## Associated Products

*Theories of Truth (Course or Curricular Material)***Title**: Theories of Truth

**Author**: Saul Kripke

**Abstract**: The topic of this seminar is truth in the sense formulated by Tarski, that is, as a semantic notion (if one doesn’t like the idea of truth being a semantic notion, one could think of it as the notion of ‘expressing a truth’). As is well known, there are problems, generated by various paradoxes, the most famous being the Liar. We will discuss, among other things, Tarski’s original approach and how it might be extended. The relevance of Gödel’s work, and alternative ways of looking at the (first) Gödel incompleteness theorem. And, of course, my own work in this area, which in addition to a treatment of truth, mentions some other ways of looking at the Gödel incompleteness theorem. I also hope to discuss the relevance of various fixed points and alternative valuation schemes. In addition, the view, advocated by Yablo and others, that Truth Tellers ought to be definitely false, not indeterminate, and how this might be developed in my own approach. If time permits, we may discuss later developments, alternatives or extensions of my own work (such as the revision theory of truth, Hartry Field’s approach, our own Graham Priest’s dialetheist treatment, etc.)

**Year**: 2018

**Primary URL**:

https://www.gc.cuny.edu/Page-Elements/Academics-Research-Centers-Initiatives/Doctoral-Programs/Philosophy/Courses/Spring-2018#kripke**Audience**: Graduate

*Truth and the Liar Paradox (Course or Curricular Material)***Title**: Truth and the Liar Paradox

**Author**: Hartry Field, Saul Kripke, and Graham Priest

**Abstract**: Between the 1930s and the 1970s there was a general consensus amongst logicians that the best solution to the Liar and related paradoxes was Tarskian: no language can be allowed to contain its own truth predicate. In the 1970s this consensus disappeared, and it is now more generally held that an appropriate solution should accommodate a language with its own truth predicate. How that should be done is, of course, another matter.
In this course, we will be reading and discussing a number of papers that deal with that issue from a variety of different perspectives. Topics to be discussed include (hopefully): classical vs non-classical logic, definitions of truth vs axiomatic theories, fixed point constructions, dialetheism, conditionals and restricted quantification, revenge paradoxes, sub-structural solutions.

**Year**: 2019

**Primary URL**:

http://as.nyu.edu/philosophy/philosophy-courses/Graduate-Courses-Fall-2019.html**Audience**: Graduate

*Elementary Recursion Theory and its Applications to Formal Systems (Course or Curricular Material)***Title**: Elementary Recursion Theory and its Applications to Formal Systems

**Author**: Saul Kripke

**Abstract**: This class will consist in my own introductory approach to recursion (computability) theory. Some of its basic results, though very easily recognized as true by experts, are not usually given as foundational in textbooks. My approach tries to tie recursion theory to basic ideas in formal logic.
Topics to be covered include: the intuitive concept of computability and its formal counterparts, the status of Church’s Thesis, my RE language, the basic ‘generated sets theorem’ and the ‘upwards generated sets theorem’, the enumeration theorem, the road from the inconsistency of the unrestricted comprehension principle to the Gödel – Tarski theorems, the narrow and broad languages of arithmetic, Cantor’s diagonal principle, different versions of Gödel’s Theorem, an enumeration theorem for partial recursive functions, languages with a recursively enumerable but non-recursive set of formulae, the uniform effective form of Gödel’s theorem, the second incompleteness theorem, the self-reference lemma, the Tarski-Mostowski-Robinson theorem, the enumeration operator fixed-point theorem, the first and second recursion theorems, and the jump operator.
If time permits, we may be able to cover the arithmetical hierarchy and the jump hierarchy, the ω-rule, hyperarithmetical and ∆_1^1 sets, Borel sets, Π_1^1 sets, normal form theorems, the Baire category theorem, incomparable degrees, and related topics.
Requirements: a solid background in first order logic and a degree of mathematical sophistication will be presupposed.

