Author: Yale Weiss

Care-theoretic semantics: Problems and non-deterministic solutions (Thomas Ferguson)

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.

Logic and inference in the sender-receiver model (Shawn Simpson)

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.

First-order logics over fixed domain (Gregory Taylor)

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.

On Kripke’s proof of Kripke completeness (Melvin Fitting)

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”.

Neopragmatism and logic: A deflationary proposal (Lionel Shapiro)

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.

Lewis on accommodation and representation de re (Gary Ostertag)

The Logic and Metaphysics Workshop will meet on March 6th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 9206) for a talk by Gary Ostertag (CUNY/Mount Sinai).

Title: Lewis on accommodation and representation de re

Abstract: Recall Lumpl, the lump of clay out of which the statue Goliath is fashioned. While (1) ‘Lumpl could have survived a squashing’ is true, (2) ‘Goliath could have survived a squashing’ is false, it being after all essential to Goliath, but not to Lumpl, that it be a statue. We have here an example of what David Lewis (1986) called “the inconstancy of representation de re”. For Lewis, the inconstancy does not amount to inconsistency, but rather points to the context-sensitivity of de re modal predication: (1) and (2) make implicit, context-sensitive reference to different counterpart relations. Once we recognize this, Lewisians argue, it becomes clear how our intuitive truth-conditional judgments are fully consistent. As I show, however, the conversational rule that triggers the implicit reference not only fails to license the reference shift, it effectively prohibits it. The upshot is that counterpart theory is deprived of a central motivation.

Spring 2023 Schedule

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. The provisional schedule is as follows:

Feb 27. Lionel Shapiro (UConn), Room 9205

Mar 6. Gary Ostertag (CUNY/Mount Sinai), Room 9206

Mar 13. Melvin Fitting (CUNY), Room 9205

Mar 20. Shawn Simpson (Pitt), Room 9205

Mar 27. Gregory Taylor (CUNY), Room 9205

Apr 3. Thomas Ferguson (Czech Academy of Sciences), Room 9205

Apr 10. Bradley Armour-Garb (SUNY Albany), Room 9205 Meeting Cancelled

Apr 17. Branden Fitelson (Northeastern), Room 9205

Apr 24. Andrea Iacona (Turin), Room 9205

May 1. Samara Burns (Columbia), Room 9205

May 10. SPECIAL WEDNESDAY SESSION (9:00-4:00). Mark Colyvan (Sydney), Heinrich Wansing (Bochum), and Daniel Skurt (Bochum), Room 9100 (Kelly Skylight Room)

May 15. Maciej Sendłak (Warsaw), Room 9206

Reification as identity? (Martin Pleitz)

The Logic and Metaphysics Workshop will meet on December 5th from 4:15-6:15 (NY time) via Zoom for a talk by Martin Pleitz (Muenster).

Title: Reification as identity?

Abstract: Abstract objects like properties and propositions, I believe, are the result of reification, which can intuitively be characterized as the metaphysical counterpart of nominalization (as in the shift, e.g., from ‘is a horse’ to ‘the property of being a horse’; cf. Schiffer, Moltmann), and occurs paradigmatically in the well-known bridge laws for instantiation, truth, etc. (e.g., something instantiates the property of being a horse iff it is a horse). So far, I have been working on an account of reification in terms of the technical notions of encoding & decoding, as some regulars at the L+M workshop may recall. In my upcoming talk, I wish to embed reification more clearly in higher-order metaphphysics and explore an alternative idea: Can reification be construed as identification across metaphysical categories? E.g., can the object that is the property of being a horse be identified, in some sense, with Frege’s concept horse, which is a non-objectual item because ‘is a horse’ is not a singular term? In my presentation I will argue for an affirmative answer. For this, I will sketch an ultra-generalized logic of equivalence, which has as its special cases (i) the well-known logics of first-order identity and equivalence, (ii) recent logics of generalized identities (à la Rayo, Linnebo, Dorr, Fine, Correia, Skiles, …) which connect higher-order items of the same type, and (iii) the logic of my proposed cross-level equivalences which connect items of different types. In a second step, I will re-construe reification as the cross-level equivalence that holds between higher-order items and abstract objects of the appropriate sort and argue that this account of reification as identity has certain advantages.

Modal pluralism and higher-order logic (William McCarthy)

The Logic and Metaphysics Workshop will meet on November 28th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 7314) for a talk by William McCarthy (Columbia).

Title: Modal pluralism and higher-order logic

Abstract: Modal pluralism is the view that there are a variety of candidate interpretations of the predicate ‘could have been the case that’ which give intuitively different answers to paradigmatic metaphysical questions (‘intuitively’ because the phrase means subtly different things on the different interpretations). It is the modal analog of set-theoretic pluralism, according to which there are a variety of candidate interpretations of ‘is a member of’.  Of course, if there were a broadest kind of counterfactual possibility, then one could define every other kind as a restriction on it, as in the set-theoretic case.  It would then be privileged in the way that a broadest kind of set would be, if there were one.  Recently, several authors have purported to prove from higher-order logical principles that there is a broadest kind of possibility. In this talk we critically assess these arguments.  We argue that they rest on an assumption which any modal pluralist should reject: namely, monism about higher-order logic. The reasons to be a modal pluralist are also reasons to be a pluralist about higher-order quantification. But from the pluralist perspective on higher-order logic, the claim that there is a broadest kind of possibility is like the Continuum Hypothesis, according to the set-theoretic pluralist.  It is true on some interpretations of the relevant terminology, and false on others.  Consequently, the significance of the ‘proof’ that there is a broadest kind of possibility is deflated.  Time permitting, we will conclude with some upshots of higher-order pluralism for the methodology of metaphysics.

Note: This is joint work with Justin Clarke-Doane.

The origins of conditional logic: Theophrastus on hypothetical syllogisms (Marko Malink and Anubav Vasudevan)

The Logic and Metaphysics Workshop will meet on November 21st from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 7314) for a talk by Marko Malink (NYU) and Anubav Vasudevan (University of Chicago).

Title: The origins of conditional logic: Theophrastus on hypothetical syllogisms

Abstract: Łukasiewicz maintained that “the first system of propositional logic was invented about half a century after Aristotle: it was the logic of the Stoics”. In this talk, we argue that the first system of propositional logic was, in fact, developed by Aristotle’s pupil Theophrastus. Theophrastus sought to establish the priority of categorical over propositional logic by reducing various modes of propositional reasoning to categorical form. To this end, he interpreted the conditional “If φ then ψ” as a categorical proposition “A holds of all B”, in which B corresponds to the antecedent φ, and A to the consequent ψ. Under this interpretation, Aristotle’s law of subalternation (A holds of all B, therefore A holds of some B) corresponds to a version of Boethius’ Thesis (If φ then ψ, therefore not: If φ then not-ψ). Jonathan Barnes has argued that this consequence renders Theophrastus’ program of reducing propositional to categorical logic inconsistent. In this paper, we show that Barnes’s objection is inconclusive. We argue that the system developed by Theophrastus is both non-trivial and consistent, and that the propositional logic generated by Theophrastus’ system is exactly the connexive variant of the first-degree fragment of intensional linear logic.