The logic of social choice (Rohit Parikh)

The Logic and Metaphysics Workshop will meet on December 11th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 4419) for a talk by Rohit Parikh (CUNY).

Title: The logic of social choice

Abstract: Logic entered social choice theory through Kenneth Arrow who was a student of the logician Alfred Tarski at City College of New York. Arrow’s impossibility result, which was axiomatic in nature, showed that there is no rational procedure to define the popular choice when there are three or more candidates. Arrow’s result led to a rich field. However, subsequent work has concentrated on what happens when voters face a slate of three or more candidates. There is not enough work on a theory of candidate slates themselves. Thus an election with just Donald Trump and Joe Biden is seen as unproblematic since there are only two candidates. The actual quality of the candidates does not matter. We will propose a method which depends on the actual quality of a candidate. Then it becomes a dominant game theoretic strategy for each party to nominate as good a candidate as possible. The goodness of a candidate is defined in terms of a dot product of two vectors: the candidate’s position and the position of a typical voter.

Use and mention in formal languages (James Walsh)

The Logic and Metaphysics Workshop will meet on December 4th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 4419) for a talk by James Walsh (NYU).

Title: Use and mention in formal languages

Abstract: Quine’s distinction between use and mention is one of the cornerstones of analytic philosophy. The distinction is typically motivated with examples from natural language, but Quine also applied the distinction to the formal languages studied in mathematical logic. I will argue that such expressions are not used in Quine’s sense, so the distinction cannot appropriately be applied to them. Accordingly, the standard practice of placing quotation marks around expressions of formal languages is incorrect. This technical point serves as a springboard for discussing the role that formal languages play in mathematical logic.

Truthmakers for modals: Meaning, truth, modals and quantifiers (Mircea Dumitru)

The Logic and Metaphysics Workshop will meet on November 27th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 4419) for a talk by Mircea Dumitru (Bucharest).

Title: Truthmakers for modals: Meaning, truth, modals and quantifiers

Abstract: First, I shall give a sketch of a general theory of truthmaking. Then, I shall raise some issues for the theory when it deals with modal language and point to some specific answers. In the remaining part I shall get into ramifications of this topic and discuss issues pertaining to meaning, truth and quantification in modal contexts and discourse.

Note: The subject of this talk was changed on Nov. 19, 2023. The previous title was “Truth with and without satisfaction”.

Vagueness and Frege (Marian Călborean)

The Logic and Metaphysics Workshop will meet on November 20th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 4419) for a talk by Marian Călborean (Bucharest).

Title: Vagueness and Frege

Abstract: A constant of Frege’s writing is his rejection of indeterminate predicates in natural language. I follow Frege’s remarks on vagueness from the early “Begriffsschrift” to his mature works, drawing parallels with contemporary theories of vagueness. I critically examine Frege’s arguments for the inconsistency of natural language and argue that the inability to accommodate vagueness and precision in his mature ontology and semantics is mainly due to heuristic rules which he took as essential, not to a deep problem in his fundamental apparatus.

Against zero-grounding (Alex Skiles)

The Logic and Metaphysics Workshop will meet on November 13th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 4419) for a talk by Alex Skiles (Rutgers).

Title: Against zero-grounding

Abstract: A number of philosophers believe that there is an intelligible distinction between ungrounded truths, which are not grounded in any truths at all, and zero-grounded truths, which are grounded, yet there are no truths that they are grounded in. Rather being a mere academic curiosity, these philosophers have also argued that the notion of zero-grounding can be put to serious metaphysical work. In this paper, we present two arguments against the intelligibility of zero-grounding, and then reject several attempts to make zero-grounding intelligible that have been suggested by its proponents.

Note: This is joint work with Tien-Chun Lo and Gonzalo Rodriguez-Pereyra.

On logics of acceptance and rejection (Alex Citkin)

The Logic and Metaphysics Workshop will meet on November 6th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 4419) for a talk by Alex Citkin (Metropolitan Telecommunications).

Title: On logics of acceptance and rejection

Abstract: In his book Formalization of Logic, Carnap suggested the following process of refutation: for any set of formulas Γ and any formula α, if Γ ⊢ α and α is rejected, reject Γ. Thus, in contrast to the Łukasiewicz’s approach to refutation, the predicate of rejection is defined on sets of formulas rather than just formulas. In addition to a predicate of rejection, we introduce a predicate of acceptance which is also defined on sets of formulas, and this leads us to constructing two-layered logical systems, the ground layer of which is a conventional deductive system (providing us with means for derivation), and the top layer having predicates of acceptance and rejection. In the case when the set of accepted formulas coincides with the set of theorems of the underlying logic and the set of rejected formulas coincides with the sets of non-theorems, we obtain a conventional deductive system. The predicate of acceptance can be non-adjunctive, and this allows us to use such systems as an alternative approach to defining Jaśkowski style discursive logics.

