## Thursday, November 27, 2008

### A modal argument for the soul

Thanks to Jeff Ketland, Agnieszka Rostalska and I will be giving two talks on December 2, 2008 in Edinburgh at the philosophy department. One of them will report what I wrote about Yablo's stuff, another will be something I worked on with Agnieszka Rostalska, Swinburne's modal argument for the existence of souls. Below is not a full version of the paper, but an abbreviated version that reveals the main gist of it.

1. INTRODUCTION

Modal logic is often used (and sometimes misused) in philosophical arguments. An interesting example, where the language of quantified propositional modal logic is put to work, is Swinburne’s argument for the existence of souls. It is interesting for at least two reasons: (i) he argues for the existence of his soul from the assumption that it is logically possible that he survives the destruction of his body, and hence, he insists that a claim about logical possibility has important existential consequences, and (ii) he fails at providing a compelling argument, but his argument isn’t trivially flawed, so it is quite interesting to see what went wrong. In these respects it is similar to (a version of) Anselm’s ontological argument which argues for a very strong conclusion from apparently simple modal premises and whose flaws nevertheless can’t be easily pointed out.

2. FORMALIZATION

Even though Swinburne’s original formulation (1986) employs formalism to a certain degree, it does not constitute a completely formalized argument whose all premises are explicitly stated. We start with giving a full formalization of Swinburne’s argument. As it turns out, it is valid: its conclusion follows from the premises, given a very modest logic (it’s not stronger that the quantified propositional version of T).

First, a few abbreviations:

C Swinburne is a Conscious person and exists in 1984.

D Swinburne’s body is Destroyed in the last instant of 1984.

S Swinburne has a Soul in 1984.

E Swinburne Exists in 1985.

84(p) Sentence p is about 1984.

com(p) Sentence p is (logically) compatible with C D ♦(p C D)

Now, the proof (ML stands for basic modal logic K, CL stands for classical logic, T stands for the modal logic T):

 (1) C Prem (2) ∀p[84(p) ∧ com(p) → ♦(C ∧ D ∧ p ∧ E)] Prem (3) ¬♦(C ∧ D ∧ ¬S ∧ E) Prem (4) 84(¬S) Prem (5) □(C ∧ D → S) → □ (C → S) Prem (6) 84(¬S) ∧ com(¬S) → ♦(C ∧ D ∧ ¬S ∧ E) ∀E: (2) (7) ¬(84(¬S) ∧ com(¬S)) CL: (3),(6)

(8)

¬84(¬S) ¬com(¬S)

CL: (7)

(9)

¬com(¬S)

CL: (4),(8)

(10)

¬♦(¬S C D)

Def: (9)

(11)

□¬(¬S C D)

Def: (10)

(12)

□(C D → S)

ML: (11)

(13)

□(C → S)

CL: (5),(12)

(14)

S

T, CL: (1),(14)

3. THE SUBSTITUTION OBJECTION

Having fixed these details, let’s take a look at the main objection against Swinburne’s argument, put forward by Alston and Smythe (1994) , Zimmerman (1991) and Stump and Kretzmann (1996). Basically, the problem is that (2) implies a specific instance of it:

(15) 84(M) com(M) → ♦(C D M E)

where:

M Swinburne is purely material (at all times) in 1984.

Now, is (15) true? Arguably, M is about 1984, and is compatible with the claim that Swinburne is a conscious person whose body is later completely destroyed. So the antecedent seems true. However, it doesn’t seem very likely that it is possible that Swinburne is purely material, conscious, and yet he survives the complete destruction of his body. So, prima facie, this substitution instance falsifies (2).

