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Seminar Volker Halbach and Tim Williamson
Michaelmas term 2016, Wednesdays, 11am-1pm, Ryle Room
We will cover some central topics in the philosophy of logic. Topics may include semantic paradoxes and self-reference, logical consequence , unrestricted quantification, deviant logics, higher-order logic, modal logic and its applications in metaphysics, free logic.
At the beginning of each class we will introduce the topic by presenting an article or book chapter, which all participants will be expected to have read in advance. This will be followed by a discussion.
The following timetable is provisional.
Week 1 (12 October): Paradoxes and self-reference I: the diagonal lemma
Paradoxes and self-reference I: the diagonal lemma and self-reference
Volker Halbach has prepared some slides. In the slides the basic technique of diagonalization (Gödel's trick) that is at the root of all more formal treatments of the semantic paradoxes. It would be useful if you could read the first part (up to slide 22). There it is explained how to obtain a sentence that says about itself that it has a certain property (truth, necessity, etc). The diagonal lemma is the starting point for almost all discussions of the semantic paradoxes (liar paradox, Curry's paradox, etc). I'll present this part also in class, and there will be opportunity to ask questions. We can then discuss its consequences for theories of truth, necessity, knowledge, and so on. The slides contain only the technical core, and there are plenty of philosophical questions surrounding this technical core.
There is also a more explicit version. This is the draft of a part of a book VH is currently writing. The material does not presuppose anything beyond a basic logic course with the possible exception of function symbols, which are not covered in the Logic Manual, for instance. Here is a quick and dirty introduction together with some other preliminaries that should help you to understand my notation. There are probably still quite a few typos.
Week 2 (19 October): Paradoxes and self-reference II: some paradoxes
Self-reference, Yablo's paradox, and other paradoxes
We continue with the slides and look at some well-known paradoxes. Some have claimed that all semantic paradoxes involce self-reference. For an informal account see here.
Week 3 (26 October): Deviant Logics
Week 4 (2 November): Logical Consequence
Main text: John Etchemendy: "Models, Semantics, and Logical Truth", Linguistics and Philosophy 11 (91-106) 1988
If you prefer to read a more detailed account, Etchemendy's most influential text is the monograph: Etchemendy, John, 1990, The Concept of Logical Consequence, Cambridge, MA: Harvard University Press
He analyzed and criticized Tarski's theory of logical consequence in: "Tarski on Truth and Logical Consequence", Journal of Symbolic Logic 53 (1988), 51-79.
Week 5 (9 November): Free Logic
Karel Lambert: "Free logics" in Lou Goble (ed.), The Blackwell Guide to Philosophical Logic, Blackwell Publishers, 2001, 258-279.
Week 6 (16 November): Higher-Order logic
Stewart Shapiro: "Classical logic II: Higher-order logic" in Lou Goble (ed.): The Blackwell Guide to Philosophical Logic, Blackwell Publishers, 2001, 33-54.
Week 7 (23 November): Unrestricted Quantification
Kit Fine: "Relatively Unrestricted Quantification" in Agustín Rayo & Gabriel Uzquiano (eds.): Absolute Generality, Oxford University Press, 2006, 20-44.
Week 8 (30 November): Modal Logic
John P. Burgess: "Quinus ab omni naevo vindicatus" in Ali A. Kazmi (ed.): Meaning and Reference, University of Calgary Press, 1998, 25-66.