Author: Yale Weiss

Deductive Systems with Unified Multiple-Conclusion Rules (Alex Citkin)

The Logic and Metaphysics Workshop will meet on March 2nd from 4:15-6:15 in room 7395 of the CUNY Graduate Center for a talk by Alex Citkin (Metropolitan Telecommunications).

Title: Deductive Systems with Unified Multiple-Conclusion Rules

Abstract: Some people fight for the rights of animals, I am fighting for the rights of rejected propositions. Following the approach suggested by Brentano and accepted and developed by Lukasiewicz, I study the deductive systems that treat asserted and rejected propositions equally, in the same way. By “statement,” we understand the expressions of form +A – “A being asserted”, and -A$ – “A being rejected”, where A is a proposition. Accordingly, by a “unified logic,” we understand a consequence relation between sets of statements and statements. We introduce the unified deductive systems which can be used to define the unified logics. Unified deductive system consists of axioms, anti-axioms, and the multiple conclusion inference rules which premises and conclusions are the statements rather than the propositions. In particular, we study the deductive systems that contain the coherency rule, which means that one cannot assert and reject the same proposition at the same time, and the fullness rule, which means that each proposition is either asserted or rejected. Inclusion of these rules though does not enforce the law of excluded middle, or the law of non-contradiction on the propositional level.

A Truthmaker Semantics for Modal Logics (Dongwoo Kim)

The Logic and Metaphysics Workshop will meet on February 24th from 4:15-6:15 in room 7395 of the CUNY Graduate Center for a talk by Dongwoo Kim (CUNY).

Title: A Truthmaker Semantics for Modal Logics

Abstract: This paper attempts to provide an exact truthmaker semantics for a family of normal modal propositional logic. The new semantics can be regarded as an “exactification” of the Kripke semantics in the sense of Fine (2014). For it offers an account of the accessibility relation on worlds in terms of the banning and allowing relations on states. The main idea is that an exact truthmaker for “Necessarily P” is a state that bans the exact falsifiers of P from obtaining, and an exact truthmaker for “Possibly P” is a state that allows the exact verifiers of P to obtain.

The Power of Naive Truth (Hartry Field)

The Logic and Metaphysics Workshop will meet on February 3rd from 4:15-6:15 in room 7395 of the CUNY Graduate Center for a talk by Hartry Field (NYU).

Title: The Power of Naive Truth

Abstract: While non-classical theories of truth that take truth to be transparent have some obvious advantages over any classical theory that evidently must take it as non-transparent, several authors have recently argued that there’s also a big disadvantage of non-classical theories as compared to their “external” classical counterparts: proof-theoretic strength. Some of them have concluded that this gives a decisive advantage to classical logic theories.  Williamson has argued this too. While conceding the relevance of proof-theoretic strength to the choice of logic, I will argue that there is a natural way to beef up extant internal theories so as to remove their proof-theoretic disadvantage. Given this, the resulting internal theories should seem preferable to their external counterparts.

A Deontic Logic for Two Paradoxes of Deontic Modality (Melissa Fusco, joint work with Arc Kocurek)

The Logic and Metaphysics Workshop will meet on February 10th from 4:15-6:15 in room 7395 of the CUNY Graduate Center for a talk by Melissa Fusco (Columbia).

Title: A Deontic Logic for Two Paradoxes of Deontic Modality

Abstract: In this paper, we take steps towards axiomatizing the two dimensional deontic logic in Fusco (2015), which validates a form of free choice permission (von Wright 1969, Kamp 1973; (1) below) and witnesses the nonentailment known as Ross’s Puzzle (Ross 1941; (2) below).

(1) You may have an apple or a pear ⇒ You may have an apple, and you may have a pear.

(2) You ought to post the letter = ̸⇒ You ought to post the letter or burn it.

Since <>(p or q) = (<>p ∨ <>q) and [ ](p) ⇒ [ ](p ∨ q) are valid in any normal modal logic – including standard deontic logic – the negations of (1)-(2) are entrenched in modal proof systems. To reverse them without explosion will entail excavating the foundations of the propositional tautologies. The resulting system pursues the intuition that classical tautologies involving disjunctions are truths of meaning, rather than propositional necessities. This marks a departure from the commitments the propositional fragment of a modal proof system is standardly taken to embody.

Note: This is joint work with Arc Kocurek (Cornell).

Spring 2020 Schedule

The Logic and Metaphysics Workshop will be meeting on Mondays from 4:15 to 6:15 in room 7395 of the Graduate Center, CUNY (365 5th Avenue). The provisional schedule is as follows (* indicates a change):

Feb 3. Hartry Field, NYU

Feb 10. Melissa Fusco, Columbia

Feb 17. NO MEETING (GC CLOSED)

Feb 24. Dongwoo Kim, GC (CUNY)

Mar 2. Alex Citkin, Metropolitan Telecommunications

Mar 9. Antonella Mallozzi, Providence College

Mar 16. David Papineau, GC (CUNY)*

Mar 23. Jenn McDonald, GC (CUNY)

Mar 30. Mircea Dimitru, Bucharest*

Apr 6. Eoin Moore, GC (CUNY)

Apr 13. SPRING RECESS (NO MEETING)

Apr 20. Michał Godziszewski, Munich

Apr 27. Michael Glanzberg, Rutgers

May 4. Matteo Zichetti, Bristol

May 11. Lisa Warenski, GC (CUNY)

May 18. PROBABLY NO MEETING

 

Logic in Fiction (Mark Colyvan)

The Logic and Metaphysics Workshop will meet on December 9th from 4:15-6:15 in room 7314 of the CUNY Graduate Center for a talk by Mark Colyvan (Sydney).

