Editing Syntax (logic) (section)

==== Syntactic consequence within a formal system ====

A formula A is a '''syntactic consequence'''<ref name="google">{{cite book|title=Frege: Philosophy of Language|author=Dummett, M.|date=1981|publisher=Harvard University Press|isbn=9780674319318|url=https://books.google.com/books?id=EYP7uCZIRQYC|page=82|access-date=2014-10-15}}</ref><ref name="google2">{{cite book|title=Aristotle and Logical Theory|author=Lear, J.|date=1986|publisher=Cambridge University Press|isbn=9780521311786|url=https://books.google.com/books?id=lXI7AAAAIAAJ|page=1|access-date=2014-10-15}}</ref><ref name="google3">{{cite book|title=The Cambridge Companion to Carnap|author1=Creath, R.|author2=Friedman, M.|date=2007|publisher=Cambridge University Press|isbn=9780521840156|url=https://books.google.com/books?id=87BcFLgJmxMC|page=189|access-date=2014-10-15}}</ref><ref name="uniba">{{cite web|url=http://www.swif.uniba.it/lei/foldop/foldoc.cgi?syntactic+consequence|title=syntactic consequence from FOLDOC|publisher=swif.uniba.it|access-date=2014-10-15|url-status=dead|archive-url=https://web.archive.org/web/20130403201417/http://www.swif.uniba.it/lei/foldop/foldoc.cgi?syntactic+consequence|archive-date=2013-04-03}}</ref> within some formal system <math> \mathcal{FS}</math> of a set Г of formulas if there is a [[Formal proof|derivation]] in [[formal system]] <math> \mathcal{FS}</math> of A from the set Г.

:<math>\Gamma \vdash_{\mathrm FS} A</math>

Syntactic consequence does not depend on any [[interpretation (logic)|interpretation]] of the formal system.<ref>Hunter, Geoffrey, Metalogic: An Introduction to the Metatheory of Standard First-Order Logic, University of California Press, 1971, p. 75.</ref>