Logical Form and Logical Constants

2000 ◽  
pp. 142-161
Author(s):  
P. F. Strawson
Keyword(s):  
Logical Form ◽  
Logical Constants

Logical constants

2018 ◽  
Author(s):  
Timothy McCarthy
Keyword(s):  
Fundamental Problem ◽  
Logical Consequence ◽  
Logical Form ◽  
Logical Truth ◽  
Semantic Property ◽  
Truth Conditions ◽  
Property A ◽  
Logical Constants ◽  
Language L

A fundamental problem in the philosophy of logic is to characterize the concepts of ‘logical consequence’ and ‘logical truth’ in such a way as to explain what is semantically, metaphysically or epistemologically distinctive about them. One traditionally says that a sentence p is a logical consequence of a set S of sentences in a language L if and only if (1) the truth of the sentences of S in L guarantees the truth of p and (2) this guarantee is due to the ‘logical form’ of the sentences of S and the sentence p. A sentence is said to be logically true if its truth is guaranteed by its logical form (for example, ‘2 is even or 2 is not even’). There are three problems presented by this picture: to explicate the notion of logical form or structure; to explain how the logical forms of sentences give rise to the fact that the truth of certain sentences guarantees the truth of others; and to explain what such a guarantee consists in. The logical form of a sentence may be exhibited by replacing nonlogical expressions with a schematic letter. Two sentences have the same logical form when they can be mapped onto the same schema using this procedure (‘2 is even or 2 is not even’ and ‘3 is prime or 3 is not prime’ have the same logical form: ‘p or not-p’). If a sentence is logically true then each sentence sharing its logical form is true. Any characterization of logical consequence, then, presupposes a conception of logical form, which in turn assumes a prior demarcation of the logical constants. Such a demarcation yields an answer to the first problem above; the goal is to generate the demarcation in such a way as to enable a solution of the remaining two. Approaches to the characterization of logical constants and logical consequence are affected by developments in mathematical logic. One way of viewing logical constanthood is as a semantic property; a property that an expression possesses by virtue of the sort of contribution it makes to determining the truth conditions of sentences containing it. Another way is proof-theoretical: appealing to aspects of cognitive or operational role as the defining characteristics of logical expressions. Broadly, proof-theoretic accounts go naturally with the conception of logic as a theory of formal deductive inference; model-theoretic accounts complement a conception of logic as an instrument for the characterization of structure.

Dialogical logic

2018 ◽  
Author(s):  
Erik C.W. Krabbe
Keyword(s):  
Winning Strategy ◽  
Logical Consequence ◽  
Logical Form ◽  
Logical Constant ◽  
Critical Dialogue ◽  
Logical Constants ◽  
Dialogue Game ◽  
Dialogical Logic ◽  
Formal Dialogue

Dialogical logic characterizes logical constants (such as ‘and’, ‘or’, ‘for all’) by their use in a critical dialogue between two parties: a proponent who has asserted a thesis and an opponent who challenges it. For each logical constant, a rule specifies how to challenge a statement that displays the corresponding logical form, and how to respond to such a challenge. These rules are incorporated into systems of regimented dialogue that are games in the game-theoretical sense. Dialogical concepts of logical consequence can then be based upon the concept of a winning strategy in a (formal) dialogue game: B is a logical consequence of A if and only if there is a winning strategy for the proponent of B against any opponent who is willing to concede A. But it should be stressed that there are several plausible (and non-equivalent) ways to draw up the rules.

scholarly journals Logical Form, Truth Conditions, and Adequate Formalization

Disputatio ◽  
2020 ◽  
Vol 12 (58) ◽  
pp. 209-222
Author(s):  
Mario Gómez-Torrente
Keyword(s):  
Logical Form ◽  
Truth Conditions ◽  
Logical Constants

Abstract I discuss Andrea Iacona’s idea that logical form mirrors truth conditions, and that logical form, and thus truth conditions, are in turn represented by means of adequate formalization. I criticize this idea, noting that the notion of adequate formalization is highly indefinite, while the pre-theoretic idea of logical form is often much more definite. I also criticize Iacona’s claim that certain distinct sentences, with the same truth conditions and differing only by co-referential names, must be formalized by the same formula (in the same context). I criticize this claim, noting that it imposes implausible demands on adequate formalization. Finally, I offer some brief remarks on the connection between Iacona’s ideas and the distinction between logical and non-logical constants.

