[FOM] Psychological basis of Intuitionism

Kreinovich, Vladik vladik at utep.edu
Tue Jun 4 18:08:41 EDT 2013

I think what you are describing is an old somewhat dogmatic constructivism.

A more plausible approach (which is sometimes called computable math) is not to claim that nothing non-constructive exists, but rather to analyze  what is constructible (e.g., computable) and what is not. For that, intuitionistic logic and mathematics are also very helpful; there are known rather subtle differences between constructive and intuitionistic math, but they are so subtle that they rarely appear in questions about constructability to different mathematical constructions.
On Mon, Jun 3, 2013 at 4:35 PM, <sambin at math.unipd.it<mailto:sambin at math.unipd.it>> wrote:
The key point is that nothing exists unless we construct it, in whatever way.

This is a step I have never been able to follow, namely that existence of mathematical objects depends on a mind that constructs them. I find it awfully subjective and would in fact brand it as a form of solipsism. If mathematics is the art of hypothetical reasoning, surely then we must develop mathematics which is open to all possibilities, including the one in which mathematics has an independent and objective nature, and moreover allows for existence without construction. (This of course is not to be confused with our ability to perceive such objectivity or our inability to comprehend such illusive forms of existence. In any case, metaphysical conclusions based on the limited nature of minds seem misguided.)

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