**Year**: 2020

**Primary URL**:

https://www.gc.cuny.edu/Page-Elements/Academics-Research-Centers-Initiatives/Doctoral-Programs/Philosophy/Courses/Spring-2020#kripke**Audience**: Other

*Ungroundedness in Tarskian Languages (Article)***Title**: Ungroundedness in Tarskian Languages

**Author**: Saul A. Kripke

**Abstract**: Several writers have assumed that when in “Outline of a Theory of Truth” I wrote that “the orthodox approach” – that is, Tarski’s account of the truth definition – admits descending chains, I was relying on a simple compactness theorem argument, and that non-standard models must result. However, I was actually relying on a paper on ‘pseudo-well-orderings’ by Harrison (Transactions of the American Mathematical Society, 131, 527–543 1968). The descending hierarchy of languages I define is a standard model. Yablo’s Paradox later emerged as a key to interpreting the result.

**Year**: 2019

**Primary URL**:

https://link.springer.com/article/10.1007%2Fs10992-018-9486-x**Access Model**: Subscription only.

**Format**: Journal

**Periodical Title**: Journal of Philosophical Logic, 43(3).

**Publisher**: Springer

*Video recordings of Saul Kripke's Spring 2018 Seminar "Theories of Truth" (Film/TV/Video Broadcast or Recording)***Title**: Video recordings of Saul Kripke's Spring 2018 Seminar "Theories of Truth"

**Writer**: Saul Kripke

**Director**: Romina Padro

**Abstract**: The topic of this seminar is truth in the sense formulated by Tarski, that is, as a semantic notion (if one doesn’t like the idea of truth being a semantic notion, one could think of it as the notion of ‘expressing a truth’). As is well known, there are problems, generated by various paradoxes, the most famous being the Liar. We will discuss, among other things, Tarski’s original approach and how it might be extended. The relevance of Gödel’s work, and alternative ways of looking at the (first) Gödel incompleteness theorem. And, of course, my own work in this area, which in addition to a treatment of truth, mentions some other ways of looking at the Gödel incompleteness theorem. I also hope to discuss the relevance of various fixed points and alternative valuation schemes. In addition, the view, advocated by Yablo and others, that Truth Tellers ought to be definitely false, not indeterminate, and how this might be developed in my own approach. If time permits, we may discuss later developments, alternatives or extensions of my own work (such as the revision theory of truth, Hartry Field’s approach, our own Graham Priest’s dialetheist treatment, etc.).

**Year**: 2018

**Primary URL**:

https://saulkripkecenter.org**Primary URL Description**: Website of the Saul Kripke Center.

**Access Model**: Available to the general public upon request at the Saul Kripke Center.

**Format**: Video

**Format**: Digital File

*Video recordings of the 2019 Fall seminar, “Truth and the Liar Paradox”. (Film/TV/Video Broadcast or Recording)***Title**: Video recordings of the 2019 Fall seminar, “Truth and the Liar Paradox”.

**Writer**: Hartry Field, Saul Kripke, and Graham Priest

**Director**: Yale Weiss

**Producer**: Romina Padro

**Abstract**: Between the 1930s and the 1970s there was a general consensus amongst logicians that the best solution to the Liar and related paradoxes was Tarskian: no language can be allowed to contain its own truth predicate. In the 1970s this consensus disappeared, and it is now more generally held that an appropriate solution should accommodate a language with its own truth predicate. How that should be done is, of course, another matter.
In this course, we will be reading and discussing a number of papers that deal with that issue from a variety of different perspectives. Topics to be discussed include (hopefully): classical vs non-classical logic, definitions of truth vs axiomatic theories, fixed point constructions, dialetheism, conditionals and restricted quantification, revenge paradoxes, sub-structural solutions.

**Year**: 2019

**Primary URL**: ttps://saulkripkecenter.org

**Primary URL Description**: Saul Kripke Center Website.

**Access Model**: Available upon request to the general public upon at the Saul Kripke Center.

**Format**: Digital File

*Video recordings of the seminar, Elementary Recursion Theory and its Application to Formal Systems (Film/TV/Video Broadcast or Recording)***Title**: Video recordings of the seminar, Elementary Recursion Theory and its Application to Formal Systems

