It seems that in Recoltes et Semailles, he does go into quite a bit of philosophizing. the only thing of relevance I've found is that he notes how Riemann "in passing" said how he thought perhaps the "True" reality is often just too complex for our minds and so we come up with fictions like the continuum to explain these sensory experiences and organize it into a coherent view not opposed to our comprehension.

This seems to be in support of a Herbartian view of reality where spatial forms or rather "measure" in general is a way of symbolically representing the true ideas behind them. Almost Platonic in a sense.

If anybody, knows more(since my French is not adequate to read all his works), it would be interesting to know. He was a great mathematician and seems to have held opinions on lots of things which just aren't accessible to those who aren't French fluent.

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    The "philosophizing" in Recoltes et Semailles is mostly that only in the colloquial sense of the word, it is the same in his correspondence with Serre. He wrote La Clef des Songes, reviewed by Landsburg, on the questions of God, dreams and creativity. McLarty has a nice piece on his "philosophy" of mathematical research, The Rising Sea. But there is nothing on the sort of ontology you are looking for. – Conifold Dec 24 '19 at 1:05

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