Entia et Nomina

Godelizing the Yablo sequence

2011-12-03T06:18:00.001+01:00

Ever couldn't sleep or eat thinking what happens when truth is replaced with provability in the omega liar? Now you can put your qualms to rest, this issue (needless to say, of ultimate relevance to Great Philosophical Questions) has been handled! Cezary Cieslinski and I have finished drafting a paper about this. (Of course, the entailment of corollaries about The Meaning of Life is so obvious that we didn't bother stating them.)

The paper is available here.

Abstract. We investigate what happens when `truth' is replaced with `provability' in Yablo's paradox. By diagonalization, appropriate sequences of sentences can be constructed. Such sequences contain no sentence decided by the background consistent and sufficiently strong arithmetical theory. If the provability predicate satisfies the derivability conditions, each such sentence is provably equivalent to the consistency statement and to the Godel sentence. Thus each two such sentences are provably equivalent to each other. The same holds for the arithmetization of the existential Yablo paradox. We also look at a formulation which employs Rosser's provability predicate.

Lesniewski book draft

2011-11-27T07:20:00.001+01:00

Finally, I have finished drafting and proofreading a book about Lesniewski's systems. To some extent it is based on my PhD thesis, but it has gone through major revisions and around 1/3 of it is new material. Anyway, if you feel like accessing the draft in exchange for a promise to let me know what you think by June 2012, please get in touch.

Synopsis. Stanisław Leśniewski (1886--1939), a Polish logician, a representative of the Lvov-Warsaw school and Alfred Tarski's PhD supervisor, developed his philosophically (and nominalistically) motivated foundations of mathematics as an alternative to the system of Principia Mathematica. He constructed three systems: a generalized propositional calculus called Protothetic, his own (higher-order) logic of predication dubbed Ontology, and a theory of parthood known as Mereology. This books presents, explicates and critically discusses Leśniewski's work and some more recent developments stemming from it. In contrast to the technical literature of the subject, this book is accessible to philosophy students with basic logic training.

The TE paper now available in Synthese

2011-11-18T09:38:00.001+01:00

The draft about logic and platonic thought experiments I talked about before has now been superseded by the final version now available (open access) in Synthese. Here.

(By the way, Springer normally charges around 2000 Euro for publishing open access. But if at least one of your affiliations is with a Polish academic institution, it's free. I'm not sure why.)

A conference on Mereology, spring 2012

2011-10-15T05:51:00.000+02:00

Janusz Czelakowski, Tomasz Połacik and Marcin Selinger are organizing the 17th conference on Applications of Logic in Philosophy and Foundations of Mathematics. This edition is about Mereology. It's planned for May 7-11, 2012 and it will take place in a very pleasant mountain town in Poland. More details here.

Yablo's paradox: Bueno & Colyvan vs. Ketland

2011-08-19T21:45:00.001+02:00

I am looking at the debate between Jeff Ketland on one hand and Bueno & Colyvan on the other, pertaining to the consistency of Yablo sentences. (See HERE for a wider list of references compiled by Jeff. While I think B&C have a few brilliant remarks, I also think their arguments are sometimes unsatisfactory, and I want to comment on these points. This is all rather sketchy, and presumably half-baked.

1. The provability of the existence of the Yablo sequence.

B&C complain:

"it's not clear...how we know that the Yablo list exists. Priest's argument seems to presuppose the existence of the list, in order to establish that to derive a contradiction from the latter, a fixed-point construction is required." (Analysis 63, 156).

For me, it seems like a very unusal approach to the diagonal lemma (DL). DL is an existence claim: it says that given a certain formula, another formula satisfying a certain equivalence exists. My impression is that DL is used by Priest to prove the existence of Yablo sentences, and the fact that certain equivalences hold for the formulas (part of the application of DL under consideration) whose existence has been thus proved is used in the derivation of a contradiction. But let's move on.

Ketland (Analysis 64,166-167) says:

"...if one extends the language L of arithmetic by adding a 1-place prediate symbol T to form a language LT, the uniform diagonalization theorem shows that there is an LT-formula Yx() such that the Uniform Fixed-Point Yablo Principle is provable in PA."

Some notational details aside, he means that PA proves

(x)[Y(x) <-> (y>x)~T(Y(y))]

He continues:

"To stress, it is a theorem of mathematical logic that the Yablo list exists."

B&C (in an unpublished (?) ms "Yablo's paradox rides again", available HERE) pick on this sentence by saying:

"...what is Ketland taking mathematical logic to be? Given the context, and his argument that the existence...follows from PA supplemented with a truth predicate, presumably he considers that combination to amount to mathematical logic. But, clearly, this combination is quite a bit more than mathematical logic - unless one assumes, without argument, the truth of logicism!"

Okay, sure, Ketland was probably a bit hasty when he said the existence of Yablo sequence is a theorem of logic: for it is conditional upon PA extended with a truth predicate. (Although, this of course hinges on what you mean by mathematical logic). Anyway, his main point holds: the existence of the Yablo sequence is not assumed without argument, it is proven within a relatively uncontroversial theory which no side of the debate wants to reject (and indeed if you look at the quote I gave, Ketland's statement is conditional).

B&C continue: "Still, if the list is a theorem of Peano arithmetic suppelemented with a truth predicate, isn't that enough? Not really." The problem is that they didn't say what it is not enough FOR. I think it is definitely enough to respond to their qualm about the existence of the sequence.

To be fair, we find out what it is not supposed to be sufficient for soon enough. B&C, on the assumption that the use of DL is a mark of self-reference, point out that using DL for proving the existence of the sequence doesn't show the sequence to be self-referential, at least unless you also show that any way of specifying the sequence has to use a fixed point construction. (They move on to sketching a way of specifying the sequence without a fixed point; evaluate it on your own).

2. The consistency of the Yablo sequence.

One of Ketland's main claims is that the sequence isn't really inconsistent: rather, it's omega-inconsistent (for a proof see his Sythese paper from 2005, vol. 145, 295-302). B&C attack this claim. They focus on an argument given by Ketland earlier (Analysis 64, 165-172), where he relied on the compactness theorem and used the claim that every finite subset of Yablo sentences is consistent. They oppose:

"There is a very interesting mistake in this argument, though. While it is true that each finite subset of Yablo sentences is not paradoxical, it is not true that each subset is satisfiable. Consider, for example, the subset consisting of just the first two sentences ... Since there is no s_k for k>2 in this set, s_2 is vacuously true. But this means that s_1 is straightforwardly false. That is, [the set] is not satisfiable. [but it] is not paradoxical ...: there is a consistent valuation function." (B&C, "Yablo's paradox rides again")

I'm not convinced. The fact that no S_k with k>2 is in the set doesn't make s_2 vacuously true: such s_{k}s still exist (well, we can prove that on uncontroversial assumptions, see point 1), only NOT IN THIS SET. Just like the fact that you're temporarily considering the set of even numbers doesn't make the odd numbers come out of existence.

3. The inconsistency of Yablo sequence.

B&C still claim that the sequence is inconsistent. They start with assuming each instance of a Yablo biconditional:

Y_i <-> (m>i) ~T(Y_m)

and each instance of the local disquotation (for i in omega):

T(Y_i) <-> Y_i

This gives them each instance of:

T(Y_i)<-> (m>i)~T(Y_m)

Then, the crucial move occurs: they say that "since each instance was arbitrary", the uniform homogeneus Yablo Principle is derivable:

(n)[T(Y_n)<-> (m>n)~T(Y_m)]

And this one is clearly inconsistent (see Ketland 2005 for a proof).

But here is a problem: the uniform homogeneus Yablo principle doesn't follow directly from the local instances. It follows on the assumption that the model of arithmetic you're looking at is standard (and indeed, the instances weren't completely arbitrary: they were restricted to standard numerals). But this is exactly what Ketland's 2005 consistency proof hinges on: the Yablo sequence can be satisfied in a non-standard model!

4. Non-standard numbers

In their 2003 (alleged) derivation of contradiction B&C move from the untruth of s_1 to the truth of some sentence s_k with k>1. In his 2004 response Ketland claims from the untruth of s_1 that it doesn't deductively follow that "there is at least one true sentence in the Yablo list" (2004:171). B&C insist that the negation of s_1 simply is equivalent to the claim that for some k>1 s_k is true (and they're right), from which they infer that there is a true sentence on the Yablo list. B&C rejoin (ms):

"if Ketland is right, and k might stand for a non-standard natural number, so what? The nonstandard models of the natural numbers are also well-ordered, and that's all that matters here. There will still be a first true sentence in the list independent of whether the index ranges over standard or non-standard numbers. And our argument goes through either way."

Well, Ketland's response is slightly misleading, for it doesn't emphasize the (possible) difference between being on the Yablo list, and being a Yablo sentence. On one interpretation (interpretation A) the Yablo list is the list of Yablo sentences obtained for natural numbers as indices. In another (B) the Yablo list is just the set of all Yablo sentences, ordered by the less-then relation, no matter whether the numbers involved are standard or not.

Now, on interpretation (A) Ketland is right: just because for some k>1 s_k is true, it doesn't follow that some sentence on Yablo list is true, because k, the witness, might be non-standard.

But on interpetation (B), Ketland's response is inadequate, and B&C's point partially holds. It does follow that for some k>1 s_k is true.

This doesn't mean they can derive a contradiction, though! In their reasoning they relied on the local Yablo disquotation principle which for n in omega says:

T(Y_n) <-> Y_n

The thing is, if k is non-standard, the local disquotation principle doesn't apply to it, and this blocks the inference.

Of course, in response you might start with the uniform Yablo disquotation principle:

(x)[T(Y(x)) <-> Y(x)]

and this will allow you to deduce a contradiction (Ketland 2005 admits that much).

Anyway, Ketland's main point still holds: the sequence BY ITSELF is consistent, as long as you don't use uniform Yablo fixed-point principle, or uniform Yablo disquotation principle. Whether we should go for the uniform or only for the local is a separate question I don't intend to tackle here.

The myth-busting paper on definitions, final version

2011-04-26T14:37:00.002+02:00

Busting a myth about Lesniewski and definitions, a paper I wrote with Severi Hamari (I talked about it a while ago) is now forthcoming in History and Philosophy of Logic. I also posted an updated version of the paper on my academia profile.

One important change is that the discussion of Nemesszeghys's views in section 9 contained a serious error. I missed it proofreading the first 20 times, but managed to catch this right before submition.
Minor modifications are here and there.
Another change is that we streamlined the references and provided more bibliographical details.

Abstract A theory of definitions which places the eliminability and conservativeness requirements on definitions is usually called the standard theory. We examine a persistent myth which credits this theory to S. Lesniewski, a Polish logician. After a brief survey of its origins, we show that the myth is highly dubious. First, no place in Lesniewski’s published or unpublished work is known where the standard conditions are discussed. Second, Lesniewski’s own logical theories allow for creative definitions. Third, Lesniewski’s celebrated ‘rules of definition’ lay merely syntactical restrictions on the form of definitions: they do not provide definitions with such meta-theoretical requirements as eliminability or conservativeness. On the positive side, we point out that among the Polish logicians, in the 1920s and 30s, a study of these meta-theoretical conditions is more readily found in the works of J. Lukasiewicz and K. Ajdukiewicz.

An Episode in the History of Polish Art and Logic

2011-04-12T16:48:00.002+02:00

Stanisław Ignacy Witkiewicz (aka Witkacy) (1885 – 1939) was a Polish painter, playwright, novelist and philosopher. He did a variety of things which not too many of us would describe as the usual day in the office: he wrote a manual (well, sort of) on using drugs (aka Unwashed Souls) and actually used drugs while painting. Some of my favorite pieces are spread over this post (HT to http://artyzm.com, where you can find more of them)).

Interestingly, Witkacy interacted with some of the Polish logicians, including Leon Chwistek (known for his work on type theory) and Alfred Tarski. He even painted portraits of both of them. Chwistek:

Tarski's portrait seems to be in Tarski's home in Berkeley (correct me if I'm wrong). But Victor W. Marek has posted a picture of it (here, 11th picture from the top).

(Nota bene, the above is not a portrait of Tarski! You actually have to follow the link to see it! ;))

Now, to the point. Witkacy read Tarski's 1933 and scribbled his comments on the margins (sorry, both things in Polish). The Warsaw University Library has recently made a copy available online. The comments are pretty cute, some of them quite funny, but my guess is Witkacy at some point got lost in the text. It's not quite clear whether he was on drugs while reading. My favorite page contains Witkacy's illustration of the concept of metalanguage (see here for a better version):

(Some other marginalia are also available, see the list here)

Reading "Language, sense and nonsense"

2011-04-11T15:00:00.004+02:00

For a while now, I've been forcing myself to read Language, Sense and Nonsense. A Critical Investigation into Modern Theories of Language by G. P. Baker and P.M.S. Hacker. I started reading it, because the main theses sounded interesting and controversial: the authors clam that modern philosophy of language and linguistics are based on false identification of main problems and severe misconceptions.

The book is meant to show that "the most of what goes by the name of `theories of meaning' or `scientific study of language' needs not remedial readjustment, but wholesale abandonment." [x] The authors criticize modern linguistics and philosophy of language on account of assuming that (i) any natural language has a deep structure of a "(correct) formal, function-theoretic, logical calculus" [2], (ii) the task of the philosophy of language is to construct a theory of its meaning which would elicit "the underlying principles of construction of any language in virtue of which we can construct and understand the infinite array of meaningful sentences" [3], (iii) that our ability to understand an infinite assembly of sentences shows the existence of compositional meaning principles, (iv) that there is a sharp distinction between syntax, semantics and pragmatism [6]. Why did I have to force myself? Well, for one, they are pointlessly and rhetorically rude:

If the true Philosopher's Stone is at last almost within our reach, if a theory of meaning, once properly constructed, holds within it the key to the great problems of philosophy, if grammar holds the key to the structure of the human mind, then indeed this wonderful insight and advance must be hailed with fanfares. And philosophers, together with theoretical linguists, must bend their wills to a united effort to grasp this treasure. then they may go on to explain the deep mysteries of our ability to understand new sentences, to discover what really exists (e.g. whether events are essential for our `ontology'), to reveal what is innately known to the human mind, to uncover the true logical form of our thoughts and the essential nature of our understanding. But the Last Trumpet has been blown with tiresome regularity in the history of philosophy, and false prophets have been legion. If the promises held out by the possibility of constructing a theory of meaning are false promises, and if the very idea of such a theory of meaning as is currently envisaged is incoherent, then this too must be proclaimed, the incoherences made clear and the hopes dashed. For then, far from being at last upon the true path of science, theorists are merely pursuing yet another monstrous chimera.
[...]
[W]e shall focus upon just those topics which are introduced in most theories of meaning with the barest of explanation, taken to be altogether perspicuous and treated with nonchalance. We shall probe the seemingly clear notion of the truth-conditions of a sentence, which is commonly taken to be the key to any cogent semantic theory. We shall place pressure upon the apparently obvious distinction, within every sentence, between its descriptive content [...] and its force. We shall test the soundness of the supposition that a language is a system, a calculus consisting of a network of hidden rules tacitly employed whenever we speak or understand what is spoken. And we shal examine whether the question of how it is possible to understand setences never heard before really is as deep as it is commonly taken to be. In general we shall resist by argument the theorists' habit of frog-marching the neophyte straight to a ceremony of initiation ito the full mysteries of the modern science of language. We shall unmask their conceptual conjuring tricks and break the mesmerizing force of their incantations by critical questioning. Our method will be the clarification of concepts. [11-12]

A few other samples of their style:

The issues we examine are important ... The misconceptions we identify ramify widely, contributing greatly to the barren mythology of late twentieth century culture. Hence this book is written with more polemical passion than is common in the typical reserved and detached forms of academic philosophy. For this we make no apology. [x]

It was rather unclear to me how the popularity of the criticized view justifies the unusually polemical style. In this case, people being criticized are more likely to be convinced by cold, calculated arguments rather than by rhetorical and emotional ramblings.

Another sample:

[W]e [...] demonstrate a readiness to demolish large parts of what pass for significant modern intellectual achievements. But our ultimate purpose is not to persuade linguists or philosophers that their theories are false... It is rather to suggest that their endeavours are futile because pointless and misconceived. [13].

Sometimes, you can forgive the style, if the arguments are good. But these really aren't. Most of them are superficial and hasty straw-man strategies which are unlikely to convince anyone who doesn't buy into treating insults as real arguments.

For a while, I was thinking about writing a short paper pointing out what went wrong in the book. But when I gave it some thought, I decided that it really wouldn't be short, and that since the book dates back to 1984, I wouldn't be addressing a really new and living concern either. Then, I also discovered a review in Mind (New Series, Vol. 94, No. 374 (Apr., 1985), pp. 307-310) by Jane Heal, and it turns out that it pretty much sums up my views about the book (below, the key fragment):

The first thing to be said about these books is that they are extremely aggressive in tone. The violence and frequency of pejorative terms is striking. Phrases like 'grotesque conceptual confusions' (LSN p. I2), 'wastelands of the intellect' (LSN p. 13), or 'frantic attempts to justify the bogus demands of a misguided theory' (LSN p. 94) are to be found peppered throughout the books. Where they do not condemn outright Baker and Hacker proceed by sneer, by loaded rhetorical question and by self-congratulation ('The several criticisms add up to a devastating indictment' LSN p. 24I).
This might be no more than robust intellectual knockabout. If one thinks something is nonsense one should be entitled to say so. But Baker and Hacker go further and cast aspersions not only on the intelligence but also on the intellectual integrity of their opponents. They are accused of 'intellectual opportunism' (LSN p. 9), 'conceptual conjuring tricks' (LSN p. 12), 'mystery mongering' (LSN p. I9), and so on. One might say of such abuse that it is totally out of place in a work with serious pretensions to philosophical scholarship. One could remark further that the repugnance it excites will lose Baker and Hacker what small chance they had of gaining converts. But from the point of view of the philosophical enterprise neither of these is the gravest charge. The real danger is that hostility will prevent them approaching their subject in such a spirit that they can feel the genuine attractions of the opposing views and hence put themselves in a position to see the real weaknesses there, if any; some level of sympathetic understanding is a prerequisite for truly efficacious demolition. Have Baker and Hacker avoided this danger? Have they, despite all the faults, something important to say?
The general problem area they have identified in both books is important; the correct interpretation of Wittgenstein's views on rules and meaning and their relevance to modern theoretical approaches to language are topics that many philosophers rightly want to see debated. But the detailed handling of the issues by Baker and Hacker is constantly disappointing. In effect they discharge an enormous blunderbuss of arguments in the direction of their opponents. Most of the missiles spray out wildly into space and even those that are on target do not wound fatally.

Munich group and blog

2011-03-30T12:03:00.001+02:00

Probably you all know about the new research group at Ludwig-Maximilians Universitat in Munich (Munich Center for Mathematical Philosophy). More info about the group can be found in the most recent volume of The Reasoner (vol 5 no 4, April 2011).

What you might not know yet is that the group started a new blog, M-Phi. (The administrators kindly invited me to contribute - since I might have hard time matching the high level of contributions it might take a while before I actually post anything there).

Ontological Proofs Today, website up and running

2011-03-28T18:11:00.000+02:00

Some time ago I mentioned a conference on ontological proofs. Now, their website is up and running. (submission deadline: April 30).

Postdoc in logic and phil of sci, Calgary

2011-03-18T23:24:00.000+01:00

The Department of Philosophy at the University of Calgary invites applications for a one-year postdoctoral fellowship starting on September 1, 2011. The area of specialization is logic or the philosophy of science. The fellow will be expected to have a well-defined research project, teach one course in the area of specialization, and participate in the research activities of the Department. All requirements for the PhD must have been completed by the starting date and no earlier than September 2007. The stipend is $50,000 Canadian per year. Applications will be accepted until April 15, 2011 or until the position is filled. Details.

"Platonic" thought experiments: how on earth?

2011-03-07T10:30:00.003+01:00

I have posted a draft of the TE paper online now (the title is the same as the title of this post). Here.

Abstract. Brown (1991a,b, 2004, 2008) and Bishop (1999) argue that thought experiments (TE) in science cannot be arguments and cannot even be represented by arguments. They rest their case on examples of TEs which either proceed through a contradiction to each a positive resolution (Brown calls such TEs "platonic") or are used by different people with opposite results. This, supposedly, makes it impossible to represent them as arguments for logical reasons: there is no logic that can adequately model such phenomena. (Brown further argues that this being the case, "platonic" TEs provide us with irreducible insight into the abstract realm of laws of nature). I argue against this approach by describing how "platonic" TEs can be modeled within the logical framework of adaptive proofs for prioritized consequence operations. To show how this mundane apparatus works, I use it to reconstruct one of the key examples used by Brown, Galileo's TE involving falling bodies. I also address Bishop's qualms about the clock-in-the-box TE which Einstein and Bohr employed when they disagreed about the uncertainty principle.

