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.

Understanding Causal Inference (David Papineau)

The Logic and Metaphysics Workshop will meet on March 7th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 5382) for a talk by David Papineau (King’s).

Title: Understanding Causal Inference

Abstract: The current pandemic has focused attention on the techniques used by epidemiologists and other non-experimental scientists to infer causal hypotheses from correlational data. These techniques, which hinge on assumptions about the way causal connections manifest themselves in conditional and unconditional correlations, pose an obvious philosophical challenge. What is it about causation that allows them to work? None of the mainstream accounts of causation—counterfactual, process, dispositional, regularity—casts any light on this question. Probabilistic and interventionist theories of causation do offer a direct response to the challenge, by positing a constitutive connection between causes and correlations, but I shall argue that these theories do not dig deep enough. Instead I shall develop an older idea—which goes back to H.A. Simon in the 1950s—that relates causal relationships to systems of structural equations with probabilistically independent exogenous variables. The attraction of this structural equations approach is that it allows us to view the correlational patterns as fallible evidence for causal relationships, rather than constitutive of them. I shall consider whether this approach can lead to a full reduction of causation and how it might accommodate quantum mechanical unpredictability.

Ignorance as an excuse, formally (Ekaterina Kubyshkina)

The Logic and Metaphysics Workshop will meet on February 14th from 4:15-6:15 (NY time) via Zoom for a talk by Ekaterina Kubyshkina (Campinas).

Title: Ignorance as an excuse, formally

Abstract: In the current literature on epistemology there is a lively debate on which type of ignorance may provide a moral excuse. A good candidate is the one in which an agent has never considered or thought about a true proposition p. From a logical perspective, it is usual to model situations involving ignorance by means of epistemic logic. However, no formal analysis was provided for ignorance as an excuse. First, we will argue that if ignorance is expressed via standard modalities of knowledge and belief, one is unable to represent ignorance as an excuse. Secondly, we fill this gap by providing an original logical setting for modelling this type of ignorance. In particular, we introduce a complete and sound logic in which ignorance is expressed as a primitive modality. Semantically, the logic is characterized by Kripke semantics with possibly incomplete worlds. Moreover, in order to consider the conditions of a possible change of an agent’s ignorance, we will extend the setting by considering public announcements.

Frame Definability in Finitely-Valued Modal Logics (Guillermo Badia)

The Logic and Metaphysics Workshop will meet on February 7th from 4:15-6:15 (NY time) via Zoom for a talk by Guillermo Badia (Queensland).

Title: Frame Definability in Finitely-Valued Modal Logics

Abstract: In this paper we study frame definability in finitely-valued modal logics and establish two main results via suitable translations: (1) in finitely-valued modal logics one cannot define more classes of frames than are already definable in classical modal logic, and (2) a large family of finitely-valued modal logics define exactly the same classes of frames as classical modal logic (including modal logics based on finite Heyting and MV-algebras). In this way one may observe, for example, that the celebrated Goldblatt–Thomason theorem applies immediately to these logics. In particular, we obtain the central result from [B. Teheux. Modal definability for Łukasiewicz validity relations. Studia Logica 104 (2): 343–363 (2016)] with a much simpler proof and answer one of the open questions left in that paper. Moreover, the proposed translations allow us to determine the computational complexity of a big class of finitely-valued modal logics.

Note: This is joint work with Carles Noguera and Xavier Caicedo.