Title: Logic in Fiction

Abstract: This paper will address the question of whether the logic of a fiction can be specified as part of the fiction. For example, can one tell a fictional story in which it is part of the story that the logic in question is, say, K3? It seems unproblematic that we can do this. After all, we can tell a story about a world with a different geometry from ours, different physical laws, and even different numbers of dimensions (e.g. the two-dimensional world of Flatland). While allowing fictions to specify their own logics seems a natural extension of such science fiction, there are problems looming. Fictions are, by their very nature, incomplete. Specifying that the logic in question is classical is to embrace, amongst other things, classical principles such as excluded middle. But if the fictional world is incomplete, in what sense can it be part of the story that excluded middle holds? We would, in effect, be specifying that the incomplete situation described in the fiction is complete. Imposing excluded middle where it doesn’t belong leads to contradiction. These are especially pressing issues for (particular kinds of) fictionalism about mathematics.

On the Notion of Diachronic Emergence (Jessica Wilson)

The Logic and Metaphysics Workshop will meet on December 2nd from 4:15-6:15 in room 7314 of the CUNY Graduate Center for a talk by Jessica Wilson (Toronto).

Title: On the Notion of Diachronic Emergence

Abstract: Though most accounts of emergence take this to be a broadly synchronic phenomenon, it has been recently maintained that there are distinctively diachronic forms of emergence (see, e.g., O’Connor and Wong’s 2005 account of strong emergence, Mitchell’s 2012 dynamic self-organization account of emergence, and Humphreys’ and Sartenaer and Guay’s 2016 accounts of ‘transformational emergence’). Here I argue that there is no need for a distinctively diachronic notion of emergence, as purported cases of such emergence can either be subsumed under broadly synchronic accounts, or else are better seen as simply cases of causation.

Memory and Intuitionistic Logic (Vincent Alexis Peluce)

The Logic and Metaphysics Workshop will meet on November 25th from 4:15-6:15 in room 7314 of the CUNY Graduate Center for a talk by Vincent Alexis Peluce (CUNY).

Title: Memory and Intuitionistic Logic

Abstract: L.E.J. Brouwer writes, “people try by means of sounds and symbols to originate in other people copies of the mathematical constructions and reasonings which they have made themselves; by the same means they try to aid their own memory. In this way the mathematical language comes into being, and as its special case the language of logical reasoning” (1907). More is left to be said, however, about the relation between the Brouwerian subject and logical language. In this talk we discuss the usual account of this relation and some problems with that view. We then propose an alternative.

An Unorthodox Solution to the Hintikka-Kripke Problem (Matías Bulnes)

The Logic and Metaphysics Workshop will meet on November 18th from 4:15-6:15 in room 7314 of the CUNY Graduate Center for a talk by Matías Bulnes (CUNY).

Title: An Unorthodox Solution to the Hintikka-Kripke Problem

Abstract: The Hintikka-Kripke problem consists in reconciling Hintikka’s semantics for doxastic operators and Kripke’s semantics for alethic operators. The problem arises from their treatment of identity. While the necessity of identities was one of the main innovations of Kripke’s semantics, Hintikka needs identities to be contingent to explain the opacity of doxastic operators. Yet alethic and doxastic operators are combined effortlessly in everyday discourse. In the talk, I will first discuss various attempts at reconciliation within the orthodoxy about opacity, and raise objections to them. Then, I will propose an unorthodox idea: rather than thinking of doxastic operators as introducing new possible worlds with different identities, think of them as introducing new logical spaces with different domains of objects. This achieves reconciliation by circumscribing the necessity of identities to the logical space of each agent. To assess this idea viz-a-viz its competitors, we will have to reexamine some fundamental concepts of the problem of opacity, such as the concepts of language and semantics.

Talking about Reification (Martin Pleitz)

The Logic and Metaphysics Workshop will meet on November 11th from 4:15-6:15 in room 7314 of the CUNY Graduate Center for a talk by Martin Pleitz (Hamburg).

Title: Talking about Reification

Abstract: Reification is the systematic association of a non-object with an object that encodes it. Therefore the reificationist must be a trans-objectist – i.e., anyone who thinks that there are instances of reification must also think that some items are not objects. As exemplified by Frege’s puzzle of the concept horse, non-objects and reification are notoriously difficult to talk about. Therefore I will begin my presentation by outlining a formal language that enables the trans-objectist and the reificationist to speak in a way that is not self-undermining. I will go on and employ the framework to give a uniform diagnosis of the set theoretic and semantic paradoxes in terms of static reification that is an alternative to Graham Priest’s Inclosure Schema, and sketch how dynamic reification can provide a uniform solution to the paradoxes as well as a general account of the constitution of abstract objects. In order to achieve this it will be crucial to import some tools of Procedural Postulationism, a dynamic account of the ontology of mathematics developed by Kit Fine.