Many thanks to Christian Strasser, Frederik Van De Putte, Erik Weber, Rawad Skaff and Joke Meheus for reading and discussing with me earlier versions of this manuscript and to all the people who discussed this topic with me: Graham Priest, Diderik Batens, Anouk Barberousse, Peter Simons, Margherita Arcangeli, Gillman Payette, and the audiences in Geneva, Paris and Ghent, where I gave talks based on this material.

Philosophica Journal (Ghent) available online

2011-02-28T19:57:00.002+01:00

Some volumes of a philosophical journal based in Ghent are now freely available here.

Teddy bears, guns and modal logic

2011-02-25T01:06:00.000+01:00

It's the time of the year when a new semester starts in Poland and I'm in Gdansk for a while (it's annoyingly and unusually cold, it feels like Calgary for some reason - seems I haven't escaped after all. Damn you, global warming!). Anyway, one of the courses I'm teaching is non-classical logic and I'm using Graham Priest's awesome book. If you've ever taught modal logics, you probably observed that it's sometimes difficult to get the students to remember which normal modal logic is related to which properties of the accessibility relation. Here's a trick I invented last year, feel free to use it (just give credit where it's due).

First off, Priest uses Greek letters to denote the main properties of the accessibility relation:

\rho stands for reflexivity
\sigma stands for symmetricity
\tau stands ofr transitivity
\eta stands for extendability

The main logics worth remembering in a basic course are T, D, B, S4 and S5:

- T is determined by the class of \rho-models
- D is determined by the class of \eta-models
- B is determined by the class of \rho\sigma-models
- S4 is determined by the class of \rho\tau-models
- S5 is determined by the class of \rho\sigma\tau-models

Here's a mnemotechnic to help people remember this.

First, you want people to remember the ordering of the logics:

T, D, B, S4, S5

instead, (make them) memorize:

TeDdy Bear with 45S

The coding here is quite obvious.

Next, you want people to remember the ordering:

\rho, \eta, (\rho \sigma), (\rho \tau), \(rho \sigma \tau)

instead, (make them) memorize:

RESTs

R stands for \rho, E stands for \eta, S stands for \sigma, T stands for \tau.

Thus, the matching of modal logics with properties of the accessibility relations is encoded by:

a Teddy bear with 45s rests.

Two problems:

You still have to remember that the first two logics are just \rho and \eta, and that the remaning one involve \rho
You have to remember to repeat "st", because it stands for "first \sigma, then \tau, then \sigma and \tau together".

Now, get people to imagine a teddy bear with a gun (preferably with a 45).

One option is to use this (source):

Another is to use this:

Or you can use this:

(I was also thinking of taking a picture of a teddy bear with a 45, I have everything I need apart from a teddy bear and a 45.)

Of course, the key sentence is not the best English phrase (I think there are at least some fragments of Yeats' poetry which trump its genius; not so sure about J. Conrad though), and there are some weak points (it doesn't extend easily to non-normal modal logics, you have to remember at least two extra assumptions I mentioned, and so on). So, if you have a better mnemotechnic, please share.

Reichenbach on the philosophical insignificance of G's second incompleteness theorem

2011-02-16T00:59:00.000+01:00

Nowadays, one standard answer to various exaggerated claims about Gödel's second incompleteness theorem (the unprovability of consistency) is that even if an interesting mathematical theory could prove its own consistency, this wouldn't help us much because inconsistent theories also prove their own consistency, (so we would still have no idea whether the theory is consistent). (For instance, I think this sort of remarks, without further references, can be found in Franzen's and Smith's books, but I don't have them handy now).

In a somewhat uninspired moment of mine, I wondered why this rather straightforward observation didn't get through to the wider philosophical audience earlier and when it was formulated. The earliest mention I run into so far (although, it's not like I spent days browsing stuff systematically) is in Reichenbach's 1948 unpublished lecture notes (which, by now, have been published in 1978). The fragment comes from the first volume:

This would mean that the proof of consistency of the language L could be given within L. A simple analysis shows that this would not improve the situation, since in this case our proof of consistency of L would be of value only if we were sure that L is consistent. In case L were not consistent, we could also deduce the statement of the consistency of L, with the qualification that then the negation of the statement were deducible too. Thus if the consistency of L were deduced within L, this fact would not prove the consistency of L.

So, one reason might be that the remark occurred in lecture notes which were unpublished for a while (by the way, if you know of Reichenbach's point being published earlier, I'd appreciate a reference), and even when they were published, it was in a two-volume set of Reichenbach's papers, which very few non-specialist would buy (or grab from a library shelf, for that matter).

But I don't think this is the whole story. The point is simple enough and certainly came to minds of many bright people who gave the issue proper consideration. The reason why this is often omitted by (hack?) philosophers is not that they are too dumb to get this point (well, at least some of them aren't). Rather it is that wishful thinking sometimes prevents people from considering objections to their view. The perspective of reaching strong philosophical conclusions by relying on some fancy mathematical apparatus, which (they think) would lend splendor to the philosophical claims themselves, is quite tempting.

Another reason is that Reichenbach's point applies to cases where one wants to claim that mathematics is somehow epistemologically flawed and that there is no mathematical certainty because mathematics cannot prove its own consistency. (... and if real mathematical knowledge is unattainable, then no knowledge is, science is useless, blah blah, blah...). It doesn't help much when one wants to suggest that since we, humans, can establish consistency claims, and mathematical "devices" cannot, our minds are not computing machines. In this argument, it seems that no deep epistemological considerations of the former sort are needed.

Incidentally, it seems that despite the fact that I've seen some philosophers using both strategies in one passage (or breath) both stances are incompatible. Either you say that mathematics is unreliable and then you cannot rely on it in an argument against computational theories of mind, or you rely on mathematics, give an argument in philosophy of mind, but cannot simultaneously deny the reliability of mathematics. (By the way, (1) even if you do the latter, you admit that mathematics can be done reliably by humans and the fact that a mathematical theory cannot prove its consistency has no bearing on whether humans can use it sensibly, (2) the sketched argument against computational theories of mind also doesn't work, but that's a whole different story).

CLMPS registration - what's up with that?

2011-01-31T00:08:00.002+01:00

Like some of you I had to spend some time submitting my stuff to one of the biggest logic events these years, CLMPS. What I found slightly surprising is how complicated the submission procedure is.

1. Before you submit your materials you have to actually register as a participant. This seems slightly impractical, especially since some of people probably decide whether they will participate only when they find out whether their proposal has been accepted.

2. When you register, you have to fill a pretty detailed form which contains all sorts of unusual questions:

you're supposed to mark your function at a conference (for instance you may choose "participant without contributed paper" or "participant with contributed paper). While some people will know their status, some people will have no idea before the submission and acceptance notification.
They also ask you whether you plan to attend the opening ceremony and the welcome banquet on July 19,
which concert you prefer to attend on July 23,
which trip you will be in a mood for on July 24,
how many people will accompany you at the conference,
what your exact arrival and departure dates are, and
which kind of hotel and what kind of room you want to stay in.

I mean, seriously, what happened to spontaneity? I have no idea what the answer to all those questions is in my case. Ah, but there is a note in case I change my mind:

Please note that demands for modification of your registration data after payment must be submitted to the LOC in writing by mail, fax or e-mail. No modification will be possible through the registration form. Also note that no modification will be possible after May 31^st, 2011.

I'm inclined to think that at some point the organizers will be swamped receiving all kinds of messages from people who will decide to change their plans and, say, go to a jazz concert rather than a classical concert, or to come with a partner, or to come one day later, or stay in a different room, and so on. I know the conference will have a lot of participants and the organizers need some head start on getting things ready, but isn't this a bit too much? And won't it, eventually, devour more of their time, given the need to deal with later changes case-by-case? Why not move the form modification deadline to May 31? Has anyone had any experience with earlier events in this series and the submission procedures? Has it always been like that?

Handbook of the History and Philosophy of Logic vol. 10 online

2011-01-25T13:06:00.004+01:00

In case you haven't noticed, Stephan Hartmann, one of the editors, made preprints from the ~~forthcoming~~ rather newly published volume on inductive logic available online. His Bayesian Epistemology is also a good read.

Ontological Proofs Today, Bydgoszcz

2011-01-17T13:34:00.002+01:00

Mirosław Szatkowski, Anthony Anderson, Jonathan Lowe, Dariusz Łukasiewicz, Richard Swinburne and Daniel von Wachter are putting together a conference in Bydgoszcz (Poland), titled Ontological Proofs Today (6-8 Sept 2011).

Alas, parts of the details are available only in Polish and the information available isn't too specific. But I would expect them to update the info some time soon. In case you have more urgent queries, I guess you can always drop the organizers a line.

Vickers and the criterion of arithmetical truth

2011-01-13T13:58:00.008+01:00

I'm reading The problem of induction by John Vickers. The entry is quite comprehensive and enjoyable. There is a thing which seems a bit hasty, though. Vickers, at some point, makes a distinction between the problem of finding a method for distinguishing reliable inductive habits and the problem of saying what the difference between reliable and unreliable inductive habits is. While the distinction is quite sensible, I'm not sure what to think about the example Vickers uses to clarify it (section 2):

The distinction can be illustrated in the parallel case of arithmetic. The by now classic incompleteness results of the last century show that the epistemological problem for first-order arithmetic is insoluble; that there can be no method, in a quite clear sense of that term, for distinguishing the truths from the falsehoods of first-order arithmetic. But the metaphysical problem for arithmetic has a clear and correct solution: the truths of first-order arithmetic are precisely the sentences that are true in all arithmetic models.

A few remarks come to mind:

Prima facie, the incompleteness of first order arithmetic (let's fix our attention on first-order true arithmetic TA1) would show that the epistemological problem of finding a method of deciding whether an arithmetical claim is true is unsolvable only if the only way to find out whether an arithmetical sentence is true would have to employ a complete axiomatization of true arithmetical sentences.
Another way to put his is that I'm not sure if incompleteness itself entails the lack of epistemological criterion; after all there are negation-incomplete and decidable theories (think of the set of theorems of classical propositional logic). Yes, negation-completeness entails decidability, but the converse doesn't hold.
For instance, if second-order model-theoretic consequence relation were decidable, we would have a decision method for first-order arithmetical truth despite the incompleteness theorem. It would suffice to check if a first-order arithmetical claim is a model-theoretic consequence of the axioms of second-order Peano arithmetic (which, modulo second-order semantic consequence, is complete).
Perhaps one could circumvent the above concern by saying that if there were any epistemological criterion for arithmetical truth, then the true arithmetic would be recursively axiomatizable. This, alas, isn't immediately obvious and is quite sensitive to what your background epistemology is. In a scenario where one can have a direct contact with God (assume there is one) and God correctly responds to any queries we have about arithmetical truth, we do have some epistemological criterion for arithmetical truth, but this fact alone tells us nothing about the axiomatizability of arithmetical truth.
Now, the set of first-order arithmetical truths in fact is undecidable. But this follows rather from the Church-Turing thesis, the undefinability of truth and the arithmetical definability of all recursive sets. If the set of FO arithmetical truths were recursive, it would be definable. But Tarski's theorem already states that it isn't. So the set of FO arithmetical truths isn't recursive, so by the Church-Turing thesis it is not decidable.
Still, there is a gap between the claim that the set of arithmetical truths is undecidable and the claim that the epistemological problem for first-order arithmetics is unsolvable. This follows only if every epistemologically respectable criterion of arithmetical truth has to be a decision method. While this seems quite likely to me, there is still some maneuvering space for all those people/crackpots who disagree.
It seems there is more to epistemological concerns about arithmetic than just incompleteness. If the incompleteness theorem failed, this would show that there are complete, sufficiently strong and consistent arithmetical theories. This by itself doesn't give us a full-blown epistemological criterion for arithmetical truth, because we also need some epistemological account of why the axioms of a given complete theory are true (after all, there are complete and false theories).
Another worry is that Vickers defines FO arithmetical truths as those claims that hold in "all arithmetic models". Presumably he means all models of first-order arithmetic. The problem with this definition is that there are non-standard FO arithmetical models. For instance, I like to think that the Godel sentence for Peano Arithmetic is true. Yet, there is a model in which it is false. So Vickers's definition would exclude the Godel sentence from arithmetical truths. Also, since there are models in which the negation of the Godel sentence for PA is false, it also wouldn't be included in the set of arithmetical truths on Vickers's definition, thus yielding the set of arithmetical truths incomplete.

The CTT paper, final version

2010-12-13T11:28:00.002+01:00

The writing process of the paper on the Church-Turing thesis, random processes and platonism has come to an end. The paper is forthcoming in Philosophia Mathematica. A more or less final version of the paper is available here. (wrt to earlier versions, I added a bunch of remarks and answers to possible counterarguments, explained what Church randomness is and why Church-random sequences are not Turing-computable and elaborated on the intuitive source of the conceptual conflation involved).

Many thanks to Leon Horsten, Liesbeth De Mol, Robert Thomas, Jeffrey Ketland, Gualtiero Piccinini, Stanisław Dercz and two anonymous referees for discussion and comments.

Possibility and the burden of proof

2010-11-19T09:02:00.004+01:00

If I didn't run into this sort of arguments often enough, I wouldn't be writing about this. Some time ago, Gualtiero Piccinini (whose computability-related stuff I really enjoy reading) posted a question about known good arguments for the existence of afterlife. Joshua Carl Davis commented:

I make an argument in my book Metaphysics and the Meaning of Life that there is an afterlife. The argument goes as follows: 1) It is always valid to argue from actuality to possibility (a logical principle dating to Medieval times), 2) I exist now therefore it is possible for me to exist again. While this does not prove the immortality of the soul, it switches the burden of proof to the other side and, I believe it is an overwhelming burden. The argument is given on page 282. The book is available on Amazon. Good luck to you.

Eric Thomson gives a pretty straightforward explanation of what went wrong there.

ET argues that equally well the fact that one didn't exist before they were born shifts the burden to the other side.
ET points out that establishing possibility doesn't automatically shift the burden of the proof.
ET indicates that the possibility of future existence doesn't follow from the actual existence by the principle that JCD refers to.

As for point 1, JCD responds:

As for your first point, which to you is more certain: "I exist now" or "I did not exist before I was born"? That should indicate which is the stronger argument.

The problem is, a reductio argument of this sort cannot be refuted by saying one of the premises is less certain than other. Suppose someone gives an argument: "P - therefore, by my magical strategy, Q", and someone else responds: "The magical strategy doesn't fly: I can equally well argue: Z - therefore, by the same magical strategy, not Q". Now, saying that Z is less certain than P doesn't help. As long as Z and P are both true, the reductio works and shows that the magical strategy (let's not hesitate to use the technical term) sucks.

What has to be done to defend the magical strategy? Well, once one is convinced it works and accepts P, plain modus tollens will force them to reject Z. This is a problem because if this is what happens, the magical strategy gives an argument: "P - therefore by my magical strategy, Q. But if Z were true, then by my magical strategy, Q would be false. Therefore, Z is false". Apply this to the case in question and it turns out that JCD can save his argument against this reductio only by denying Z. But to save an argument for life after death by assuming life before birth will not be a convincing strategy to many.

As for point 2, I wouldn't have much to add. It is perhaps metaphysically possible that BSG is true and JCD is a cylon travelling in time (and perhaps across possible worlds), but this doesn't shift the burden of the proof: he doesn't have to focus on proving that he isn't. I am still allowed to assume he isn't, unless proven otherwise. (In general, the burden shift JCD proposes would be pretty bad in court: innocent unless proven guilty would turn into guilty unless proven innocent given the possibility of guilt.)

JCD addresses ET's point 2 as follows:

As regards your second point, I do believe the burden of proof is switched. My existence is already a possibility based on the fact that I currently exist. The argument only illustrates that the burden is, was, has always been, on the other side. It's the difference between saying there will be another lion or there will be a unicorn.

Now,"I do believe the burden of proof is switched" and "The argument only illustrates that the burden is, was, has always been, on the other side." is not an adequate response, it is just a restatement of JCD's claim (actually, its strengthening). I'm not even sure if it's consistent to say that the burden is switched and that it has always been on the other side.

How about "My existence is already a possibility based on the fact that I currently exist"? Well, ET claims: mere possibility doesn't shift the burden. JCD's claim is consistent with this. I can say that existence is already based on the fact that I exist and yet maintain that this doesn't shift the burden. ET doesn't deny the possibility of JCD's existence, so stating it has nothing to do with ET's objection.

Perhaps, what JCD means is that we already know that our existence is possible (well, we do exist), whereas we don't have a compelling reason to believe that our non-existence is. If this was true, then indeed, the burden of proving the possibility of non-existence would be on JCD's opponents. Alas, the experience of the fragility of human existence is quite common, and so are prima facie consistent thoughts about death of the body as the end of life. If JCD claims human non-existence is impossible, an argument is needed.

As for point 3, JCD's reasoning goes from P to Possibly P and from Possibly P to Possibly P and Q: I exist. Therefore, it is possible that I exist. Therefore, it is possible that I exist after my body dies. Of course, the first move is valid (you don't have to conjure medievals to see that), but the second one isn't (just take Q to be not-P, for instance; or any sentence that metaphysically excludes P, if you prefer).

Evolutionary arguments do go astray (sometimes)

2010-11-16T15:34:00.002+01:00

Norton (Why thought experiments do not transcend empiricism. In Hitchcock, C., editor, Contemporary Debates in the Philosophy of Science, pages 44–66, Blackwell) when talking about developing non-classical logics to model certain aspects of thought experiments gives the following, as he calls it, evolutionary argument:

I think there are some reasons to believe that no new, exotic logic is called for. In outlining the general notion of logic above, I recalled the evolutionary character of the logic literature in recent times. New inferential practices create new niches and new logics evolve to ﬁll them. Now the activity of thought experimenting in science was identiﬁed and discussed prominently a century ago by Mach (1906) and thought experiments have been used in science actively for many centuries more. So logicians and philosophers interested in science have had ample opportunity to identify any new logic that may be introduced by thought experimentation in science. So my presumption is that any such logic has already been identiﬁed, in so far as it would be of use in the generation and justiﬁcation of scientiﬁc results. I do not expect thought experiments to require logics not already in the standard repertoire. This is, of course, not a decisive argument. Perhaps the logicians have just been lazy or blind. It does suggest, however, that it will prove diﬃcult to extract a new logic from thought experiments of relevance to their scientiﬁc outcomes – else it would already have been done! (pp. 54-55)

To gains some perspective on this argument, consider the following “evolutionary” argument. Norton, among other things, works on the philosophy of relativity. Now, relativity theory has been around, pretty much, since the same time when Mach wrote about thought experiments. So philosophers interested in science have had ample opportunity to identify and solve any philosophical issue that may be introduced by relativity theory. So, in this ﬁeld, any philosophically interesting claim has already been made and any philosophically argument has been given, and Norton’s work in philosophy or relativity is redundant. Unless, of course, philosophers of science since the discovery of relativity theory have just been lazy or blind.

A geeky note about multilingual support for WinEdt 6.0

2010-11-02T02:39:00.008+01:00

So WinEdt 6.0 has been out for a while now. It's a good piece of software, and I've been using various versions of WinEdt since 2003 (sometimes I use emacs with auctex, but for larger projects, I definitely prefer WinEdt).

Anyway, if you often switch between languages, you have to play around to get WinEdt to open your files with appropriate dictionaries. This is where modes kick in. It so happens that the explanation that WinEdt provides for this stuff isn't too clear, so here is a step-by-step procedure that will get you multilingual support for WinEdt 6.0.

