back to ideas for this text


Single Idea 3192

[from 'On Formally Undecidable Propositions' by Kurt Gödel, in 17. Mind and Body / C. Functionalism / 2. Machine Functionalism ]

Full Idea

Gödel in his completeness theorem for first-order logic showed that a certain set of syntactically specifiable rules was adequate to capture all first-order valid arguments. No semantics (e.g. reference, truth, validity) was necessary.

Gist of Idea

Basic logic can be done by syntax, with no semantics

Source

report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Georges Rey - Contemporary Philosophy of Mind 8.2

Book Reference

Rey,Georges: 'Contemporary Philosophy of Mind' [Blackwell 1997], p.212


A Reaction

This implies that a logic machine is possible, but we shouldn't raise our hopes for proper rationality. Validity can be shown for purely algebraic arguments, but rationality requires truth as well as validity, and that needs propositions and semantics.

Related Idea

Idea 19059 In standard views you could replace 'true' and 'false' with mere 0 and 1 [Dummett]