Iconicity and Logical Form

1994 ◽  
Vol 16 (1) ◽  
pp. 53-64
Author(s):  
Chrsitopher Hookway
Keyword(s):  
Logical Form

The Structure of Truth

2020 ◽  
Author(s):  
Donald Davidson
Keyword(s):  
Philosophy Of Language ◽  
Logical Form ◽  
Historical Document ◽  
Truth Theory ◽  
Ontological Commitments ◽  
Theory Of Meaning ◽  
First Time

Donald Davidson’s 1970 Locke Lectures appear in print for the first time in this volume, accompanied by an introduction highlighting their significance as a snapshot of his evolving views in the philosophy of language and describing their relationship to the work he published during his lifetime. The lectures comprise an invaluable historical document that illuminates how Davidson was thinking about the theory of meaning, the role of a truth theory therein, the ontological commitments of a truth theory, the notion of logical form, and so on, at a pivotal moment in the development of his thought. Unlike Davidson’s previously published work, they are written so as to be presented to an audience as a fully organized and coherent exposition of his program in the philosophy of language. Had these lectures been widely available in the years following 1970, the reception of Davidson’s work, especially in the philosophy of language, might have been very different. Given the systematic nature of the presentation of Davidson’s semantic program in these lectures, it is hoped that they will be of use to those encountering his thought for the first time.

ON THE NOTION OF CANONICAL DERIVATIONS FROM OPEN ASSUMPTIONS AND ITS ROLE IN PROOF-THEORETIC SEMANTICS

2015 ◽  
Vol 8 (2) ◽  
pp. 296-305 ◽  
Author(s):  
NISSIM FRANCEZ
Keyword(s):  
Natural Deduction ◽  
Proof System ◽  
Logical Constants ◽  
Local Completeness ◽  
Definition Of ◽  
The Impact

AbstractThe paper proposes an extension of the definition of a canonical proof, central to proof-theoretic semantics, to a definition of a canonical derivation from open assumptions. The impact of the extension on the definition of (reified) proof-theoretic meaning of logical constants is discussed. The extended definition also sheds light on a puzzle regarding the definition of local-completeness of a natural-deduction proof-system, underlying its harmony.

Affixation and Logical Form

1994 ◽  
Vol 11 ◽  
pp. 25-36
Author(s):  
Frank Drijkoningen
Keyword(s):  
Logical Form

AL-FĀRĀBĪ'S KITĀB AL-ḤURŪF AND HIS ANALYSIS OF THE SENSES OF BEING

2008 ◽  
Vol 18 (1) ◽  
pp. 59-97 ◽  
Author(s):  
STEPHEN MENN
Keyword(s):  
Second Order ◽  
First Person ◽  
Logical Syntax ◽  
Logical Constants ◽  
First Order ◽  
Propositional Truth ◽  
Arabic Word ◽  
Ideal Language ◽  
The Senses

Al-Fārābī, in the Kitāb al-Ḥurūf, is apparently the first person to maintain that existence, in one of its senses, is a second-order concept [ma‘qūl thānī]. As he interprets Metaphysics Δ7, ‘‘being'' [mawjūd] has two meanings, second-order ‘‘being as truth'' (including existence as well as propositional truth), and first-order ‘‘being as divided into the categories.'' The paronymous form of the Arabic word ‘‘mawjūd'' suggests that things exist through some existence [wujūd] distinct from their essences: for al-Kindī, God is such a wujūd of all things. Against this, al-Fārābī argues that existence as divided into the categories is real but identical with the essence of the existing thing, and that existence as truth is extrinsic to the essence but non-real (being merely the fact that some concept is instantiated). The Ḥurūf tries to reconstruct the logical syntax of syncategorematic or transcendental concepts such as being, which are often expressed in misleading grammatical forms. Al-Fārābī thinks that Greek more appropriately expressed many such concepts, including being, by particles rather than nouns or verbs; he takes Metaphysics Δ to be discussing the meanings of such particles (comparable to the logical constants of an ideal language), and he takes these concepts to demarcate the domain of metaphysics. This explains how al-Fārābī's title can mean both ‘‘Book of Particles'' and ‘‘Aristotle's Metaphysics.''

Sign in / Sign up

Export Citation Format

Share Document