Published online by Cambridge University Press: 15 January 2014
The best known and most widely discussed aspect of Kurt Gödel's philosophy of mathematics is undoubtedly his robust realism or platonism about mathematical objects and mathematical knowledge. This has scandalized many philosophers but probably has done so less in recent years than earlier. Bertrand Russell's report in his autobiography of one or more encounters with Gödel is well known:
Gödel turned out to be an unadulterated Platonist, and apparently believed that an eternal “not” was laid up in heaven, where virtuous logicians might hope to meet it hereafter.
On this Gödel commented:
Concerning my “unadulterated” Platonism, it is no more unadulterated than Russell's own in 1921 when in the Introduction to Mathematical Philosophy … he said, “Logic is concerned with the real world just as truly as zoology, though with its more abstract and general features.” At that time evidently Russell had met the “not” even in this world, but later on under the infuence of Wittgenstein he chose to overlook it.
One of the tasks I shall undertake here is to say something about what Gödel's platonism is and why he held it.
A feature of Gödel's view is the manner in which he connects it with a strong conception of mathematical intuition, strong in the sense that it appears to be a basic epistemological factor in knowledge of highly abstract mathematics, in particular higher set theory. Other defenders of intuition in the foundations of mathematics, such as Brouwer and the traditional intuitionists, have a much more modest conception of what mathematical intuition will accomplish.
Writings of Gödel
The bibliographical references to Gödel's writings are those used by the editors in the Collected Works. The latter are cited as CW with a volume number, but Gödel's published writings are cited in original pagination (given in the margins of CWI and II), his unpublished writings by page number in CW III, if applicable, manuscript page otherwise. The following are the items cited:
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