Kurt Gödel
A logician who gave a formal version of the ontological proof.
Life
A logician and mathematician born in Brno and died in Princeton, Kurt Gödel proved his incompleteness theorems in 1931: in any consistent formal system rich enough for arithmetic, some true statements remain unprovable. In 1940 he also showed that the continuum hypothesis cannot be refuted from the usual axioms. A Platonist, he held mathematical objects to be real and, around 1970, wrote out a formal version of the ontological proof of God's existence.
Main works
Proves that no consistent formal system rich enough for arithmetic can prove all the truths it expresses.
Defends mathematical realism: sets exist and can be grasped by a kind of intuition.
A formal modal-logic version of the argument of Anselm and Leibniz, written around 1970 and published in the Collected Works.
In his own words
« Despite their remoteness from sense experience, we do have something like a perception also of the objects of set theory, as is seen from the fact that the axioms force themselves upon us as being true. »
« A probable decision about its truth is possible also in another way, namely, inductively by studying its "success." Success here means fruitfulness in consequences »
Positions
click a row to see the evidenceHe wrote out a formal ontological proof of a God-like being and privately held that God exists.
Gödel, "Ontological Proof" (notes c. 1970, Collected Works III)
Mathematical objects are real, and we know them by a kind of intellectual perception, not by the senses.
Gödel, "What is Cantor's Continuum Problem?" (1947, rev. 1964)
Some mathematical truths are reachable with certainty, yet his incompleteness theorems show no fixed formal system can prove them all.
Gödel, "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I" (1931)
He argued the human mind may exceed any machine, which points beyond a purely mechanical view of the mind.
Gödel, Gibbs Lecture "Some basic theorems on the foundations of mathematics and their philosophical implications" (1951)