**Writer**: Saul Kripke

**Director**: Romina Padro

**Producer**: Romina Padro

**Abstract**: This class will consist in my own introductory approach to recursion (computability) theory. Some of its basic results, though very easily recognized as true by experts, are not usually given as foundational in textbooks. My approach tries to tie recursion theory to basic ideas in formal logic.
Topics to be covered include: the intuitive concept of computability and its formal counterparts, the status of Church’s Thesis, my RE language, the basic ‘generated sets theorem’ and the ‘upwards generated sets theorem’, the enumeration theorem, the road from the inconsistency of the unrestricted comprehension principle to the Gödel – Tarski theorems, the narrow and broad languages of arithmetic, Cantor’s diagonal principle, different versions of Gödel’s Theorem, an enumeration theorem for partial recursive functions, languages with a recursively enumerable but non-recursive set of formulae, the uniform effective form of Gödel’s theorem, the second incompleteness theorem, the self-reference lemma, the Tarski-Mostowski-Robinson theorem, the enumeration operator fixed-point theorem, the first and second recursion theorems, and the jump operator.
If time permits, we may be able to cover the arithmetical hierarchy and the jump hierarchy, the ω-rule, hyperarithmetical and ∆_1^1 sets, Borel sets, Π_1^1 sets, normal form theorems, the Baire category theorem, incomparable degrees, and related topics.

**Year**: 2020

**Primary URL Description**: Saul Kripke Center website.

**Access Model**: Available upon request to the general public at the Saul Kripke Center.

**Format**: Digital File

*Kripke’s Fixed Point Construction and the V-Curry Paradox. (Conference/Institute/Seminar)***Title**: Kripke’s Fixed Point Construction and the V-Curry Paradox.

**Author**: Brian Cross Porter

**Abstract**: In this paper, I propose a solution to the v-curry paradox, using Kripke’s fixed point construction for truth (1975) and Kripke semantics for modal logic. The basic idea will to be to run Kripke’s transfinite construction for a truth predicate over all models of L, and then use those models as worlds in an S5 modal frame, and then define a validity predicate using and the truth predicate. The resulting construction avoids the v-curry paradox without rejecting structural contraction or transitivity.

**Date Range**: 2018

**Primary URL**:

https://philosophy.commons.gc.cuny.edu/event/saul-kripke-center-young-scholars-series-brian-cross-porter-kripkes-fixed-point-construction-and-the-v-curry-paradox/**Primary URL Description**: The lecture was part of the young Scholars Series, sponsored by the Saul Kripke Center. For a detailed description of the event, see ACCOMPLISHMENTS/What was accomplished under these goals?/Point 3.f).

*WORKSHOP ON META-INFERENCES (Conference/Institute/Seminar)***Title**: WORKSHOP ON META-INFERENCES

**Author**: Sponsored by the Saul Kripke Center and the New York Institute of Philosophy at NYU.

**Abstract**: WORKSHOP ON META-INFERENCES
Some have thought that one can save classical logic for inferences by denying it for meta-inferences (roughly speaking). The presentations discussed advantages and disadvantages of this view.

**Date Range**: Thursday 26 September, 2019.

**Location**: CUNY, Graduate Center.

**Primary URL**:

https://saulkripkecenter.org/index.php/blog/*Digital Transcripts of Saul Kripke's Princeton Seminars on the Theory of Truth (1987-1989) (Database/Archive/Digital Edition)***Title**: Digital Transcripts of Saul Kripke's Princeton Seminars on the Theory of Truth (1987-1989)

**Author**: Saul Kripke

**Abstract**: One of Kripke’s most significant contributions to philosophy can be found in his treatment of the concept of truth in his article “Outline of a Theory of Truth.”
In his “Outline,” Kripke gave a new and revolutionary solution to the Liar paradox and related paradoxes that preserves the intuitive notion of truth to a great extent. But Kripke’s “Outline” is just that: an outline. It omits many of the details of Kripke’s philosophical views, as well as much of the specific mathematical machinery needed for fleshing them out.
Fortunately, Kripke addressed the gaps and covered a great deal of new ground in four seminars given at Princeton University in the Spring semester of 1987, the Spring semester of 1988, the Fall semester of 1988, and the Spring semester of 1989. These seminars comprise a total of forty-two classes completely devoted to the theory of truth.
It should be noted that in these seminars, delivered more than ten years after the publication of the “Outline”, Kripke goes beyond completing the agenda he had set up in the ‘70s. He addresses objections directed at his own theory, introduces modifications, and discusses rival theories that appeared after the publication of the “Outline”. For instance, in response to objections that the truth-teller sentence (‘This very sentence is true’) ought to be regarded as false since there is no reason to think it true, Kripke shows how this could be accommodated in his theory.
The Digital Transcripts of Saul Kripke's Princeton Seminars on the Theory of Truth (1987-1989) include all the original typewritten manuscripts. Unfortunately, because the manuscripts contain a wealth of formal symbolism, it was impossible to use a program for automatically converting the manuscripts to digital form and the process had to be done manually. The completely retyped digital version incorporates handwritten comments in the margins, additional proofs, and has been checked against the audio of the seminars.

