Existential Import and Relations of Categorical and Modal Categorical Statements

Raclavský, Jiří

doi:10.12775/llp.2017.026

Cited by 2 publications

(4 citation statements)

References 29 publications

(38 reference statements)

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“…The exact behaviour of constructions was described in [20,21] in terms of Henkin-style modeltheoretic semantics, see Sec. 6 (Appendix), in which the notions of type and model are used (see below).…”

Section: Language and Semantics Of Tt *mentioning

confidence: 99%

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Puzzles of Existential Generalisation from Type-theoretic Perspective

Raclavský

2022

Electron. Proc. Theor. Comput. Sci.

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The present paper addresses several puzzles related to the Rule of Existential Generalization, (EG). In solution to these puzzles from the viewpoint of simple type theory, I distinguish (EG) from a modified Rule of Existential Quantifier Introduction which is derivable from (EG). Both these rules are often confused and both are considered as primitive but I show that (EG) itself is derivable from the proper Rule of Existential Quantifier Introduction. Moreover, the latter rule must be primitive in logical systems that treat both total and partial functions, for the universal and the existential quantifiers are not interdefinable in them. An appropriate natural deduction for such a system is deployed. The present logical system is simpler than the system recently proposed and applied by the present author. It utilises an adequate definition of substitution which is capable of handling not only a higher-order quantification, but also (hyper)intensional contexts.

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Section: Language and Semantics Of Tt *mentioning

confidence: 99%

“…An object belonging to type τ of order n is called an nth-order τ-object. The full definition of the notions of type and order can be found in [21] or [20]; I only state here its core.…”

Section: Language and Semantics Of Tt *mentioning

confidence: 99%

Puzzles of Existential Generalisation from Type-theoretic Perspective

Raclavský

2022

Electron. Proc. Theor. Comput. Sci.

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“…where ϕ [t] indicates a formula that contains term t. The rule (∃-I) may be primitive in various ND, but must be primitive in ND for partial logics (such as the ND proposed below) alongside the introduction rule for ∀, since ∀ and ∃ are not interdefinable in partial logics. To illustrate, the formula ¬∃xBK(x), where BK is the predicate "be (identical to) the KF", is currently true, while ∀x¬BK(x) is false since not every individual is decidable as (not) being BK (to work properly, the law for the exchange of quantifiers must be adjusted using the strong truth predicate [see, e.g., Raclavský, , 2018).…”

Section: Wiles Knows That Fermat Believedmentioning

confidence: 99%

“…The exact behaviour of constructions can be described in terms of Henkin-style denotational semantics for L TT * [see Raclavský, 2018Raclavský, , 2020.…”

Section: The Logic For Fine-grained Hyperintensionalitymentioning

confidence: 99%

The Rule of Existential Generalisation and Explicit Substitution

Raclavský¹

2021

LLP

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The present paper offers the rule of existential generalization (EG) that is uniformly applicable within extensional, intensional and hyperintensional contexts. In contradistinction to Quine and his followers, quantification into various modal contexts and some belief attitudes is possible without obstacles. The hyperintensional logic deployed in this paper incorporates explicit substitution and so the rule (EG) is fully specified inside the logic. The logic is equipped with a natural deduction system within which (EG) is derived from its rules for the existential quantifier, substitution and functional application. This shows that (EG) is not primitive, as often assumed even in advanced writings on natural deduction. Arguments involving existential generalisation are shown to be valid if the sequents containing their premises and conclusions are derivable using the rule (EG). The invalidity of arguments seemingly employing (EG) is explained with recourse to the definition of substitution.

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Existential Import and Relations of Categorical and Modal Categorical Statements

Cited by 2 publications

References 29 publications

Puzzles of Existential Generalisation from Type-theoretic Perspective

Puzzles of Existential Generalisation from Type-theoretic Perspective

The Rule of Existential Generalisation and Explicit Substitution

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