# Truth, Semantic Closure, and Conditionals

Standefer, Shawn (2014) Truth, Semantic Closure, and Conditionals. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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## Abstract

Almost all theories of truth place limits on the expressive power of languages containing truth predicates. Such theories have been criticized as inadequate on the grounds that these limitations are illegitimate. These criticisms set up several requirements on theories of truth. My initial focus is on the criticisms and why their requirements should be accepted.

I argue that an adequate theory of truth should validate intuitive arguments involving truth and respect intuitive evaluations of the semantic statuses of sentences. From this starting point, I analyze the arguments in favor of several common requirements on theories of truth and formulate some minimal requirements on theories of truth. One is a logic neutrality requirement that says that a theory must be compatible with a range of logical resources, such as different negations. Another is the requirement that the theory validate certain laws governing truth, such as the T-sentences.
These two requirements rule out many theories of truth.
The main problem is that many theories lack an adequate conditional, the addition of which is, in fact, precluded by those theories.

I argue that the revision theory of truth can satisfy my criteria when augmented with a pair of conditionals, which are defined using a modification of the framework of circular definitions of the revision theory. I distinguish two roles for conditionals in theories of truth and argue that the conditionals of the proposed theory fill those roles well. The conditionals are interdefinable with a modal operator. I prove a completeness theorem for the calculus $C_0$ of \emph{The Revision Theory of Truth} modified with rules for this operator. I examine the modal logic of this operator and prove a Solovay-type completeness theorem linking the modal logic and a certain class of circular definitions.

I conclude by examining Field's recent theory of truth with its new conditional.
I argue that Field's theory does not meet my requirements and that it fails to vindicate some of Field's own philosophical views. I close by proposing a framework for studying Field's conditional apart from his canonical models.

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## Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
Standefer, Shawnsms105@pitt.eduSMS105
ETD Committee:
Committee ChairGupta, Anilagupta@pitt.eduAGUPTA
Committee MemberBelnap, Nuelbelnap@pitt.eduBELNAP
Committee MemberBrandom, Robertrbrandom@pitt.eduRBRANDOM
Committee MemberShaw, Jamesjrs164@pitt.eduJRS164
Date: 3 February 2014
Date Type: Publication
Defense Date: 20 August 2013
Approval Date: 3 February 2014
Submission Date: 5 September 2013
Access Restriction: 5 year -- Restrict access to University of Pittsburgh for a period of 5 years.
Number of Pages: 246
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Philosophy
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Philosophical logic, truth, paradox, semantics, conditional, revision theory
Date Deposited: 03 Feb 2014 16:29