[FOM] Psychological basis of Intuitionism

Antonino Drago drago at unina.it
Wed Jun 5 18:28:23 EDT 2013

> My question is not about the philosophical conviction but rather
> psychological mechanisms. For example, studies on expertise indicate
> experts have superior pattern matching skills relating to the areas
> they are experts in. How do mathematicians develop general pattern
> matching abilities?
> D. E. (Steve) Stevenson, PhD

Do you know Michael A. Arbib Arbib's wotks? For. ex.
Piagetian perspective on mathematical construction Synthese 84 (1):43 - 58 
(1990) Abstract  In this paper, we offer a Piagetian perspective on the 
construction of the logico-mathematical schemas which embody our knowledge 
of logic and mathematics. Logico-mathematical entities are tied to the 
subject's activities, yet are so constructed by reflective abstraction that 
they result from sensorimotor experience only via the construction of 
intermediate schemas of increasing abstraction. The axiom set does not 
exhaust the cognitive structure (schema network) which the mathematician 
thus acquires. We thus view truth not as something to be defined within the 
closed world of a formal system but rather in terms of the schema network 
within which the formal system is embedded. We differ from Piaget in that we 
see mathematical knowledge as based on social processes of mutual 
verification which provide an external drive to any necessary dynamic of 
reflective abstraction within the individual. From this perspective, we 
argue that axiom schemas tied to a preferred interpretation may provide a 
necessary intermediate stage of reflective abstraction en route to 
acquisition of the ability to use formal systems in abstracto.

      Antonino Drago

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