[FOM] Psychological basis of Intuitionism
Kreinovich, Vladik
vladik at utep.edu
Thu Jun 6 16:21:01 EDT 2013
Sorry for not being clear, I DID NOT mean to say that YOUR papers are dogmatic, what I meant was that old constructivist papers were often dogmatic, in the sense that they treated all non-constructive mathematical results as meaningless. Most modern papers on constructivism no longer do that, especially since it turns out that many non-constructive results from classical mathematics can be reformulated in constructive terms, by using appropriate double negations of existence and or, and by using pseudo-functions instead of functions.
And yes, you are right, there are different versions of constructivism, it could be computability, it could be something more general.
________________________________________
From: sambin at math.unipd.it [sambin at math.unipd.it]
Sent: Thursday, June 06, 2013 2:05 PM
@ Vladik
It is not nice to charge a colleague of being dogmatic and old
fashioned before reading the papers he suggests. Understanding your
remarks as a question, my answer is that it all depends on what one
means by construction. My version of constructivism is not scholastic.
In my opinion, construction should not be limited to what is reducible
to Turing computability (which indeed would be dogmatic).
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