The Logic and Metaphysics Workshop will meet on May 10th from 10:00-4:00 (NY time) in-person at the Graduate Center (Kelly Skylight Room) for a special Wednesday session. The program:

10:00-11:30: Heinrich Wansing (Bochum)

Title: Quantifiers in connexive logic (in general and in particular)

Abstract: Connexive logic has room for two pairs of universal and particular quantifiers: one pair are standard quantifiers; the other pair are unorthodox, but we argue, are well-motivated in the context of connexive logic. Both non-standard quantifiers have been introduced previously, but in the context of connexive logic they have a natural semantic and proof-theoretic place, and plausible natural language readings. The result are logics which are negation inconsistent but non-trivial.

Note: This is joint work with Zach Weber (Otago).

11:30-12:30: Lunch

12:30-2:00: Daniel Skurt (Bochum)

Title: RNmatrices for modal logics

Abstract: In this talk we will introduce a semantics for modal logics, based on so-called restricted Nmatrices (RNmatrices). These RNmatrices, previously used in the context of paraconsistent logics, prove to be a versatile tool for generating semantics for normal and non-normal systems of modal logics. Each of these semantics have sound and complete Hilbert-style calculi. The advantage of RNmatrices is that they provide a unifying framework for modal logics with or without first-order Kripke-frame conditions.

Note: This is joint work with Marcelo Coniglio (Campinas) and Pawel Pawlowski (Ghent).

2:00-2:30: Break

2:30-4:00: Mark Colyvan (Sydney/LMU)

Title: Explanatory and non-explanatory proofs in mathematics

Abstract: In this paper I look at the contrast between explanatory and non-explanatory proofs in mathematics. This is done with the aim of shedding light on what distinguishes the explanatory proofs. I argue that there may be more than one notion of explanation in operation in mathematics: there does not seem to be a single account that ties together the different explanatory proofs found in mathematics. I then attempt to give a characterization of the different notions of explanation in play and how these sit with accounts of explanation found in philosophy of science.

The Logic and Metaphysics Workshop will meet on May 1st from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 9205) for a talk by Samara Burns (Columbia).

Title: Understanding (and) surveyability

Abstract: In this talk I will discuss the notion of surveyable proof. Discussions of surveyability emerge periodically in recent philosophical literature, but the notion of surveyable proof can be traced back to Descartes. Despite this long history, there is still disagreement about what features a proof must have in order to count as surveyable. This disagreement arises, in part, because there is still significant vagueness regarding the problem that unsurveyability poses for the epistemology of mathematics. I identify three features of justification in mathematics that could be at issue in the surveyability debate: a priority, internalism, and certainty. Each of these features is prima facie troubled by unsurveyable proof. In each case, however, I’ll argue that unsurveyable proof does not pose any real issue. I will suggest that the surveyability debate should not be framed in terms of justification at all, and that the problem is really about mathematical understanding.

The Logic and Metaphysics Workshop will meet on April 24th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 9205) for a talk by Andrea Iacona (Turin).

Title: Inferentialism and connexivity

Abstract: In my talk I will investigate the relationships between two claims about conditionals that by and large are discussed separately. One is the claim that a conditional holds when its consequent can be inferred from its antecedent, or when the latter provides a reason for accepting the former. The other is the claim that conditionals intuitively obey some characteristic connexive principles, such as Aristotle’s Thesis and Boethius Thesis. Following a line of thought that goes back to Chrysippus, I will suggest that these two claims may coherently be understood as distinct manifestations of a single basic idea, namely, that a conditional holds when its antecedent is incompatible with the negation of its consequent. The account of conditionals that I will outline is based precisely on this idea.

The Logic and Metaphysics Workshop will meet on April 17th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 9205) for a talk by Branden Fitelson (Northeastern).

Title: Probability and logic/meaning: Two approaches

Abstract: In this talk, I will compare and contrast two approaches to the relation between probability and logic/meaning.  First, I will examine the Traditional (“Kolmogorovian”) Approach of setting up probability calculi, which presupposes semantic/logical notions and defines conditional probability in terms of unconditional probability.  Then, I will discuss the Popperian Approach, which does not presuppose semantic/logical notions, and which takes conditional probability as primitive.  Along the way, I will also discuss the prospects (and pitfalls) of adding an Adams-style conditional to various probability calculi.