In this philosophy, mathematics is just a formal game played by formal rules. When we say that something exists, for instance, we are just saying that from some set of axioms, we can prove a statement about existence. It is irrelevant to us whether the axioms are true or the thing "really" exists. All that matters is that we successfully followed the rules of the formal game.
The "simultaneity of the nonsimultaneous" (to borrow from Bloch) in 1930: the triumphant and festive present (Hilbert) confronting the past (Du-Bois-Reymond) with fate already sealed (Gödel).
The past:
>Du Bois-Reymond's investigations of electrical properties of the nervous system had led him to long-standing fundamental questions, especially the nature of matter and force and the relationship between mental phenomena and their physical aspects. He recognized scientists’ general belief that when we do not know a solution—ignoramus in Latin—nevertheless, under certain circumstances, we could know. However, he countered, concerning riddles of the material world such as these two, we must decide in favor of a harder truth: ignorabimus—we shall never know. Du Bois-Reymond reported later that his 1872 speech had excited considerable controversy and his ignorabimus slogan had become a sort of shibboleth in natural philosophy.
The present declaration by Hilbert:
>[...] This conviction of the solvability of every mathematical problem is a powerful incentive to the worker. We hear within us the perpetual call: There is the problem. Seek its solution. You can find it by pure reason, for in mathematics there is no ignorabimus.
And then the barely noticeable turn of events:
>Besides the meeting of the Society of German Natural Scientists and Physicians, the other three conferences at Königsberg in early September of 1930 were:
Second Conference on Epistemology of the Exact Sciences,
Annual Meeting of the German Mathematical Society, and
Annual Meeting of the German Physical Society.
The first of these was the most momentous of the four, a major step in bringing the adherents of the Vienna Circle of philosophers to both inner agreement and public notice. Their program challenged and eventually helped supplant much of the type of philosophy discussed and developed in the German universities in the late 19th and early 20th centuries. On September 6, two days before Hilbert’s speech, the young Austrian logician Kurt Gödel (1906-1978) presented his completeness theorem, which filled a major gap in Hilbert’s finitist foundation of mathematics. In a round-table discussion on the next day, the day before Hilbert spoke, Gödel modestly announced his first incompleteness theorem.
[0]https://old.maa.org/press/periodicals/convergence/david-hilb...
perihelions•8mo ago
https://en.wikipedia.org/wiki/University_of_Göttingen#%22Gre...
And it's prophetic, when he speaks (in translation)
>"The achievements of industry, for example, would never have seen the light of day had the practical-minded existed alone and had not these advances been pursued by disinterested fools".
Because who was it Nazis purged from Hilbert's Göttingen? Szilárd; Einstein; Teller—the future of industry, born of abstract theories and of sciences pursued for their own sake.
esafak•8mo ago