Maximal Non-trivial Sets of Instances of Your Least Favorite Logical Principle

2020 ◽  
Vol 117 (1) ◽  
pp. 30-54 ◽  
Author(s):  
Lucas Rosenblatt ◽  
Keyword(s):  
Classical Theory ◽  
Theories Of Truth ◽  
Logical Principle ◽  
Valid Principle

The paper generalizes Van McGee's well-known result that there are many maximal consistent sets of instances of Tarski's schema to a number of non-classical theories of truth. It is shown that if a non-classical theory rejects some classically valid principle in order to avoid the truth-theoretic paradoxes, then there will be many maximal non-trivial sets of instances of that principle that the non-classical theorist could in principle endorse. On the basis of this it is argued that the idea of classical recapture, which plays such an important role for non-classical logicians, can only be pushed so far.

NOTES ONω-INCONSISTENT THEORIES OF TRUTH IN SECOND-ORDER LANGUAGES

2013 ◽  
Vol 6 (4) ◽  
pp. 733-741 ◽  
Author(s):  
EDUARDO BARRIO ◽  
LAVINIA PICOLLO
Keyword(s):  
Classical Theory ◽  
Second Order ◽  
Revision Theory ◽  
Theories Of Truth ◽  
First Order ◽  
Order Case ◽  
Desirable Feature ◽  
Conceptual Problems ◽  
Inconsistent Theories

It is widely accepted that a theory of truth for arithmetic should be consistent, butω-consistency is less frequently required. This paper argues thatω-consistency is a highly desirable feature for such theories. The point has already been made for first-order languages, though the evidence is not entirely conclusive. We show that in the second-order case the consequence of adoptingω-inconsistent truth theories for arithmetic is unsatisfiability. In order to bring out this point, well knownω-inconsistent theories of truth are considered: the revision theory of nearly stable truthT#and the classical theory of symmetric truthFS. Briefly, we present some conceptual problems withω-inconsistent theories, and demonstrate some technical results that support our criticisms of such theories.

The Power of Naive Truth

2020 ◽  
pp. 1-34
Author(s):  
HARTRY FIELD
Keyword(s):  
Classical Theory ◽  
Theories Of Truth ◽  
Natural Way

Abstract Nonclassical theories of truth that take truth to be transparent have some obvious advantages over any classical theory of truth (which must take it as nontransparent on pain of inconsistency). But several authors have recently argued that there’s also a big disadvantage of nonclassical theories as compared to their “external” classical counterparts: proof-theoretic strength. While conceding the relevance of this, the paper argues that there is a natural way to beef up extant internal theories so as to remove their proof-theoretic disadvantage. It is suggested that the resulting internal theories are preferable to their external counterparts.

Let all social partners in the social support process count: New perspectives on classical theory

2013 ◽  
Author(s):  
Liu-Qin Yang ◽  
Robert R. Wright ◽  
Liu-Qin Yang ◽  
Lisa M. Kath ◽  
Michael T. Ford ◽  
...  
Keyword(s):  
Social Support ◽  
Classical Theory ◽  
The Social ◽  
Social Partners

The Calder´on-Zygmund Theory I: Ellipticity

2017 ◽  
Author(s):  
Brian Street
Keyword(s):  
Classical Theory ◽  
Singular Integral ◽  
Singular Integrals ◽  
Differential Operators ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Single Parameter ◽  
Partial Differential ◽  
Translation Invariant ◽  
Partial Differential Operators

This chapter discusses a case for single-parameter singular integral operators, where ρ‎ is the usual distance on ℝn. There, we obtain the most classical theory of singular integrals, which is useful for studying elliptic partial differential operators. The chapter defines singular integral operators in three equivalent ways. This trichotomy can be seen three times, in increasing generality: Theorems 1.1.23, 1.1.26, and 1.2.10. This trichotomy is developed even when the operators are not translation invariant (many authors discuss such ideas only for translation invariant, or nearly translation invariant operators). It also presents these ideas in a slightly different way than is usual, which helps to motivate later results and definitions.

Reprise

2018 ◽  
Author(s):  
Paul M. Pietroski
Keyword(s):  
Modern Logic ◽  
Theories Of Truth ◽  
Theories Of Meaning

This chapter summarizes the main themes. Humans naturally acquire generative procedures that connect meanings with pronunciations. These meanings are neither concepts nor extensions. Meanings are composable instructions for how to access and assemble concepts of a special sort. In particular, phrasal meanings are instructions for how to build monadic (i.e., predicative) concepts that are massively conjunctive. Theories of meaning should not be confused with theories of truth. Lexicalization is a process of introducing concepts that can be combined via simple operations whose inputs must be monadic or dyadic. In theorizing about meanings, we can and should eschew much of the powerful typology and combinatorial operations that the founders of modern logic introduced for very different purposes.

Sign in / Sign up

Export Citation Format

Share Document