An approach to property-talk for property nominalists (Brad Armour-Garb)

The Logic and Metaphysics Workshop will meet on October 30th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 4419) for a talk by Brad Armour-Garb (SUNY Albany).

Title: An approach to property-talk for property nominalists

Abstract: Properties, understood as immanent universals that are repeatable entities which distinct objects can each have at the same time and in different places, are weird, so weird, in fact, that if we could do without them, we probably should do so. An alternative to an approach that sanctions properties might suggest a deflationary view of property-talk according to which the raison d’être of our use of ‘property’ is that it serves a quasi-logical function that is akin to what alethic deflationists claim about truth-talk. Deflationists about property-talk normally subscribe to a form of property nominalism, which rejects the sort of property realism that takes properties to be immanent universals. In this talk, after highlighting some of the weirdness of, or worries for, property realism and explaining why certain forms of property nominalism should not be abided, I highlight the expressive role of property-talk and go on to explain how property-talk performs its roles by introducing what I call “adjectival predicate-variable deflationism” (“APVD”). As I will show, by incorporating APVD into a version of what I have called a “semantic-pretense involving fictionalism” (“SPIF”), we capture the full range of property-talk instances without compromising property nominalism. Time permitting, I will also highlight a virtue of my view, which another form of property nominalism cannot accommodate. If property nominalism is correct, then we should endorse the SPIF account of property-talk that I will develop in this talk.

Note: This is joint work with James A. Woodbridge.

Diachronic reasoning with conditionals (Melissa Fusco)

The Logic and Metaphysics Workshop will meet on October 23rd from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 4419) for a talk by Melissa Fusco (Columbia).

Title: Diachronic reasoning with conditionals

Abstract: I will discuss a hybrid decision theory, coinciding sometimes with (traditional) Evidential Decision Theory, but usually with (traditional) Causal Decision Theory, which is inspired by recent work on unified and fully compositional approaches to the probabilities of conditionals. The hybrid theory features a few other loci of interest: the partitionality of acts A ∈ {A} fails, and close attention is paid to how one might (dis)confirm chance hypotheses under the umbrella of the Principal Principle. On this theory, the probabilities of conditionals play a role in underwriting a theory of imaging that follows Skyrms’s Thesis (Skyrms, 1981, 1984). Moreover, the credences it is epistemically rational to assign to these conditionals guides updating on one’s own acts. This implies some departures from Conditionalization, which I defend on epistemological grounds.

Maximal deontic logic (Yale Weiss)

The Logic and Metaphysics Workshop will meet on October 16th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 4419) for a talk by Yale Weiss (CUNY).

Title: Maximal deontic logic

Abstract: The worlds accessible from a given world in Kripke models for deontic logic are often informally glossed as ideal or perfect worlds (at least, relative to the base world). Taking that language seriously, a straightforward but nonstandard semantic implementation using models containing maximally good worlds yields a deontic logic, MD, considerably stronger than that which most logicians would advocate for. In this talk, I examine this logic, its philosophical significance, and its technical properties, as well as those of the logics in its vicinity. The principal technical result is a proof that MD is pretabular (it has no finite characteristic matrix but all of its proper normal extensions do). Along the way, I also characterize all normal extensions of the quirky deontic logic D4H, prove that they are all decidable, and show that D4H has exactly two pretabular normal extensions.

Whence admissibility constraints? From inferentialism to tolerance (Brett Topey)

The Logic and Metaphysics Workshop will meet on October 2nd from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 4419) for a talk by Brett Topey (Salzburg).

Title: Whence admissibility constraints? From inferentialism to tolerance

Abstract: Prior’s invented connective ‘tonk’ is sometimes taken to reveal a problem for certain inferentialist approaches to metasemantics: according to such approaches, the truth-theoretic features of our expressions are fully determined by the rules of inference we’re disposed to follow, but admitting the ‘tonk’ rules into a language would lead to intuitively absurd results. Inferentialists tend to insist that they can avoid these results: there are constraints on what sets of inference rules can be admitted into a language, the story goes, and the rules governing disruptive expressions like ‘tonk’ are defective and so illegitimate. I argue, though, that from an inferentialist perspective, there’s no genuine sense in which rules like the ‘tonk’ rules are defective; those who endorse the relevant sort of inferentialism turn out to be committed to Carnap’s principle of tolerance. I then sketch an argument to the effect that this, despite appearances, isn’t a problem for inferentialism.

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