David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
Learn more about PhilPapers
Ratio 12 (3):279–295 (1999)
If logical truth is necessitated by sheer syntax, mathematics is categorially unlike logic even if all mathematics derives from definitions and logical principles. This contrast gets obscured by the plausibility of the Synonym Substitution Principle implicit in conceptions of analyticity: synonym substitution cannot alter sentence sense. The Principle obviously fails with intercepting: nonuniform term substitution in logical sentences. 'Televisions are televisions' and 'TVs are televisions' neither sound alike nor are used interchangeably. Interception synonymy gets assumed because logical sentences and their synomic interceptions have identical factual content, which seems to exhaust semantic content. However, intercepting alters syntax by eliminating term recurrence, the sole strictly syntactic means of ensuring necessary term coextension, and thereby syntactically securing necessary truth. Interceptional necessity is lexical, a notational artifact. The denial of interception nonsynonymy and the disregard of term recurrence in logic link with many misconceptions about propositions, logical form, conventions, and metalanguages. Mathematics is distinct from logic: its truth is not syntactic; it is transmitted by synonym substitution; term recurrence has no essential role. The '=' of mathematics is an objectual relation between numbers; the '=' of logic marks a syntactic relation of coreferring terms.
|Keywords||mathematical truth logical truth logical form synonymy identity equality|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Roger Wertheimer (2000). The Synonymy Antinomy. In A. Kanamori (ed.), The Proceedings of the Twentieth World Congress of Philosophy. Philosophy Document Center. pp. 67-88.
Roger Wertheimer (1994). Synonymy Without Analyticity. International Philosophical Preprint Exchange.
Shannon Dea (2006). "Merely a Veil Over the Living Thought": Mathematics and Logic in Peirce's Forgotten Spinoza Review. Transactions of the Charles S. Peirce Society 42 (4):501-517.
Christopher Menzel (1998). Logical Form. In Edward Craig (ed.), Routledge Encyclopedia of Philosophy. Routledge.
Kevin C. Klement (2004). Propositional Logic. Internet Encyclopedia of Philosophy.
Added to index2009-01-28
Total downloads183 ( #22,305 of 1,924,984 )
Recent downloads (6 months)34 ( #11,494 of 1,924,984 )
How can I increase my downloads?