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Snow is white iff \(\dots\) Predication and perception. (La neige est blanche ssi \(\dots\) PrĂ©dication et perception.) (French) Zbl 0941.03004

Summary: The paper tackles the problem of the links between the formal (logical) syntax and semantics of perceptive judgements and their perceptive (geometrical) content. In the most elementary situations, the perceptive content is reducible to a qualitative filling-in of spatial domains (objects’ extensions) by sensible qualities (colors, textures, etc.). These filling-ins are describable by sections of suitable fibrations, which are particular cases of sheaves. The problem is therefore to understand how a logical syntax can be semantically interpreted in terms of sections of sheaves. This is possible in the framework of topos theory.

MSC:

03A05 Philosophical and critical aspects of logic and foundations
18B25 Topoi
03G30 Categorical logic, topoi
91E10 Cognitive psychology
91E30 Psychophysics and psychophysiology; perception
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