The Birth of Analytic Philosophy

Modern analytic philosophy begins with the German mathematician and logician Gottlob Frege, whose project of logicism sought to show that arithmetic could be derived entirely from logic, without appeal to intuition or experience. In his Begriffsschrift (1879) Frege invented a new formal notation for quantification and inference that laid the groundwork for modern predicate logic, and in Die Grundlagen der Arithmetik (1884) he argued that numbers are logical objects, definable in terms of classes and the notion of one-to-one correspondence. His later Grundgesetze der Arithmetik attempted to carry out this reduction in full formal detail, but the project was famously derailed when Bertrand Russell discovered, in 1901, that Frege's system permitted the construction of a paradoxical class — the class of all classes that do not contain themselves — now known as Russell's paradox. Independently of logicism, Frege made a second lasting contribution in his 1892 essay 'Über Sinn und Bedeutung' ('On Sense and Reference'), distinguishing between the sense (Sinn) of an expression, its mode of presentation or cognitive content, and its reference (Bedeutung), the object it picks out. The classic illustration is that 'the morning star' and 'the evening star' both refer to the planet Venus, sharing a Bedeutung, yet differ in Sinn, which is why the identity statement linking them is informative rather than a trivial repetition.