Philosophy of logic

Following the developments in formal logic with symbolic logic in the late nineteenth century and mathematical logic in the twentieth, topics traditionally treated by logic not being part of formal logic have tended to be termed either philosophy of logic or philosophical logic if no longer simply logic.

Compared to the history of logic the demarcation between philosophy of logic and philosophical logic is of recent coinage and not always entirely clear. Characterisations include

• Philosophy of logic is the area of philosophy devoted to examining the scope and nature of logic.^[1]
• Philosophy of logic is the investigation, critical analysis and intellectual reflection on issues arising in logic. The field is considered to be distinct from philosophical logic.
• Philosophical logic is the branch of study that concerns questions about reference, predication, identity, truth, quantification, existence, entailment, modality, and necessity.^[2]
• Philosophical logic is the application of formal logical techniques to philosophical problems.^[3]

This article outlines issues in philosophy of logic or provides links to relevant articles or both.

Introduction

This article makes use of the following terms and concepts:

• Type–token distinction
• Use–mention distinction

Truth

Parmenides said To say that that which is, is not or that which is not is, is a falsehood; and to say that which is, is and that which is not is not, is true^[4]

This apparent truism has not proved unproblematic.

Truthbearers

Logic uses such terms as true, false, inconsistent, valid, and self-contradictory. Questions arise as Strawson (1952) writes^[5]

(a) when we use these words of logical appraisal, what is it exactly that we are appraising? and (b) how does logical appraisal become possible?

See also: Sentence, Statement, Proposition.

Tarski's definition of Truth

See:

• Semantic theory of truth § Tarski's Theory
• T-schema
• Stanford Encyclopedia of Philosophy entry on Tarski's Truth Definitions
• Self-reference:2.1 Consequences of the Semantic Paradoxes in Stanford Encyclopedia of Philosophy

Analytic Truths, Logical truth, Validity, Logical consequence and Entailment

Since the use, meaning, if not the meaningfulness, of the terms is part of the debate, it is possible only to give the following working definitions for the purposes of the discussion:

• A necessary truth is one that is true no matter what the state of the world or, as it is sometimes put, in all possible worlds.^[6]
• Logical truths are those necessary truths that are necessarily true owing to the meaning of their logical constants only.^[7]
• In formal logic a logical truth is just a "statement" (string of symbols in which no variable occurs free) which is true under all possible interpretations.
• An analytic truth is one whose predicate concept is contained in its subject concept.

The concept of logical truth is intimately linked with those of validity, logical consequence and entailment (as well as self-contradiction, necessarily false etc.).

• If q is a logical truth, then p therefore q will be a valid argument.
• If p1, p2, p3 ... pn therefore q is a valid argument then its corresponding conditional will be a logical truth.
• If p1 & p2 & p3 ... pn entails q then If (p1 & p2 & p3 ... pn) then q is a logical truth.
• If q is a logical consequence of p1 & p2 & p3 ... pn if and only if p1 & p2 & p3 ... pn entails q and if and only if If (p1 & p2 & p3..pn) then q is a logical truth

Issues that arise include:

• If there are truths that must be true, what makes them so?
• Are there analytic truths that are not logical truths?
• Are there necessary truths that are not analytic truths?
• Are there necessary truths that are not logical truths?
• Is the distinction between analytic truth and synthetic truth spurious?

See also

Paradox

Meaning and reference

See

• Sense and reference
• Theory of reference
• Mediated reference theory
• Direct reference theory
• Causal theory of reference (section References)
• Descriptivist theory of names (section References)
• Saul Kripke (section References)
• Frege's Puzzle (section New Theories of Reference and the Return of Frege's Puzzle)
• Gottlob Frege (section References)
• Failure of reference (section References)
• Rigid designator (section Causal-Historical Theory of Reference)
• Philosophy of language (section References)
• Index of philosophy of language articles
• Supposition theory (section References)
• Referring expression
• Meaning (philosophy of language)
• Denotation and Connotation
• Extension and Intension
• Extensional definition
• Intensional definition
• Metacommunicative competence
• Absent referent

Names and descriptions

• Failure to refer
• Proper name (philosophy)
• Definite description
• Descriptivist theory of names
• Theory of descriptions
• Singular term
• Term logic § Singular terms
• Empty name
• Bas van Fraassen § Singular Terms, Truth-value Gaps, and Free Logic
• The Foundations of Arithmetic § Development of Frege's own view of a number
• Philosophy of language § references
• Direct reference
• Mediated reference theory

