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Showing posts from November, 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

Modallogicisoftenused(andsometimesmisused)inphilosophicalarguments. 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 hesurvivesthedestructionofhisbody,andhence,heinsiststhataclaimaboutlogical possibility has important existential consequences, and(ii) he fails at providing a compelling argument, but his argumen…

Summer school - conditionals

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


Conditionals: Philosophical and Linguistic Issues

Application deadline:16 February, 2009

Course Directors:Barry Loewer, Rutgers, Philosophy Department, New Brunswick, USA
Jason Stanley, Rutgers, Philosophy Department, New Brunswick, USA

Faculty:Dorothy Edgington, University of Oxford, Faculty of Philosophy, Magdalen College and University of London, Birkbeck College, UK
Alan Hajek, Australian National University, Research School of Social Sciences, Philosophy Program, Canberra, Australia
Angelika Kratzer, University of Massachusetts, Department of Linguistics, Amherst, USA
Robert 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 condi…

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 )
(…

Chwistek on contradiction

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…

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. …