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What is the category system

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Vitaliy Dolgorukov
Vitaliy Dolgorukov

The document discusses the concept of categories from Aristotle through Kant to modern formal semantics. It outlines Kant's view of categories as pure concepts of understanding and describes how formal semantics uses type theory to define semantic categories. It also discusses how natural language expressions are assigned semantic types and how type-shifting operators allow expressions to take on different types depending on context.

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What is the System of Categories ? From Kant to Formal Semantics Vitaliy Dolgorukov ( HSE, Faculty of Philosophy) Bridge to Logic II, 26.01.2011
[object Object],[object Object],'What is the System of Categories? From Kant to Formal Semantics', Bridge to Logic II,26.01.2011, Vitaliy Dolgorukov, HSE, Faculty of Philosophy
Categories as « pure concept of understanding » ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],'What is the System of Categories? From Kant to Formal Semantics', Bridge to Logic II,26.01.2011, Vitaliy Dolgorukov, HSE, Faculty of Philosophy
Category as semantic type ,[object Object],[object Object],'What is the System of Categories? From Kant to Formal Semantics', Bridge to Logic II,26.01.2011, Vitaliy Dolgorukov, HSE, Faculty of Philosophy
Ajdukewich ,[object Object],[object Object],'What is the System of Categories? From Kant to Formal Semantics', Bridge to Logic II,26.01.2011, Vitaliy Dolgorukov, HSE, Faculty of Philosophy
Formal semantics: from uniform semantic type to type-shifting ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],'What is the System of Categories? From Kant to Formal Semantics', Bridge to Logic II,26.01.2011, Vitaliy Dolgorukov, HSE, Faculty of Philosophy
Type-shifting ,[object Object],[object Object],[object Object],'What is the System of Categories? From Kant to Formal Semantics', Bridge to Logic II,26.01.2011, Vitaliy Dolgorukov, HSE, Faculty of Philosophy
[object Object],'What is the System of Categories? From Kant to Formal Semantics', Bridge to Logic II,26.01.2011, Vitaliy Dolgorukov, HSE, Faculty of Philosophy lift : j-> λ P[P(j)] ( total; injective) lower : maps a function onto its generator (partial; surjective) lower (lift (j)) = j ident : j -> λ x[x = j] (total; injective) iota : P -> ι x[P(x)] (partial; surjective) iota(ident(j)) = j nom : P-> ∩ P (Chierchia) (almost total; injective) pred : x-> ∪ x (Chierchia) (partial; surjective) pred (nom(P)) = P
'What is the System of Categories? From Kant to Formal Semantics', Bridge to Logic II,26.01.2011, Vitaliy Dolgorukov, HSE, Faculty of Philosophy
'What is the System of Categories? From Kant to Formal Semantics', Bridge to Logic II,26.01.2011, Vitaliy Dolgorukov, HSE, Faculty of Philosophy
BE: λPλx[{x}∈ P] ,[object Object],[object Object],[object Object],[object Object],[object Object],'What is the System of Categories? From Kant to Formal Semantics', Bridge to Logic II,26.01.2011, Vitaliy Dolgorukov, HSE, Faculty of Philosophy
[object Object],[object Object],'What is the System of Categories? From Kant to Formal Semantics', Bridge to Logic II,26.01.2011, Vitaliy Dolgorukov, HSE, Faculty of Philosophy
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],'What is the System of Categories? From Kant to Formal Semantics', Bridge to Logic II,26.01.2011, Vitaliy Dolgorukov, HSE, Faculty of Philosophy

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What is the category system

  • 1. What is the System of Categories ? From Kant to Formal Semantics Vitaliy Dolgorukov ( HSE, Faculty of Philosophy) Bridge to Logic II, 26.01.2011
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  • 5.
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  • 7.
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  • 9. 'What is the System of Categories? From Kant to Formal Semantics', Bridge to Logic II,26.01.2011, Vitaliy Dolgorukov, HSE, Faculty of Philosophy
  • 10. 'What is the System of Categories? From Kant to Formal Semantics', Bridge to Logic II,26.01.2011, Vitaliy Dolgorukov, HSE, Faculty of Philosophy
  • 11.
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  • 13.