Logic and Metaphysics Workshop

The Logic and Metaphysics Workshop will meet on May 15th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 9206) for a talk by Maciej Sendłak (Warsaw).

Title: Explanatory realism and counterfactuals

Abstract: In my talk, I want to propose a novel approach to the question of counterfactuals. This is grounded in two assumptions, imported from the philosophy of science. The first one has it that to explain a phenomenon is to show how it depends on something else. The second states that the correct explanation ought to be contrastive. This means that a good explanation justifies the occurrence of a phenomenon and – at the same time – excludes occurrence of some other states of affairs. I am going to argue that – together with the assumption that conditionals express a dependence relation between A and C – the above gives ground for analysis of counterfactuals. According to this proposal: “A>C” is true at the world of evaluation iff there is a relation of dependence that hold between referents of A and C, and the same relation of dependence holds in the world of evaluation.

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.

The Logic and Metaphysics Workshop will meet on April 3rd from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 9205) for a talk by Thomas Ferguson (Czech Academy of Sciences).

Title: Care-theoretic semantics: Problems and non-deterministic solutions

Abstract: In this talk I will present the details of a project of care-theoretic semantics in which a linguistic feature of care–rather than truth–is understood as the fundamental semantic property. I will review the details, including how adopting a bounds consequence position in which bounds are determined by considerations of topic allows one to determine both a theory of inference and theory of meaning on the basis of care alone. I will consider two challenges to the project: that of the reconciliation of topic-theoretic and truth-theoretic bounds (in which we need to acknowledge cases in which a position crosses both types of bounds) and sui generis monstrous content (in which two anodyne sentences together yield a content-theoretic violation). I will show that in both cases intuitions suggest the use of Nmatrices in the style of Avron and consider the merits of their employment in the care-theoretic setting.

The Logic and Metaphysics Workshop will meet on March 20th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 9205) for a talk by Shawn Simpson (Pitt).

Title: Logic and inference in the sender-receiver model

Abstract: The sender-receiver model was developed by David Lewis to tackle the question of the conventionality of meaning. But many people who cared about the conventionality of meaning did so because they thought it was intimately connected to the conventionality of logic. Since Lewis’s work, only a few attempts have been made to say anything about the nature of logic and inference from the perspective of the sender-receiver model. This talk will look at the what’s been said in that regard, by Skyrms and others, and suggest a few general lessons.

The Logic and Metaphysics Workshop will meet on March 27th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 9205) for a talk by Gregory Taylor (CUNY).

Title: First-order logics over fixed domain

Abstract: What we call first-order logic over fixed domain was initiated, in a certain guise, by Peirce around 1885 and championed, albeit in idiosyncratic form, by Zermelo in papers from the 1930s.  We characterize such logics model- and proof-theoretically and argue that they constitute exploration of a clearly circumscribed conception of domain-dependent generality.  Whereas a logic, or family of such, can be of interest for any of a variety of reasons, we suggest that one of those reasons might be that said logic fosters some clarification regarding just what qualifies as a logical concept, a logical operation, or a logical law.

The published paper is available here: https://doi.org/10.1111/theo.12382.

The Logic and Metaphysics Workshop will meet on March 13th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 9205) for a talk by Melvin Fitting (CUNY).

Title: On Kripke’s proof of Kripke completeness

Abstract: Saul Kripke announced his possible world semantics in 1959, and published his proof of axiomatic completeness for the standard modal logics of the time in 1963.  It is very unlike the standard completeness proof used today, which involves a Lindenbaum/Henkin construction and produces canonical models.  Kripke’s proof involved tableaus, in a format that is difficult to follow, and uses tableau construction algorithms that are complex and somewhat error prone to describe. I will first discuss Kripke’s proof, then the historical origins of the modern version.  Then I will show that completeness, proved Kripke style, could actually have been done in the Lindenbaum/Henkin way, thus simplifying things considerably.  None of this is new but, with the parts collected together it is an interesting story. “In my end is my beginning”.

The Logic and Metaphysics Workshop will meet on February 27th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 9205) for a talk by Lionel Shapiro (UConn).

Title: Neopragmatism and logic: A deflationary proposal

Abstract: Neopragmatists seek to sidestep metaphysical puzzles by shifting the target of philosophical explanation from the objects we think and talk about to the functions of expressions and concepts in our cognitive economy. Logical vocabulary can serve as a target for neopragmatist inquiry, and it has also posed obstacles to neopragmatist accounts of other vocabulary. I will argue that the obstacles can be addressed by adopting a neopragmatist perspective toward logical relations, such as logical consequence, and toward propositional content. Doing so calls into question two purported constraints on explanations of the functions of logical connectives. I will sketch an account made possible by rejecting those constraints, one according to which logical connectives serve to express dialectical attitudes. The proposal is deflationary in two ways: it rests on an extension of deflationism from truth to logical relations, and it aims to deflate some of neopragmatists’ theoretical ambitions.