The completeness of the first-order functional calculus

Henkin, Leon

doi:10.2307/2267044

Cited by 449 publications

(219 citation statements)

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“…The model-existence theorems of Henkin (1949Henkin ( , 1950 allow us to argue for results just as disturbing as radical inscrutability, even granted constraints of eligibility. It is an epistemic possibility that the actual world is Pythagorean: that an interpretation that depicts our words as picking out integers matches the intended interpretation on grounds of fi tting with "total theory" and beats it on grounds of eligibility.…”

Section: Resultsmentioning

confidence: 99%

“…The result at the heart of the argument for radical inscrutability, due to Henkin (1949Henkin ( , 1950, is the following: if T is a syntactically consistent theory, then T has a model-that is, an interpretation under which every sentence is true.…”

Section: An Alternative Argument For Radical Inscrutabilitymentioning

confidence: 99%

“…To begin with, then, we can appeal to the Henkin constructions that are possible for simple type theories (Henkin 1950). The techniques involved are generalizations of those described here, and the effect is the same for our purposes.…”

Section: The Existence Of Pythagorean Worldsmentioning

confidence: 99%

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Eligibility and Inscrutability

Williams¹

2007

The Philosophical Review

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The philosophy of intentionality asks questions such as: in virtue of what does a sentence, picture, or mental state represent that the world is a certain way? The subquestion I focus upon here concerns the semantic properties of language: in virtue of what does a name such as 'London' refer to something or a predicate such as 'is large' apply to some object?This essay examines one kind of answer to this "metasemantic" 1 question: interpretationism, instances of which have been proposed by Donald Davidson, David Lewis, and others. I characterize the "twostep" form common to such approaches and briefl y say how two versions described by David Lewis fi t this pattern. Then I describe a fundamental challenge to this approach: a "permutation argument" that contends, by interpretationist lights, there can be no fact of the matter about lexical

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Section: Resultsmentioning

confidence: 99%

Section: An Alternative Argument For Radical Inscrutabilitymentioning

confidence: 99%

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Eligibility and Inscrutability

Williams¹

2007

The Philosophical Review

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“…We claim that completeness also holds: a proof (a nontrivial variant of the Henkin construction, see [Henkin, 1949]) will appear elsewhere.…”

Section: Axmentioning

confidence: 88%

Modal Change Logic (MCL): Specifying the reasoning of knowledge-based systems

Fensel

Groenboom

Lavalette

1998

Data & Knowledge Engineering

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Abstract.We investigate the formal specification of the reasoning process of knowledge-based systems in this paper. We analyze the corresponding parts of the KADS specification languages KARL and (ML) 2 and deduce some general requirements. The essence of these languages is that they integrate a declarative specification of inferences with control information. The languages differ in the way they achieve this integration and each of them has shortcomings. We propose a unifying semantical framework that integrates the core of the different solutions and overcomes their problems. We define a semantics and axiomatization with the Modal Change Logic (MCL). The main contribution of the paper is not to introduce yet another specification language. Instead we aim at four goals: (1) defining a framework for describing the dynamic reasoning behavior of knowledge-based systems which integrates existing approaches; (2) defining a semantics for the specification of the dynamic reasoning behavior of a knowledge-based system within the states as algebras setting that overcomes several shortcomings and ad-hoc solutions of existing approaches; and (3) providing an axiomatization that enables the development of mechanized proof support. (4) Through conceptual and semantical clarity, we investigate the relationships to similar work in software engineering and database engineering opening possibilities for further cross-fertilization of these fields.

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“…We think that this is a good notion of logical consequence, for it immediately ensures an intuitively desirable property, to wit, that relations of logical consequence be preserved upon extension of a language. Furthermore, strong completeness may be established for it merely by definitional modifications of the strong completeness proof for the ordinary domainand-values notion of logical consequence of Henkin [4]. Indeed, any reader familiar with Henkin's proof, will recognize immediately how much of our "new-names" notion of logical consequence is derivative from Henkin, for the addition of new names was the profound trick which made his proof go through.…”

mentioning

confidence: 98%