What is a Truth Value And How Many Are There?

@article{Cook2009WhatIA,
  title={What is a Truth Value And How Many Are There?},
  author={Roy T. Cook},
  journal={Studia Logica},
  year={2009},
  volume={92},
  pages={183-201}
}
  • R. Cook
  • Published 2009
  • Mathematics, Computer Science
  • Studia Logica
Truth values are, properly understood, merely proxies for the various relations that can hold between language and the world. Once truth values are understood in this way, consideration of the Liar paradox and the revenge problem shows that our language is indefinitely extensible, as is the class of truth values that statements of our language can take – in short, there is a proper class of such truth values. As a result, important and unexpected connections emerge between the semantic… Expand

Topics from this paper

Vagueness, Truth and Permissive Consequence
We say that a sentence A is a permissive consequence of a set of premises Γ whenever, if all the premises of Γ hold up to some standard, then A holds to some weaker standard. In this paper, we focusExpand
The No-No Paradox Is a Paradox
The No-No Paradox consists of a pair of statements, each of which ‘says’ the other is false. Roy Sorensen claims that the No-No Paradox provides an example of a true statement that has no truthmaker:Expand
Chapter 21 Vagueness , Truth and Permissive Consequence
We say that a sentence A is a permissive consequence of a set of premises ! whenever, if all the premises of ! hold up to some standard, then A holds to some weaker standard. In this paper, we focusExpand
SUPER LIARS
  • P. Schlenker
  • Computer Science
  • The Review of Symbolic Logic
  • 2010
TLDR
A theory is developed which seeks to take literally the quantificational form of the negative expression something other than true, and develops the theory within a generalization of the Strong Kleene Logic, augmented with negations that each have a nonmonotonic semantics. Expand
A UNIFIED THEORY OF TRUTH AND PARADOX
  • Lorenzo Rossi
  • Computer Science, Mathematics
  • The Review of Symbolic Logic
  • 2019
TLDR
A unified theory oftruth and paradox is developed, that is a theory of truth that also provides a unified account of paradoxical sentences, that yields a way of interpreting all three kinds of paradoxicals sentences, as well as unparadoxical sentences within a single model. Expand
Possible predicates and actual properties
  • R. Cook
  • Mathematics, Computer Science
  • Synthese
  • 2014
TLDR
An enriched deflationist account of properties—the Infinitary Deflationary Conception of Existence—supports the standard semantics for models with countable first-order domains, and allows one to prove the categoricity of the second-order Peano axioms. Expand
EMBRACING THE TECHNICALITIES: EXPRESSIVE COMPLETENESS AND REVENGE
TLDR
A much richer formal language is developed, and semantics for that language is created, and an extremely powerful expressive completeness result is proved for the system in question. Expand
UvA-DARE ( Digital Academic Repository ) Vagueness , truth and permissive consequence
We say that a sentence A is a permissive consequence of a set of premises Γ whenever, if all the premises of Γ hold up to some standard, then A holds to some weaker standard. In this paper, we focusExpand
Extendability and Paradox
TLDR
This essay reviews revenge as it arises in the set-theoretic setting, and develops an analogy between the problems of expressive incompleteness and revenge affecting proposals to resolve the semantic paradoxes, and the always incomplete and extendable nature of domains of sets on the modal structural approach to set theory. Expand
Should Anti-Realists be Anti-Realists About Anti-Realism?
On the Dummettian understanding, anti-realism regarding a particular discourse amounts to (or at the very least, involves) a refusal to accept the determinacy of the subject matter of that discourseExpand
...
1
2
...

References

SHOWING 1-10 OF 13 REFERENCES
The seas of language
1. What is a Theory of Meaning? (I) 2. What is a Theory of Meaning? (II) 3. What do I Know When I Know a Language? 4. What does the Appeal to Use do for the Theory of Meaning? 5. Language and TruthExpand
Doubt truth to be a liar
I. TRUTH 1. Aristotle on the Law of Non-Contradiction 2. Theories of Truth 3. Trivialism II. NEGATION 4. Contradiction 5. Boolean Negation 6. Denial and Rejection III. RATIONALITY 7. Rational BeliefExpand
What Vagueness Consists In
The main question of the paper is that ofwhat vagueness consists in. This question must be distinguished from other questions about vagueness discussed in the literature. It is argued that familiarExpand
Vagueness: A Minimal Theory
Vagueness is given a philosophically neutral definition in terms of an epistemic notion of tolerance. Such a notion is intended to capture the thesis that vague terms draw no known boundary acrossExpand
Logic, Semantics, Metamathematics: Papers from 1923 to 1938
TLDR
This edition of The Concept of Truth in Formalized Languages includes a new preface and a new analytical index for use by philosophers and linguists as well as by historians of mathematics and philosophy. Expand
On Formally Undecidable Propositions of Principia Mathematica and Related Systems
TLDR
This document is a translation of a large part of Gödel’s proof, where the notation used by Gödel has been largely replaced by other notation. Expand
Revenge of the liar : new essays on the paradox
Prolegomenon to future revenge 1. Embracing revenge: on the indefinite extendibility of language 2. The liar paradox, expressibility, and possible languages 3. Solving the paradoxes, escaping revengeExpand
Outline of a Theory of Truth
TLDR
The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academic journals and scholarly literature from around the world, supported by libraries, scholarly societies, publishers, and foundations. Expand
Embracing Revenge: On the Indefinite Extensibility of Language
  • 2007
Clarifying the Logic of Clear Cases
  • 2005
...
1
2
...