Download appropriate dictionaries. They are available here. Extract (if needed) and save the file(s) somewhere. It doesn't really matter where, just make sure you know where it is. Say you want to install Polish and download pl_huge.dic saving it at C:\Program Files\WinEdt Team\WinEdt\Dict\pl_huge.dic.
Run WinEdt 6, go to Options. Under Editor: Mouse, Modes, Defaults you will find Modes. Open the file.
Now, what I do, is I look at the submodes and add a line: MODE=":PL|*.pl.tex" This creates a submode PL which is assigned automatically to all files ending with .pl.tex
I also replace corresponding lines for US and UK English, using: MODE=":UK|*.uk.tex" and MODE=":US|*.us.tex"
That way, whenever I have a file in Polish I save it as name.pl.tex, if I have a file in American English, I save it as name.us.tex, and so on.
This sets the modes right. Now dictionaries. In the Options tree go to Dictionary Manager and then to Word Lists.
Then you add something like this to the list:

DICTIONARY="Polish"

FILE="C:\Program Files\WinEdt Team\WinEdt\Dict\pl_huge.dic"

ENABLED=1

MODE_FILTER="PL"

LOAD_ON_START=1

SAVE_ON_EXIT=1

ADD_NEW_WORDS=1

USE_FOR_COMPLETION=1

ALLOW_COMPOUNDED_WORDS=1

The first line just gives your setting a name. The second locates the dictionary file (that's why you need to remember where you saved it). The mode filter tells you for which modes this dictionary is active.

8. Now you also have to turn off your English dictionaries for the Polish file and switch them on for US and UK submodes. That is, you look at all English dictionaries listed and make sure their mode filter contains appropriate submode. Thus, for example:

DICTIONARY="English (common)"

FILE="%B\Dict\English\eng_com.dic"

ENABLED=1

MODE_FILTER="US"

LOAD_ON_START=1

SAVE_ON_EXIT=1

ADD_NEW_WORDS=0

USE_FOR_COMPLETION=1

ALLOW_COMPOUNDED_WORDS=1

Then, you save all the changes you've made in the options sections, restart WinEdt to make sure it loads its settings anew and check if language selection works properly. Make sure the files you use have appropriate extensions.

If you think something's still off, feel free to include mode declaration in the beginning of each file. Just include % -*- TeX:US -*- (or % -*- TeX:PL -*- or...) in your preamble.

Applications of Logic in Philosophy and Foundations of Mathematics CFP

2010-10-19T13:29:00.002+02:00

If structural completeness is your thing, Janusz Czelakowski, Tomasz Połacik and Marcin Selinger are organizing a conference focusing on such issues. It will take place in a nice small mountain town in Poland (Szklarska Poręba) 9-13 may, 2011. The conference is about to be bilingual, so feel free to take a look at the CFP and maybe drop them a line.

Second Entia et Nomina Workshop CFP

2010-10-11T12:07:00.004+02:00

This is the second time Gdansk University is organizing Entia et Nomina, a logico-philosophical workshop. Most likely, it is also the last time the language is Polish. Next time, we plan to switch to English. So, English speakers - stay tuned. Polish speakers - CFP below:

EntiaEtNomina2011CFP

PhDs in Logic, CFP

2010-10-08T09:59:00.001+02:00

17-18 February 2011, PhDs in Logic III, Brussels, Belgium (deadline: 15 November 2010)

PhDs in Logic is an annual two-day graduate conference and winter school in logic. Each year we invite four established professors to do a tutorial on their work in two one-hour sessions. We also give about ten PhD students the opportunity to do a thirty-minute presentation on (a) their own work or (b) an overview of some topic in their field.

The current conference will feature the tutorials by Eric Pacuit (*Epistemic Logic*), Sonja Smets (*Quantum Logic*), Mai Gehrke (*Algebraic Logic*) and Peter Koepke (*Set Theory*). PhD students in logic with a background in philosophy, computer science, or mathematics are the intended audience for these tutorials. They are also the type of students we have in mind for our thirty-minute student sessions.

Students interested in doing a talk should send a 500-1000 word abstract to phdsinlogic+abstractsgmail.com by November 15th, 2010.

For more information, visit our website at http://www.vub.ac.be/phdsinlogic2011/.

Busting a myth about Lesniewski and definitions

2010-10-02T17:58:00.003+02:00

Some time ago I run into a few logicians chatting at a conference about how Lesniewski formulated the standard theory of definitions. For some reason I felt obliged to say a few words about this. One thing let to another, and this ended up in a footnote to Gupta's entry on definitions at the Stanford Encyclopedia (see footnote three). A few more coincidences and I started writing a paper about this with Severi Hamari. After a freakish number of revisions (around 20) we finally agreed on a version, and I posted it on academia.

Many thanks for their comments to John MacFarlane, Nuel Belnap, Wilfrid Hodges, Paolo Mancosu, Oystein Linnebo and Jan von Plato (I hope I didn't forget anyone).

Abstract:

A theory of deﬁnitions which places the eliminability and conservativeness requirements on deﬁnitions is usually called the standard theory. We examine a persistent myth which credits this theory to S. Lesniewski, a Polish logician. After a brief survey of its origins, we show that the myth is highly dubious. First, no place in Lesniewski’s published orunpublished work is known where the standard conditions are discussed. Second, Lesniewski’s own logical theories allow for creative deﬁnitions. Third, Lesniewski’s celebrated ‘rules of deﬁnition’ lay merely syntactical restrictions on the form of deﬁnitions: they do not provide deﬁnitions with such meta-theoretical requirements as eliminability or conservativeness. On the positive side, we point out that among the Polish logicians, in the 1920s and 30s, a study of these meta-theoretical conditions is more readily found in the works of J. Lukasiewicz and K. Ajdukiewicz.

History and Philosophy of Computing, Ghent, Nov 7-10, 2011

2010-10-02T17:36:00.001+02:00

From 7-10 November 2011 the Centre for Logic and Philosophy of Science organizes an International Conference on the History and Philosophy of Computing.

AIMS AND SCOPE

The computing sciences collect the most diverse complex of experts: philosophers, logicians, historians, mathematicians, computer scientists, programmers, engineers. The number of involved subjects grows accordingly: from foundational issues to their applications; from philosophical questions to problems of realizability and design of specifications; from theoretical studies of computational barriers to the relevance of machines for educational purposes.

A historical awareness of the evolution of computing not only helps to clarify the complex structure of the computing sciences, but it also provides an insight in what computing was, is and maybe could be in the future. Philosophy, on the other hand, helps to tackle some of the fundamental problems of computing, going from the limits of the “mathematicizing power of homo sapiens”to the design of feasible and concrete models of interactive processes.

The aim of this conference is to bring together these two streams: we are strongly convinced that an interplay between the researchers with an interest in the history and philosophy of computing can crucially add to the maturity of the field.

We plan to have up to 30 contributed papers to be presented at the conference. We welcome contributions from logicians and philosophers or historians of science as well as from philosophically and/or historically aware computer scientists and mathematicians.

Topics of the conference include:

The birth, evolution and future of computation
Philosophical, foundational and practical issues of computability in logic, mathematics and computer science
Computation in the sciences

More details on deadlines and submissions can be found at:

http://www.computing-conference.ugent.be
computing.conference@ugent.be

INVITED SPEAKERS:

Bill Aspray (University of Texas)

Martin Davis (New York University)

Fairouz Kamareddine (Heriot-Watt University Edinburgh)

Sybille Krämer (Freie Universität Berlin)

Giovanni Sambin (Universita' di Padova)

Raymond Turner (University of Essex)

CONFERENCE CHAIRS:

Liesbeth De Mol and Giuseppe Primiero

PROGRAMME COMMITTEE:

G. Alberts (Amsterdam)

S. Artemov (New York)

M. Campbell-Kelly (Warwick)

A. Eden (Essex)

L. Floridi (Oxford & Hertfordshire)

R. Kahle (Lisbon)

B. Loewe (Amsterdam)

J. Meheus (Ghent)

E. Myin (Antwerp)

S. Negri (Helsinki)

V. de Paiva (Palo Alto)

S. Smets (Groningen)

G. Sundholm (Leiden)

C. Toffalori (Camerino)

J.P. van Bendegem (Brussels)

M. van Dyck (Ghent)

B. van Kerkhove (Brussels & Hasselt)

E. Weber (Ghent)

SUPPORT

A number of Students Grants will be available through our Sponsor and Supporting Associations. More details to come on the webpage of the conference.

Church-Turing against Platonism - extensive revision

2010-09-24T11:39:00.003+02:00

The note I mentioned a while ago went through serious revisions and extensions. The main points stand, but I added extra content, explanations and arguments to turn this into something more resembling a paper. Here is THE NEW VERSION. (HT to Leon Horsten for his comments)

My top ten pieces of software

2010-08-27T14:28:00.005+02:00

And now for something completely different. A brief list of neat pieces of software I've been using (widely understood to include online services).

WinEdt (6.0) - my favorite LaTeX editor. I've been trying to use quite a few different editors, but this one really works for me. It's not freeware, it's not Linux-compatible (as you could figure out from its name). But I like how you can set up your own macros, how it uses bookmarks, and how it handles large multi-file projects.
Allway Sync - a neat program (freeware in its moderate version) that helps you to synchronize your files across different units. If you switch between computers more than a few times a week, this one's really cool. What I've done is I configured it to check my flash disk automatically once I plug it in on any computer I'm using and to automatically update the files. Saves lots of time and helps to avoid file version mix-ups.
PDFX-Change - a nice PDF viewer with convenient commenting options - quite useful for on-screen proofreading and grading, if you care about saving paper or if you work with people over the Internet.
FreeMind - a java-based mind-mapping software. I use it to organize papers I've read (you can include local or external links). It is kinda cool to draw arrows between papers, add comments, group them according to topic and so on. Sometimes I also use it to outline papers.
TimeGT - For a long time I was looking for a nice task management software. I tried quite a few different ones, but eventually settled on this one. It is complicated enough to handle my task groupings, but sufficiently user friendly to allow me spend less time organizing my tasks than actually performing them. Also, it is GTD-compatible.
Speaking of GTD, GTD for gmail is a nice add-on that helps one to survive email storms. It works quite well for Firefox. The Chrome version is still a bit shaky, but things are looking bright.
GoogleReader really helps me to keep track of all those interesting blog posts on all those neat blogs I'm following (only now I have 572 unread items). It's also an excellent procrastinating tool when you don't feel like really working, but don't wanna feel guilty about not doing anything useful. You can also find your friends and follow their recommendations.
StyleWriter (4.0) - only recently I started using this interesting piece of proofreading software. What's quite nice about it is that it focuses on avoiding pompous and wordy phrases, lengthy sentences and such. It actually helps me to keep my writing simple(r). Alas, it's not freeware. Another problem is, it doesn't handle LaTeX too well, so I have to play around with my text before I run it by StyleWriter.
JabRef reference manager. It works quite well with bibtex databases, and it is not too bad as a pdf manager.
Speaking of references, Mendeley certainly deserves a honorable mention (I wrote about it some time ago). Come to think of it, I'm quite disappointed by how it can't handle switching between computers and changing local folders, so I'm waiting for a better version before I start using it seriously.

How not to use the Church-Turing thesis against platonism

2010-08-04T09:56:00.004+02:00

Recently, I've written up a quick note explaining why an argument against platonism, based on the Church-Turing thesis and deployed by Olszewski (1999) doesn't work. It's here. Abstract below.

Olszewski [1999] claims that the Church-Turing thesis can be used in an argument against platonism in philosophy of mathematics. I argue that the argument relies on the illegitimate conﬂation of eﬀective computability with computability by any means, and that even if it worked, it would not be an argument against platonism, but rather against any realism about truth-value of mathematical sentences.

Some Polish classics online

2010-08-04T09:46:00.003+02:00

The Polish Virtual Library of Science made quite a few classical volumes available. Among them, some historical volumes of Acta Arithmetica, Annales Polonici Mathematici, Fundamenta Mathematicae, Mathematical Monographs series, Mathematical Dissertations and Studia Mathematica. Here. Of special interest, Kuratowski's and Sierpinski's works in the Mathematical Monographs series. Here. Alas, some of the stuff is in French and some is in Polish.

Watch out in Kirchberg

2010-07-15T23:22:00.003+02:00

Soon, some of you might be headed to Kirchberg for the yearly Wittgenstein Symposium organized by the Austrian Ludwig Wittgenstein Society.

What you might know is that if you want to, you might bring your tent and camp for free near the swimming pool in this lovely village during the event.

What you might not know is that if you do, this involves some risk. In 2008 when I was there, our rather international camp was attacked by a bunch of young nationalists yelling scheissen Polaken raus and such (even though, only some of us were actually Polish). So, my advice, enjoy the event, it's definitely worth it, but be careful and don't walk around alone at night.

Gender gap in class

2010-06-12T15:13:00.004+02:00

Having read about final gaps at Oxford, I got a tad self-consciouss and run the stats for the two largest classes I taught this year. It turns out that in Logic women are 1.17 points (out of 100) ahead of men, and in a course where we do stuff on theories of truth men are 2.14 points (also out of 100) ahead. I feel relieved.

Befriending numbers nominalistically

2010-05-28T12:30:00.005+02:00

I probably should've posted this sooner. On Monday I'm giving a talk at Oxford, criticizing Nathan Salmon's argument against nominalism, to be found in his recent paper in Analysis titled Numbers versus Nominalists. Feel free to pop in if you're around. Details below.

Rafal Urbaniak (Ghent University/ Gdansk University) 'Yellow card for Salmon'
Monday, 31 May, 16:30 - 18:30, Ryle Room, Faculty of Philosophy,10 Merton Street, Oxford.

Nathan Salmon (Numbers versus nominalists, Analysis 68.3:177-182,2008) argues that nominalists cannot plausibly deny the inference from(A) `there are exactly two Martian moons' to (B) `something is such that it is number two and there are exactly that many Martian moons'.He insists that the latter claim commits one to the existence ofnumbers. Salmon in effect argues that nominalism faces a rather serious challenge, for (as he claims) the inference can be denied only at the expense of giving up on higher-order logic, which is very unlikely to be an independently motivated strategy. After briefly describing Salmon's argument I will sketch a variant ofthe nominalist position on which the troublesome and apparently committing sentence is ambiguous between a statement that is derivable from (A) but non-committing, and another, which is committing but (onthe nominalist's view) not derivable from (A), even if the nominalistfinds higher-order logic a reliable source of legitimate inferences

Boredom in philosophy

2010-05-18T21:57:00.002+02:00

In Florida Philosophical Review David McNaughton has an amusing and somewhat to the point paper about why philosophy tends to be tedious and boring. Here.

Why is so much philosophy so tedious? Not, or not simply, because it is technical and complex, but because—too often—it displays mere cleverness. Implausible theories are defended against objections by ever more sophisticated technical fiddling with the details. Originality and creativity are in short supply. I argue that this is bad for philosophy, bad for philosophers, and almost inevitable given various structural features of the profession which require early and prolific publication. As a profession we are autonomous—we could change our structures if we chose.

Łukasiewicz at Harvard, 1926

2010-05-07T18:17:00.006+02:00

I was browsing a volume of a Polish philosophical journal (Ruch Filozoficzny) dating back to 1928, looking for something quite unrelated when I came across Łukasiewicz's report about the Sixth International Congress of Philosophy, Harvard, Sept 13-17, 1926, which, as it turns out, he attended. I did find his report slightly unusual, so here's a juicy bit, in my rough translation:

Almost everything made the worst impression on me. Perhaps this was only bad luck. I wasn't present and the most interesting talks by Driesch, Weyl and Whitehead, which took place before my arrival. Although, having seen the content in print, I infer that perhaps I wouldn't have gained much had I actually heard them. From what I've experienced, a few details.

In the plenary session, Bougle from Sorbonne was talking about philosophy and peace movement, and E. Becher from Munich about darwinism and international relations. Both talks were on the level of newspaper articles; and the topics were more propagandistic than scientific. Becher said that Darwin's theory cannot be applied to human societies, because at war it is the bravest who perish, and the weak hide behind the lines. It came across my mind that had the Germans won, one could find a philosopher who'd say that according to Darwin's theory the bravest have the right to live and the weakest have to die. In the logic session Schiller from Oxford was trying to eradicate the difference between facts and values saying that facts become values and values become facts. I didn't understand anything and even now I think he was only playing with words. J. E. Heyde from Gryfia [not sure what place Ł meant, RU] was teaching in Rehmke's spirit how to solve the "ultimate" "problem of knowledge". He emphasized that what is not extended cannot occupy space. I reminded him that mathematicians don't take points to be extended and yet they locate them in space. He seemed surprised, opposed softly, and eventually said that he'd like to correspond with me about this. I gave him my address. So far, no message. Other talks weren't any better, maybe except for an interesting talk about the meaning of the concept of probability by C. J. Ducasse from Providence, Rhode Island.

On the last day, in the logic section, after five boring talks a short discussion took place. I spoke, giving critical remarks about the talks and expressed the view that the level of philosophical conferences is way lower than the level of other scientific conventions. A few people nodded, in general my impression was they didn't get it.

My only profit from the congress is that it supported my conviction that philosophy, as it is nowadays practiced, and as it has always been practiced, can have various values, can be uplifting, can satisfy your heart's needs, but is devoid of the most important value I think it should have: scientific value.

J. H. Sobel (1929-2010)

2010-04-26T21:36:00.003+02:00

Only now I have learned that Jordan Howard Sobel has passed away. A brilliant philosopher of religion, epistemologist and logician. I had the pleasure of attending his talk in 2007 in Vancouver (SEPA annual meeting) and chatting with him at dinner. His Logic and Theism is definitely to be recommended. Rest in peace...

Frege's slingshot, a minor fix (in case you care about details)

2010-04-16T10:21:00.004+02:00

In one of the classes, I'm talking about slingshot arguments, and I was thinking about a possibly clear way of laying out Frege's argument that (if sentences have denotations) propositions aren't in general denotations of sentences, showing why the conclusion technically speaking doesn't follow, and how once an extra assumption is added the argument flies. Here's the result. (If you know and understand Frege, this probably won't surprise you, but I'm only concerned with a way of presenting this to students here).

Frege in On Sense and Nominatum argues:

Thus far we have considered sense and nominatum only of such expressions, words, and signs which we called proper names. We are now going to inquire into the sense and the nominatum of a whole declarative sentence. [...] Is this thought to be regarded as the sense or the nominatum of the sentence? Let us for the moment assume that the sentence has a nominatum! If we then substitute a word in it by another word with the same nominatum but a different sense, then this substitution cannot affect the nominatum of the sentence. But we realize that in such cases the proposition is changed; e.g., the proposition of the sentence "the morning star is a body illuminated by the sun" is different from that of "the evening star is a body illuminated by the sun''. Someone who did not know that the evening star is the same as the morning star could consider the one proposition true and the other false. The proposition can therefore not be the nominatum of the sentence; it will instead have to be regarded as its sense.

To put this in a step-wise manner: consider two sentences:

[A] The morning star is a body illuminated by the sun.

[B] The evening star is a body illuminated by the sun.

The assumptions are:

[F1] If one can accept a sentence p but deny a sentence q simultaneously (in a given context), p and q do not express the same proposition.

[F2] Substitution of co-referential designators in larger expressions preserves the denotation of whole expressions.

[F3] In one and the same context, one can accept [A] and deny [B].

[F4] The morning star = The evening star

The first two steps in reasoning are quite straightforward. From [F1] and [F3] it follows:

[F5] [A] and [B] express different propositions.

and from [F2] and [F4] we obtain:

[F6] [A] and [B] have the same denotation.

Now for the slightly problematic step (supposedly from [F5] and [F6]):

[F7] The proposition expressed by [A] is not the denotation of [A] and the proposition expressed by [B] is not the denotation of [B]

To see why [F7] doesn't follow from [F5] and [F6], let's represent these more formally. "D(p)" stands for "the denotation of "p" " and "S(p)" stands for "the proposition expressed by (the sense of) "p" ".

[F5'] S(A) ≠S(B)

[F6'] D(A)=D(B)

[F7'] D(A)≠S(A) & D(B)≠S(B)

Now consider two models, in which:

[model 1] D(A)=S(A) & D(B)≠S(B)

[model 2] D(B)=S(B) & D(A)≠S(A)

In each of those models [F5'] and [F6'] are true, and yet [F7'] false (it's helps to draw a diagram here). Of course, there are at least two worries. One is that each of the models is not too uniform: the denotation of one of the sentences is identical with its sense, whereas the denotation of the other isn't identical with its sense. Another worry is that there are no clear reasons why any of these situations is to be preferred over the other. Hence, it seems sensible to use an extra assumption which captures the idea that the answer to the question whether denotations of sentences are their senses should have a general answer, that is, that either all sentences denote their senses, or no sentence does:

[F+] D(A)=S(A) ⇔D(B)=S(B)

In fact, [F7'] follows from [F5'], [F6'] and [F+]. For suppose that [F5'], [F6'] and [F+] are true and yet [F7'] is false:

[F7-] ~[D(A)≠S(A) & D(B)≠S(B)]

DeMorgan applied to [F7-] gives us:

[F7-a] D(A)=S(A) v D(B)=S(B)

Now, let's do a proof by cases. Suppose:

[A1] D(A)=S(A)

With [F+] this entails:

[A2] D(B)=S(B)

But transitivity of identity applied to [A1], [F6'] and [A2] gives us:

[A3] S(A)=S(B)

which contradicts [F5'].

