## Tuesday, July 28, 2009

### Tahko's paper on modal epistemology online

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.

## Saturday, July 18, 2009

### Leszek Kołakowski has passed away

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]

## Friday, July 17, 2009

### Marriage and Domestic Partnership

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.

## Wednesday, July 15, 2009

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:

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).

## Wednesday, July 8, 2009

### NCM 09 (part 1)

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.

$\small \mbox{For any } \Gamma \mbox{ and } \Delta, \mbox{ asserting each formula in } \Gamma \\ \mbox{ and denying each in } \Delta \\ \mbox{ is a clash.}$

The rules we buy into unconditionally are at least these:

$\mbox{\textsc{Identity:}}\,\, \Gamma, A \vdash A, \Delta \\ \mbox{\textsc{Cut:}}\,\, \Gamma \vdash A, \Delta \,\, \Gamma, A \vdash \Delta \Rightarrow \Gamma \vdash \Delta$

There are two interesting negation rules:

$\mbox{[]\neg L]}\,\,\,\,\,\,\,\,\, \Gamma \vdash A, \Delta \Rightarrow \Gamma, \neg A \vdash \Delta \\ \mbox{[]\neg R]}\,\,\,\,\, \,\,\,\,\, \Gamma,A \vdash \Delta \Rightarrow \Gamma \vdash \neg A, \Delta$

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:

$T\vdash A \Rightarrow A \in T$.

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,

$A\vdash U \Rightarrow A\in U.$

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:

$T \vdash A, U \Rightarrow A\in T \\ T, A\vdash U \Rightarrow A \in U$

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.

## Monday, July 6, 2009

### Lecture notes on PA

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

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).

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.

## Sunday, July 5, 2009

### A few papers reach daylight

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.

## Saturday, July 4, 2009

### Rating Journals, again

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.