Formal and material consequence

• The problem of the material conditional: see Material conditional

Logical constants and connectives

Quantifiers and quantificational theory

Modal logic

Deviant logics

Classical v. non-classical logics

Philosophical theories of logic

• Conceptualism
• Constructivism
• Dialetheism
• Fictionalism
• Finitism
• Formalism
• Intuitionism
• Logical atomism
• Logicism
• Nominalism
• Realism
• Platonic realism
• Structuralism

Other Topics

• Leibniz's Law: see Identity of indiscernibles
• Vacuous names
• Do predicates have properties?: See Second-order logic
• Sense, Reference, Connotation, Denotation, Extension, Intension
• The status of the Laws of Logic
• Classical Logic
• Intuitionism
• Realism: see Platonic realism, Philosophical realism
• The Law of Excluded Middle: see Law of excluded middle
• Modality, Intensionality and Propositional Attitude
• Counter-factuals
• Psychologism

See also

• Logic
• Is logic empirical?
• Type-token distinction
• Use–mention distinction
• Pierce's type-token distinction
• Concatenation theory

Resources

• Haack, Susan. 1978. Philosophy of Logics. Cambridge University Press. (ISBN 0-521-29329-4)
• Quine, W. V. O. 2004. Philosophy of Logic. 2nd ed. Harvard University Press. (ISBN 0-674-66563-5)
• Alfred Tarski. 1983. The concept of truth in formalized languages, pp. 152–278, Logic,semantics, metamathematics, papers from 1923 to 1938, ed. John Corcoran (logician), Hackett,Indianapolis 1983.

References

1. Audi, Robert, ed. (1999). The Cambridge Dictionary of Philosophy (2nd ed.). CUP.
2. Lowe, E. J.. Forms of Thought: A Study in Philosophical Logic. New York: Cambridge University Press, 2013.
3. Russell, Gillian Thoughts, Arguments, and Rants, Jc's Column.
4. Aristotle, Metaphysics,Books Γ, Δ, Ε 2nd edition 1011b25 (1993) trans Kirwan,: OUP
5. Strawson, P.F. (1952). Introduction to Logical Theory. Methuen: London. p. 3.
6. Wolfram (1989) p. 80
7. Wolfram (1989), p. 273

Important figures

Important figures in the philosophy of logic include (but are not limited to):

Aristotle George Boole George Boolos Rudolf Carnap Gordon Clark Alonzo Church Augustus De Morgan Michael Dummett

Gottlob Frege Kurt Gödel Georg Hegel Immanuel Kant Gottfried Leibniz David Lewis John Stuart Mill

Charles Sanders Peirce Alvin Plantinga Arthur Prior Willard Van Orman Quine Bertrand Russell Alfred Tarski Ludwig Wittgenstein

Philosophers of logic

W.V.O. Quine Bertrand Russell Ludwig Wittgenstein

Michael Dummett Hilary Putnam Saul Kripke

Charles Sanders Peirce Alfred Tarski Donald Davidson

Augustus De Morgan Gordon Clark Aristotle

Literature

• Fisher Jennifer, On the Philosophy of Logic, Thomson Wadworth, 2008, ISBN 978-0-495-00888-0
• Goble, Lou, ed., 2001. (The Blackwell Guide to) Philosophical Logic. Oxford: Blackwell. ISBN 0-631-20693-0.
• Grayling, A. C., 1997. An Introduction to Philosophical Logic. 3rd ed. Oxford: Blackwell. ISBN 0-631-19982-9.
• Jacquette, Dale, ed., 2002. A Companion to Philosophical Logic. Oxford Blackwell. ISBN 1-4051-4575-7.
• Kneale, W&M (1962). The development of logic. Oxford.
• McGinn, Colin, 2000. Logical Properties: Identity, Existence, Predication, Necessity, Truth. Oxford: Oxford University Press. ISBN 0-19-926263-2.
• Quine, Willard Van Orman (1970). Philosophy Of Logic. Prentice Hall: New JerseyUSA.
• Sainsbury, Mark, 2001. Logical Forms: An Introduction to Philosophical Logic. 2nd ed. Oxford: Blackwell. ISBN 0-631-21679-0.
• Strawson, PF (1967). Philosophical Logic. OUP.
• Alfred Tarski,1983. The concept of truth in formalized languages, pp. 152–278, Logic,semantics, metamathematics, papers from 1923 to 1938, ed. John Corcoran (logician), Hackett,Indianapolis 1983.
• Wolfram, Sybil, 1989. Philosophical Logic: An Introduction. London: Routledge. 290 pages. ISBN 0-415-02318-1, ISBN 978-0-415-02318-4
• Journal of Philosophical Logic, Springer SBM

External links

• Routledge Encyclopedia of Philosophy entry