An argument for the other case is analogous. Suppose:

[B1] D(B)=S(B)

An application of [F+] yields:

[B2] D(A)=S(A)

Transitivity of identity applied to [B1], [F6'] and [B2] gives us:

[B3] S(A)=S(B)

which contradicts [F5'].

If you find this formulation useful, feel free to use it in class (it would be nice if you let me know if you do, though).

A historical remark on the nominal description theory

2010-03-29T21:27:00.003+02:00

I haven't been posting in a while, being swamped with teaching duties and so on. Right now, I'm looking at M. Morris's An Introduction to the Philosophy of Language, which in those respects that currently interest me contains, I think, more material than, say, Miller's or Lycan's textbooks (having said that, these books on the other hand have other virtues). On pp 86ff Morris is talking about what he calls a simple nominal description theory, according to which a name n connotes the description `the object called n' (or something to that effect). This, of course, seems to violate Kripke's non-circularity restriction; yet, it has been interestingly developed by K. Bach (Thought and Reference). Anyway, my point is rather short and historical - although this view hasn't been associated with anyone in the Frege-Russell period, this sort of approach has been around for a while, and I'm quite positive that at least Lesniewski hold that view. Here's a relevant bit from L's 1911 paper, in my translation:

J.S. Mill says that not all names have connotations. Among those which have no connotations are, according to Mill, proper names such as, e.g., Paul, Caesar on the one hand, and some of the names of attributes on the other. If this were really so, one could foresee certain difficulties in regarding as analytic those positive existential propositions whose subjects are just such names without connotation. Yet even the names which I have mentioned and which according to Mill have no connotation, in my opinion, have connotation; proper names connote the property of possessing a name which sounds like the given proper name, whereas the names of attributes regarded by Mill as lacking connotation, connote either the property of possessing such names, or the property of complete identity with entities which bear such names. Thus, e.g., the name ‘Paul’ connotes the property of having the name ‘Paul’, the name ‘redness’ connotes the property of having the name ‘redness’. Instead of ‘Paul’ we can then say ‘a being which has the name ‘Paul”, instead of ‘redness’ — a being which is completely identical with beings that bear the name ‘redness’. . . I shall touch here upon Husserl’s thesis that one proper name, e.g., Socrates’, can name various objects only because it is ambiguous, just as names such as ‘redness’; I do not think this is the case — these names would be equivocal only if, while denoting various objects, they also connoted different properties. In fact the word ‘Socrates’, while denoting different objects, connotes always one property, that is the property of bearing the name ‘Socrates’.

Knowability volume online

2010-03-05T09:15:00.001+01:00

I see a volume of Synthese devoted to knowability issues is now available online. Cool.

The History of Categorical Logic

2009-12-26T00:59:00.002+01:00

Through the paralyzing paradoxes of Professor Polaro I have learned that The History of Categorical Logic by Jean-Pierre Marquis and Gonzalo E. Reyes is available online for free. So far I just took a quick look, but it seems like a good read. Here.

Nominalist Neologicism

2009-12-21T17:03:00.003+01:00

My visit to Bristol is over, I'm back home (i.e. in Poland) for a few weeks. I used some of the spare time to finish drafting the first paper that I worked on with Oystein Linnebo last semester (stay tuned for another one).

The paper is titled Nominalist Neologicism and contains the core of the modal-iterative approach to abstraction principles that I've been advocating over the last year or so. It's based on a talk I gave in Frankfurt (Trends in the Philosophy of Mathematics), so the style is a bit relaxed.

If you plan to take a look at it, please let me know in a comment below this post, so that I know I should expect feedback from you. The deadline is Jan 15, so if you have any comments, please share them with me by Jan 10.

Here.

deRosset's stuff on modalities

2009-12-07T15:52:00.002+01:00

I see Louis deRosset has posted a few nice pieces related to modalities on his website. These include "Possible worlds I: Modal Realism", "Possible Worlds II: Nonreductive Theories of Possible Worlds" and his dissertation "Modal Primitivism: A study in the metaphysics of Necessity and Possibility". Here.

Philosophical Tales

2009-11-30T14:51:00.006+01:00

Recently my favorite method of procrastination involved reading Philosophical Tales: Being an Alternative History Revealing the Characters, the Plots, and the Hidden Scenes That Make Up the True story of Philosophy. Even if not always charitable and not always historically adequate, it's quite amusing. Below, some fragments that I find entertaining (the selection is slightly random, though):

Thomas Aquinas was very overweight, suffered from dropsy, and had one large eye and one small eye which made him look lopsided. As a child he was silent most of the time and, when he did speak, it was often unrelated to the conversation. So, he decided to become a philosopher-monk. And, as such, he was very successful.

After he [Aquinas] drove away the temptress, two angels came to him and fastened a chastity belt around his waist.” Or so at least embellishes our other theological expert at Trinity Communications on the Internet, along with advice to readers to “Buy or fashion your own chastity belt, easy to make from braided yarn or thin, soft rope.” (Adding that “St. Joseph chastity belts are available at some Catholic shops,” which Aquinas would not have approved of, being against shops and trading generally.) But at least there is agreement on Aquinas’s good character, albeit it still remains a challenge for people who think that sex is that bad to work out how to continue existing once the present batch has died out....
In the afternoon, Kant would take a long walk along the river, accompanied by his servant, Lampe, carrying an umbrella in case it rained. Kant’s rule that everyone must be treated as an end in themselves and never merely as a ‘means’ to an end (“there can be nothing more dreadful than that the actions of a man should be subject to the will of another”) evidently did not apply to servants carrying umbrellas
Even in bed, the rules had to be followed: Kant had a system for rolling himself up in his sheets so that they ﬁ tted tightly around him. Kant, it will be noted, slept for less than seven hours. He wrote a little booklet about health matters, warning against the dangers of too much sleep. He explained that as each person had only a certain amount of sleep in them, if they used it all up by lying in bed, they WOULD DIE EARLY. (My parents should have told me that ...)
In the Critique of Practical Reason (1786) Kant’s thought leaves the physical universe behind to find a proof for the existence of heaven and the afterlife. He points out that since justice is the good ﬂourishing and the wicked being punished, and that this does not happen on Earth, as we can see by looking around us, then it must take place “in the next world.” This is sublime reasoning. And so to the less than fully appreciated Kantian treatise on the beautiful and the sublime. Night is sublime, day is beautiful. The sea is sublime, the land is beautiful, men are sublime, women are beautiful – and so on. Lots of professors wrote treatises like that at the time, it was almost compulsory.
...the best known is what he calls the categorical imperative:

Act only according to a maxim by which you can at the same time will that it shall become a general law.

...when Kant’s version appears in the Metaphysic of Morals (1785), the imperative is also offered to decide all moral issues. Curiously, though, it seems to collapse at the most easy tests. For example, it allows things that surely should be banned, while outlawing things that don’t seem to matter very much. A rule, for instance, that all children under 5 who disturb philosophers should be beaten with a stick and have their tongues cut out is approved by the ‘rule’ since it is universalizable, but borrowing is forbidden, as if everyone borrowed, it would lead to a run on the bank.
Pompous Footnote

1 Prior to Kant, as Bertrand Russell also notes, philosophers were gentlemen, addressing an audience of amateurs in the language of the everyday. After Kant, philosophy became a dialogue (indeed, often a monologue), conducted in technical language and obscure terms.
Montaigne constantly referred to himself as a way of both ridiculing and excusing his views. Des Cartes uses the same device to distance himself from anticipated criticism, and also to create the dramatic story of the author’s ‘enlightenment’ after some six days reﬂecting on the nature of the world in a warm oven room.
The famous words cogito ergo sum (which render themselves so elegantly in English as “I think, therefore I am”) never appear in the original version of the Meditations, only in a later and indeed rather casual translation. The actual words used are better translated as: “let the Demon deceive me as much as he may, he will never bring it about that I am nothing so long as I think I am something. So, after considering everything very thoroughly, I must conclude that this proposition, I am, I exist, is necessarily true, every time that I say it, or conceive it in my mind.”(1)

Pompous Footnote
1 Ego sum, ego existo, quoties a me profertur, vel mente concipitur, necessario esse verum is the original Latin text of 1641, for purists. The French version of the principle in the Discourses is superﬁcially nearer to “I think, therefore I am,” being “Je pense, donc je suis,” but an accurate translation of this is not “I think, therefore I am,” but “I am thinking, therefore I exist.” Anyway, the ‘cogito’ does not refer to this text but to the argument in the Meditations. So that’s clear.
Bertrand Arthur William Russell, Third Earl of somewhere or other, son of a Victorian prime minister, and Professor of Philosophy at Trinity College, Cambridge, is still considered there, if not much anywhere else, as “profoundly inﬂ uential in the development of philosophy in the twentieth century.” His special expertise is said to have been in the area of philosophical logic; indeed, he is credited with having coined the term, although as the words have long currency individually, and the activity preceded him by 2,000 years, it is hard to see how his arrangement can count as a novelty. Nevertheless, says Nicholas Grifﬁn, writing in the Routledge Encyclopedia of Philosophy, he was indisputably responsible for a number of “important logical innovations,” prime amongst which was a way to “reparse sentences continuing the phrase ‘so-and-so’ into a form in which the phrase did not appear.” Such achievements deserve further examination.
As a philosopher, Russell sometimes speaks absolute nonsense. Russell seems to have been aware of this, hence his “impish grin” whilst offering increasingly ludicrous examples. Not so his heirs. They issue their dull arrangements with a seriousness born of a serene lack of self-knowledge. Fortunately aside from his logic, Russell did other things. The same is not true of his followers.
Whilst there at Cambridge, Wittgenstein became an institution within an institution, celebrated both for his unorthodox personal style and for his revolutionary approach to teaching. Refusing to lecture but offering only to hold seminars, his ascetic ofﬁce had few books, equipped instead with the famous deckchair. Those who attended his seminars became his ‘disciples’, and showed their commitment by dressing the same way – tweed jackets, ﬂ annel trousers, no ties. (The clothes, like the philosophy, were not for girls . . .) After each session, he would invite selected conﬁdants to join him at ‘the ﬂicks’, where he would sit in the middle of the front row (nearest the screen) munching on a pork pie. As for Cambridge’s ofﬁcial social gatherings, Wittgenstein declined to attend the ‘dinners’ of the university, although he did agree to participate in the ‘Moral Science Club’ from time to time, including one infamous evening when, to murmurs of approval from his disciples, he demanded of Karl Popper that he provide an example of a ‘moral rule’, gesticulating with a poker for emphasis. Popper supposedly said, “Not threatening visiting speakers with pokers,” and Wittgenstein threw the poker down and stormed out (followed by disciples).
... today the ofﬁcial hagiography neglects some facts. Wittgenstein did give away ‘control’ of his inherited millions, but only to his sisters, and so it was that during World War II, even as the Nazi project was at its most clear and most appalling, he was still able to arrange that a large chunk of the Wittgenstein family fortune – not, say, three ingots of gold (as we all might send) but three tons of the stuff – was made available to the Nazi war effort. In return, the family received official ‘non-Jewish’ status.
Yet, despite favoring one absolute authority, Hobbes dismantled the claims of kings to divine favor, and for doing this (amongst other reasons) he was considered by many of his contemporaries to be, if not actually an atheist, certainly a dangerous heretic. After the Great Plague of 1666, when 60,000 Londoners died, followed by the Great Fire straight afterwards, a parliamentary committee was set up to investigate whether his writings might have brought the two disasters on the realm. As a result of its ﬁndings, he was forbidden to write any more books about matters relating to “human conduct” and so had to publish his work abroad instead.
A report in the Journal des Savants of March 4, 1686, records that one young lady had refused “a perfectly eligible suitor” because “he had been unable, within a given time, to produce any new idea about squaring the circle.”
No one knows now exactly what he was accused of, but one of his early biographers, Colerus, describes how Spinoza, relaxed by smoking a pipe, or when he wanted to “rest his mind” rather longer, looked for some spiders which had gotten into a fight with one another, or (failing that) he put flies into a spider’s web, “and then watched the battle with so much enjoyment that he sometimes burst out laughing.” Such diversions there were before there was telly.

Miscellanea Logica: new series

2009-11-28T02:31:00.006+01:00

Through Philos-L I've learned that the new series of Miscellanea Logica is out - for a while I though the enterprise was pretty much dead, but the new series is up and running, chief-edited by Jaroslav Peregrin, a cool logician, known also to some as the - brilliant - logician - who - made - us - make - unintended - loops - on - an - otherwise - marvelous - hike - in - Czech - mountains - in 2007 - nevertheless ("hey, haven't we passed by that tree-cutting machine some time ago?" - "No, there's plenty of those around here" - "all of them with a blue blouse inside and this sticker?") ... anyway, I see that the new series is available online for free! HERE! Check it out. :)

Managing pdfs with Mendeley

2009-11-19T10:56:00.003+01:00

Recently, I've been playing around with Mendeley, a pdf file manager. It does have some very neat features: it allows one to catalogue their pdf files in one database, it keeps a copy of the catalogue (and files, up to 500 MB) online, it inludes an internal pdf browser and provides nice search & filtering options, it allows one to share groups of pdfs with up to 10 other people; it is also possible to comment on pdfs and share those comments as well. Another nice feature is that the package includes a file manager which (if you want) can organize copies of imported files, so that you end up with one organized folder with all your pdfs and positions in your catalogue are linked to them. You can also decide to generate a bibtex file (or bibtex files) as you go, if you like to use LaTeX. When you add files, you can automatically do a google scholar search for file details, it works pretty well. Overall, I think the authors have done a pretty good job. I decided to import all my pdfs into the database. The whole thing, however, is in its beta stage and there are some minor issues - here are some remarks:

There is no explicit "work offline" option, and if you change the library and restart the program, it connects automatically with the server and uploads the changes. Sometimes, I'm connected with internet only by a wireless stick, and I don't want my library to automatically synchronize with the server while adding pdfs and editing pdf intro.
The program crashes once in a while (in my case, it's more like 3-5 times a day). Luckily, no data loss occurs.
The bibtex file that the program generates is kinda weird, you have to take a look at it and correct it by hand. File links in Bibtex don't work when you open the file with JabRef. In the original database it's difficult to make a distinction between those capitalizations that are to be preserved in Bibtex. If you imported your files from a bibtex database, in the new database most likely the entries will get new keys. Still, it's easier to correct the entry and copy it to your "real" bibtex file than to create a new one, so I rather enjoy the bibtex-related features.
The internal pdf browser isn't too elaborate - I wouldn't mind having at least "go to page", "go to next page", "go to previous page" buttons. Also, it would be nice if the browser supported bookmarks.
The file organizer options, even though they include organizing files into folders by journal, author or year, don't allow you to organize files by collection.

I do think, however, that overall this is a pretty cool stuff and I'm sure, given some time, it will become even better.

What we don't need to save ordinary conditionals from

2009-11-07T17:12:00.002+01:00

It’s been a while since I posted anything. Mostly this is because life has been pretty hectic lately. In September we spent a few weeks in Gdańsk, but now we’re moving every few weeks between various places in the UK, visiting different universities and trying to get some research done meanwhile. This semester I’m mostly based in Bristol as a British Academy Visiting Fellow, working with Oystein Linnebo on the dynamic approach to abstraction principles, and doing some directed reading (on groundedness with Hannes Leitgeb and on axiomatic theories of truth with Leon Horsten). These days, however, we’re hanging out in Scotland, currently visiting Arche Research Centre in St. Andrews, taking off for a few other places tomorrow.

I gave a talk here on Tuesday about nominalistic approaches to neologicism, and decided to stick around for the Arche/CSMN graduate conference. Today, I managed to catch a talk by Ernest Lepore followed by an interesting talk about counterfactuals by Daniel Berntson (with a commentary by Guðmundur Andri Hjálmarsson). Daniel’s talk was titled Saving Ordinary Counterfactuals and was devoted to the problems that quantum indeterminacy (or related phenomena) are supposed to raise for our intuitions about ordinary counterfactuals. The whole thing was very clear and quite interesting. I do have one minor worry, though - I don’t think the problem that Daniel is trying to address exists... Counterfactually: if there were such a problem, Daniel’s approach would be a neat way to approach it. But let’s start from the beginning...

The problem

Intuitively we accept the counterfactual:

(1) If I were to throw a champagne glass off the top of Empire State Building, it would break.

Supposedly, quantum mechanics informs us also that:

(2) There is some chance that a glass thrown off the top of the Empire State Building will quantum tunnel to the moon without breaking.

If indeterminism is true and (2) expresses objective probability, (2) seems to entail (3):

(3) If I were to throw a champagne glass of the top of the Empire State Building, it might safely quantum tunnel to the moon.

This entails:

(4) If I were to throw a champagne glass off the Empire State Building, it might not break.

Now, Daniel suggests that "(4) puts pressure on us to give up (1)" and that there is an "inescapable clash" in the infelicitous assertion (5):

(5) If I were to throw a champagne glass off the Empire State building, it would break; and furthermore, it might not break.

The strategy

In order to save the truth of (1) within the Lewis-Stalnaker approach, Daniel suggests replacing:

A>B iff all of the closest A-worlds are B-worlds.

with

A>B iff the vast majority of the closest A-worlds are B-worlds.

The underlying idea now would be that (1) is made true because most of the closest worlds where the glass is dropped are worlds where it is broken, whereas (4) emphasizes that not all closest possible worlds are worlds where the glass is broken.

Say we put aside the issue of how we are to count possible worlds and they ratios if there are infinitely many of those. There still are some problems that come along with this solution. Most prominently, agglomeration (A>B, A>C hence A>B&C) and transitivity (A>B, A^B>C hence A>C) fail. To fix these issues, Daniel introduces the notion of being almost true, and says that certain claims, even though they aren’t strictly speaking true on this semantics, are still almost true, like when we have a counterfactual which doesn’t preserve probability ratio, but whose consequent is only slightly less probable than the antecedent. There are some bells and whistles to play around with here, but this should be enough for the set-up.

The worry

First, observe that a necessary (but not obviously sufficient) condition for thinking that (5) is a problem is the acceptance of (1) and (4). Strictly speaking, so far Daniel has shown how to preserve the truth of (1), but didn’t say explicitly how to make sense of (4).

In fact, Daniel introduces might-conditionals by saying:

A >m> B iff ~(A>~B)

That is, a might conditional A >m> B is supposed to come out true iff it is not the case that ~B is true in the vast majority of the closest A-worlds.

Alas, this reading of might-conditionals doesn’t support the truth of (4), because given that all the relevant worlds where the glass is broken are worlds where it is not the case that it tunnels safely to the moon, (4) still comes out false if it is to be read as a might-conditional.

Second, it’s not clear where the clash really is. I would certainly be worried if I had intuitive reasons to believe:

(5’) If I were to throw a champagne glass off the Empire State building, it would break; and furthermore, it wouldn’t break.

But so far, I don’t. (5) certainly doesn’t entail (5’). Given that (4) shouldn’t be constructed as a might-counterfactual if its truth is to be preserved, what job exactly is "might" doing in (4) and (5)?

Well, I’m inclined to say that that are at least two ways to accept (1), (4) and (5) even if we play along with non-probabilistic Lewis-Stalnaker semantics.

Story 1. (1) says that in every closest possible world, where I drop the glass, it’s broken, whereas (4) says that there are still some accessible but less similar worlds, where even though the glass is dropped, it’s not broken.
Story 2 (1) says that in every closest possible world, where I drop the glass, it’s broken, and (4) says that it is possible that the glass is dropped and not broken.

Personally, I prefer story 2, because it assigns less content to "might", and because (5) as it is, when read along the reading suggested in story 2, entails that the world where the glass is broken is not the closest one anyway.

I don’t even have the intuitions that (5) displays any sort of clash to start with. Imagine I say:

If I were to join you for conference drinks tonight, I would be hungover the next day. Well, in fact, it’s highly unlikely that I would decide to drink only water, in which case I might feel good the next day even if I go. So if I were to join you for conference drinks tonight, I might feel good the next day, but I think I wouldn’t.

This doesn't seem to contain any contradiction whatsoever.

Interestingly, we did a poll and around half of the audience thought that (5) was problematic, and around half that it wasn’t.

