Totality=Every; Dependence=Some; Choice=Any; Chance=A (Elia Zardini)

The Logic and Metaphysics Workshop will meet on May 2nd from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 5382) for a talk by Elia Zardini (Madrid).

Title: Totality=Every; Dependence=Some; Choice=Any; Chance=A

Abstract: I’ll first propose an interpretation of the multiplicative/additive distinction among operators arising in a logical framework lacking the structural property of contraction (focusing mostly on the quantifiers): multiplicative operators represent interaction among their operands (with universal quantification representing totality and particular quantification representing dependence) whereas additive operators represent selection (with universal quantification representing choice and particular quantification representing chance). I’ll then argue that reflection on the behaviour of natural-language determiners points towards a very natural working hypothesis that associates: multiplicative universal affirmative with ‘every’; multiplicative particular affirmative with ‘some’; additive universal affirmative with ‘any’; additive particular affirmative with ‘a’. I’ll illustrate the fruitfulness of this hypothesis with four examples, from the epistemic, normative, attitudinal and stative domains respectively.

Neo-Pragmatism about Truth (Julian Schlöder)

The Logic and Metaphysics Workshop will meet on May 9th from 4:15-6:15 (NY time) via Zoom for a talk by Julian Schlöder (UConn).

Title: Neo-Pragmatism about Truth

Abstract: Deflationists about truth hold that the function of the truth predicate is to enable us to make certain assertions we could not otherwise make. Pragmatists claim that the utility of negation lies in its role in registering incompatibility. The pragmatist insight about negation has been successfully incorporated into bilateral theories of content, which take the meaning of negation to be inferentially explained in terms of the speech act of rejection. One can implement the deflationist insight in the pragmatist’s theory of content by taking the meaning of the truth predicate to be explained by its inferential relation to assertion. There are two upshots. First, a new diagnosis of the Liar, Revenges and attendant paradoxes: the paradoxes require that truth rules preserve evidence, but they only preserve commitment. Second, one straightforwardly obtains axiomatisations of several supervaluational hierarchies, answering the question of how such theories are to be naturally axiomatised. This is joint work with Luca Incurvati (Amsterdam).

Modal Frame Incompleteness: An Account through Second Order Logic (Mircea Dumitru)

The Logic and Metaphysics Workshop will meet on May 16th from 4:15-6:15 (NY time) via Zoom for a talk by Mircea Dumitru (Bucharest).

Title: Modal Frame Incompleteness: An Account through Second Order Logic

Abstract: Propositional modal logic is usually viewed as a generalization and extension of propositional classical logic. The main argument of this paper is that a good case can be made that modal logic should be construed as a restricted form of second order classical logic. The paper makes use of the embedding of modal logic in second order logic and henceforth it goes on examining one aspect of this second order connection having to do with an incompleteness phenomenon. The leading concept is that modal incompleteness is to be explained as a kind of exemplification of standard order incompleteness. Moreover the modal incompleteness phenomenon is essentially rooted in the weaker expressive power of the language of sentential modal logic as compared to the stronger expressive power of the language of second order logic.

Logical Suppression Anew (Tore Fjetland Øgaard)

The Logic and Metaphysics Workshop will meet on April 25th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 5382) for a talk by Tore Fjetland Øgaard (Bergen).

Title: Logical Suppression Anew

Abstract: Val Plumwood and Richard Sylvan argued from their joint paper The Semantics of First Degree Entailment and onward that the variable sharing property is but a mere consequence of a good entailment relation; indeed they viewed it as a mere negative test of adequacy of such a relation, the property itself being a rather philosophically barren concept. Such a relation is rather to be analyzed as a sufficiency relation free of any form of premise suppression. Suppression of premises, therefore, gained center stage. Despite this, however, no serious attempt was ever made at analyzing the concept. A first rigorous analysis of their notion of suppression was given in Farewell to Suppression-Freedom. Therein it was shown that Plumwood and Sylvan’s notion of suppression is in fact properly weaker than variable sharing. I will in the current talk explore ways of strengthening the suppression criterion. One plausible way of doing so, I will argue, yields a principle equivalent to the standard variable sharing property. I hope to show, then, that the notion of suppression is not as unfruitful as I previously made it out to be.

From Truthmaker to Menu Semantics (Justin Bledin)

The Logic and Metaphysics Workshop will meet on April 11th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 5382) for a talk by Justin Bledin (Johns Hopkins).

Title: From Truthmaker to Menu Semantics

Abstract: The logical foundations of English and other natural languages are often assumed to have an essentially truth-theoretic character where the meanings of connectives and quantifiers are grounded in the truth and falsity of sentences. In this talk, I explore a fundamentally different perspective that shifts the focus from the truth value to the ‘menu’. Under this alternative conception of the logic of natural language, speakers manifest their logical competence by, metaphorically speaking, constructing and combining menus of items in various types throughout the grammar. The logical connectives are ‘menu constructors’: negation can be used to express that items are ‘off’ the menu, conjunction produces combinations of ‘on-menu’ items, and disjunction introduces choice between items. My point of departure for this truth displacing project is, oddly enough, recent work in ‘truthmaker’ or ‘exact’ semantics. What I try to do is build a bridge between the standard theory of truthmaker semantics (van Fraassen 1969; Fine 2017), which assigns menus of truthmakers and falsemakers at the sentential level, and compositional semantics in the general style of Montague. One of the most striking aspects of the theory is its treatment of noun phrases, as both quantificational and non-quantificational NPs are all assigned both denotations and ‘anti-denotations’ drawn or constructed from a rich entity space populated by both positive and negative individuals and their sums. Towards the end of the talk, I will try to bring out the explanatory power of menu semantics by applying it to a couple of problem areas in natural language quantification.

