Re: A quiet query from a visitor

Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> writes:

If you are looking for intuitionists: Aatu Koskensilta (I think so).

While I have a healthy interest in intuitionism I am by no stretch of
imagination an intuitionist, in the sense that I would hold that
classical mathematics is in some sense unjustified and would confine
myself to intuitionistically valid reasoning.

It is traditional for intuitionists (and constructivists) of certain
bent to moan and groan about how classical mathematics is "a fantasy",
"theological", "God's mathematics" and so on. There is of course no
necessity to connecting such expressions of one's dislike of certain
kind of concepts, modes of reasoning, mathematical ideas, to
intuitionism. Intuitionistic reasoning and classical mathematics are
simply two very different ways of conceiving mathematics and the
meaning of mathematical statements. It is entirely possible to find
both of these conceptions of interest, and to see that some principle
or other might be entirely and utterly compelling on the classical
interpretation and wholly unacceptable on the intuitionistic
understanding.

In the spirit of free inquiry, rationality and all things good, I
refuse to place myself in any of the traditional "schools" of
philosophy of mathematics or foundations. I simply accept mathematics
at face value -- content in my dogmatic slumber, so to speak -- and in
my philosophical moments try to make sense of it in simple,
down-to-earth terms, exercising my best judgement and good sense,
without any need for elaborate philosophical systems. Almost
invariably such systems are much more obscure and doubtful than the
straightforward observations about some aspects of our mathematical
practice and reasoning they purport to explain or -- shudder --
justify.

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.

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