The "Modal argument" paper is forthcoming

2009-09-19T10:31:00.005+02:00

A paper we wrote with Agnieszka Rostalska (I very roughly outlined an early version here) is forthcoming in Philo. A rather final draft of the paper is available online here. The paper is devoted to the clarification and criticism of Swinburne's modal argument for the existence of the soul. Before I paste the abstract and acknowledgments below, one more remark.

When giving this paper at various places, one sort of reactions encountered came from people with good background in logic, but no previous experience with philosophy whatsoever. The reaction boils down to a rather blind stare and comments like "who cares about arguments for the existence of the soul?" or "Why is anyone doing this stuff?". The answers are simple. "Philosophers." to the first question. "Because it's more interesting than using complex mathematical tools to solve problems that only two to three people in the world care about." to the second one.

I prefer to use slightly less elaborate mathematical machinery to deal with philosophically motivated issues than to get into very complex and hermetic issues in, say, inaccessible set theory or computer science. This doesn't mean they aren't interesting. I just find philosophical problems more entertaining and important. And I think it is, in a sense, the responsibility of a philosopher and a logician to spend some time looking at what philosophical arguments are around about claims people care about and what can be said about their correctness, instead of locking themselves in the ivory tower of elaborate and detached purely mathematical problems. But again, it's a matter of choice.

Abstract

Richard Swinburne (Swinburne and Shoemaker 1984; Swinburne 1986) argues that human beings currently alive have non-bodily immaterial parts called souls. In his main argument in support of this conclusion (modal argument), roughly speaking, from the assumption that it is logically possible that a human being survives the destruction of their body and a few additional premises, he infers the actual existence of souls. After a brief presentation of the argument we describe the main known objection to it, called the substitution objection (SO for short), which is raised by Alston and Smythe (1994), Zimmerman (1991) and Stump and Kretzmann (1996). We then explain Swinburne's response to it (1996). This constitutes a background for the discussion that follows. First, we formalize Swinburne's argument in a quantified propositional modal language so that it is logically valid and contains no tacit assumptions, clearing up some notational issues as we go. Having done that, we explain why we find Swinburne's response unsatisfactory. Next, we indicate that even though SO is quite compelling (albeit for a slightly different reason than the one given previously in the literature), a weakening of one of the premises yields a valid argument for the same conclusion and yet immune to SO. Even this version of the argument, we argue, is epistemically circular.

Acknowledgments

We would like to express our gratitude to all the people who discussed these issues with us and commented on earlier versions of this paper. We are grateful to participants of the events where the paper has been presented: Workshop & Young Researcher's Day in Logic, Philosophy and History of Science in Brussels, 2008, Jeffrey Ketland's Omega-seminar in Edinburgh, 2008, and Formal Methods in the Epistemology of Religion in Leuven, 2009. The main ideas of this paper originated after a number of discussions about philosophy of religion and mind with Professor Jack MacIntosh (Calgary). Comments provided by Professor Richard Swinburne (Oxford), who was in the audience when this paper was presented in Leuven in June 2009, were also very helpful, and it was interesting to learn that Professor Swinburne agrees with all our main points, apart from our final assessment of the modified argument. It was Lara Buchak (Berkeley) who observed that our version of the argument developed in response to SO results from a weakening of one of the premises. We also owe gratitude to Paul Draper for his invaluable editorial comments.

Trends in Philosophy of Mathematics (day 3, talk 1)

2009-09-12T19:10:00.001+02:00

On the third day the schedule was a bit more complicated, we had to choose between one of two parallel sessions. The choice was difficult, so I will be unable to comment on some of really interesting talks that I was unable to attend. If I don’t talk about a certain talk it’s because I was unable to make it to it because the alternative talk was more related to what I’m working on. For now, the first talk of the day.

Assadian: Crispin Wright and his Hero

Wright, defending the epistemic accessibility of prima facie impredicative Hume’s Principle tells a story of a fictional character (named Hero) who initially knows second-order logic and possesses a bunch of sortal concepts referring to concrete objects, but doesn’t understand the concept of number. Wright then argues that the Hero can process in stages in order to gain the understanding of the concept of natural numbers.

Stage 1 - The Hero introduces HP for the initial domain that he possesses a grasp of.

Stage 2 - The Hero now understands without circularity the truth conditions of Nx:Fx = Nx:Gx, where neither F nor G contain further occurrences of further numerical terms. The Hero also knows that Nx:Fx=s is false for any term s referring to an object present at Stage 1. In this sense, he seems able to solve the Caesar Problem for he comes to accept:

(NE) no object whose identity is grounded in anything else than HP can be identical to a number.

Stage 3 - The Hero moves on to understanding truth conditions of identity statements of terms containing embedded occurrences of numerical operators.

Assadian takes issue with Wright’s account of how the Hero learns NE, which is of key importance in solving CP. NE seems to hinge on the possession of a complete characterization of natural numbers (=identity conditions for them), and this is not something that the Hero can have at stage 2. For it seems that to understand the claim that the characterization of numbers doesn’t go beyond its identity conditions dictated by HP, one has to be able to grasp those identity conditions already.On the other hand, understanding of complex terms containing embedded numerical operators seems to require that NE be already known, if CP is to be solved. Moreover, if NE is not available at stage 2, the Hero is unable to solve CP at that stage.

A slightly different neologicist approach to the problem is to assume that different sorts of objects in general have different criteria of identity - once one postulates the existence of maximal categories of that sort and ads some fairly convincing assumptions about them, two theorems can be proven. The first says that for any category C for any two objects that fall under that category, they are identical iff they satisfy identity conditions corresponding to that category. The other one says that no object belongs to two different categories. It is needed if we are to exclude the possibility that both numbers and persons constitute a single larger category with its specific identity conditions.

Assadian argues that even though if those theorems are present, CP is solved, it’s quite implausible that those theorems are available to the Hero at stage 2, because theorem 2 already says something about the whole category of all numbers and their identity conditions. On the other hand, if those theorems are to be introduced only at stage 3, it is unclear why the Hero would be able to solve CP already in stange 2 to start with.

Although I generally agree that non-iterative approaches to abstraction principles have been so far unable to solve CP (among the iterative ones there’s Linnebo’s and mine, and I think mine can handle CP and it is quite unclear whether Linnebo’s does - but this is a whole different story), I really would have to see the proofs in detail - what would have to be checked is whether (i) the assumptions used to prove theorems 1 and 2 are convincing, (ii) theorems 1 and 2 follow from those assumptions, (iii) theorems 1 and 2 really allow to solve CP (i.e. to prove negations of mixed identity statements, or something to that effect), and (iv) whether no undesired consequences follow from the same assumptions. But the stuff seems interesting.

Qualms about the (non-)circularity of NE aside, what I’m rather worried about is the justification of the framework in which NE even makes sense. I mean, I have pretty hard time understanding the idea of objects such that there is nothing else to learn about them apart from their rather coarse-grained identity conditions. I am perfectly fine with coarse-grained or relative identity claims, or true fake identity between fake singular terms, but the idea that there really are objects such that the only way we can learn anything about them is through abstraction principles seems suspicious. Of course, it is an attempt to deal with epistemic challenges to Platonism about mathematics, but I don’t think a blunt answer of the sort "How can we know something about numbers? Well, we learn something about them through abstraction principles and there’s nothing else to learn" is satisfactory. I would need a more elaborate and convincing metaphysical story which would convince me to accept the existence of such things, and which would explain why those objects should enjoy this particular status.

The adaptive logics book has moved

2009-09-05T16:25:00.001+02:00

Due to server issues, the book I mentioned before has moved. Here. I also fixed the original link.

Live from Trends in Logic VII (day 2)

2009-09-03T04:15:00.003+02:00

Today we had four quite exciting talks. The first one, given by Oystein Linnebo (Bristol) was devoted to A Partial Defense of Frege's Basic Law V. Oystein started off with the intuitions that there is some pressure to accept Frege's BLV (which says that extensions of two concepts are identical iff exactly the same objects fall under that concept). After criticizing the limitation-of-size approach to restricted versions of the comprehension principle, he went modal-and-iterative about BLV. That is, BLV was used to capture how new sets are formed at new stages using the objects already existing in previous stages, and modal operators were thrown in to express the intuition that we're talking about the possible ways our set-formation process can go. This gives a fairly intuitive criterion for a plurality determining a set: it has to have the same elements across possible worlds. Proof-theoretically, once you take S4.2 as the underlying modal logic, throw in some trans-world extensionality principles for pluralities and sets and introduce the potential plural collapse ("it is necessary that for any xx it is possible that there is a y such that y is the set of xx's"), you can get (a reinterpretation of) Zermelo set theory minus infinity and foundation.

The second talk, by Leon Horsten, was devoted to the relation between numbers and counting systems. Leon defended and described the view dubbed computational structuralism: it's kinda like structuralism, but you take arithmetic to be about the structure of arithmetical notational systems. The basic idea is that if one has a recursively introduced notational systems (so that the symbol denoting the successor is computable), and the addition function is also computable, the system is isomorphic to the intended omega-sequences.

Michael Resnik and Stewart Shapiro both talked about qualms that arise around identity conditions for structures and their elements (or positions in them). Resnik, roughly, was arguing that in certain contexts identity claims (and questions about identity) of certain structures doesn't make sense, whereas Shapiro was rather inclined to say that it's not as much the identity questions that are misled, but rather that certain terms may seem and behave like singular terms, despite referring indeterminately to many objects.

Live from Trends in Logic VII

2009-09-02T00:05:00.003+02:00

It's the first day of Trends in Logic VII, aka Trends in the Philosophy of Mathematics. So far, we're past an opening, an opening leture by Ryszard Wójcicki, and a splendid conference dinner.

Ryszard Wójcicki, an excellent "hardcore" logician known for his work on consequence operations and Polish-style meta-theory of propositional calculi, has recently decided to think about more philosophical issues. He was talking about Two sources of mathematical truth. The main gist was that the key "source" of mathematical truth was "conceptual realities" (the other source being empirical domains). Alas, I didn't quite get what being a source of truth is, how conceptual realities are supposed to be different from mathematical structures, what their ontological status is, and why they're supposed to exist. Having said that, it was interesting to hear a real "hardcore" researcher say what he thinks about the philosophical status of his own field.

My general impression is that if a "hardcore" scientist of any specific sort suddenly starts to philosophize, it's bound to be slightly weird stuff from the philosopher's perspective (it's not as bad as a philosopher trying to do science, though). What slightly surprised me was that this also holds for logicians. On the other hand, I do think that one of the problems that analytic philosophy in Poland is facing is that there are many excellent logicians doing highly technical stuff but having no philosophical interests or well developed intuitions, and there are many philosophers with highly developed intuitions, but with almost no grasp of logic or attention to arguments and details whatsoever.

A rant about "deductive"

2009-08-26T11:34:00.006+02:00

or
Don't diss the logician

I’m on my way back from The Second Conference on Concept Types and Frames in Language, Cognition and Science in Dusseldorf. It was a nice conference that gathered linguists, cognitivists, philosophers of science and logicians interested in the functional approach to concepts.

One of the things that surprised me was that both experienced cognitivists (like Paul Thagard) and younger researchers still stick to the distinction between inductive and deductive types of reasoning and attach that much importance to it. Interestingly, “deductive” in their use has a pejorative content and the term is sometimes used condescendingly to emphasize that whatever it is that logicians do is boring and useless and that pretty much the only source of insight and real knowledge are “inductive inferences” taking place in “the real brain”. So, here’s a short rant about this sort of attitude (Frederik is reading over my shoulder and tossing in his remarks).

To start with, I don’t think I know a logician alive who still uses the word “deductive” in any serious ahistorical context. This is because the notion is so worn out that different people associate it with many different things. Instead, more specific terms are used that separately capture different things that you might mean when you say “deductive”.

Roughly, a consequence operation is, for instance, often simply thought of as a set of pairs of sets of sentences. It is called structural if it’s closed under substitution. That’s one thing that you might have in mind: deductive means defined in terms of rules (and maybe axioms) which essentially make no distinction between formulas of the same syntactic form. Another way you can think about these things is to require that a deductive consequence should be simply truth-preserving (vaguely: it’s impossible that the consequence is false when the premises are true). This interpretation is not syntactic, but rather model-theoretic. A truth-preserving consequence doesn’t have to be structural and a structural consequence doesn’t have to be truth-preserving. Another sense you might associate with being deductive is being both structural and truth-preserving (in which case, you still get a multitude of consequence operations, depending on what language and model theory you pick, and what you take to belong to your logical vocabulary). Yet another interpretation you can take is to say that something is a deductive consequence of a given set of premises if it follows from them by classical logic – this notion is sometimes used by those cognitivists who think that logic is classical logic. Although this consequence is structural, whether it’s truth-preserving when it comes to natural language is a matter of what you think about the correctness of certain natural language inferences. For instance, you might be a relevantist – in which case you’re inclined to say that the classical logic allows you to infer too much. Yet another notion simply requires a deductive consequence to satisfy Tarski’s conditions, or some of them, or some of them and some other conditions of a similar type. Yet another idea is to make no reference to a formal system whatsoever and assume that a sentence A is a deductive consequence of a sentence B iff “If B, then A” is analytic (standard qualms about analyticity aside). So in general, the logician’s conceptual framework is full of notions more precise than “deductive”, and the word “deductive” seems unclear and a tad outdated.

But let us even suppose we fix on the notion of being deductive as being validated by classical logic (this seems to be the best you can do if you want to make it easy for the cognitivits to argue that deductive inferences are uninformative). Why on earth would you think that deductive reasoning can only give you boring and useless consequences that you already were aware of, unless you say so because what you take to be the most prominent example of a deduction is one of the slightly obvious syllogisms, most likely employing Socrates and his mortality?

The thing is, human beings are not logically omniscient (I myself, for instance, often feel dumb when I stare at a deductive proof I can’t grasp after half an hour). In fact, the history of mathematics is a good source of examples where prima facie well-understood premise sets led to surprising consequences. Just because the truth of a conclusion is guaranteed by the truth of the premises doesn’t mean that once we believe the premises we actually are aware that they lead to this conclusion. Take the Russell’s paradox. A rather bright dude named Frege spent years without noticing a fairly simple reasoning whose conclusion was to him somewhat surprising. Take Godel’s incompleteness theorem(s). A rather known set of mathematical truths together with a bit of slightly complicated deductive reasoning led to one of the most important discoveries in the 20th century logic, which stunned a bunch of other not-too-dumb mathematicians. If you still think that deductive inferences give nothing but boring and obvious conclusions, think again!

Two points about the opposition between the deductive and the inductive. First of all, unless you define inductive as non-deductive, the distinction is not exhaustive. For instance, if inductive inferences are supposed to be those that lead to a general conclusion, we’re missing non-deductive inferences with particular conclusions (like in History, one uses certain general assumptions and knowledge about present facts to surmise something particular about the past). In this sense, the deductive-reductive distinction introduced by the Lvov-Warsaw school sounds a bit neater (look it up).

Another thing is that people often speak of inductive inferences as if they didn’t have anything to do with deduction (the following point was made by Frederik). Quite to the contrary, certain facts about what is deducible and what isn’t lie always in the background when you’re assessing the plausibility of an inductive inference. For instance, you want the generalization you introduce to explain certain particular data you’re generalizing from, and one of the most obvious analysis of explanation uses the notion of deducibility. Also, you don’t want your new generalization to contradict your other data and other generalizations you have introduced before: but hey, isn’t the notion of consistency highly dependent of your notion of derivability?

Having said that, I also have to emphasize that this doesn't mean that I take non-deductive inferences (whatever they are) to be uninteresting; indeed, the question of how we come to accept certain beliefs other than by deducing them (whatever this consists in) from other beliefs is a very hard and interesting problem. What I oppose to, rather, is drawing cut and dry lines between these types of reasoning and saying that only one of them is interesting.

A book on adaptive logics in progress...

2009-08-22T18:32:00.004+02:00

Diderik Batens is working on a book about adaptive logics. He made drafts of first few chapters available online and invites comments. Here.

Frames, Frames and Frames

2009-08-17T16:25:00.004+02:00

1. The paper on dynamic frames has been accepted and is forthcoming in the Logic Journal of the IGPL. As I understand their self-archiving policy, it can't be publicly accessible for 12 months after it's published by OUP. Hence, I'm making the final version available now, it'll be available till the official publication. If you feel like grabbing it before it disappears, it's here.

2. In the same vein, in Ghent this Friday (August 21) we're having a mini-workshop on frame theory. If you're around at that time, feel free to swing by. There's gonna be an outing afterwards.

Title: Frames, Frames and Frames

Time: Friday, August 21. 17:00-19:00 (There will be three talks, 30 minutes each + discussion)

Place: Room 2.19, Centre for Logic and Philosophy of Science, Universiteit Gent, Blandijnberg 2

Talks:

1. Capturing dynamic frames. It's based on the paper I just mentioned: I explain what frames are, how certain frames can be expressed by sets of first-order, formulas, and how an adaptive strategy can be applied to a reasoning with a conceptual framework when faced with an anomaly.
2. Induction from a single instance and dynamic frames. It reports the content of a joint paper with Frederik Van De Putte; basically, we discuss how the background knowledge needed for a distinction between plausible and implausible cases of induction from a single instance can be formulated within frame theory, and how the theory provides a nice framework for talking about this sort of reasoning as relying on certain second-order inferences.
3. Similarity and dynamic frames. I'm talking about Bugajski's algebraic semantics for similarity relation, indicate its weaknesses, and provide a relational semantics that's simpler and which satisfies more of Williamson's requirements for 4-place similarity relation. Then, I discuss Bugajski's argument to the effect that interesting similarity structures can be generated by a set of properties only if those properties aren't sharp. To criticize it, I describe how non-trivial similarity structures can be generated by sets of sharp properties, if these are viewed within the framework of dynamic frame theory.

NCM 09 (part 2)

2009-08-10T19:35:00.004+02:00

... and the postponed report on Non-Classical Mathematics 2009 continues...

The second talk was given by Giovanni Sambin. He talked about his minimalist foundation and about a way constructive topology can be developed over a minimalist foundation. It's quite interesting to see how much stuff can be done constructively. Also, Giovanni is a devoted and areally charming constructivist. I was chatting with him at a pub one night and only by finding myself almost converted to constructivism I knew it was time to go home.

By the way, among many inaccurate things that are being said about Godel's theorem (like these) you can find a remark that Godel's incompleteness and undefinability proofs/theorems don't work in intuitionistic mathematics. Actually, they do. And the person to talk to is Giovanni, who worked out all the details making sure everything is constructive.

Arnon Avron talked about a new approach to Predicative Set Theory. Roughly,the underlying principles of the predicative mathematics are:

I. Higher-order constructs are acceptable only when introduced through non-circular definitions referring only to constructs introduced by previous definitions.

II. The natural number sequence is a well understood concept and as a totality it constitutes a set.

It is well known that Feferman has pursued the project and has shown how a large part of classical analysis can be developed within it. The system, however, is not too popular, partially because it uses a rather complex hierarchy of types, which makes the theory more complicated than, say, ZFC.

Arnon Avron discussed an attempt to simplify predicative mathematics by getting rid of the type hierarchy and developing a type-free predicative set theory. The idea is that the comprehension schema is restricted to those formulas that satisfy a syntactically defined safety relation between formulas and variables. The relation resembles a syntactic approximation to the notion of domain-independence used in database theory, and the intuition is that acceptable formulas define a concept in an acceptable way independent of any extension of the universe.

A replacement for Journal Wiki

2009-08-10T11:56:00.002+02:00

Here is a new database (by Andrew Cullison) gathering data pertaining to philosophy journal experience. I mentioned its being in preparation before. Now it seems to be up and running (although, the journal wiki data import is yet about to happen). It is certainly more user-friendly than its predecessor.

Tahko's paper on modal epistemology online

2009-07-28T14:31:00.003+02:00

I see Tuomas Tahko, besides posting a bunch of pictures from his recent trip, posted also his paper on modal epistemology. It's quite interesting. Title and details below.

Two-Dimensional Modal Semantics, Conceivability, and Modal Epistemology

ABSTRACT The combination of two-dimensional modal semantics and conceivability purports to be very powerful: it upholds modal rationalism, explains a posteriori necessity, and even accounts for metaphysical impossibilities—all this while committing to only one modal space, conceptual modality. In this paper I will examine whether two-dimensional modal semantics and conceivability can produce a complete account of modal epistemology and argue that they cannot. We will see that the framework fails to account for metaphysical modality or to deal with metaphysically substantial, essentialist statements because it is unable to distinguish between trivial and substantial modal truths.