Causal Relativism (Jenn McDonald)

The Logic and Metaphysics Workshop will meet on April 4th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 5382) for a talk by Jenn McDonald (Columbia).

Title: Causal Relativism

Abstract: In this talk, I defend a kind of causal relativism. I argue that actual causation cannot be taken to hold simpliciter between two particular things (‘things’ such as events, states-of-affairs, etc.).  Instead, actual causation holds only relative to a background space of possibilities – a modal profile The argument applies generally to any difference-making analysis of actual causation.  But I will use the framework of structural equation models to make the case.   I first demonstrate that structural equation models represent situations in this way – as relative to some modal profile or other.  This observation is underappreciated in the literature.  I show how it raises a problem for all extant analyses of actual causation in terms of these models.  This problem is best responded to by a kind of causal relativism, or so I will argue.  Notably, the problem cannot be avoided by rejecting a structural equation framework.  While the framework is useful for its illustration, the problem arises for any analysis governed by the idea that a cause is what makes a difference in an effect’s occurrence.

Necessity, Essence and Explanation (Dongwoo Kim)

The Logic and Metaphysics Workshop will meet on March 28th from 4:15-6:15 (NY time) via Zoom for a talk by Dongwoo Kim (CUNY).

Title: Necessity, Essence and Explanation

Abstract: I shall discuss some of the relations between metaphysical modality, essence and explanation. The essentialist approach to metaphysical modality seeks to give an account of necessity (and thus of possibility) as having its source in essence. But what is essence, and in what sense and how does it give rise to necessity? In their recent paper “Essential Properties are Super-Explanatory: Taming Metaphysical Modality” (2020), Marion Godman, Antonella Mallozzi and David Papineau have attempted to address these issues with respect to aposteriori necessities concerning kinds. According to their account, the essence of a kind consists in the super-explanatory property—a single property that is causally responsible for a multitude of commonalities shared by the instances of the kind. And they argue that this super-explanatory notion of essence offers a principled account of aposteriori necessities concerning kinds. In this talk, I am going to argue that their account is not satisfactory. I shall examine two main arguments of GMP that the super-explanatory property of a kind is metaphysically necessary and argue that they both are fallacious. Along the way, a general problem will emerge that applies to any account that tries to explicate the notion of essence in terms of an explanatory relation.

Why Mathematics Works so Well (Noson Yanofsky)

The Logic and Metaphysics Workshop will meet on March 21st from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 5382) for a talk by Noson Yanofsky (CUNY).

Title: Why Mathematics Works so Well

Abstract: A major question in philosophy of science involves the unreasonable effectiveness of mathematics in physics. Why should mathematics, created or discovered, with nothing empirical in mind be so perfectly suited to describe the laws of the physical universe? To answer this, we review the well-known fact that the defining properties of the laws of physics are their symmetries. We then show that there are similar symmetries of mathematical facts and that these symmetries are the defining properties of mathematics. By examining the symmetries of physics and mathematics, we show that the effectiveness is actually quite reasonable. In essence, we show that the regularities of physics are a subset of the regularities of mathematics.

Avicenna motivates two new logics (Wilfrid Hodges)

The Logic and Metaphysics Workshop will meet on March 14th from 4:15-6:15 (NY time) via Zoom for a talk by Wilfrid Hodges (Queen Mary).

Title: Avicenna motivates two new logics

Abstract: The logician Avicenna (Ibn Sina in Arabic) tells us that some thousand and twenty years ago he discovered a group of previously unknown logics. He seems to have been the first logician – at least west of India and after the ancient Greeks – who made any such claim. We will examine two of these new logics and his motivations for them. The first new logic, discovered in around 994 when Avicenna was about eighteen years old, was rediscovered by Boole in the mid 19th century. We will study some features of it that were important to Avicenna (and to some recent logicians) but apparently missed by Boole. The second new logic, probably from around 1000, seems to be the earliest logic with inference rules that act below the surface levels of the formulas. It was impossible to state the inference rules correctly before Frege introduced the notion of scope, but we will see how far Avicenna got.

Paraconsistency with some detachment (Michael Burton)

The Logic and Metaphysics Workshop will meet on February 28th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 5382) for a talk by Michael Burton (Yale).

Title: Paraconsistency with some detachment

Abstract: In this talk, a proof-of-concept logic is presented that is like first-order LP (the “logic of paradox”) except things behave classically within the scope of universal quantifiers. This logic’s material conditional does not, in general, detach, but much can be deduced with it. Structures for this logic are classical first-order structures equipped with a congruence relation, giving this logic a connection to Priest’s collapsing lemma for LP. Some possible improvements to this logic are then discussed. One of these involves separating classicality from universal quantification, having classicality be mediated instead by operators that interact with variable assignments. Finally, the relevance of logics of this kind to various logical paradoxes is discussed.