The Logic and Metaphysics Workshop will meet on October 16th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 4419) for a talk by Yale Weiss (CUNY).
Title: Maximal deontic logic
Abstract: The worlds accessible from a given world in Kripke models for deontic logic are often informally glossed as ideal or perfect worlds (at least, relative to the base world). Taking that language seriously, a straightforward but nonstandard semantic implementation using models containing maximally good worlds yields a deontic logic, MD, considerably stronger than that which most logicians would advocate for. In this talk, I examine this logic, its philosophical significance, and its technical properties, as well as those of the logics in its vicinity. The principal technical result is a proof that MD is pretabular (it has no finite characteristic matrix but all of its proper normal extensions do). Along the way, I also characterize all normal extensions of the quirky deontic logic D4H, prove that they are all decidable, and show that D4H has exactly two pretabular normal extensions.
The Logic and Metaphysics Workshop will meet on October 2nd from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 4419) for a talk by Brett Topey (Salzburg).
Title: Whence admissibility constraints? From inferentialism to tolerance
Abstract: Prior’s invented connective ‘tonk’ is sometimes taken to reveal a problem for certain inferentialist approaches to metasemantics: according to such approaches, the truth-theoretic features of our expressions are fully determined by the rules of inference we’re disposed to follow, but admitting the ‘tonk’ rules into a language would lead to intuitively absurd results. Inferentialists tend to insist that they can avoid these results: there are constraints on what sets of inference rules can be admitted into a language, the story goes, and the rules governing disruptive expressions like ‘tonk’ are defective and so illegitimate. I argue, though, that from an inferentialist perspective, there’s no genuine sense in which rules like the ‘tonk’ rules are defective; those who endorse the relevant sort of inferentialism turn out to be committed to Carnap’s principle of tolerance. I then sketch an argument to the effect that this, despite appearances, isn’t a problem for inferentialism.
The Logic and Metaphysics Workshop will meet on September 18th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 4419) for a talk by Will Nava (NYU).
Title: Non-classicality all the way up
Abstract: Nearly all non-classical logics that have been studied admit of classical reasoning aboutthem. For example, in the logic K3, A or not-A is not a valid schema. However, ‘A or not-A’ is K3-valid or not K3-valid—this is, in some sense, a valid claim. In this talk, I introduce a simple framework for thinking about the logic of a given logic. This allows for a measure of the non-classicality of a logic—one on which almost all familiar non-classical logics are of the lowest grade of non-classicality. I’ll then discuss some strategies for generating and theorizing logics of higher grades of non-classicality, as well as some motivation for taking these logics seriously.
The Logic and Metaphysics Workshop will meet on September 11th from 4:15-6:15 (NY time) in-person at the Graduate Center (Philosophy Program Thesis Room in 7113) for a talk by Francesco Paoli (Cagliari).
Title: Logical metainferentialism
Abstract: Logical inferentialism is the view that the meaning of the logical constants is determined by the rules of inference that govern their behaviour in proofs – in particular, sequent calculus proofs, according to the preferences of several recent authors. When it comes to the nuts and bolts, however, the view is tenable only if certain aspects – concerning e.g. harmony criteria for rules, normal forms, or proof-theoretic validity – are clarified. Sequent calculus inferentialists generally do so in terms of proofs from axioms, not of derivations from assumptions. Although the merits of this approach are already debatable in traditional settings, recent work on sequent calculi without Identity or Cut has revealed further shortcomings. Logical metainferentialism revises inferentialism in this more general perspective. In this talk, we will sketch the basics of this view and argue that, from this vantage point, the claim that LP is the “One True Logic” may appeal even to the inferentialistically inclined logician.
The Logic and Metaphysics Workshop will be meeting on Mondays from 4:15 to 6:15 (NY time) unless otherwise indicated. Talks will be in-person only at the CUNY Graduate Center (Room 4419). The provisional schedule is as follows:
Sep 4. NO MEETING
Sep 11. Francesco Paoli (Cagliari)
Sep 18. Will Nava (NYU)
Sep 25. NO MEETING
Oct 2. Brett Topey (Salzburg)
Oct 9. NO MEETING
Oct 16. Yale Weiss (CUNY)
Oct 23. Melissa Fusco (Columbia)
Oct 30. Brad Armour-Garb (SUNY Albany)
Nov 6. Alex Citkin (Independent Scholar)
Nov 13. Alex Skiles (Rutgers)
Nov 20. Marian Călborean (Bucharest)
Nov 27. Mircea Dumitru (Bucharest)
Dec 4. James Walsh (NYU)
Dec 11. Rohit Parikh (CUNY)
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).
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).
2:30-4:00: 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.