B.Phil.
Seminar Volker Halbach and Alexander Paseau
Logic and Philosophy of Logic
Hilary term 2019, Monday, 11am-1pm, Ryle Room
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.
Topics to be discussed in the seminar will include a review of metatheoretic results,
logical constants, logical consequence, semantic paradoxes, operator and
predicate conception of modalities, and self-reference. The following plan is preliminary and we are happy to adapt it to the preferences of the participants.
Week 1 (14 January): Review of metatheoretic results
As preparation for the remaining topics, we will briefly go over some topics, including 2nd-order logic, compactness, infinitary logics, decidability, and basics of modal logic. Alex Paseau has prepared some notes, which can be downloaded from here.
Week 2 (21 January): Formalisation and Logical Consequence
Alex Paseau has prepared two papers for this week on Formalisation and Capturing Consequence.
Week 3 (28 January): The Problem of Logical Constants I
In the first half of the class we talk about the following seminal paper:
Tarski, Alfred (1986), ‘What are logical notions?’, History and Philosophy of Logic 7, 143–154. edited by John Corcoran.
For the second half, Alex Paseau has produced some brief notes on inferentialism.
Week 4 (4 February): The Problem of Logical Constants II
We continue with the discussion of criteria for logical constants. We focus on the following article:
G. Sher (2013), 'The Foundational Problem of Logic', The Bulletin of Symbolic Logic 19, pp. 145-98.
There is a vast literature on this topic. Depending on time, we might also look a the following:
McGee, Vann (1996), ‘Logical operations’, Journal of Philosophical Logic 25, 567–580.
Week 5 (11 February): The Substitutional Theory of Logical Consequence
The main text is:
There is also a formal version:
Week 6 (18 February): Modalities as operators and predicates
We discuss the formalization of modal notions such as necessity, apriority, provability, knowledge as predicates and sentential operators.
Halbach, Volker and Philip Welch (2009), ‘Necessities and Necessary Truths: A Prolegomenon
to the Metaphysics of Modality’, Mind 118, 71–100.
There is a recent monograph about this topic:
Johannes Stern: Toward Predicate Approaches to Modality, Trends in Logic Vol. 44, Springer, 2016
Week 7 (25 February): Diagonalization and modal paradoxes
Large parts of philosophical logic revolve around Gödel's diagonal lemma, which allows us to prove the existence of what is often called ‘self-referential’ sentences such as the liar sentence. The usual setting for proving the diagonal lemma is arithmetical. Sentences and expressions in generl are coded as numbers and then the diagonal lemma is proved in an arithmetical theory. However, for the purposes of many philosophical debates the detour through arithmetic with all its complications can be avoided. Quine, Smullyan and others have given highly simplified version. I present one particular form. The idea is taken from a joint book draft coauthored with Graham Leigh.
There are some slides again. There will not be sufficient time to go through all of them, but you might find some of the additional slides useful.
Week 8 (4 March): Many-sorted logic
It was suggested we could talk about many-sorted logic, more precisely about first-order many-sorted logic.
For a first idea see:
There are several papers, but we probably look at the following:
T. Barrett and H. Halvorson: ‘Quine’s conjecture on many sorted logic’, Synthese 194 (2017), 3563–3582
The proofs in this paper a somewhat painful, but it should be possible to get an idea about what Morita equivalence is without reading the proofs.
Dominik Ehrenfels has prepared some slides.