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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.