4. SWINBURNE’S RESPONSE AND ITS FAILURE

Swinburne’s response to this objection is worth being quoted in full:

Like all worthwhile arguments, mine purported to start from premises which many an opponent [sic] might grant . . . as they stand . . . to establish a conclusion which he did not previously recognize. I suggested that most people not already having a ﬁrm philosophical position on the mind/body issue will grant my premises. But someone already having a ﬁrm philosophical position contrary to mine can challenge my premiss (2) by inserting a p which he claims to be compatible with C and D and which he claims will show the premiss to be false, where p states a philosophical thesis about the very issue in dispute, contrary to the one which I am seeking to prove. Examples include “I am purely material in 1984” of Alston and Smythe, or “I am identical with my body or some part of it” of Zimmerman. Now of course I claim that no such p is compatible with C ∧ D. Since I put forward premisses (2) and (3) as purported necessary truths, my argument was designed to show that (given C) S is a necessary truth. The claim therefore that any p of the above type is compatible with C ∧ D amounts to the denial of my conclusion. Now it is true that my argument will not convince anyone who claims to be more certain that the conclusion is false than that the premises are true. But then that does not discredit my argument — for no argument about anything will convince someone in that position. My argument was designed for those prepared to set aside philosophical dogma concerned explicitly with the mind/body issue, and rely only on philosophical theses and intuitions about logical possibility relating to other or wider issues. (Swinburne 1996: 71)

So, basically, Swinburne denied:

(16) ♦(M C D)

claiming that it is not logically possible that he is purely material and conscious and his body is destroyed. But if by ♦ he means logical possibility (or, as he called it, ‘coherent describability’), he doesn’t seem to be right when he says that to affirm (16) one has to have a firm philosophical position. To the contrary, to reject (16) one already has to assume that C and D alone entail logically that Swinburne is not material. Unless Swinburne can provide an independent argument to show that this indeed is the case, we have no reason to accept his rejoinder.

5. ANOTHER DEFENSE AGAINST THE SUBSTITUTION OBJECTION

There are at least two ways we can make a material conditional true: by making its antecedent false, or by making its consequent true. Swinburne’s strategy was to do the former. However, it might seem a more plausible move to do the latter and insist that our reading of logical possibility is so weak that not only (16) comes out true, but also it is the case that:

(17) ♦(C D M E)

For indeed, on the face of it, there is no purely logical incoherence in the description of a situation where Swinburne is purely material and conscious in 1984, his body is destroyed in the last instant of 1984 and yet he continues to exist in 1985. Perhaps, the story might continue, God decided to “teleport” Swinburne to another body while destroying his previous body, or just actually gave him a soul while destroying his body.

Alas, this move won’t take us very far. If Swinburne is purely material in 1984, he certainly doesn’t have a soul in 1984. That is, M makes ¬S true. Hence, if (17) is true, so is:

(18) ♦(C D ¬S E)

But it is easy to observe that if that were the case, we would falsify (3), thus making the argument unsound.

Perhaps, in the argument, instead of speaking about being about 1984’ we should rather speak about being true about 1984’? Let’s abbreviate:

tr84(p) 84(p) p

Now, we have to check if we can run the argument in this setting. Instead of (2), take:

(2a) p[tr84(p) com(p) → ♦(C D p E)]

Next, mimic the initial proof, eliminating the universal quantifier from (2a):

(6a) tr84(¬S) com(¬S) → ♦(C D ¬S E)

From (3) and (6a) substituting ¬S for p we obtain:

(7a) ¬(tr84(¬S) com(¬S))

De Morgan’s law applied to (7a) gives us:

(19) ¬tr84(¬S) ¬com(¬S)

At this point we split the disjunction into a proof by cases. Suppose ¬tr84(¬S). By definition, this means that either ¬84(¬S) or ¬¬S. But (4) says that 84(¬S). So, ¬¬S and hence S. Suppose on the other hand that ¬com(¬S). In this case we land back at (9) and proceed with the argument exactly the same way as before, obtaining S. Hence the whole disjunction in (19) entails S, given the rest of the premises.

This strategy deals nicely with the substitution objection. To believe that M falsifies (2a) one has to believe that tr84(M), and yet to deny that ♦(C ∧ D ∧ M ∧ E). But to accept tr84(M), one already has to assume that M is true, and to deny that ♦(C ∧ D ∧ M ∧ E) one has to believe that it is impossible that M is true and yet Swinburne survives the destruction of his body. So, in order to believe that M falsifies (2a) one would have to believe that Swinburne won’t survive, which actually means having a firm position.

