Unrestricted Logical Inferentialism

Shadows of Syntax ◽

10.1093/oso/9780190086152.003.0003 ◽

2020 ◽

pp. 55-94

Author(s):

Jared Warren

Keyword(s):

Logical Constants ◽

Bad Company ◽

Metaphysics Of Logic

This chapter develops and defends an unrestricted inferentialist theory of the meanings of logical constants. Unlike restricted inferentialism, unrestricted inferentialism puts no constraints on which rules can determine meanings. The foundations of inferentialism are also discussed, including various types of holism and the distinction between basic and derivative rules. In order to develop and defend a detailed inferentialist theory of logic, this chapter provides an inferentialist account of the “logical” constants, solves Carnap’s categoricity problem for the meanings of logical constants, and provides inferentialist approaches to both the psychology and metaphysics of logic. Finally, the chapter briefly discusses the challenge to unrestricted inferentialism posed by tonk and related types of bad company. Building on the foundation provided by Part I (chapters 1-2) of the book, this chapter provides a freestanding development and defense of logical inferentialism.

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The tangled web of agency

Behavioral and Brain Sciences ◽

10.1017/s0140525x17001170 ◽

2018 ◽

Vol 41 ◽

Author(s):

Alain Pe-Curto ◽

Julien A. Deonna ◽

David Sander

Keyword(s):

Two Dimensions ◽

Bad Company

AbstractWe characterize Doris's anti-reflectivist, collaborativist, valuational theory along two dimensions. The first dimension is socialentanglement, according to which cognition, agency, and selves are socially embedded. The second dimension isdisentanglement, the valuational element of the theory that licenses the anchoring of agency and responsibility in distinct actors. We then present an issue for the account: theproblem of bad company.

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

The Review of Symbolic Logic ◽

10.1017/s1755020315000027 ◽

2015 ◽

Vol 8 (2) ◽

pp. 296-305 ◽

Cited By ~ 7

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.

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

Arabic Sciences and Philosophy ◽

10.1017/s0957423908000477 ◽

2008 ◽

Vol 18 (1) ◽

pp. 59-97 ◽

Cited By ~ 8

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.''

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