Leszek Kołakowski has passed away

2009-07-18T13:29:00.002+02:00

Leszek Kołakowski, an important figure in political philosophy and an interesting Polish thinker has passed away.

Brian Leiter, despite his severe criticism of Kołakowski actually cared to post a short note about this, too. [pointed out by Ziel of the Polish blog Jakies Przepisywania z Prasy Wszelakiej fame in personal communication]

Marriage and Domestic Partnership

2009-07-17T11:28:00.003+02:00

Okay, I know, this isn't logic-related. Anyway, I see Elizabeth Brake's (University of Calgary) Stanford Encyclopedia entry on Marriage and Domestic Partnership is now available.

Leitgeb, "about", Yablo (again)

2009-07-15T16:07:00.004+02:00

A paper I already mentioned has been accepted and is coming out in Logique et Analyse soon. I'm keeping the copyright and I like open-access stuff, so the most recent version is available here. Title and (updated) abstract below:

Leitgeb, "about", Yablo

Leitgeb (2002) objects against the clarity of the debate about the alleged (non-)circularity of Yablo's paradox, arguing that there are actually two notions of self-reference and circularity at play. One, on which Yablo's paradox is not circular, is defined via the reference of the constituents of a sentence, and another, on which the paradox is circular, is defined via syntactic mappings and fixed points. More importantly, Leitgeb argues that both definitions aren't satisfactory and that before we can undertake a serious debate about the circularity of Yablo's paradox we first need to clarify the notions involved. I will focus on Leitgeb's criticism of the first definition and will argue that the problems arise not as much on the level of our definition of circularity as on the level of our definition of reference of sentences (aboutness). Leitgeb's main worry is the failure of a requirement called `Equivalence Condition', which says that if a formula is self-referential, any formula logically equivalent to it should also be self-referential. I will argue that preservation under logical equivalence is unreasonable with respect to self-reference, but is indeed needed with respect to aboutness. Since Leitgeb's own tentative notion of aboutness doesn't satisfy the requirement, I will suggest another approach which fixes this problem. I also explain why the intuitions that circularity should satisfy the equivalence condition are misled. Next, I argue that the new notion of aboutness is not susceptible to slingshot arguments. Finally, I compare it with Goodman's notion of absolute aboutness, emphasizing those features of Goodman's approach that make his notion inapplicable in the present discussion.

I would like to express my gratitude to all the people who discussed earlier versions of this paper with me: Hannes Leitgeb, Jeffrey Ketland, Karl Georg Niebergall, Diderik Batens, Joke Meheus, Maarten Van Dyck, Stefan Wintein, Martin Bentzen, Christian Strasser, Ghent Centre for Logic and Philosophy of Science members, and the participants of PhDs in Logic workshop (Gent 2009).

NCM 09 (part 1)

2009-07-08T12:07:00.008+02:00

As promised, I begin a series of posts about Non-Classical Mathematics 2009. (I've just started using this LaTeX editor for internet, so the formulas look kinda weird, I should get used to this system within a couple of weeks).

The conference started with Greg Restall's talk titled Theories, Co-Theories & Bi-Theories in Non-Classical Mathematics. In the non-classical setting the assertion of a negation of a formula and its denial are different things. Those who accept gluts will assert negations of certain formulas without denying the formulas themselves. Those who accept gaps will deny certain formulas without asserting their negations.

Now, in a setting of a mathematical theory we're dealing with a consequence operation such that for any A and B, if A entails B, then asserting A and denying B is a clash. This generalizes to sets of formulas.

The rules we buy into unconditionally are at least these:

There are two interesting negation rules:

Both rules hold if there are no gaps and no gluts. If there are gaps, [~R] doesn't work. If there are gluts, [~L] doesn't hold, and if there are both gaps and gluts, none of the rules works. Perhaps, one might want to add other inference rules, but let's not be bothered by these issues.

Recall now that T is a theory iff for any A:

.

In the non-classical setting, if you want to avoid clash (which you want to avoid even if you allow for gaps or gluts), you should assert whatever belongs to the theory you're committed to. A theory, however, doesn't tell you which formulas you should deny (for instance, ~A belonging to the theory only tells you that you should assert the negation of A, but from this, it still doesn't follow that you shouldn't assert A itself).

Greg then goes on to introducing theory-like notions that help one not only to tell what assertions one has to make, but also what has to be denied. The first one is the notion of a cotheory. U is a cotheory iff for every A,

The intuition here is that U is a set of unassertable sentences, and the definition mirrors the fact that if something is not to be asserted, then nothing that entails it should be asserted either.

Now, combine these two notions to construct a thing that tells you what to accept and what to reject. is a bitheory iff for every A:

Again, the intuition is that T is what's to be accepted, and U is what's to be denied.

The rest of Greg's talk was devoted to applying this ideas to non-classical theories of numers, classes and truth.

Lecture notes on PA

2009-07-06T18:47:00.003+02:00

I see Konrad Zdanowski (who worked with M. Mostowski) is now at Paris 7 and has posted his lecture notes on Peano Arithmetic. Here. Neat.

Elsevier turned to the dark side

2009-07-06T16:52:00.003+02:00

Not a long time ago, Elsevier was shown to be quite dishonest, publishing a fake journal for money. Here's another embarassing thing about Elsevier which should convince you that open-access, independent online journals are becoming a serious alternative to the old-school venues (thanks to Brian Leiter for linking).

Change & contradiction

2009-07-06T11:55:00.003+02:00

Over at Blog&~Blog, Ben Burgis has a nice post about Graham Priest's theory of change. He also raises certain difficulties for the theory. One of the objections is that if we admit that change involves contradiction, then Priest probabilistic argument for classical re-capture ("contradictions are rare, so we are most of the cases allowed to use classical rules, even if they aren't really valid") seems to fail. Even though I'm not a dialetheist myself, I'm still wondering how damaging this objection is, so I posted a comment with a sketch of a possible way out for the dialetheist. More remarks over at Blog&~Blog.

A few papers reach daylight

2009-07-05T12:35:00.005+02:00

My long-in-the-drawer mini-trilogy about doxastic synonymy and slingshot arguments has finally reached daylight, published in The Reasoner. Here (starting on p. 4), here (starting on p. 5), and here (starting on p. 4). (I started thinking about these things in 2006 in a seminar on truth given by Prof. Ali Kazmi).

I must say, my experience with The Reasoner is quite positive, and not because they accepted the paper(s), but rather because:

Their feedback was really quick (three weeks or so).
Nevertheless, I had three competent reviewers.
Their helpful comments were forwarded to me together with an initial R&R.

Given that there are places where your paper might be stuck for almost a year, or places that either don't justify their negative decisions or send along pretty weird reviews, The Reasoner's way of handling things is certainly praiseworthy. Of course, this result is partially obtained by severe wordcount limits; yet saying stuff in as few words as possible is quite an interesting challenge. So, if you have something interesting to say and it doesn't take too many words, The Reasoner is a venue worth considering!

One more thing, I also see that the paper on definability of identity in higher-order languages (I talked about it some time ago) is now officially available through the Australasian Journal of Logic. AFAIK (two papers with AJL), feedback time and quality are really good, and I really like its being open access.

Rating Journals, again

2009-07-04T08:41:00.004+02:00

Some time ago I advertised Philosophy Journals Wiki. As Douglas Portmore (who started the project) points out, it has certain disadvantages. Over at PEA Soup he discusses these things and points to an interesting attempt to replace Wiki with something more convenient.

p.s. I will get around to posting about NCM 09. Soon.

Non-Classical Mathematics 2009 (introductory remarks)

2009-06-19T17:57:00.005+02:00

Finally, I can write something about what's going on now. I'm in Hejnice, lodged in a cell (it's quite comfortable though) in a monastery pretty much in the middle of Czech mountains. I was here two years ago, but this time I have wireless internet access. It's pretty cool.

So, what's going on? Well, it seems, Non-classical Mathematics (surprisingly??) attracted more mathematicians than philosophers and logicians. In fact, most of the people present here are rather mathematically-minded. This, of course, is not a complaint. For a philosopher (or a philosophically-minded logician, for that matter), dealing with mathematicians is a bit of a challenge though. They usually spend less time looking for philosophical motivations for their work and more time doing real mathematics. This means, if you're a philosopher, listening to mathematical talks will require more effort. You have to overcome the first impression that people sometimes get into extremally complicated technical issues without explaining why we should be interested in them. I mean, I'm pretty sure these people know what they're doing and why they're doing that, but the standards they employ for motivation of technical work are a bit different. Also, this stuff is often more complicated than most of more philosophically motivated work, so it's a bit more difficult to follow (which means, it's easy for me to feel slightly retarded when faced with all those technical results).

There are, however, also certain clearly positive aspects to this experience. For instance, a few brief conversations I had here confirm my view that doing mathematics doesn't require one to have a clear philosophical position about what mathematics is about (I mean, this is not deeply surprising, I've talked with mathematicians before). For instance, a guy who works on weak set theories, when asked about his view on what set theory is about, said cheerfully something like "I don't care, you know, it's a theory, I play around with it, prove stuff and that's it - what else would I need to know?". It's refreshing. This also means that philosophers of mathematics can still claim there's something for them to do.

This reminds me of P. F. Strawson's remark about analysis of concepts used by specific theorists:

The scientific specialist [...] is perfectly capable of explaining what he is doing with the special terms of his specialism. He has an explicit mastery, within the terms of his theory, of the special concepts of his theory [...] the specialist may know perfectly well how to handle these concepts inside his discipline, i.e. be able to use them perfectly correctly there, without being able to say, in general, how he does it. Just as we, in our ordinary relations with things, have mastered a pre-theoretical practice without being necessarily able to state the principles of the practice, so he, the scientific specialist, may have mastered what we may call a theoretical practice without being able to state the principles [...] a mathematician may discover and prove new mathematical truths without being able to say what are the distinctive characteristics of mathematical truth or of mathematical proof [...] even operating within his own specialism, a specialist was bound to employ concepts [...] from the fact that he there employs them quite correctly, it by no means follows that he can give a clear and general account or explanation of what is characteristic of their employment in his specialism. [Analysis and Metaphysics]

There is a downside to it. If you discuss philosophical aspects of mathematical concepts, mathematicians quite likely won't give a rat's ass about it. I mean, it's to be expected, just like you don't expect a competent kettle user to be interested in someone's specification of sufficient and necessary conditions for something to be a kettle (or an ink-spiller to be interested in philosophically interesting ways of spilling ink). Just like a mathematician might have a hard time convincing philosophers that the complex questions he's trying to answer actually matter, a philosopher might have a hard time convincing mathematicians that philosophical considerations about mathematics have some relevance.

Of course, there is no clear-cut distinction between the mathematicians and the philosophers. I presented a very simplified sketch of some aspects of the extremes of a very interesting and often fruitful tension.

Anyway, all this seems to have some bearing on the Burgess-Rosen critique of nominalist reconstructions of mathematical theories. The gist of the critique is this: when you give a reconstruction, you either give something different from what mathematicians actually have in mind, and thus, you put forward a revolutionary view of mathematics (which is highly impractical, because you're suggesting new textbooks have to be written, mathematics in schools should be changed, etc.), or you are claiming that your theory is an actual analysis of what they're doing, and then you have to show that this really is what they have in mind. Now, it seems to me that mathematicians usually don't have anything philosophical in mind at all when they're doing mathematics, just like we don't have a correct analysis of our every-day concepts when we use them. Thus, giving a nominalistic reconstruction is neither a suggestion that mathematics should be revised (in fact, I believe, a correct nominalistic story about mathematics should rather suggest that everything's okay with mathematics and it shouldn't be changed), nor a theory of what mathematicians have in mind. It's rather a proposal as to how a philosopher can make sense of mathematical activity and mathematical truth without being commited to abstract objects. And what would making sense consist in? Well, telling a nominalistically acceptable story which would be consistent with one's philosophical views and which would allow one to understand on the philosophical level how mathematics can be true and yet applicable. Sort of.

Having said all this, I will switch back to the reporting mode now and post some more detailed remarks on the content of the talks some time soon.

FMER, Leuven, June 10-12, cont'd

2009-06-19T16:03:00.002+02:00

Day 3, after lunch

Lara Buchak (joint with Branded Fitelson who couldn't make it to the conference) -Is it rational to have faith? - Lara was trying to cash out what having faith commits one to, and on the analysis she presented faith in X requires that one not actively look for further evidence for the truth or falsity of X. This move seems to collide with the expected utility theory of rationality. Then, she argued that the claim that expected utility maximisers should always perform cost-negligible experiments neglects the phenomenon of risk aversion. It turns out that for individuals who take risk into account in a certain way it is sometimes rational to refrain from gathering further evidence.

One issue was raised, if I remember well, by Joshua - namely, if this is the way you understand faith, Richard Swiburne doesn't have faith, for he actively looks for evidence pertaining to the truth of religion. Perhaps (now that I think of it) this can be circumvented by saying that faith in X would require one not to actively look for further evidence for the falsity of X (it depends how one construes Swiburne's thought, but one way to see this is to think that he does actively look for evidence in support of religion, but doesn't actively look for evidence against religion).

Another issue is that the notion of evidence in/against religion is quite elusive. Lara used an example of prayers: pray for something and see if you get it. But it seems that (at best) what you're testing this way is the conjunction of some of your religious beliefs and the claim that your will agrees with the will of God). Also, what counts as test or evidence for or against religion is highly theory-dependent. You can go Swinburnian about this and think that no actual event whatsoever is evidence against religion, because given certain considerations, everything that is happening should be happening if (his version of) theism is true. You can go more Tooleyan about this, and count every event that prima facie should not happen as evidence against the truth religion. Perhaps it's just me being confused, but I don't think we have a good understanding of a test that both a theist and an atheist would agree upon, so that the cost of its performing is negligible (given the negligibility requirement, for instance, Hick-style die-and-see-what-happens is out of the question).

The conference started with a slightly apologetic talk by Swinburne. It ended with a rather atheistic talk by Herman Philipse. He gave a series of short arguments against the claim that there is a C-inductive argument from the Big-bang to the existence of God. Briefly,i f h is theism, e is the occurence of big bang, and k is tautological background knowledge, Swinburne argues that Pr(e|h&k)>Pr(e|k). The first point that Philipse makes is that given that God would want to create humans and the fact that given the cosmic singularity, the probability that it will result in there being humans is quite low, it seems that Pr(e|h&k) is very low. Another point raises pertaining to Swinburne's claim that Pr(e|k) is very low. Since Pr(e|k)=Pr(e|h&k)Pr(h|k) + Pr(e|~h&k)P(~h|k) we need to know the prior probability Pr(e|~h&k) and Pr(~h|k). Philipse argued that Pr(e|~h&k)> Pr(e|h&k). He also attacked Swinburne's use of simplicity criterion. Since this was directed against Swinburne who was present, quite an interesting discussion followed.

As for Bayesian-style arguments for/against God's existence, I'm rather sceptical. The problem is, even if the math adds up, they all rest on primitive assessment of probability of things like "big bang occurs" relative to the existence of God, or relative to the negation of his existence, and many other probabilities of this sort. When asked questions like "what's the probability that intelligent beings like humans exist given the hypothesis that there is no god and no multiverse?" or "What's the probability that Big Bang occurs given the hypothesis that God exists", I'm just inclined do say: I have no idea. I would love it if (a) someone explained to me the notion of probability at play, and (b) showed me how on this notion of probability, the probability claims involved can be assessed without hand-wavy and practically untestable extra assumptions. Perhaps I'm just a frequentist and haven't seen too many worlds being created. My bad.

FMER, Leuven, June 10-12, cont'd

2009-06-19T15:26:00.003+02:00

Day 3, before lunch

Edward Wierenga talk titled Developing Molinism employed fairly complex modal stuff (you know, actuality, counterfactuals and all that) to help formulate Molinism, the view that God has a knowledge of propositions that are intermediate between being necessarily true and independent of God's will or creative ativity, and contingently true propositions dependent on God's will. These are contingent true propsitions not dependent upon God's will (in the intended interpretations: propositions about future but free actions of men).

This knowledge is often taken to be a knowledge about certain counterfactuals (like "If Adam were placed in the Garden of Eden, he would freely eat the forbidden fruit"). This knowledge would assist God in devising the world so that it is the best world possible without interfering with human free decisions. The technical problem is that it's difficult to find right truth-conditions for counterfactuals of this sort which satisfy all the desiderata. Wierenga first discussed his original view (that Plantinga's conditionals of world actualizations can do the job) and criticized it, and then presented another suggestion, employing tense considerations.

Paul Bartha talking about Many gods, many wagers, discussed in detail the many-gods objection against Pascal's wager. He then argued that given the evolutionary stability condition on probabilistic reasoning (roughly, the condition is that after making a bet, no further probability considerations of the state of affairs after making the bet will make you change your mind) the many-god objection doesn't raise any difficulties that the classical version of Pascal's argument already encounters.

David Glass - Can evidence for design be explained away? - An obvious way to counter a design argument is to provide an alternative explanation. For instance, evolution theory is taken to render inconvincing certain design arguments. The problem is, certain version of design arguments are compatible with alternative explanations - why accept both? Well, don't if there's no need to do that! The technical question, however, is when one explanation is good enough to render the other redundant. Are there cases where it is better to accept both explanations than only one of them?

David addresses these issues within the Bayesian framework. Even if two explanations are marginally independent they typically become negatively dependent when one conditions on the evidence they explain. So, if one explanation is found to be true, this lowers the probability of the other explanation. There are, however, two important possible outcomes. Say a design hypothesis D has a certain prior probability Pr(D). Next, suppose it receives confirmation from evidence E so that Pr(D|E)>Pr(D). Then, we find out that an alternative explanation A is true. This undermines Pr(D|E&A). In the first case, Pr(D|A&E) is not higher than Pr(D), and so the initial confirmation of D by E has been completely negated. In the second, Pr(D|E&A) is higher than Pr(D) but lower than Pr(D|E). Given than only the first kind of outcome counts as explaining away, it turns out that it is very difficult to come up with an alternative theory that completely explains away the evidence for design.

FMER, Leuven, June 10-12, cont'd

2009-06-19T14:46:00.003+02:00

This is getting overwhelming. I haven't finished posting about FMER and I'm already at another conference (Non-classical mathematics) that I also would love to blog about. I'll do my best to complete the FMER mini-series as soon as possible.

Day 2, after lunch

Alan Hajek talked about Blaise and Bayes. He first surveyed a few variants of arguments usually given as reconstructions of Pascal's wager in terms of "dominance" and "expected utility". It was fun, especially since he also showed that they're invalid, for some slightly surprising but equally obvious reasons. He discussed certain emendations that can be made to salvage the wager.

Joshua Thurow's talk was titled Does religious disagreement actually aid the case for theism? Disagreement trailblazing for the miraculous. He pointed out that disagreement about an inferentially-based belief may not automatically force one to suspend judgment en block. Divide the evidence for and against religions into two sets: A - the testimony to the occurrence of miracles, B - everything else. Suppose there is enough disagreement about the evidence in B that considered alone B supports suspending judgment in all religious belief. Then, using Bayes's theorem, Joshua argued that if A includes even moderate testimonial evidence for the occurrence of a miracle, then A and B together support whatever theositic religion is most supported by the testimony in A.

Michael Tooley discussed The probability that God exists. He employed Canapian-style structure-description approach to inductive logic to arrive at an upper bound on the probablitiy that God exists given only the information that the world contains n events each of which is such that in the light of the totality of known rightmaking and wronkmaking properties, it would be morally wrong to allow the event in question.

Given that there are n such events and that there are k unknow morally significant properties, the probability that none of those n actions is wrong all things considered, argues Tooley, is less than (k/k+1)(1/n+1). So, he argued, the probability that God exists must be less than 1/n+1.

One idealizing assumption that Tooley seems to take is that the total moral status of an action is assessed in terms of the number of morally relevant properties (rightmaking vs. wrongmaking), known or unknown. I think it's unlikely a theist would buy into this: they might insist that some (especially unknown) properties are more important and mere counting them (especially since it's not really obvious how you individuate properties so that counting makes sense) won't help to assess the moral status of an action.

