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
Abstracts:
“Giving as Spending and Spending as Giving: Buddhism and the Politics of Spending during the Chosŏn Dynasty”
Juhn Ahn, University of Michigan
The impact of the Koryŏ-Chosŏn transition on the Buddhist establishment in Korea is generally understood in current scholarship to have been a negative one. It is all too often assumed that Buddhist monasteries, who enjoyed great economic prosperity under Koryŏ’s culture of giving, were forced to undergo a radical reduction in size and number and their wealth confiscated to replenish the empty royal fisc. There is also a tendency to assume that this systematic restructuring of the Buddhist establishment, often dubbed its “decline,” was orchestrated and executed by a small group of reform-minded Neo-Confucian scholar-officials who saw Buddhism as an economic parasite and cause of unnecessary spending. It is true that the Buddhist establishment never again enjoyed the kind of wealth that it once did during the Koryŏ, but this paper argues that we should not take this as a sign of decline or the necessary outcome of state suppression. Instead, this paper will turn its attention to the politics of spending that continued to shape and reshape the Chosŏn court and show that the politics of spending provided the Buddhist establishment with an opportunity—an opportunity that it did in fact use—to redefine the conditions of its existence.
“Court Lady Ch’ŏn Ilch’ŏng (1848 – 1934) in the Making of Modern Korean Buddhism”
Hwansoo Kim, Yale University
In this talk, I will introduce the work of a forgotten Korean Buddhist laywoman who served as one of the highest-ranking ladies in the court of the late Chosŏn dynasty. I will demonstrate that Court Lady Ch’ŏn (1848 – 1934) was as integral to modernizing Korean Buddhism during the pre-colonial and colonial era as the Korean Buddhist monastics with whom she worked. By examining Ch’ŏn’s seminal role in the incipient stage of modern Korean Buddhism, the history of female Buddhist leadership can be extended.
Ch’ŏn primarily worked with the Korean monk and leader Yi Hoegwang (1862-1933), drawing on a wide network of relationships both inside and outside the court to help him establish the first modern institution of Korean Buddhism, build the first modern temple in central Seoul, and open a Buddhist clinic. However, because Yi was later condemned by historiography as the worst of Buddhists who had collaborated with Korea’s colonizer, Ch’ŏn’s leadership and legacy were likewise stigmatized and sidelined. This talk seeks to restore Ch’ŏn’s centrality as a Buddhist modernizer, thereby giving balance to a largely male-centered and ethno-centric history and lengthening the lineage of lay female leadership in the transformation of Korean Buddhism in the early twentieth century.
“Buddhism and State Violence in Modern Korea”
Jin Y. Park, American University
Historically, Korean Buddhism has been known as “State Protection Buddhism” (護國佛敎). The seemingly positive character of this description also points to the limitations of Korean Buddhism’s role in the broader context of society. A state should exist to protect its members, but history has witnessed that the state can and did exercise its power against its members. Which members did the Korean government support, and which were sacrificed in the process? What role did Korean Buddhism play in the unfolding of that history?
This presentation deals with Buddhism’s response to state violence in modern Korea. Through an analysis of a specific instance of state violence and Korean Buddhism’s response, the presentation tries to gauge Korean Buddhism’s capacity to engage with the socio-political milieu of human existence.
Co-sponsored by
The Academy of Korean Studies, Seoul Korea; Weatherhead East Asian Institute; the Department of East Asian Languages and Cultures; The Institute for Religion, Culture, and Public Life; The Department of Religion; The Center for Buddhism and East Asian Religion
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
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
Well-known ties between arithmetical proof and intuitionistic logic make it natural to think of provability in terms of intuitionistic logic and hence absolute provability in terms of one of its extensions. For this reason, we propose Intuitionistic Tense Logic, or tINT, to study absolute provability. We delineate tINT models and a Hilbert-style system, and then prove soundness and completeness. We then use the tINT framework to discuss and compare ideas of absolute provability of authors in the literature.
The Saul Kripke Center is pleased to announce that Vincent A. Peluce (PhD student, Philosophy, CUNY Graduate Center) will deliver the fourth Saul Kripke Center Young Scholars Series talk on Thursday, December 5, 2019, from 2:00 to 4:00 in room 9206 of the CUNY Graduate Center.
This will be the third (and, time permitting, some material from the fourth) of a series of lectures that I aim to write up formally as a book. We will begin with a brief review of the most familiar theory of Chinese aesthetics: works of art are the products of sensitive human beings who cannot suppress their sincere responses to emotional stimuli. If art is understood as a sincere statement of this kind by a great genius, it stands to reason that, by correctly interpreting the work, one can communicate with that genius’s mind (xin 心) even after his or her death–and, likewise, that an artist today can communicate with audiences yet unborn. Art is thus timeless and offers the possibility of incorporeal immortality. If there is extra time, I will also survey two interrelated phenomena that I call meta-criticism and meta-writing (since there are no technical terms for them in Chinese). Meta-criticism, i.e. criticism of criticism, is a major feature of Chinese theories about art. Meta-criticism must be related to meta-writing, or the practice of writing about writing while exemplifying the very styles and techniques that one recommends: for example, artfully rhyming a couplet about rhyming.
With responses from: SANDRA SHAPSHAY (Hunter College, CUNY)
The Fall dates for the Comparative Philosophy seminar:
September 20 – Justin Tiwald (San Francisco State University)
October 11 – Richard Kim (Loyola University, Chicago
November 8 – Sungmoon Kim (City University of Hong Kong)
December 6 – Paul R. Goldin (University of Pennsylvania)
More details (such as titles, abstracts, and respondents) to follow. Looking forward to seeing you soon.
Hagop Sarkissian
Associate Professor & Chair, Department of Philosophy, The City University of New York, Baruch College
Associate Professor, Department of Philosophy, CUNY Graduate Center
Co-Director, Columbia Society for Comparative Philosophy
https://www.cbs.columbia.edu/cscp/