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.
Logic and Metaphysics Workshop:
September 2 GC Closed NO MEETING
September 9 Yael Sharvit, UCLA
September 16 Ole Hjortland and Ben Martin, Bergen
September 23 Alessandro Rossi, StAndrews
September 30 GC Closed NO MEETING
October 7 Dongwoo Kim, GC
October 14 GC Closed NO MEETING
October 21 Rohit Parikh, GC
October 28 Barbara Montero, GC
November 4 Sergei Aretmov, GC
November 11 Martin Pleitz, Muenster
November 18
November 25
December 2 Jessica Wilson, Toronto
December 9 Mark Colyvan, Sydney
December 16 MAYBE A MEETING; MAYBE NOT
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.
Logic & Metaphysics Workshop
September 2 GC Closed NO MEETING
September 9 Yael Sharvit, UCLA
September 16 Ole Hjortland and Ben Martin, Bergen
September 23 Alessandro Rossi, StAndrews
September 30 GC Closed NO MEETING
October 7 Dongwoo Kim, GC
October 14 GC Closed NO MEETING
October 21 Rohit Parikh, GC
October 28 Barbara Montero, GC
November 4 Sergei Aretmov, GC
November 11 Martin Pleitz, Muenster
November 18
November 25
December 2 Jessica Wilson, Toronto
December 9 Mark Colyvan, Sydney
December 16 MAYBE A MEETING; MAYBE NOT
Recently, Rebecca Kukla – among others – has argued that consent language is too narrow to adequately capture the ethical obligations and failures arising in the context of sex. Instead, she offers more nuanced scripts for the kinds of communication that occur throughout sex, not just at the beginning. I agree with Kukla that consent language is too narrow; however, I argue that she overlooks the fact that intimate personal communication requires an emotional attunement to context precisely because it cannot be fully scripted. To demonstrate this I turn to Cavell’s category of the passionate utterance which gestures at this dynamic dimension of performatives, but doesn’t deliver a detailed account. In this paper I will expand on Cavell’s idea of the passionate exchange in order to shed light on the active interpretive role of the audience, and how it contributes to performative success.
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.
Logic and Metaphysics Workshop
September 2 GC Closed NO MEETING
September 9 Yael Sharvit, UCLA
September 16 Ole Hjortland and Ben Martin, Bergen
September 23 Alessandro Rossi, StAndrews
September 30 GC Closed NO MEETING
October 7 Dongwoo Kim, GC
October 14 GC Closed NO MEETING
October 21 Rohit Parikh, GC
October 28 Barbara Montero, GC
November 4 Sergei Aretmov, GC
November 11 Martin Pleitz, Muenster
November 18
November 25
December 2 Jessica Wilson, Toronto
December 9 Mark Colyvan, Sydney
December 16 MAYBE A MEETING; MAYBE NOT
There is a broad consensus that Aristotle introduced the concept of matter in order to develop a consistent account of substantial change. However, it is disputed which role matter fulfills in substantial change. According to the traditional interpretation, matter persists while taking on or losing a substantial form. According to a rival interpretation, matter does not persist in substantial change; instead, it is an entity from which a new substance can emerge and which ceases to exist in this process. In my view, both interpretations are problematic in the light of Aristotle’s broader ontological project and are at odds with the way Aristotle describes the substantial generation of living beings. On the basis of Aristotle’s biological theory, I will suggest that Aristotelian matter is a continuant in substantial generation, but does not satisfy the common criteria for persistence that apply to individual substances.
Anna Schriefl
Anna Schriefl is Wissenschaftliche Mitarbeiterin (assistant professor) at the University of Bonn, and currently a visiting scholar at the New School. She has published a book about Plato’s criticism of money and wealth, and most recently an introduction into Stoicism (both in German).
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.
Logic and Metaphysics Workshop
September 2 GC Closed NO MEETING
September 9 Yael Sharvit, UCLA
September 16 Ole Hjortland and Ben Martin, Bergen
September 23 Alessandro Rossi, StAndrews
September 30 GC Closed NO MEETING
October 7 Dongwoo Kim, GC
October 14 GC Closed NO MEETING
October 21 Rohit Parikh, GC
October 28 Barbara Montero, GC
November 4 Sergei Aretmov, GC
November 11 Martin Pleitz, Muenster
November 18 Matias Bulnes, CUNY
November 25 Vincent Peluce, CUNY
December 2 Jessica Wilson, Toronto
December 9 Mark Colyvan, Sydney
December 16 MAYBE A MEETING; MAYBE NOT
September 2 GC Closed NO MEETING
September 9 Yael Sharvit, UCLA
September 16 Ole Hjortland and Ben Martin, Bergen
September 23 Alessandro Rossi, StAndrews
September 30 GC Closed NO MEETING
October 7 Dongwoo Kim, GC
October 14 GC Closed NO MEETING
October 21 Rohit Parikh, GC
October 28 Barbara Montero, GC
November 4 Sergei Aretmov, GC
November 11 Martin Pleitz, Muenster
November 18 Matias Bulnes, CUNY
November 25 Vincent Peluce, CUNY
December 2 Jessica Wilson, Toronto
December 9 Mark Colyvan, Sydney
December 16 MAYBE A MEETING; MAYBE NOT
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.
Logic and Metaphysics Workshop
September 2 GC Closed NO MEETING
September 9 Yael Sharvit, UCLA
September 16 Ole Hjortland and Ben Martin, Bergen
September 23 Alessandro Rossi, StAndrews
September 30 GC Closed NO MEETING
October 7 Dongwoo Kim, GC
October 14 GC Closed NO MEETING
October 21 Rohit Parikh, GC
October 28 Barbara Montero, GC
November 4 Sergei Aretmov, GC
November 11 Martin Pleitz, Muenster
November 18 Matias Bulnes, CUNY
November 25 Vincent Peluce, CUNY
December 2 Jessica Wilson, Toronto
December 9 Mark Colyvan, Sydney
December 16 MAYBE A MEETING; MAYBE NOT
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.
Logic and Metaphysics Workshop
September 2 GC Closed NO MEETING
September 9 Yael Sharvit, UCLA
September 16 Ole Hjortland and Ben Martin, Bergen
September 23 Alessandro Rossi, StAndrews
September 30 GC Closed NO MEETING
October 7 Dongwoo Kim, GC
October 14 GC Closed NO MEETING
October 21 Rohit Parikh, GC
October 28 Barbara Montero, GC
November 4 Sergei Aretmov, GC
November 11 Martin Pleitz, Muenster
November 18 Matias Bulnes, CUNY
November 25 Vincent Peluce, CUNY
December 2 Jessica Wilson, Toronto
December 9 Mark Colyvan, Sydney
December 16 MAYBE A MEETING; MAYBE NOT