Time Travel paper online

2009-06-15T14:33:00.005+02:00

At FMER I had an opportunity to chat with Michael Tooley about time travel. Two years ago I had this paper about Tooley's example of loopless time travels and conditional logics. Michael put forward this example to indicate that if Lewis-Stalnaker semantics for conditional logics is adequate, then there are impossible cases of backward causation even without causal loops. Later on the argument was interpreted as an argument against the adequacy of conditional logics from the possibility of time travel (I recall that seemed to be the interpretation of Charles Cross, I was commenting on his talk at WCPA 2006 in Vancouver).

My point was that the impossibility of the situation described not only follows from basic assumptions of LS semantics, not only can be proven syntactically as holding in many conditional logics (that was Charles' observation), but also can be proven using fairly weak assumptions, weaker that those of Charles, and that the possibility of the situation is not very intuitive to start with (thus I rather sided with Michael, emphasizing that even without causal loops time travel can be tricky).

The chat reminded me about this paper, so I dug it up and posted to my academia profile. It's here.

FMER, news from the trenches (cont'd)

2009-06-15T13:26:00.003+02:00

Here's Day 2, before lunch. ^*

The day started with a talk by Benjamin Jantzen titled Peirce on Miracles: The Failure of Bayesian Analysis. Benjamin started with a brief explanation of Hume’s criticism, according to which no testimony could be sufficient to justify belief in a miracle, given that the probability of fraudulent or mistaken testimony is always greater than the probability of the miracle occurring. He then considered Hume’s argument as an instance of Bayesian probabilistic inference. The basic idea is that the probability of a miracle having occurred given various testimonies to that effect is computed from the probability that each witness would report accurately given the occurrence of the miracle, the joint probability of the occurrence of such a collection of testimonies, and the antecedent probability of the miracle. Finally, Ben argued that given the Peircean criticism of the Bayesian approach, the probabilistic analysis of this sort is seriously flawed. The main gist of the criticism is that:

There is no such a thing as the objective veracity of a witness. To apply the Bayesian method we need to know the probability that a witness judged accurately and told the truth in a particular instance. The details of that instance cannot be replicated even in principle, so we have no class of sufficiently similar events to build a sample space (this objection hinges on Peirce’s frequentist account of probability).
Even if we grant such a thing exists, it doesn’t satisfy the independencies required by the method of balancing likelihoods employed in the argument. What leads one witness into error tends to lead others into the same error.
History tends to preserve only the positive assertions of the extraordinary and biases the computed posterior probability. When we hypothetize the occurrence of a miracle on the basis of some set of testimonies, we are not rational in using those same testimonies to determine the probability that this hypothesis is true.

The main positive lesson is that after constructing an abductively valid hypothesis we should gather independent data for an inductive phase.

Lydia and Tim McGrew talked about The Reliability of Witnesses and Testimony to the Miraculous. They started with Condorcet’s formula for the probability of an event:

pt/pt+(1-p)(1-t)

where p is the antecedent probability of the event and t is the reliability of truthfulness of the witness. Then, they tracked subsequent changes that led to the formation of Bayes’s Theorem. Indeed, Condorcet’s account seems like a particular instance of B’s theorem, given the similarity between his formula and:

P(H)P(tH|H)/P(H)P(tH|H)+P(~H)P(tH|~H)

In particular, Condorcet’s formula is a special case resulting from three limiting assumptions.

The witness is equireliable – he is equally likely to tell the truth about H regardless of whether it occurs.
The witness is forthcoming – he would not be silent on the subject of H had it not occurred.
Testimony regarding H is restricted to YES or NO.

Lydia and Tim followed the history of the debate surrounding testimony and miracles (Babbage, Reid, Bentham, Hume, Campbell, Venn, Holder, Earman) , showing how it led to the rejection of these assumptions.

Finally, they argued that the move from Condorcet’s formula to Bayesian factors is correct and that the factors should not be construed as modeling witness’ reliability, but rather a function of a wider range of epistemically relevant factors.

^* If you're one of the speakers and think your view is misrepresented, drop me a line.

FMER, Leuven, June 10-12, News from the Trenches

2009-06-14T16:24:00.008+02:00

Formal Methods in the Epistemology of Religion took place in Leuven, June 10-12 2009. The conference was amazing, I really had a blast. I was transiting from Ghent every day, and the schedule was quite intense, so only now I have a few moments to write about it.

Jake Chandler (of the choice & inference fame) and Victoria Harrison, with the financial support of the Centre for Logic and Analytical Philosophy have pulled off an excellent event, gathering together many prominent scholars working on formal stuff and philosophy of religion.

Most of the talks were related to Bayesian epistemology and its applications. It’s not the framework I usually deal with, so I've learned a lot. Also, after Prof. Swinburne’s talk I had the opportunity to give a talk about his modal argument in his presence, criticize his views, and see how he responds. That was pretty cool.

Anyway, here are some general remarks about the conference. I’ll start with Day 1 (the conference started in the afternoon, so there were only three talks), and comment about the other two days in near future.

DAY 1

The day hit off with a lecture given by Richard Swinburne, Bayes, God, and multiverse. Swinburne, employing Bayes’s theorem, explicated a probabilistic argument for God’s existence, arguing that given the empirical evidence we have, the relative assessment of the posterior probability of God’s existence is higher than the probability of godless multiverse and than the probability of a unique (and godless) universe (he referred to fine-tuning etc. here).

The second talk was delivered by me (on behalf of Agnieszka Rostalska and myself, it’s a joint paper but Agnieszka couldn't make it). I presented a formalization of Swinburne’s modal argument for the existence of the soul, and suggested another variant that avoids the main objection directed against it (it can be viewed as a weakening of one of the premises - thanks to Lara Buchak for this observation). I also argued that even this weakened version is epistemically too strong to convince anyone who allows the mere possibility of material conscious beings.

Some time ago, an anonymous referee of this paper said that the new version of the argument is not “much of an addition to the literature, since the modification which the author offers to Swinburne is one which it would be most implausible to suppose that he would wish to make”. In response to that: Swinburne was there when I was giving the talk and agreed that the modification which we offer is the one he would like to make for the same reasons for which we say it’s better (our further discussion pertained to our assessment of the revised argument, and Prof. Swinburne eventually suggested that he has a different argument which he will send in my direction some time soon - I'm looking forward to seeing it). The bottom line, if you want to state a conditional without any possibility of falsification, make sure your antecedent cannot be made true.

Graham Oppy talked about the Epistemological foundations of Koons’ cosmological argument. Koons argued that any exception to the principle of general causation that is narrow enough to avoid a collapse into global scepticism about empirical knowledge is also narrow enough to permit the construction of a successful proof of God’s existence. Oppy analyzed Koons’ arguments. Specifically, he took issue with Koons’ claim that in order to be justified in believing that one’s belief that p and the grounds for one’s belief that p are caused, one needs to be justified in believing that it is highly likely that any of the situations in one’s knowledge net is caused. Oppy discussed related epistemogical issues involved in Koons argument for the claim that we are in position to accept a priori a (defeasible) principle of causality.

Philosophy Journal Information

2009-06-05T16:55:00.002+02:00

Before submitting a paper, it's good to check out what experience with that journal other people had: how long you're likely to wait, or whether you're about to get any feedback in case of rejection. Philosophy Journal Information is devoted to these things. Check it out, and don't forget to post your info!

A category theory book online.

2009-06-02T22:37:00.002+02:00

A nice book on category theory, Toposes Triples and Theories (by Michael Barr and Charles Wells) is available here.

Philosophers' Rally, Cracow 2009 (Poland)

2009-06-02T18:30:00.004+02:00

After having spent an intensive weekend in Cracow, I'm on a plane back to Brussells (well, actually, after I just got on it, all passengers were asked to disembark and identify their own luggage because we had one suitcase extra that didn’t seem to belong to anyone…) Anyway, although I was slightly frustrated with the previous large philosophical conference in Poland I went to (see more details here), I was quite delighted to attend this one (also, I like the fact that I could catch up with some of the Gdańsk students, who decided to take the trip and participate). Hence a few general comments about what Philosophers' Rally is and about philosophy in Poland in general.

As far as I know, there are two fairly regular, large and general philosophical events in Poland. One is the Philosophical Congress (the 2008 edition took place last September in Warsaw). In a way, it’s similar to large general conferences like CPA in Canada or APA in the States. What’s similar is a huge number of participants, and a wide spectrum of topics being discussed. What’s different about PC? Acceptance is based on semi-blind review of abstracts only (I’m quite positive the rejection rate is WAY lower, and what their review procedure is remains quite unclear to me), there are no pre-prepared comments after the talks, and there are no jobs interviews (philosophy job market in Poland is a topic for a whole different story). It’s usually organized by notable members of Polish philosophical community and most of the participants are faculty members from around the country (I recall, there were around 20 parallel sessions and chairs didn’t always pay attention to timing, so navigating between talks you wanted to make to was quite a complex task).

The other one is Philosophers’ Rally. It is more like a graduate conference (only, it’s really nation-wide). Apart from a bunch of invited speakers, who are faculty members, most of the participants are undergraduates, graduates and young PhDs. Most of the organizers are young and dynamic people. Acceptance is based on abstracts (I recall from a conversation with one of the organizers that the rejection ratio was around 20% and that the abstracts were sent for review to faculty members deemed competent in their respective fields; I think there were around 120 talks this year). [note: PR was on hiatus for a few years, and this is the first time it took place after its revival; also, it’s the first time they did require abstracts and did the reviewing; I think it’s a big step forward.]

From my observation, the atmosphere at a Polish philosophical conference can get quite weird (this doesn’t apply, or almost doesn’t apply to logic conferences in Poland though). The reason is, some philosophers behave as if they treated a conference like a rap battle (a lame one, too): you gotta get there, make noise, diss everyone else and show how smart you are. This on one hand leads to ad personam arguments and unjustified condescending remarks - you can actually sometimes hear a prof. telling a student something to the effect that they are wrong because they’re students, or arguments like “only an idiot would believe this”; also, certain groups whose members admire only each other (borrowing the phrase from Geach ;)) can be observed. An interesting phenomenon is that sometimes when a prof is considered important, some of their students will often follow them around, listening to what they have to say with awe even if it’s rude or utter crap, and imitating their style… weird stuff, I must say. On the other hand, this makes people take critical comments more personally, even if the comments are given with no vicious attitude and in good faith. Long story short: people often don’t make a distinction between persons and their views, and the overall culture of discussion leaves something to wish for.

Another thing which makes Polish philosophy quite different from what you usually see at an English-speaking University is the high level of continental deliberations. Approximately ½ or 2/3 of the conference topics were related to something that I don’t feel competent to describe.

Yet another observation: many of the talks, even if they are really clear and well-organized, are not devoted to making a point, claiming something, or arguing for or against anything. Rather, they focus on saying things like “A famous philosopher X said Y about Z”, or “A famous philosopher X said Y about Z, but another well-known philosopher V disagreed, but I won’t try to evaluate their arguments, I’m only presenting their views”. Although not too creative, this kind of work is useful in Poland, where accessibility to current literature (esp. books, for most of the universities have access to main journal databases) is slightly restricted for technical and pecuniary reasons. Also, if an undergraduate or a master’s student can do a good job presenting/comparing other people’s view, it’s a good exercise for them anyway.

Having said all this, I must stress that there are many young and intelligent Polish philosophers (some of them even undergraduates), who are doing sensible work on interesting topics. For instance:

• Magda Kamińska (from Gdansk, yay!) presented the knowability paradox, described Williamson’s response to it, presented a few counterintuitive weakened paradoxes that you can run even if you switch to intuitionistic logic, and argued that a re-construal of non-omniscience claims in intuitionstic logic is not a successful strategy for dealing with the problem because it violates very basic intuitions that we have about quantification in natural language.
• Bartosz Wcisło mounted a few arguments to the effect that the modality involved in the knowability paradox is uninteresting: that some Fitch-style unknowable sentences at a certain time may become knowable at a later time if you juggle around with temporary indices, and that in certain context sentences that are effectively decidable may come out Fitch-style unknowable. I don’t think the arguments worked, but fairly technical details were involved, and they are quite clever – it takes a while to figure out why this doesn’t fly.
• One of my favorites was Marta Ewa Romaneczko’s discussion of psychoanalysis. It is often claimed that it’s highly unfalsifiable and unscientific. Romaneczko in a clear and engaging manner argued to the contrary: that given certain fairly sensible approach to inter-theoretical falsification, falsifiability is available for many psychoanalytical claims, and that in fact there have been claims in the history of psychoanalysis that have been considered falsified and withdrawn when faced with data.

Many other familiar topics have been also discussed: metaphysical issues surrounding counting objects and constitution (Łukasz Krawiranda), availability of contingent identity with rigid designators (Błażej Skrzypulec), criteria of identity (Adam Andrzejewski), the relation between predicates and properties (Krzystof Posłajko, who also asked a wonderful question about deduction theorems in paraconsistent logics in my workshop), Frege’s notion of truth (Tomasz Pawlik), counterfactuals as the source of modal knowledge (Katarzyna Kuś), technical issues pertaining to probabilistic reasoning about causality (Leszek Wroński), empty names and their behavior within the framework of causal theory of reference (Rafał Ciok), the epistemology of thought experiments (Katarzyna Kobos), the physical acceptability (or its lack) of Lewis’ modal realism (Krzysztof Adamek), neo-Ryleanism about knowing-how (Bolesław Czarnecki), game-theoretic analysis of Kant’s imperative (Piotr Wilkin), Kai Nielsen’s critism of Malcom’s variant of the Ontological Argument (Jak Cieślar), semantic space hypothesis and AI programming (Krzysztof Hanusz), biological plausibility of Chomsky’s concept of linguistic competence (Piotr Wołkowski), a criticism of Dennett’s heterophenomenology from a Peircean perspective (Adrianna Smurzyńska), the question of intentionality of emotions (Paweł Bankiewicz) and the relation between epiphenomenalism and Davidson’s anomalism (Jarosław Ziółkowski).

Overall, despite certain particularities of Polish philosophical discourse (which were quite rare at Philosophers' Rally anyway), I’m quite optimistic: many young philosophers work hard on things currently discussed in the English-speaking world.

Another thing worth mentioning: apart from a few really minor glitches (which happen everywhere), the conference was really well-organized, and in this respect it stands second to none of those conferences that I’ve seen anywhere else (in fact, there even was an English-speaking section!). I would like to express my gratitude to the organizers: thanks guys for having me!

Adaptive logics in Cracow

2009-05-27T19:28:00.002+02:00

Tomorrow, I'm off to Cracow, to give two 90 minutes long workshops on adaptive logics. I think I'll talk about various ways paraconsistent logics can be obtained, the way they generate inconsistency-adaptive logics, the standard format of adaptive logics and some other examples of adaptive logics, not related to paraconsistency.

Anyway, if you're in Cracow and speak Polish, feel free to pop in (more details here). Please do remember what happens to those who ask tricky questions, though. ;)

Postdoc position in History and Philosophy of Logic

2009-05-27T10:55:00.002+02:00

There's a postdoc position in Amsterdam, related to history of logic, Bolzano, Tarski, Lesniewski etc. More details here.

"Numbers" by M. & G. Fittings online

2009-05-26T17:47:00.002+02:00

I've just noticed that a very nice book about number theory by Melvin Fitting and Greer Fitting is freely available online here. Here's a bit from the introduction.

A preface is supposed to explain why you should read the book. Like most prefaces, this one will make more sense after the fact. Nevertheless, here goes.

Most mathematicians believe (rather strongly) that numbers behave in certain well-defined ways. This belief can not be justified by personal experience. No mathematician has `seen' more than a finite, probably small, collection of numbers. Instead mathematicians justify their beliefs by giving proofs. In practice, this means that certain facts about numbers are accepted as `obvious', and used in carefully reasoned arguments for the correctness of other facts that are less obvious, or possibly not obvious at all. Since mathematicians generally are concerned to establish the nonobvious, little thought is customarily given as to why the `obvious' facts are correct.
Now, it is an observation as old as Aristotle that one can not provesomething from nothing. One must always begin with some body of `obvious' facts and proceed from there. In practice, most mathematicians contentedly place hundreds of facts in this `obvious' category in order to get on with their proper business of discovery and verification of the non-obvious.
But at least once in a mathematician's career, it is good to take a sharp look at the status of the `obvious' facts; and it is probably best to do it early, and get it over with. As we remarked above, it is not possible to do away with all assumptions, even in mathematics. But, one of the great achievements of 19th and early 20th century mathematics was the careful and precise limitation of exactly what a working mathematician must `accept on faith'. That is, it was discovered what can constitute an irreducible minimum of `obvious' facts.
It is the purpose of this book to present such an irreducible minimum, and show how most commonly assumed facts about numbers follow directly. Nonetheless, this book is a bit of a fraud, because like all mathematicians we still assume that some obvious facts are more obvious than others. This is a book about the number systems, so for our purposes we assume as `sufficiently obvious' a variety of pre-numerical facts. Specifically, we assume, without being too explicit about the matter, several principles about the behaviour of sets or collections. Now this material too has been subjected to a similar treatment, also around the turn of the century. Today one can find basic set theory developed from a small number of axioms in many books on elementary set theory. But our book is long enough already, so we elected to omit this material here. For us the issue is: given a variety of `obvious facts' from set theory, what elementary properties of numbers must one accept in order to logically derive the entire basic framework of mathematics.

Philosophy Talk

2009-05-22T22:36:00.002+02:00

Philosophy Talk is a radio show, their past programs are available online - well, you can listen online without paying, at least to those that I've tried, but it seems you have to pay to download. ;)

Their list of topics sounds pretty cool. It includes:

Beliefs gone wild
Capital punishment
The Copyright wars
Different cultures, different selves
Animal minds
Bodies for sale
Digital selves
Morality of food
We've been framed: how language shapes politics
Varietes of love
Athletic beauty
Philosophy of wine
Immigration
Marriage and monogamy
If truth is so valuable, why is there so much BS?
The erotic vs. the pornographic

and many others.

An amazing bit of poetry

2009-05-20T12:15:00.002+02:00

Here you can find an interesting poem by Geoffrey K. Pullum, Scooping the Loop Snooper, treating about the halting problem and its undecidability.

Jerzy Perzanowski has passed away

2009-05-18T19:17:00.005+02:00

During the night from 16th to 17th of May, Jerzy Perzanowski (1943-2009), a fine Polish logician and a legend of Polish logic has passed away. Brief information about his work can be found here.

Prof. Perzanowski concerned himself with applications of logic (esp. modal logics) in formal ontology. Three parts of his Locative Ontology are available here, here, and here. His essay Towards Combination Metaphysics is available here.

He also gave some thought to paraconsistent logics (he was a friend of Diderik Batens, and cooperated with the Ghent Centre for Logic and Philosophy of Science). His 50 years of parainconsistent logics is available here and his Parainconsistency, or inconsistency tamed, investigated and exploited can be found here.

Prof. Perzanowski was well known for his slightly idiosyncratic and yet very clear terminology and engaging manner of discussion (I recall a discussion we had in Warsaw in September about Godel-style ontological proofs, and man, he was difficult to argue with).

He also played a political role as one of the leading figures of the Krakow section of Solidarność.

He will be missed.

König's paradox and the modal view of plural quantification

2009-05-15T11:20:00.003+02:00

In the last chapter of this thing, I defended the view according to which plural quantification:

For some a, .....

(where a can be singular, empty, or general) can (roughly speaking) be read nominalistically as:

It is possible to introduce a (singular, empty or general) name-token, such that...

One of the prima facie reasons to reject the substitutional interpretation of plural quantification was that we run out of tokens (finite sequences over a finite alphabet), if the domain is large enough.

My solution was to distinguish between different possible worlds where possible tokens are introduced, so that (assume we believe in Real Numbers):

For every real number, it is possible that it has a name.

comes out true, whereas:

It is possible that every real number has a name.

comes out false. So the basic idea is that even if in every possible world, there are only countably many names, the union of names in all accessible possible worlds doesn't have to be countable.

Now, I've been thinking about König's paradox (this is G. Priest's formulation from his essay Paraconsistency and Dialetheism, in Handbook of the History of Logic, vol 8):

There is an uncountable infinitude of ordinal numbers, but there is only a countable number of descriptions in English. Hence, there are many more ordinal numbers than can have names. In particular to turn the screw, since the ordinal numbers are well-ordered, there is a least ordinal number that has no description. But we have just described it.

Now, in the framework I like to think in (the modal framework mentioned above), the problem doesn't seem to arise (even given the assumption that ordinal numbers actually exist, which I'm not inclined to accept but that's a different story). Why?

Well, even if in any possible situation the number of English descriptions is countable, it doesn't mean that there is an unnameable ordinal number. So say, we are at certain time t. There is a set of actually existing English tokens which describe ordinals. Then at t+1 we produce the token:

The least ordinal number that has no description.

