The Idea of a Logical Constant

1981 ◽  
Vol 78 (9) ◽  
pp. 499 ◽  
Author(s):  
Timothy McCarthy
Keyword(s):  
Logical Constant

Predicates, parts, and impermanence: a contemporary version of some central Buddhist tenets

2017 ◽  
Vol 54 (4) ◽  
pp. 475-488
Author(s):  
MATTHEW McKEEVER
Keyword(s):  
Natural Language ◽  
Recent Work ◽  
Analytic Philosophy ◽  
Buddhist Philosophy ◽  
Logical Constant ◽  
Good Sense ◽  
Buddhist Doctrine ◽  
Spatially Extended ◽  
Temporal Parts ◽  
Spatial Locations

AbstractIn this article, I argue that recent work in analytic philosophy on the semantics of names and the metaphysics of persistence supports two theses in Buddhist philosophy, namely the impermanence of objects and a corollary about how referential language works. According to this latter package of views, the various parts of what we call one object (say, King Milinda) possess no unity in and of themselves. Unity comes rather from language, in that we have terms (say, ‘King Milinda’) which stand for all the parts taken together. Objects are mind- (or rather language-)generated fictions. I think this package can be cashed out in terms of two central contemporary views. The first is that there are temporal parts: just as an object is spatially extended by having spatial parts at different spatial locations, so it is temporally extended by having temporal parts at different temporal locations. The second is that names are predicates: rather than standing for any one thing, a name stands for a range of things. The natural language term ‘Milinda’ is not akin to a logical constant, but akin to a predicate.Putting this together, I'll argue that names are predicates with temporal parts in their extension, which parts have no unity apart from falling under the same predicate. ‘Milinda’ is a predicate which has in its extension all Milinda's parts. The result is an interesting and original synthesis of plausible positions in semantics and metaphysics, which makes good sense of a central Buddhist doctrine.

scholarly journals ISOMORPHISM INVARIANCE AND OVERGENERATION

2016 ◽  
Vol 22 (4) ◽  
pp. 482-503 ◽  
Author(s):  
OWEN GRIFFITHS ◽  
A.C. PASEAU
Keyword(s):  
Logical Constant ◽  
Logical Nature ◽  
Clear Cases

AbstractThe isomorphism invariance criterion of logical nature has much to commend it. It can be philosophically motivated by the thought that logic is distinctively general or topic neutral. It is capable of precise set-theoretic formulation. And it delivers an extension of ‘logical constant’ which respects the intuitively clear cases. Despite its attractions, the criterion has recently come under attack. Critics such as Feferman, MacFarlane and Bonnay argue that the criterion overgenerates by incorrectly judging mathematical notions as logical. We consider five possible precisifications of the overgeneration argument and find them all unconvincing.

scholarly journals Tonk Strikes Back∗

2005 ◽  
Vol 3 ◽  
Author(s):  
Denis Bonnay ◽  
Benjamin Simmenauer
Keyword(s):  
Logical Constant ◽  
Double Line ◽  
Rule Based ◽  
Logical Constants ◽  
Inferential Role ◽  
The Right

What is a logical constant? In which terms should we characterize the meaning of logical words like “and”, “or”, “implies”? An attractive answer is: in terms of their inferential roles, i.e. in terms of the role they play in building inferences. More precisely, we favor an approach, going back to Dosen and Sambin, in which the inferential role of a logical constant is captured by a double line rule which introduces it as reflecting structural links (for example, multiplicative conjunction reflects comma on the right of the turnstyle). Rule-based characterizations of logical constants are subject to the well known objection of Prior’s fake connective, tonk. We show that some double line rules also give rise to such pseudo logical constants. But then, we are able to find a property of a double line rules which guarantee that it defines a genuine logical constant. Thus we provide an alternative answer to Belnap’s requirement of conservatity in terms of a local requirement on double line rules.

scholarly journals Preface. Conditional: Conceptual and Historical Analysis

Studia Humana ◽  
2017 ◽  
Vol 6 (1) ◽  
pp. 3-4
Author(s):  
Fabien Schang
Keyword(s):  
Critical Analysis ◽  
Historical Analysis ◽  
Logical Constant

Abstract The logic of conditional is developed hereby in a series of papers, contributing to a historical and critical analysis of what the logical constant is expected to mean.

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.