Unfortunately, even this version of the argument is not devoid of difficulties. Suppose we replace (2) with (2a). The assumption employed now says that no true sentence compatible with Swinburne‘s being alive and conscious in 1984 and his body being destroyed excludes the possibility of him surviving the destruction of his body. This is equivalent to the claim that any sentence about 1984 compatible with C ∧ D that excludes the possibility of Swinburne‘s survival is already false. But this indicates that this version of the argument is epistemically circular

7. SUMMARY

Here are a few points to sum up.

• Swinburne’s initial argument is valid, when given in full form.
• The substitution objection undermines one of the premises, and Swinburne’s defence against this criticism doesn’t work.
• One can defend the argument more plausibly in a different way, but this falsifies another premise of the argument.
• One can try to avoid these difficulties by running a different version of the argument. It deals better with the objections put forward so far, but it turns out to be epistemically circular.

REFERENCES

Alston, W. P. And Smythe, T.W. (1994). Swinburne’s argument for dualism. Faith and Philosophy, 11(1): 127-133

Stump, E. and Kretzmann, N. (1996). An objection to Swinburne’s argument for dualism. Faith and Philosophy, 13: 405-412

Swinburne, R. (1984). Personal Identity, chapters 1-4, The Dualist Theory, pp. 1-66, Basil Blackwell

Swinburne, R. (1986). The Evolution of the Soul. Clarendon Press.

Swinburne, R. (1996). Dualism intact. Faith and Philosophy, 13(1): 68-77

Zimmerman, D. W. (1991). Two Cartesian arguments for the simplicity of the soul. American Philosophical Quarterly, 3:217-226

## Tuesday, November 25, 2008

### Summer school - conditionals

This sounds pretty cool. I might try to be there. More details on their website.

Conditionals: Philosophical and Linguistic Issues

 Course Directors: Barry Loewer, Rutgers, Philosophy Department, New Brunswick, USAJason Stanley, Rutgers, Philosophy Department, New Brunswick, USA Faculty: Dorothy Edgington, University of Oxford, Faculty of Philosophy, Magdalen College and University of London, Birkbeck College, UKAlan Hajek, Australian National University, Research School of Social Sciences, Philosophy Program, Canberra, AustraliaAngelika Kratzer, University of Massachusetts, Department of Linguistics, Amherst, USARobert Stalnaker, Massachusetts Institute of Technology, Department of Linguistics & Philosophy, Cambridge, USA

The aims of this summer school are 1) to teach and discuss recent philosophical and linguistic advances on our understanding of conditionals and 2) to promote discussions among the faculty and participants of issues involving conditionals from the perspectives of linguistics, philosophy of language, philosophical logic, cognitive psychology, and philosophy of science 3) to help establish a network of young researchers on issues in philosophy of language and philosophical logic.

The course will cover
1. an introduction to the main ideas needed for an understanding of recent work on conditionals including the basics of modal logic, probability theory, and linguistics;
2. the main accounts of the linguistics and semantics of indicative and subjunctive conditionals;
3. the connections between probability and conditionals;
4. connections between conditionals and other philosophical concepts including laws, causation, knowledge, the direction of time.

### Chwistek on the axiom of reducibility and completeness

So, I finally found some time to read Chwistek's 1912 paper. As it turns out, after a few pages about Lukasiewicz's criticism (where Chwistek defends Aristotle, but, to my mind, quite superficially), he moves on to a description of R&W type theory with the axiom of reducibility.

The most interesting part is where he actually argues that it is inconsistent: it turns out that the argument that was in Ueber die Antinomen der Prinzipien der Mathematik, translated in McCall's volume was already (pretty much) shaped in 1912. I haven't compared those arguments in details, but prima facie, it's the same argument.

