The Logic and Metaphysics Workshop will meet on April 28th from 2:00-4:00 in-person at the Graduate Center (Room 7395) for a talk by Claudine Verheggen (York, CA).

Title: Wittgenstein’s response to Kripke’s Wittgenstein

Abstract: In response to the sceptical problem he found in the writings of Ludwig Wittgenstein, Saul Kripke argued that the only possible rejoinder was a sceptical solution. He did not consider what I take to be Wittgenstein’s way out, which is to dissolve the problem, showing that the sceptic’s conception of what it is for words to have meaning is misguided and therefore the sceptical problem unmotivated. Both sceptical solution and dissolution are committed to semantic non-reductionism. But I do not think that both are committed to semantic quietism. I argue that, whereas the sceptical solution can only lead to quietism, as it concedes that the foundational challenge the sceptic has raised cannot be met and thus only descriptive remarks about meaning are forthcoming, the dissolution of the sceptical problem opens up an alternative way of thinking about meaning, a way which generates its own problem, the resolution of which may result in constructive, albeit still non-reductionist, remarks about meaning.

The Logic and Metaphysics Workshop will meet on April 21st from 2:00-4:00 in-person at the Graduate Center (Room 7395) for a talk by Jacob McNulty (Yale).

Title: A hole within being: Consciousness as nothingness in the early Sartre

Abstract: Among Sartre’s best-known theses in Being and Nothingness is his claim that the world of experience contains what he calls “négatités,” little pools or pockets of nothingness. The most famous example of a négatité is Pierre, the friend who is absent from the café. Sartre’s conviction that there are négatités all around us has another side, often obscured from view: I mean his (apparent) conviction that we ourselves are a kind of non-being or nothingness. In this paper I try to shed some light on this Sartrean thesis by connecting it to perennial problem in metaphysics concerning the status of holes, shadows or absences — in short, non-beings. However I see more than mere analogy here. Sartre’s view, as I understand it, is that we literally are a type of hole. We are holes in the sense that we are the kinds of nonbeings that require beings as our hosts. More accurately, it is being and not beings that host the holes that we are. Ordinary holes have some particular material thing as their hosts: cheese or fabric. Yet our “host” is not any particular being (cheese or fabric) but being itself: the in-itself [en soi]. 

The Logic and Metaphysics Workshop will meet on May 5th from 2:00-4:00 in-person at the Graduate Center (Room 7395) for a talk by Luca Incurvati (ILLC).

Title: On class hierarchies

Abstract: In her seminal article ‘Proper Classes’, Penelope Maddy introduced a theory of classes validating the naïve comprehension rules. The theory is based on a step-by-step construction of the extension and anti-extension of the membership predicate, which mirrors Kripke’s construction of the extension and anti-extension of the truth predicate. Maddy’s theory has been criticized by Øystein Linnebo for its ‘rampant indeterminacy’ and for making identity among classes too fine-grained. In this paper, I present a theory of classes that builds on Maddy’s theory but avoids its rampant indeterminacy and allows for identity among classes to be suitably coarse-grained. For all the systems I discuss, I provide model theories and proof theories (formulated in bilateral natural deduction systems), along with suitable soundness and completeness results.

The Logic and Metaphysics Workshop will meet on April 7th from 2:00-4:00 in-person at the Graduate Center (Room 7395) for a talk by Allison Aitken (Columbia).

Title: Vasubandhu on intentional action: From mind-body to mind-only

Abstract: Jonathan Schaffer argues that mereological nihilism “culminates in monism.” In other words, the same sorts of parsimony considerations that motivate the rejection of real composites ultimately lead to a monist ontology. In this talk, I show how the 4th-5th century Buddhist philosopher Vasubandhu makes a similar argument, but instead of proposing an existence monism, as Schaffer does, Vasubandhu advances a type-monism–specifically, a form of metaphysical idealism on which all that exist are mental representations. I show how he exploits challenges confronting mereological nihilists when it comes to accommodating intentional action in their ontologies in order to call into question the explanatory utility of matter itself. He first uses puzzles concerning the metaphysics and causal mechanics of action to eliminatively reduce bodily action to mental action, and then leverages the same principle of parsimony that motivates his external world realist interlocutors to exclude real composites from their ontology to jettison matter from the picture altogether. I consider reasons why Vasubandhu resists existence monism and instead takes his type-monism to be the simplest sufficient ontology capable of explaining the sorts of things that matter most to him and his fellow-Buddhists, like intentional actions that are both morally significant and causally efficacious.

The Logic and Metaphysics Workshop will meet on March 24th from 2:00-4:00 in-person at the Graduate Center (Room 7395) for a talk by Davide Sutto (Oslo).

Title: The iterative conception of pluralities

Abstract: Georg Cantor informally distinguished between “consistent” and “inconsistent” multiplicities as those many things that, respectively, can and cannot be thought of as one, i.e., as a set. In this talk I propose a framework that clarifies the distinction through a contemporary development of the iterative conception of set. Reshaping Tim Button’s Level Theory by means of plural logic, I define and axiomatize the notion of a plural level. This provides an explanation of Cantor’s consistent multiplicities as level-bound pluralities, namely as those pluralities that appear at some level of the plural cumulative hierarchy of sets. Furthermore, it also yields a development of set theory from plural logic that retains the full power of the comprehension axiom schema. This feature is especially relevant as it enables a parallel understanding of inconsistent multiplicities as those pluralities that are not level-bound, that is, as proper classes.

