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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.

The Provability of Consistency (Sergei Artemov)

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

Title: The Provability of Consistency

Abstract: We revisit the foundational question “Can consistency of a theory T be established by means of T?” The usual answer “No, by Gödel’s Second Incompleteness Theorem” is based on two assumptions:

1. Gödel’s internalized consistency formula is the only way to represent consistency.
2. Any contentual reasoning within T internalizes as a formal derivation in T.

We show that already for Peano arithmetic PA both of these assumptions are false: (1) does not cover such legitimate mode of presentation as schemes (think of the Induction scheme), (2) fails for schemes. Based on these observations, we offer a proof of PA-consistency by means of PA and discuss its potential impact.

Benacerraf’s Non-Problem (Barbara Gail Montero)

The Logic and Metaphysics Workshop will meet on October 28th from 4:15-6:15 in room 7314 of the CUNY Graduate Center for a talk by Barbara Gail Montero (CUNY).

Title: Benacerraf’s Non-Problem

Abstract: Research in philosophy of mathematics over roughly the past half century can be understood, to a large degree, as a series of responses to what is commonly known as the Benacerraf problem: Given the abstract nature of mathematical entities, how can we come to have mathematical knowledge? How are we, in Benacerraf’s words,  “to bridge the chasm. . . between the entities that form the subject matter of mathematics and the human knower?” In this talk, I aim to share with you some of the reasons why I think that Benacerraf’s problem—as he presents it and as Field restates it—just may be nothing to worry about. ​

 

The Buddha versus Popper: When to Live? (Rohit Parikh)

The Logic and Metaphysics Workshop will meet on October 21st from 4:15-6:15 in room 7314 of the CUNY Graduate Center for a talk by Rohit Parikh (CUNY).

Title: The Buddha versus Popper: When to Live?

Abstract: We discuss two approaches to life: presentism and futurism. The first one, which we are identifying with the Buddha, is to live in the present and not to allow the future to hinder us from living in the ever present now. The second one, which we will identify with Karl Popper, is to think before we act, and act now for a better future. We will discuss various aspects of presentism and futurism, such as Ruth Millikan’s Popperian animal, the psychologist Howard Rachlin’s social and temporal discounting, and even the popular but controversial idea, YOLO (you live only once). The purpose of this talk is to contrast one with the other. The central question of ethics is: How should one live? Our variation on that question is: When should one live? We conjecture that the notion of flow, developed by Csikszentmihalyi, may be a better optimal choice between these two positions.

This work, which is joint with Jongjin Kim, is to appear in the Journal of Buddhist Ethics.

 

Explanation and Modality: On Why The Swampman Is Still Worrisome to Teleosemanticists (Dongwoo Kim)

The Logic and Metaphysics Workshop will meet on October 7th from 4:15-6:15 in room 7314 of the CUNY Graduate Center for a talk by Dongwoo Kim (CUNY).

Title: Explanation and Modality: On Why The Swampman Is Still Worrisome to Teleosemanticists

Abstract: Many have thought that Davidson’s Swampman scenario offers a serious problem to teleosemantics. For it appears to be possible from the scenario that there are completely ahistorical creatures with beliefs, and this apparent possibility contradicts the theory. In a series of papers (2001, 2006, 2016), Papineau argues that the Swampman scenario is not even the start of an objection to teleosemantics as a scientific reduction of belief. It is against this claim that I want to argue here. I shall argue that the explanatory power of teleosemantics rests on two conceptual pillars, namely success semantics and the etiological conception of biological function, and that the Swampman scenario questions the adequacy of the foundational conceptual commitments. Along the way, some general connection between explanation and modality will be developed that sheds a new light on Kripke’s analysis of necessary a posteriori propositions. The conclusion will be that teleosemanticists should tackle the Swampman objection head on.

 

Existence, Verbal Disputes and Equivocation (Alessandro Rossi)

The Logic and Metaphysics Workshop will meet on September 23rd from 4:15-6:15 in room 7314 of the CUNY Graduate Center for a talk by Alessandro Rossi (St Andrews).

Title: Existence, Verbal Disputes and Equivocation

Abstract: Noneism is the theory according to which some things do not exist. Following an established convention, I will call allism the negation of noneism (every thing exists). Lewis [1990] and, more recently, Woodward [2013] argued that the allism/noneism dispute turns on an equivocation about the meaning of ‘exists’ and would thereby be merely verbal. These arguments have been attacked by Priest [2005, 2011, 2013], who took the dispute to be genuine. In this paper, I will present two new arguments for the genuineness of the allism/noneism dispute. The first appeals to a recent version of logical pluralism defended by Kouri Kissel [Forth]: the two parties could be seen as engaging in a metalinguistic negotiation, that is, a normative disagreement about which meaning of ‘exists’ is best suited for a certain domain of discourse. Secondly, Williamson [1987] indicated a proof-theoretic criterion the two sides should meet in order for their dispute to count as genuine: they must share enough rules of inference governing ‘exist’ to characterise it up to logical equivalence. This challenge, I argue, can be met.