**Year**: 2018

**Primary URL**:

https://saulkripkecenter.org**Primary URL Description**: Saul Kripke Center Website

**Access Model**: Available upon request to the general public at the Saul Kripke Center

*Truth as a Fixed Point. Seminars on the Theory of Truth Volume I by Saul A. Kripke (Book)***Title**: Truth as a Fixed Point. Seminars on the Theory of Truth Volume I by Saul A. Kripke

**Author**: Saul A. Kripke

**Editor**: Eduardo Barrio and Romina Padró

**Abstract**: The first volume of the Seminars on the Theory of Truth by Saul Kripke, Truth as a Fixed Point, primarily focuses on Kripke’s criticisms of Tarski and the philosophical and mathematical development of his own theory. It fills in many details of his philosophical views omitted in Kripke’s famous paper, ‘Outline of a Theory of Truth’, as well as much of the specific mathematical machinery needed for fleshing them out. Moreover, in Truth as a Fixed Point, he goes beyond completing the agenda he had set up in the ‘70s, addressing objections and introducing modifications to his own theory.

**Year**: 2019

**Primary URL**:

https://saulkripkecenter.org**Primary URL Description**: Saul Kripke Center website.

**Access Model**: Though the publication will be subscription only, a digital version of the manuscript is available upon request at the Saul Kripke Center.

**Publisher**: Forthcoming in Oxford University Press

**Type**: Edited Volume

**Copy sent to NEH?**: Yes

*Alternative Approaches. Seminars on the Theory of Truth Volume II by Saul A. Kripke (Book)***Title**: Alternative Approaches. Seminars on the Theory of Truth Volume II by Saul A. Kripke

**Author**: Saul A. Kripke

**Editor**: Eduardo Barrio and Romina Padro

**Abstract**: The second volume of Seminars on the Theory of Truth Volume by Saul A. Kripke focuses on Kripke’s defense of his own theory against the rival proposals that appeared in its wake. In particular, he discusses at length the revision theory of truth, independently developed by Herzberger (1982) and Belnap and Gupta (1982), and compares it in detail to his own theory. In addition, the volume includes material from Kripke’s recent seminars regarding his views on other alternative theories, including those of Priest and Field.

**Year**: 2019

**Primary URL**:

https://saulkripkecenter.org**Primary URL Description**: Saul Kripke Center Website.

**Access Model**: Though the publication will be subscription only, a digital version of the manuscript will be available upon request at the Saul Kripke Center.

**Publisher**: Partial manuscript. Oxford University Press has expressed interest in continuing the publication of the series.

**Type**: Edited Volume

**Copy sent to NEH?**: Yes

*Truth Project (Web Resource)***Title**: Truth Project

**Author**: Yale Weiss

**Abstract**: Page devoted to the NEH grant, “An Edition of Seminars on the Theory of Truth by American Philosopher Saul Kripke” in the Saul Kripke Center website, describing the project and updated with news about it. We have also posted pictures, brief videos, and news on the Saul Kripke Center’s Facebook and Twitter accounts. The NEH support is acknowledged.

**Year**: 2019

**Primary URL**:

https://saulkripkecenter.org*Power Points and Handouts (Course or Curricular Material)***Title**: Power Points and Handouts

**Author**: Saul Kripke

**Abstract**: Power Points or handouts were made for the three relevant seminars, "Theories of Truth" (Spring 2018), "Truth and the Liar Paradox" (Fall 2019), and "Elementary Recursion Theory and its Applications to Formal Systems" (Spring 2020).

**Year**: 2019

**Primary URL**:

https://saulkripkecenter.org**Primary URL Description**: Available at the Saul Kripke Center upon request.

**Audience**: Graduate