Kurt Gödel, Philosopher-Scientist #2

After John Dawson’s very introductory piece there follows another introductory paper, “Kurt Gödel’s Philosophical Remarks (Max Phil)” by the editors of the volume, Gabriella Crocco and Eva-Maria Engelen. All the essays in the book, by the way, are in English — though the prose has very obviously not always been well checked by a native speaker for naturalness.

This paper starts with a preamble (1) on ‘Gödel’s philosophy and his scientific oeuvre’, followed by a central section (2) giving what the authors call a technical description of the Max Phil. Their concluding section (3) is on ‘The content of the Philosophical Remarks (=Max Phil). First insights’.

(1) We already know, e.g. from Hao Wang and from Gödel’s unsent response to the Grandjean questionnaire, something about Gödel’s negative philosophical views — we know what he was against. In particular, Gödel found himself fundamentally out of sympathy with the prevailing philosophical ideas he encountered at the Vienna Circle. What is a lot less clear is Gödel’s positive philosophy (to use our authors’ phrase). “I was a conceptual and mathematical realist”, he wrote in his draft reply to Grandjean: but what exactly does that mean?

We find other thoughts that appealed to Gödel in that page from the Nachlass, where he epitomizes  “My philosophical viewpoint” in fourteen points, given in translation by Wang (A Logical Journey, p. 316) and repeated here in an improved transcription and revised translation. But this is, let’s be honest, pretty strange. For example, we read (according to our authors):

1. The world is rational.
4. There are other worlds and rational beings, who are of the other and higher kind.
5. The world in which we now live is not the only one in which we live or have lived.
11. The higher beings are connected to the other beings by analogy, not by composition.

Taken cold, without further elaboration, it is very difficult to know what to make of such remarks — and what else is currently published of Gödel’s work doesn’t help a great deal, as  Crocco and Engelen themselves say. So the great interest of working on the Max Phil notebooks, they maintain, is in seeing if we can indeed reconstruct a systematic positive philosophical viewpoint from them (even though the remarks are often brief, allusive, and written only for Gödel’s himself). We shall see.

One quick remark about this section. Our authors mention as one of Gödel’s technical achievements that are, in Wang’s words, “disproofs of philosophical hypotheses of the age”,  the “proof of the independence of the axiom of choice from the axioms of set theory”(!) which “shows that strong realism in set theory, represented by the axiom of choice, is no less coherent than constructivism.” Oh dear. Gödel proved a consistency result not the independence result. But taking that as an unfortunate slip, the more serious point remains that a constructivist who is unhappy about the coherence of impredicative ideas, and hence about the coherence of classical impredicative ZF is hardly going to be mollified by a classical proof of the relative consistency of ZFC, is she?

(2) At the end of the Collected Works there is a catalogue of the Nachlass, which dates but otherwise says very little about the Max Phil notebooks. The second section of the present paper tells us a little more,

Fifteen out of sixteen notebooks survive, numbered 0, I-XII, XIV and XV (notebook XIII dating from 1945-1946 having been lost by Gödel himself in 1946). The character of the notebooks changes somewhat as time goes on, and it is suggested that we can consider them as falling into four groups.

Group A contains the first notebook of 80 pages, dating from 1934 to 1941,  together with notebooks I and II, 157 pages dating from 1937 to 1942 (plus another 40 pages added to notebook II devoted to ‘time management’). The first notebook contains notes on lectures Gödel has attended, and the first three three contain work plans, thoughts about working methods, “maxims for the conduct of life as a successful thinker and researcher”, as well philosophical remarks scattered across a range of topics.

Group B contains notebooks III to VIII, whose pages are consecutively numbered from p.1 to p. 680. These date from the beginning of 1941 to late 1942 and are more purely philosophical. Group C contains notebooks IX to XII, numbered separately but amounting to another 463 pages, dating from late 1942 to mid 1945 and continue in much the same pattern though there are now remarks too on relativity and quantum mechanics, and on the idea of force in physics and biology.

Group D contains the two late notebooks, XIV dating from July 1946 to May 1955 (128 pages), and  a short XV from May 1955 onwards (just 33 pages).

So all in all, that’s a significant number of pages: though I got no sense at all of how much material (when transcribed from the shorthand) is on a  typical page. Our authors add some bar charts giving the relative occurrence of headings like “Bemerkung”, “Bemerkung Philosophie”, “Bemerkung Grundlagen” and so on — but not terribly helpfully as the categories Gödel uses are pretty sweeping, and it seems that in many of the notebooks two or three headings cover the large majority of entries. The “technical description” of the Max Phil therefore doesn’t give us much of a steer about content. So what do our authors go on to say about this in their third section?

To be continued