As the biographer of the physiologist Emil du Bois-Reymond I'm delighted by the discussion of his brother Paul du Bois-Reymond's contribution to the invention of the diagonal argument.

Does anyone know if Emil's 1872 address on "The Limits of Science" encouraged his brother Paul to think along those lines?

  • $\begingroup$ Why so ? Emil du Bois-Reymond's lecture The Limits of our Knowledge of Nature is about the physical world: "With regard to the enigma of the physical world the investigator of Nature has long been wont to utter his "Ignoramus" with manly resignation. As he looks back on the victorious career over which he has passed, he is upheld by the quiet consciousness that wherein he now is ignorant, he may at least under certain conditions be enlightened, and that he yet will know. ... 1/2 $\endgroup$ – Mauro ALLEGRANZA May 28 '16 at 17:28
  • $\begingroup$ ... But as regards the enigma what matter and force are, and how they are to be conceived, he must resign himself once for all to the far more difficult confession: Ignorabimus!" 2/2 $\endgroup$ – Mauro ALLEGRANZA May 28 '16 at 17:28

The main reference for this is

McCarty, D. C. Problems and riddles: Hilbert and the du Bois-Reymonds. Synthese 147 (2005), no. 1, 63–79.

Both Paul du Bois-Reymond and Hilbert were profoundly influenced by Emil's lecture. Paul pretty much accepted the implications for mathematics, whereas Hilbert rejected them.

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  • $\begingroup$ Thank you. I am familiar with that essay. McCarty makes an argument that relies on chronology (Emil first, Paul later) and resemblance (skepticism in science, skepticism in mathematics). I suppose asking for a smoking gun is a bit too much. $\endgroup$ – Gabriel Finkelstein May 29 '16 at 18:54
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    $\begingroup$ If you are looking for a direct connection between Emil's Limits and Paul's mathematics, the obvious choice is Paul's approach to infinitesimals. He seems to have applied Emil's approach to express his own (Paul's) pessimism about ever reconciling his own embracing of infinitesimals with some of his contemporaries' opposition. The dichotomy Paul proposed here is similar to the one that would eventually evolve into the classical/intuitionistic divide. $\endgroup$ – Mikhail Katz May 30 '16 at 7:35
  • $\begingroup$ Very interesting. Emil said that we would never understand the ultimate nature of matter. Did Paul say something similar about infinitesimals? $\endgroup$ – Gabriel Finkelstein May 31 '16 at 14:58
  • $\begingroup$ I think it was more in the spirit of "we will never be able to agree about infinitesimals". $\endgroup$ – Mikhail Katz May 31 '16 at 15:42

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