The last two sections of 1912 have quite intriguing titles:

iv. Contradictions in Russell's system. The possibility of a system free of contradictions.
v. The pseudo-problem of a logic without the principle of contradiction

In section iv he basically :

(i) claims type theory without the axiom of reducibility is consistent (needless to say, no proof is given;P )
(ii) is very careful about completeness: he says it's possible there are true sentences that can't be proven in this type theory:

The system allows to prove many true sentences. These, however, won't suffice for determining the fertility of the system. To answer this question, tremendous further work is required [...] for now, I'll limit myself to the claim that the task isn't fully delusional, that is, that even if many true claims are left out, we sill have a system that does possess certain scientific value. [p. 326]

(iii) insists that after leaving out the axiom of reducibility the system is consistent, because it was because of the axiom that the contradiction arose. (but he is quite consious that this isn't a proof).

In section vi he criticizes the idea of a logic which admits contradiction (the idea occured in Łukasiewicz's book). I'll write about this when I have more time...

Interestingly, there is no mention of Lesniewski's work whatsoever.

## Tuesday, November 18, 2008

As you may (or may not) know, there was a fairly lively debate surrounding the validity of the principle of contradiction in Poland in the beginning of the twentieth century.

Main participants:

Łukasiewicz 1910, On the principle of contradiction in Aristotle.

A book. He distinguished a few senses of the principle, and criticized most of them. He also attempted to describe a society in which people wouldn't accept the principle.

Leśniewski 1912, An attempt of a proof of the principle of contradiction

A paper. This is weird stuff. He assumes the principle on the meta-lingustic level (in his words: "no contradictory proposition possesses a symbolic function") and argues for the ontological formulation. Interestingly, Łukasiewicz wrote in his diary that Lesniewski showed up at his place with the manuscript and that Łukasiewicz were convinced by Leśniewski's defence. I'm not. (see here for reasons, especially section 2.4)

Chwistek 1912, On the principle of contradiction in the light of Bertrand Russell's recent research.

A long paper. This stuff is quite rare. I had to take an 800 km long trip and dig in an archive to find a copy (which I did last week). Quite amusingly, everyone cites it, but no one gets the reference quite right (which was another reason why it was difficult to find). I haven't read it yet, but it's ca 65 pages. I'll post some comments as I go.

Anyway, I'll be translating it over the next few months (a student of mine here in Gdansk might do some bits) with the purpose of gathering all three things in one book-like publication. (Bernard Linsky already kindly agreed to write an introductory part discussing Chwistek's relations with Russell, when the translation is done). What's quite surprising is that only Lesniewski's paper has been translated. I mean, there's a sort of an English abstract of Łukasiewicz's book lying around (translated by Vernon Wedin, in Review of Metaphysics, 1971, 24, 485-509), but it's not exactly the actual book.

(There's also a book on Łukasiewicz's stuff by Fred Seddon, which I'll try to get a hold of.)

## Monday, November 10, 2008

### Definability of identity in higher-order languages

Thanks to the long weekend I finally found some time to write up a first draft of a paper that I've meant to write for quite a while. (I know, spending the long weekend doing research is a tad pathetic and geeky, but I really wouldn't have time to do this some other time). It's about a thing that seems to have been settled - the definability of identity. Below is the abstract. The full version of the paper is here.

It is a commonplace remark that the identity relation, even though not expressible in a first-order language without identity with classical set-theoretic semantics, can be defined in a language without identity, as soon as we admit second-order, set-theoretically interpreted quantifiers binding predicate variables that range over all subsets of the domain. However, there are fairly simple and intuitive higher-order languages with set-theoretic semantics (where the variables range over all subsets of the domain) in which the identity relation is not definable. The point is that the definability of identity in higher-order languages not only depends on what variables range over, but also is sensitive to how predication is construed.

## Monday, November 3, 2008

### A revised version of Leitgeb, `about'', Yablo

So, I exchanged a few emails with Hannes Leitgeb. His feedback motivated some slight (and yet, important) changes in the content. The revised version has been uploaded here.