Editing Logical positivism (section)

===Logicism===

By [[reductionism|reducing]] mathematics to logic, [[Bertrand Russell]] sought to convert the mathematical formulas of [[physics]] to [[symbolic logic]]. [[Gottlob Frege]] began this program of [[logicism]], continuing it with Russell, but eventually lost interest. Russell then continued it with [[Alfred North Whitehead]] in their ''[[Principia Mathematica]]'', inspiring some of the more mathematical logical positivists, such as [[Hans Hahn (mathematician)|Hans Hahn]] and [[Rudolf Carnap]].<ref name=Hintikka>{{cite book |last=Hintikka |first=Jaako |chapter=Logicism |title=Philosophy of Mathematics |editor1=Andrew D Irvine |publisher=North Holland |location=Burlington MA |year=2009 |url=https://books.google.com/books?id=mbn35b2ghgkC&pg=PA283 |pages=283–84}}</ref>

Carnap's early anti-metaphysical works employed Russell's [[type theory|theory of types]].<ref>{{cite journal |last=Schlick |first=Moritz |year=1932 |title=The elimination of metaphysics through logical analysis of language |journal=Erkenntnis |volume=2 |issue=1 |pages=1-31 |doi=10.1007/BF01886406}} Reprinted in {{cite book |title=Logical Positivism |last=Ayer |first=Alfred Jules |pages=60-81 |year=1959 |location=New York |publisher=Free Press}}</ref> Like Russell, Carnap envisioned a universal language that could reconstruct mathematics and thereby encode physics. Yet [[Kurt Gödel]]'s [[incompleteness theorem]] showed this to be impossible, except in trivial cases, and [[Alfred Tarski]]'s [[undefinability theorem]] finally undermined all hopes of reducing mathematics to logic. Thus, a universal language failed to stem from Carnap's 1934 work ''Logische Syntax der Sprache'' (''Logical Syntax of Language''). Still, some logical positivists, including [[Carl Hempel]], continued support of logicism.<ref name=Hintikka/>