Now, as I see it, there are two different things that can be meant here.

The least number for which no description actually existed at t.
The least number for which no English description can be introduced, i.e. for which there is no possible description.

If 1. is meant, then no problem arises, because the newly introduced description exists at t+1 but not at t. If 2. is meant, then the description introduced doesn't pick an ordinal, because there is no ordinal for which no English description can be introduced, and empty sets don't have least members. Basically, from the fact that necessarily, the number of English descriptions is countable, it doesn't follow that there are ordinals that can't be described.

Of course, they can't be simultaneously described in one possible world. Say one points this out and tries the description:

The least ordinal that can't be possibly described in a simultaneous description of (some) ordinals.

But here, again, from the uncountability of ordinals it doesn't follow that there is such a number, because there are many ways we can go about naming things, and an ordinal not named in one scenario might be named in another one.

PhilPapers Editorship

2009-05-14T07:53:00.004+02:00

The editors-in-chief (David Bourget and David Chalmers) kindly offered me (well, after I applied) the editorship of the following sections of PhilPapers (they fall under Ontology of Mathematics):

Mathematical Fictionalism
Mathematical Nominalism
Mathematical Platonism
Mathematical Structuralism
Mathematical Neo-Fregeanism
Indeterminacy in Mathematics
Indispensability Arguments in Mathematics
Numbers

and I gladly accepted. My main motivation is, this will force me to actually spend some time checking out new stuff, and to read all those interesting papers lying around that my evil procrastinating twin would never read otherwise.

If you feel like helping out and moving stuff down the branches on the categorization tree, please do so! Also, feel free to drop me a line if you know of something available online that's not listed there!

Representing consistency

2009-05-13T16:59:00.005+02:00

This is a response to Richard's remark on the previous post:

This has an unfortunate property that RCon doesn't have. If T is inconsistent, then, PA |- Con'(T). So this doesn't really have much claim to being called a consistency statement, does it?

Since it was too long to post in one piece in the comments, here it is.

Well, yeah, I didn't say it's the most useful or intuitive one. I just said it's simple. The main question is whether the formula strongly represents in T the consistency of T, no?

So if you check out Mostowski's "Thirty years of Foundational Studes" his way of defining this is this. He first assumes that T is consistent (and extends PRA). Then he says:

"We shall say that a formula F with one free variable is a weak description of a set X of integers if for any integer n the formula F(\bar n) is provable in T just in case n is an element of X. If F is a weak description of X and ~F is a weak description of the complement of X, then we call F a strong description of X in T."

Right, so what we care about in this setting is whether Pr' strongly represents in T provability in T. And indeed, it does.

A slightly different approach is not to assume the consistency of T, and to say that Pr' captures (in T) provability (in T) iff both:

If [n] (the object whose godel number is n) is a proof of [m], then T proves Pr'(n,m), and

if [n] is not a proof of [m], then T proves ~Pr'(n,m).

If T is consistent, then everything works out just fine for Pr', and if T is inconsistent, then vacuously also both conditions are satisfied, right?

(also, correct me if I'm wrong, but if T is PA, then Con'(PA) captures PA's consistency, and there's nothing wrong about PA proving Con'(PA) if PA is inconsistent.)

Now, if you call a consistency claim of T any formula that in T strongly represents T's consistency, Mostowski's formula is a consistency claim.

This all only shows that strong representation requirement isn't as hard to satisfy as one might initially think. And of course, there are other requirements you might put on formulas to count as "real" consistency claims.

A strikingly simple consistency statement

2009-05-13T12:11:00.003+02:00

Suppose T is a consistent formalization of arithmetic containing PRA (Primitive Recursive Arithmetic). Use some standard arithmetical encoding of formulas. Goedel's well-known second underivability theorem says that Con(T), the standardly constructed consistency statement for T, is not derivable in T.

There are, however, formulas equivalent to Con(T), which are derivable in T (although, the derivability conditions aren't satisfied). Usually, Rosser's or Feferman's examples are quoted; these are a bit complicated and involve reference to an ordering of formulas or proofs or axioms.

Here is another, strikingly simple non-standard consistency statement which is provable in T (due to Mostowski).

Let Pr express T's provability relation (it's the standard derivability predicate, nothing kinky is going on there). Define:

Pr'(x,y) ⇔ Pr(x,y)& ¬ Pr(x, ⌈0=S0⌉)

As T contains PRA, T proves 0≠S0. Since T is also consistent, T doesn't prove 0=S0. So ¬ Pr(x, ⌈0=S0⌉) is true of all numbers x. So Pr(x,y)& ¬ Pr(x, ⌈0=S0⌉) is true of exactly the same numbers as Pr(x,y). So Pr and Pr' have the same extension.

Now, construct the consistency statement Con'(T) as follows:

Con'(T) ⇔ ∀x ¬ Pr'(x,⌈0=S0⌉)

This boils down to:

Con'(T) ⇔ ∀x ¬[Pr(x,⌈0=S0⌉)& ¬ Pr(x,⌈0=S0⌉)]

which says that nothing is a number of a T-derivation that proves both 0=Sn and its negation. Clearly, proving Con'(T) in T doesn't require much effort.

Troubles with Elsevier

2009-05-11T19:26:00.002+02:00

Following Brian Weatherson I just allow myself to spread the word that Elsevier has been publishing fake journals for money (see here). Interesting reactions here.

Peer instruction in philosophy

2009-05-08T14:50:00.003+02:00

Here is a website devoted to something that looks like an interesting lecturing strategy. The basic idea is that every fifteen minutes or so, the lecture is interrupted and students are asked a quiz question. Then, those who got the aswers right are supposed to convince their neighbors who did not get the right answer about it. The method (i) provides the lecturer with insight into how many of the students understand the material, and (ii) makes students think harder. Here is a paper where the effectiveness of this method is studied. I might try it out some time.

Lectures online, Arche

2009-05-08T14:32:00.004+02:00

Arche research centre is posting lecture multimedia online. So far, they have Crispin Wrigh, Graham Priest and Ole Hjortland. Also, the format is pretty cool (it's sound AND slides).

Similarity, bots, uhm ...varia

2009-05-08T11:31:00.004+02:00

I'm writing a paper on modeling various kinds of similarity relations with relational models (these are modified Bugajski models, [JPL 1983 vol. 12] for similarity), so that those of Williamson's constraints on four-place similarity relations [NDJFL 1988, vol . 29] that I find convincing are satisfied.

Also, contra Bugajski, who argued that a set of properties generating a similarity relation has to contain vague properties if the resulting structure is to be non-trivial, I rather argue that even with sharp properties we get fairly intuitive and yet quite non-trivial structures, if we assume that our concepts are more like dynamic frames (a fairly new theory of concepts uses this idea and does seem to have some empirical support, see Barsalou's stuff).

Anyway, I was looking for a good similarity jokes to use as examples, found two I like:

Whats the difference between a fish and a mountain bike?
Both can swim, except for the mountain bike.

How does a shotgun with a broken firing pin resemble a government worker?
It won't work and you can't fire it.

More importantly, I stumbled upon an article about work being done by Julia Taylor and Larry Mazlack to get bots understand jokes based on puns. The task is quite non-trivial, considering the vast computational complexity of bacground knowlege searches etc.

Of course, this doesn't mean a great breakthrough is to be expected anytime soon (or anytime at all), but still, finding similarities between words and employing them efficiently in jokes isn't really that easy. The way the bot works is supposed essentialy to be this:

The program then checks to see if the message is consistent with what would make sense. If it doesn’t, the bot searches to see if the word sounds similar to a word that would fit. If this is the case, the bot flags it as humor.

Three things come to my mind: (1) defining what you mean by consistency with what would make sense and finding a way to check it might be a serious problem. (2) It's not sure whether (a) the bot is supplied with a list of similarities between words, or (b) can search its dictionary and identify words that sound similar (case (b), of course, sounds a bit more interesting). (3) It would be even more interesting if the bot could crack new jokes.

Another interesting thing I found following a link from Wikipedia (I was looking for OpenCyc to play around with, but didn't know what it was called). Wiki, while writing about Cyc mentions a fairly new application of it:

The comprehensive Terrorism Knowledge Base is an application of cyc in development that will try to ultimately contain all relevant knowledge about terrorist groups, their members, leaders, ideology, founders, sponsors, affiliations, facilities, locations, finances, capabilities, intentions, behaviors, tactics, and full descriptions of specific terrorist events. The knowledge is stored as statements in mathematical logic, suitable for computer understanding and reasoning.

So, in fact, there are moments where logic comes handy. Good to know. A slightly more serious report about how this database works is available here.

Many thanks, Greg!

2009-05-04T11:32:00.003+02:00

Some time ago, I won a slightly geeky quiz by Greg Restall by providing a false answer (well, interestingly, a false answer was needed). Today I received the prize, it's a copy of The Law of Non-Contradiction. Now I have two copies on my desk (one is from the library, though). So, many thanks, Greg!

Lesniewski and Frege's way out

2009-05-03T00:22:00.005+02:00

Recall that Frege, when faced with Russell's paradox, replaced the left-to-right direction of his Basic Law V:

{x:F(x)}={x:G(x)} → ∀x[F(x)↔G(x)]

with something like:

{x:F(x)}={x:F(x)}→∀y[[y≠{x:F(x)}]→ F(y)↔G(y)]

This move came to be referred to as Frege's way out (I think this name dates back to Quine's 1955 Mind paper, but that's just a guess).

Right now, I'm reading Giaquinto's The Search for Certainty. It's a very clear and accessible account of main debates surrounding foundations of mathematics pretty much from Dedekind and Cantor to Gödel. I really like the book, it's fun to read, the account is clear and succinct, and the author provides well-defended critical assessment of the views he discusses.

One remark. In footnote 22 (to ch. 3, part 2) Giaquinto's remarks that Lesniewski has already shown that Frege's way out still leads to contradiction.

This isn't exactly right. Strictly speaking, what Lesniewski has shown is rather that Frege's way out leads to contradiction with three additional assumptions (well, after translation from Lesniewski's language):

∀F[∃xF(x)→∃y(y={z:F(z)})]
∀F∀x,y[x={z:F(z)} & y={u:F(u)} → x=y]
∃x,y,z[x≠ y & x ≠ z & y≠z]

The first says that if something is F, then the class of F's exists. The second says that the class operator is a function (this is especially non-trivial in Lesniewski's systems), so that when you have a concept F, 'the extension of F' will name at most one object. (In a sense, assumption 2 corresponds to an instance of the right-to-left direction of Basic Law V). The third says that there are at least three distinct objects.

For an excruciatingly boring but a fairly detailed account of these (and related) things, see this paper. If you want to see a streamlined version of Lesniewski's proof on the blog, let me know in a comment and I might come up with a short version.

Infinite sums can get tricky!

2009-04-30T21:05:00.002+02:00

Here's a neat example of a reasoning taken to be a paradox in 18th century (in relation to infinitesimal calculus).

1. Consider the infinite sum:

1/2 + 1/4 + 1/8 + ... + 1/2ⁿ + 1/2ⁿ⁺¹ ...

Intuitively, it won't go above 1, and will be higher than any number below 1. So, we might take it to be 1.

2. Now consider:

1-1+1-1+1-1+...

One way to think about this sequence is this:

(1-1)+(1-1)+(1-1)+...

This way, it becomes 0+0+0+..., and hence it should equal 0.

3. Another way to break it down is to observe that -1+1=-(1-1) and substitute accordingly:

1-(1-1)-(1-1)-(1-1)...

But if we count this way, we get 1-0-0-0-0.... = 1.

4. Now, call the whole sum U.

U= 1-1+1-1+1-1+...

The reverse: -U will be obtained by reversing the signs before the summands:

-U= -1+1-1+1-1+1...

Add now 1 to each side:

1-U= 1-1+1-1+1-1+1...

But this is nothing but 1-U=U! Thus, it should follow that U=1/2.

The question some 18th-century mathematicians asked: which one is it?

Szymanik on Quantifiers

2009-04-29T10:55:00.003+02:00

Jakub Szymanik was kind enough to send me a surprise gift - a copy of his Quantifiers in TIME and SPACE (his dissertation published by ILLC). I've just discovered it in my mailbox. Thanks, Jakub! It seems fun and I look forward to reading it! Meanwhile, here is the abstract:

In the dissertation we study the complexity of generalized quantifiers in natural language. Our perspective is interdisciplinary: we combine philosophical insights with theoretical computer science, experimental cognitive science and linguistic theories.

We argue for identifying a part of meaning, the so-called referential meaning (model-checking), with algorithms. Then, we discuss the influence of computational complexity theory on cognitive tasks to motivate technical considerations which follow.

First, we study computational complexity of quantifier iteration, cumulation, resumption, branching and Ramseyification. Then we investigate the computational complexity of polyadic lifts expressing various readings of reciprocal sentences with quantified antecedents and establish a dichotomy between these readings: the strong reciprocal reading can create NP-complete constructions, while the weak and the intermediate reciprocal readings do not. We argue that this difference should be acknowledged in the Strong Meaning hypothesis.

Moreover, we study the definability and complexity of the type-shifting approach to collective quantification in natural language. We show that under reasonable complexity assumptions it is not general enough to cover the semantics of all collective quantifiers in natural language. Moreover, we suggest that some collective quantifiers might not be realized in everyday language due to their high computational complexity. Additionally, we introduce the so-called second-order generalized quantifiers to the study of collective semantics.

Theoretical discussion is followed by the empirical investigations. We study the statement known as Hintikka's thesis: that the semantics of sentences like 'Most boys and most girls hate each other' is not expressible by linear formulae and one needs to use branching quantification. We discuss possible readings of such sentences and come to the conclusion that they are expressible by linear formulae, as opposed to what Hintikka states. Next, we propose empirical evidence confirming our theoretical predictions that these sentences are sometimes interpreted by people as having the conjunctional reading.

Finally, we discuss a computational semantics for monadic quantifiers in natural language. We recall that it can be expressed in terms of finite-state and push-down automata. Then we present and criticize the neurological research building on this model. The discussion leads to a new experimental set-up which provides empirical evidence confirming the complexity predictions of the computational model. We show that the differences in reaction time needed for comprehension of sentences with monadic quantifiers are consistent with the complexity differences predicted by the model.

In general, our research explores, from different perspectives, the advantages of identifying meaning with algorithms and applying computational complexity analysis to semantic issues. It shows the fruitfulness of such an abstract computational approach for linguistics and cognitive science.

Fefermans' book on Tarski available in Polish!

2009-03-31T19:05:00.000+02:00

A Polish translation of Fefermans' Alfred Tarski: Life and Logic, translated by Joanna Golińska-Pilarek and Marian Srebrny is being published. On April 1, Warsaw University Library organizes a reception, accompanied by talks given by Jan Woleński, Mieczysław Omyła (who wrote the introduction to the Polish edition), Jan Zygmunt, Wacław Zawadowski, and THE TRANSLATORS.

If by any chance you're in Warsaw, it's in room 256 in the University Library building at Dobra 56/66 at 5 p.m. Last but not least, the posting informs, Polish doughnuts sponsored by Blikle will be served.

Pity I won't be there. :)

A contra to Putnam's 'Twin Earth'

2009-03-31T09:48:00.000+02:00

Recall than Putnam (The Meaning of 'Meaning') argued that if a new substance is discovered with a different chemical composition but the same phenomenal qualities as certain known substance, it will not fall under the same natural kind.

His thought experiment to support this claim is this: imagine a distant planet just like ours, except the water-like substance there has different, complicated chemical composition XYZ. It looks and tastes like water etc. Imagine you travel to that planet. On Putnam's reading, even though we would initially think this is water, once we discover the difference in chemical composition, we'll reject this view and reserve the term "water" for those substances which have the structure of H₂O.

Here's a historical example that these things aren't so clear-cut. For ages, the Chinese considered jade to be the most precious substance (pretty much like gold in the West). They also were very sensitive to its authenticity. Near the end of the 18th century, a large shipment of a very similar stone with unrelated composition, jadeite, made it to China. The Chinese could tell by its feel that it was a different material. They called it "new jade". They also started calling the real jade '"old jade". Interestingly, both substances came to be called jade and the new jade came to be used pretty much just like the old jade (now, jadeite is even more valued than nephrite, the original jade).

[More details about this stuff in LaPorte's very nice book, Natural Kinds and Conceptual Change.]

A cool lecture video online

2009-03-26T08:57:00.000+01:00

A video from a nice session on Time Travel (Anne French, Ken Perszyn and Nick Smith) is available here. The sever hosts also Colossal Squid Lectures (they have nothing to do with time travel, afaik, it's just the title is so cool I couldn't help but mention this).

Nicholas J. J. Smith's research website links to a few fun papers about time travel as well. Among others: Why Would Time Travellers Try to Kill their Younger Selves? and Bananas Enough for Time Travel?

A new blog on philosophy in Bristol

2009-03-18T00:11:00.000+01:00

Alexander Bird has started a new blog on philosophy-related stuff going on in Bristol. He has already posted a podcast on alternative medicine and taking science seriously.

Entia et Nomina

Godelizing the Yablo sequence

Lesniewski book draft

The TE paper now available in Synthese

A conference on Mereology, spring 2012

Yablo's paradox: Bueno & Colyvan vs. Ketland

The myth-busting paper on definitions, final version

An Episode in the History of Polish Art and Logic

Reading "Language, sense and nonsense"

Munich group and blog

Ontological Proofs Today, website up and running

Postdoc in logic and phil of sci, Calgary

"Platonic" thought experiments: how on earth?

Philosophica Journal (Ghent) available online

Teddy bears, guns and modal logic

Reichenbach on the philosophical insignificance of G's second incompleteness theorem

CLMPS registration - what's up with that?

Handbook of the History and Philosophy of Logic vol. 10 online

Ontological Proofs Today, Bydgoszcz

Vickers and the criterion of arithmetical truth

The CTT paper, final version

Possibility and the burden of proof

Evolutionary arguments do go astray (sometimes)

A geeky note about multilingual support for WinEdt 6.0

Applications of Logic in Philosophy and Foundations of Mathematics CFP

Second Entia et Nomina Workshop CFP

PhDs in Logic, CFP

Busting a myth about Lesniewski and definitions

History and Philosophy of Computing, Ghent, Nov 7-10, 2011

Church-Turing against Platonism - extensive revision

My top ten pieces of software

How not to use the Church-Turing thesis against platonism

Some Polish classics online

Watch out in Kirchberg

Gender gap in class

Befriending numbers nominalistically

Rafal Urbaniak (Ghent University/ Gdansk University) 'Yellow card for Salmon'Monday, 31 May, 16:30 - 18:30, Ryle Room, Faculty of Philosophy,10 Merton Street, Oxford.

Boredom in philosophy

Łukasiewicz at Harvard, 1926

J. H. Sobel (1929-2010)

Frege's slingshot, a minor fix (in case you care about details)

A historical remark on the nominal description theory

Knowability volume online

The History of Categorical Logic

Nominalist Neologicism

deRosset's stuff on modalities

Philosophical Tales

Miscellanea Logica: new series

Managing pdfs with Mendeley

What we don't need to save ordinary conditionals from

The "Modal argument" paper is forthcoming

Trends in Philosophy of Mathematics (day 3, talk 1)

The adaptive logics book has moved

Live from Trends in Logic VII (day 2)

Live from Trends in Logic VII

A rant about "deductive"

A book on adaptive logics in progress...

Frames, Frames and Frames

NCM 09 (part 2)

A replacement for Journal Wiki

Tahko's paper on modal epistemology online

Leszek Kołakowski has passed away

Marriage and Domestic Partnership

Leitgeb, "about", Yablo (again)

NCM 09 (part 1)

Lecture notes on PA

Elsevier turned to the dark side

Change & contradiction

A few papers reach daylight

Rating Journals, again

Non-Classical Mathematics 2009 (introductory remarks)

FMER, Leuven, June 10-12, cont'd

FMER, Leuven, June 10-12, cont'd

FMER, Leuven, June 10-12, cont'd

Time Travel paper online

FMER, news from the trenches (cont'd)

FMER, Leuven, June 10-12, News from the Trenches

Philosophy Journal Information

A category theory book online.

Philosophers' Rally, Cracow 2009 (Poland)

Rafal Urbaniak (Ghent University/ Gdansk University) 'Yellow card for Salmon'
Monday, 31 May, 16:30 - 18:30, Ryle Room, Faculty of Philosophy,10 Merton Street, Oxford.