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.
Contents
 Introduction 1

Truth 2
 Truthbearers 2.1
 Tarski's definition of Truth 2.2
 Analytic Truths, Logical truth, Validity, Logical consequence and Entailment 2.3
 Paradox 2.4
 Meaning and reference 3

Names and descriptions 4
 Formal and material consequence 4.1
 Logical constants and connectives 5
 Quantifiers and quantificational theory 6
 Modal logic 7

Deviant logics 8
 Classical v. nonclassical logics 8.1
 Philosophical theories of logic 9
 Other Topics 10
 See also 11
 Resources 12
 References 13
 Important figures 14
 Philosophers of logic 15
 Literature 16
 External links 17
Introduction
This article makes use the following terms and concepts:
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 selfcontradictory. 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
 Tschema
 Stanford Encyclopedia of Philosophy entry on Tarski's Truth Definitions
 Selfreference: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 selfcontradiction, 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 [1]
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 CausalHistorical 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, Truthvalue 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. nonclassical 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 Secondorder 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
 Counterfactuals
 Psychologism
See also
 Logic
 Is logic empirical?
 Typetoken distinction
 Use–mention distinction
 Pierce's typetoken distinction
 Concatenation theory
Resources
 Haack, Susan. 1978. Philosophy of Logics. Cambridge University Press. (ISBN 0521293294)
 Quine, W. V. O. 2004. Philosophy of Logic. 2nd ed. Harvard University Press. (ISBN 0674665635)
 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
 ^ Audi, Robert, ed. (1999). The Cambridge Dictionary of Philosophy (2nd ed.). CUP.
 ^ Lowe, E. J.. Forms of Thought: A Study in Philosophical Logic. New York: Cambridge University Press, 2013.
 ^ Russell, Gillian Thoughts, Arguments, and Rants, Jc's Column.
 ^ Aristotle, Metaphysics,Books Γ, Δ, Ε 2nd edition 1011b25 (1993) trans Kirwan,: OUP
 ^ Strawson, P.F. (1952). Introduction to Logical Theory. Methuen: London. p. 3.
 ^ Wolfram (1989) p. 80
 ^ Wolfram (1989), p. 273
Important figures
Important figures in the philosophy of logic include (but are not limited to):

Philosophers of logic
Literature
 Fisher Jennifer, On the Philosophy of Logic, Thomson Wadworth, 2008, ISBN 9780495008880
 Goble, Lou, ed., 2001. (The Blackwell Guide to) Philosophical Logic. Oxford: Blackwell. ISBN 0631206930.
 Grayling, A. C., 1997. An Introduction to Philosophical Logic. 3rd ed. Oxford: Blackwell. ISBN 0631199829.
 Jacquette, Dale, ed., 2002. A Companion to Philosophical Logic. Oxford Blackwell. ISBN 1405145757.
 Kneale, W&M (1962). The development of logic. Oxford.
 McGinn, Colin, 2000. Logical Properties: Identity, Existence, Predication, Necessity, Truth. Oxford: Oxford University Press. ISBN 0199262632.
 Sainsbury, Mark, 2001. Logical Forms: An Introduction to Philosophical Logic. 2nd ed. Oxford: Blackwell. ISBN 0631216790.
 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 0415023181, ISBN 9780415023184
 Journal of Philosophical Logic, Springer SBM
External links
 Routledge Encyclopedia of Philosophy entry