Inferentialism and the Epistemology of Logic

2020 ◽  
pp. 93-107
Author(s):  
Paul Boghossian ◽  
Timothy Williamson
Keyword(s):  
Logical Constant ◽  
Inferential Role ◽  
Timothy Williamson ◽  
Epistemology Of Logic

This essay attempts to clarify the project of explaining the possibility of ‘blind reasoning’—namely, of basic logical inferences to which we are entitled without our having an explicit justification for them. The role played by inferentialism in this project is examined and objections made to inferentialism by Paolo Casalegno and Timothy Williamson are answered. Casalegno proposes a recipe for formulating a counterexample to any proposed constitutive inferential role by imaging a subject who understands the logical constant in question but fails to have the capacity to make the inference in question; Williamson’s recipe turns on imagining an expert who continues to understand the constant in question while having developed sophisticated considerations for refusing to make it. It’s argued that neither recipe succeeds.

Basic logic: reflection, symmetry, visibility

2000 ◽  
Vol 65 (3) ◽  
pp. 979-1013 ◽  
Author(s):  
Giovanni Sambin ◽  
Giulia Battilotti ◽  
Claudia Faggian
Keyword(s):  
Sequent Calculus ◽  
Linear Logic ◽  
Logical Constant ◽  
Cut Elimination ◽  
Inference Rules ◽  
Reflection Symmetry ◽  
Basic Logic ◽  
Strict Control ◽  
Geometric Symmetry

AbstractWe introduce a sequent calculus B for a new logic, named basic logic. The aim of basic logic is to find a structure in the space of logics. Classical, intuitionistic. quantum and non-modal linear logics, are all obtained as extensions in a uniform way and in a single framework. We isolate three properties, which characterize B positively: reflection, symmetry and visibility.A logical constant obeys to the principle of reflection if it is characterized semantically by an equation binding it with a metalinguistic link between assertions, and if its syntactic inference rules are obtained by solving that equation. All connectives of basic logic satisfy reflection.To the control of weakening and contraction of linear logic, basic logic adds a strict control of contexts, by requiring that all active formulae in all rules are isolated, that is visible. From visibility, cut-elimination follows. The full, geometric symmetry of basic logic induces known symmetries of its extensions, and adds a symmetry among them, producing the structure of a cube.

Finite Axiomatizability using additional predicates

1958 ◽  
Vol 23 (3) ◽  
pp. 289-308 ◽  
Author(s):  
W. Craig ◽  
R. L. Vaught
Keyword(s):  
Order Logic ◽  
The Other ◽  
First Order Logic ◽  
Logical Constant ◽  
Finite Axiomatizability ◽  
Logical Constants ◽  
First Order

By a theory we shall always mean one of first order, having finitely many non-logical constants. Then for theories with identity (as a logical constant, the theory being closed under deduction in first-order logic with identity), and also likewise for theories without identity, one may distinguish the following three notions of axiomatizability. First, a theory may be recursively axiomatizable, or, as we shall say, simply, axiomatizable. Second, a theory may be finitely axiomatizable using additional predicates (f. a.+), in the syntactical sense introduced by Kleene [9]. Finally, the italicized phrase may also be interpreted semantically. The resulting notion will be called s. f. a.+. It is closely related to the modeltheoretic notion PC introduced by Tarski [16], or rather, more strictly speaking, to PC∩ACδ.For arbitrary theories with or without identity, it is easily seen that s. f. a.+ implies f. a.+ and it is known that f. a.+ implies axiomatizability. Thus it is natural to ask under what conditions the converse implications hold, since then the notions concerned coincide and one can pass from one to the other.Kleene [9] has shown: (1) For arbitrary theories without identity, axiomatizability implies f. a.+. It also follows from his work that : (2) For theories with identity which have only infinite models, axiomatizability implies f. a.+.

A formalization of the C-O propositional calculus

1951 ◽  
Vol 47 (4) ◽  
pp. 635-636
Author(s):  
Alan Rose
Keyword(s):  
Propositional Calculus ◽  
Logical Constant ◽  
False Statement ◽  
True Statement ◽  
Image Position

In this paper we formalize the two-valued propositional calculus with implication and the logical constant 0 (denoting a false statement), as primitives. We can define the logical constant 1 (denoting a true statement), byand we can define negation by NP = df. CP0.

HARMONISING HARMONY

2015 ◽  
Vol 8 (3) ◽  
pp. 411-423 ◽  
Author(s):  
LUCA TRANCHINI
Keyword(s):  
Logical Constant ◽  
Inversion Principle ◽  
The One

AbstractThe term ‘harmony’ refers to a condition that the rules governing a logical constant ought to satisfy in order to endow it with a proper meaning. Different characterizations of harmony have been proposed in the literature, some based on the inversion principle, others on normalization, others on conservativity. In this paper we discuss the prospects for showing how conservativity and normalization can be combined so to yield a criterion of harmony equivalent to the one based on the inversion principle: We conjecture that the rules for connectives obeying the inversion principle are conservative over normal deducibility. The plausibility of the conjecture depends in an essential way on how normality is characterized. In particular, a normal deduction should be understood as one which is irreducible, rather than as one which does not contain any maximal formula.

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