The Logic and Metaphysics Workshop will meet on March 17th from 4:00-6:00 in-person at the Graduate Center (Room 7395) for a talk by Greg Restall (St Andrews).

Title: Modal logic and contingent existence

Abstract: In this talk, I will defend contingentism, the idea that some things exist contingently. It might be surprising that this needs defence, but natural reasoning principles concerning possibility and necessity on the one hand, and the existential and universal quantifiers on the other, have led some to necessitism, the view that everything that exists, exists necessarily. Almost all recent work on modal semantics makes essential use of possible worlds models. These models have proved useful for analysing the structural properties of modal logics, but it is less clear that they fix the meaning of our modal vocabulary, given that we have no grasp of what counts as a possible world, independent of our grasp of what counts as possible. In this talk, I describe an inferentialist semantics for modal and quantificational vocabulary, not as a rival to possible worlds models, but as an explanation of how the concepts we do employ can be modelled using possible worlds. I then use this inferentialist semantics to clarify the contingentist’s commitments, and offer answers to necessitist objections.

The Logic and Metaphysics Workshop will meet on March 17th from 2:00-4:00 in-person at the Graduate Center (Room 7395) for a talk by Marian Călborean (Bucharest).

Title: Vagueness as dispersion

Abstract: Classical logic (FOL) is thought to be incompatible with the fuzzy cutoffs of vague predicates. I conceptualize vagueness as the dispersion of negative and positive cases of predicates such as “tall” across ranks defined by the preferred ordering—e.g., “having less or equal cm of height”. I distinguish vertical dispersion—both negative and positive cases of the predicate can share the same measurement—and horizontal dispersion—change happens with gradually fewer intercalations of negative and positive cases. Parallel to the non-classical approach of Cobreros et al. (2012), I introduce two classical shorthand modifiers “strictly” and “broadly”. Then, the Sorites paradox is solved by weakening the principle of tolerance to “If a person is strictly tall, anyone one less cm of height is broadly tall”, noted ∀xy.((Lxy ∧ [L]Ty) ⊃ Tx). This notational extension of FOL is conservative and can express higher-order vagueness.

The Logic and Metaphysics Workshop will meet on March 3rd from 2:00-4:00 in-person at the Graduate Center (Room 7395) for a talk by Koji Tanaka (ANU).

Title: What’s so impossible about impossible worlds?

Abstract: Imagine a world where the laws of nature (or physics) are different from those in the actual world. In such a world, Usain Bolt might run faster than the speed of light. Graham Priest argues that such a world would be a physically impossible world. By analogy, a world where the laws of logic are different from those in the actual world is said to be a logically impossible world. But what’s so impossible about such a world? I argue that there is nothing impossible about a world that is merely different from the actual world. I will show that Priest’s position conflates how to evaluate modal statements with how to identify the actual world among all worlds. After rejecting Priest’s position, I will conclude by arguing that what makes a world impossible is not the difference in laws, but the violation of those laws.

The Logic and Metaphysics Workshop will meet on March 10th from 2:00-4:00 in-person at the Graduate Center (Room 7395) for a talk by Rani Rachavelpula (Columbia).

Title: Generating gunk

Abstract: An object is gunky iff all its parts have proper parts. Since Anaxagoras, philosophers have appealed to the existence of gunk to support a range of metaphysical views. These discussions raise questions about the composition of gunk: How is gunk generated? How do we get gunk? Obviously, gunk cannot be composed of atoms. Otherwise, we have admitted objects into our ontology (i.e. atoms) with no proper parts. This has led to the widespread belief that gunk cannot be generated. It must be given. In this talk we prove this claim to be false. Though gunk cannot be generated by atoms, it can nevertheless be generated by some fundamental parts. We apply Weyl’s Equidistribution Theorem to produce a mereological model of a universe which is gunky yet generated by a single element. This dispels other misconceptions about gunk and provides a new perspective on debates about metaphysical fundamentality.

The Logic and Metaphysics Workshop will meet on February 10th from 2:00-4:00 in-person at the Graduate Center (Room 7395) for a talk by Sergei Artemov (CUNY).

Title: Consistency of PA is a serial property, and it is provable in PA

Abstract: We revisit the question of whether the consistency of Peano Arithmetic PA can be established in PA and answer it affirmatively. Since PA-derivations are finite objects, their Gödel codes are standard natural numbers, and PA-consistency is equivalent to the series ConS(PA) of arithmetical formulas “n is not a code of a proof of 0 = 1” for numerals n = 0, 1, 2, … In contrast, in the consistency formula Con(PA) “for all x, x is not a proof of 0 = 1,” the quantifier “for all x” captures standard and nonstandard numbers, Con(PA) is strictly stronger than PA-consistency. Adopting Con(PA) as PA-consistency was a strengthening fallacy: the unprovability of Con(PA) does not yield the unprovability of PA-consistency. A proof of a serial property is a selector proof: prove that each instance has a proof. We selector prove ConS(PA) thus showing that PA-consistency is provable in PA. We discuss other theories and perspectives for Hilbert’s consistency program.