Carl Friedrich Gauss said:

When a philosopher says something that is true then it is trivial. When he says something that is not trivial then it is false.

On one occasion I read that supposedly Gauss has added in parentheses that Aristotle was an exception. Do you know more about it?

If any, I'd be sure that Gauss rather said that "especially Aristotle", i.e. that "Aristotle was exceptionally bad".


QUESTION   what Gauss really said?


The quote is not accurate but Gauss actually wrote something similar to Schumacher in the letter of 1 November 1844 cited here, where he complains about concepts and definitions given in math books by philosopher that are not mathematicians, namely

[...] look around at modern philosophers [...] don't their definitions make your hair stand on end? Read in the history of ancient philosophy what the men of the days, Plato and others (I except Aristotle), gave as explanation. And even in Kant matters are often not much better; his distinction between analytic and synthetic propositions seems to me either a triviality or false.

So Gauss considers Aristotle to be the exception between ancient (and modern) philosophers in the sense that his definitions are free of confusion.

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    $\begingroup$ It is indeed surprising that Gauss seems to be putting Atistotle above Plato for clarity of definitions. Modern historians would disagree: they consider Plato's contribution to mathematics very important, unlike that of Aristotle. $\endgroup$ – Alexandre Eremenko Dec 31 '19 at 14:03
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    $\begingroup$ Gauss is citing here Hegel (author of the Science of Logic), Schelling (who criticized Hegel's view about logic), Wolff and Kant (both authors of a Logic), Nees von Esenbeck (botanist, but also author of System der spekulativen Philosophie), and Plato (no logical treatise have survived, but he dealt with truth and falseness in Theaetetus and with the nature of definitions in many dialogues, like Euthyphro), so my personal opinion is that here Gauss is appreciating Aristotle as the author of the Organon, which is actually a pretty clear logic textbook. $\endgroup$ – user6530 Dec 31 '19 at 15:48
  • $\begingroup$ Thank you U6530, +1, and let me wait for eventual later answers. I see that Aristotle was appreciated by Gauss for just one item, for its logical narration. I would also like to know about any Plato's original contribution to mathematics, was there any? Any at all? $\endgroup$ – Wlod AA Dec 31 '19 at 19:37
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    $\begingroup$ @WlodAA be aware of the fact that Gauss' appreciation of Organon is only a personal deduction. On the other hand it's well known that Gauss' view on infinity is close to that of Aristotle: both refuse actual infinity in mathematcs, whose demonstrative needs are well served (in their view) by potential infinity. About Plato, this can be the subject for another question, but remember that Plato was not a mathematician. $\endgroup$ – user6530 Dec 31 '19 at 20:21
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    $\begingroup$ I'm not so sure about the rejection of actual infinity in Greek tradition. In Aristotle's Physics, Book III, we found: some as the Pythagoreans and Plato make the infinite a principle in the sense of a self-subsistent substance, and not as a mere attribute of some other thing. Only the Pythagoreans place the infinite among the objects of sense[...], Plato [...] that the infinite is present not only in the objects of sense but in the Forms also. [...] Anaxagora and Democritus [...] that the infinite is continuous by contact $\endgroup$ – user6530 Dec 31 '19 at 21:33

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