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Workshop on Substructural Logics, Hierarchies Thereof, and Solutions to the Liar

The Logic and Metaphysics Workshop and the Saul Kripke Center are hosting a day of talks on substructural Logics, hierarchies thereof, and solutions to the Liar on Friday, October 30, 2020. The schedule, NY time, will be as follows (abstracts can be accessed here):

10.00. Strict/Tolerant and Tolerant/Strict Logics, Melvin Fitting, CUNY.

11.40. Expressibility and the (Un)paradoxicality Paradoxes, Will Nava, NYU.

1.20. Lunch Break.

2.00. What is Meta-inferential Validity?, Chris Scambler, NYU.

3.40. Supervaluations and the Strict-Tolerant Hierarchy, Brian Porter, CUNY.

5.20. End (virtual gathering).

Talks will be on Zoom, and are open to all interested. A link will be sent out on the mailing lists of the Logic and Metaphysics Workshop and the Saul Kripke Center the day before. People not on either of those lists who want to receive the link should email Graham Priest (priest DOT graham AT gmail DOT com). PLEASE FEEL FREE TO PASS ON THIS ANNOUNCEMENT.

The Metaphysics of Epistemic Norms (Lisa Warenski)

The Logic and Metaphysics Workshop will meet on October 26th from 4:15-6:15 (NY time) via Zoom for a talk by Lisa Warenski (CUNY).

Title: The Metaphysics of Epistemic Norms

Abstract: A metanormative theory inter alia gives an account of the objectivity of normative claims and addresses the ontological status of normative properties in its target domain.  A metanormative theory will thus provide a framework for interpreting the claims of its target first-order theory.  Some irrealist metanormative theories (e.g., Gibbard 1990 and Field 2000, 2009) conceive of normative properties as evaluative properties that may attributed to suitable objects of assessment (doxastic states, agents, or actions) in virtue of systems of norms.  But what are the conditions for the acceptability of systems of norms, and relatedly, correctness of normative judgment?  In this paper, I take up these questions for epistemic norms.  Conditions for the acceptability of epistemic norms, and hence correctness of epistemic judgment, will be based on the critical evaluation of norms for their ability to realize our epistemic aims and values.  Epistemic aims and values, in turn, are understood to be generated from the epistemic point of view, namely the standpoint of valuing truth.

A Note on Synonymy in Proof-Theoretic Semantics (Heinrich Wansing)

The Logic and Metaphysics Workshop will meet on November 2nd from 4:15-6:15 (NY time) via Zoom for a talk by Heinrich Wansing (Bochum).

Title: A Note on Synonymy in Proof-Theoretic Semantics

Abstract: The topic of identity of proofs was put on the agenda of general (or structural) proof theory at an early stage. The relevant question is: When are the differences between two distinct proofs (understood as linguistic entities, proof figures) of one and the same formula so inessential that it is justified to identify the two proofs? The paper addresses another question: When are the differences between two distinct formulas so inessential that these formulas admit of identical proofs? The question appears to be especially natural if the idea of working with more than one kind of derivations is taken seriously. If a distinction is drawn between proofs and disproofs (or refutations) as primitive entities, it is quite conceivable that a proof of one formula amounts to a disproof of another formula, and vice versa. The paper develops this idea.

Models, Model Theory, and Modeling (Michael Glanzberg)

The Logic and Metaphysics Workshop will meet on October 19th from 4:15-6:15 (NY time) via Zoom for a talk by Michael Glanzberg (Rutgers).

Title: Models, Model Theory, and Modeling

Abstract: In this paper, I shall return to the relations between logic and semantics of natural language.  My main goal is to advance a proposal about what that relation is.  Logic as used in the study of natural language—an empirical discipline—functions much like specific kinds of scientific models. Particularly, I shall suggest, logics can function like analogical models.  More provocatively, I shall also suggest they can function like model organisms often do in the biological sciences, providing a kind of controlled environment for observations.  My focus here will be on a wide family of logics that are based on model theory, so in the end, these claims apply equally to model theory itself.  Along the way towards arguing for my thesis about models in science, I shall also try to clarify the role of model theory in logic.  At least, I shall suggest, it can play distinct roles in each domain. It can offer something like scientific models when it comes to empirical applications, while at the same time furthering conceptual analysis of a basic notion of logic.

A Metainferential Hierarchy of Validity Curry Paradoxes (Brian Cross Porter)

The Logic and Metaphysics Workshop will meet on October 12th from 4:15-6:15 (NY time) via Zoom for a talk by Brian Cross Porter (CUNY).

Title: A Metainferential Hierarchy of Validity Curry Paradoxes

Abstract: The validity curry paradox is a paradox involving a validity predicate which does not use any of the logical connectives; triviality can be derived using only the structural rules of Cut and Contraction with intuitively plausible rules for the validity predicate. This has been used to argue that we should move to a substructural logic dropping Cut or Contraction. In this talk, I’ll present metainferential versions of the validity curry paradox. We can recreate the validity curry paradox at the metainferential level, the metametainferential level, the metametametainferential level, and so on ad infinitum. I argue that this hierarchy of metaninferential validity curry paradoxes poses a problem for the standard substructural solutions to the validity curry paradox.

Mathematical Information Content (Oliver Marshall)

The Logic and Metaphysics Workshop will meet on October 5th from 4:15-6:15 (NY time) via Zoom for a talk by Oliver Marshall (UNAM).

Title: Mathematical Information Content

Abstract: Alonzo Church formulated several logistic theories of propositions based on three alternative criteria of identity (1949, 1954, 1989, 1993). The most coarse grained of these criteria is Alternative (2), according to which two propositions are identical iff the sentences that express them are necessarily materially equivalent. Alternative (1) is more discerning. According to Alternative (1), two propositions are identical iff the sentences that express them can be obtained from one another by the substitution of synonyms for synonyms and λ-conversion. Church said that he intended this to limn a notion of proposition closely related to Frege’s notion of gedanke, but added that it will not be sufficiently discerning if propositions in the sense of Alternative (1) are taken as objects of assertion and belief (1993). Alternative (0), the most discerning criterion, says that two propositions are identical iff the sentences that express them can be obtained from one another by the substitution of synonyms for synonyms. I argue that Alternative (1) does indeed provide insight into one of the topics that concerned Frege (1884) – namely, abstraction. Then I discuss various counterexamples to Church’s criteria (including one due to Paul Bernays, 1961). I close by proposing a criterion of identity for mathematical information content based on the various examples under discussion.

Coin flips, Spinning Tops and the Continuum Hypothesis (Daniel Hoek)

The Logic and Metaphysics Workshop will meet on September 28th from 4:15-6:15 (NY time) via Zoom for a talk by Daniel Hoek (Virginia Tech).

Title: Coin flips, Spinning Tops and the Continuum Hypothesis

Abstract: By using a roulette wheel or by flipping a countable infinity of fair coins, we can randomly pick out a point on a continuum. In this talk I will show how to combine this simple observation with general facts about chance to investigate the cardinality of the continuum. In particular I will argue on this basis that the continuum hypothesis is false. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. A classic theorem from Banach and Kuratowski (1929), tells us that it follows, given the axioms of ZFC, that there are cardinalities between countable infinity and the cardinality of the continuum. (Get the paper here: https://philpapers.org/archive/HOECAT-2.pdf).

Arithmetical Semantics for Non-Classical Logic (Yale Weiss)

The Logic and Metaphysics Workshop will meet on September 21st from 4:15-6:15 (NY time) via Zoom for a talk by Yale Weiss (CUNY).

Title: Arithmetical Semantics for Non-Classical Logic

Abstract: I consider logics which can be characterized exactly in the lattice of the positive integers ordered by division. I show that various (fragments of) relevant logics and intuitionistic logic are sound and complete with respect to this structure taken as a frame; different logics are characterized in it by imposing different conditions on valuations. This presentation will both cover and extend previous/forthcoming work of mine on the subject.

Cantor’s Theorem, Modalized (Chris Scambler)

The Logic and Metaphysics Workshop will meet on September 14th from 4:15-6:15 (NY time) via Zoom for a talk by Chris Scambler (NYU).

Title: Cantor’s Theorem, Modalized

Abstract: I will present a modal axiom system for set theory that (I claim) reconciles mathematics after Cantor with the idea there is only one size of infinity. I’ll begin with some philosophical background on Cantor’s proof and its relation to Russell’s paradox. I’ll then show how techniques developed to treat Russell’s paradox in modal set theory can be generalized to produce set theories consistent with the idea that there’s only one size of infinity.

(The slides are available here.)

Fall 2020 Schedule

The Logic and Metaphysics Workshop will be meeting on Mondays from 4:15 to 6:15 (NY time) entirely online. The provisional schedule is as follows:

Sep 14. Chris Scambler, NYU

Sep 21. Yale Weiss, CUNY

Sep 28. Daniel Hoek, Virginia Tech

Oct 5. Friederike Moltmann, CNRS Oliver Marshall, UNAM

Oct 12. Brian Porter, CUNY

Oct 19. Michael Glanzberg, Rutgers

Oct 26. Lisa Warenski, CUNY

Nov 2. Heinrich Wansing, Bochum

Nov 9. Eoin Moore, CUNY

Nov 16. Nick Stang, Toronto

Nov 23. Behnam Zolghadr, Hamburg

Nov 30. Mircea Dumitru, Bucharest

Dec 7. Jennifer McDonald, CUNY