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 arena 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 and metalogic.^{[citation needed]}
• Philosophical logic is the branch of logic concerning aspects other than or outside of formal logic.^{[citation needed]}
• Philosophical logic is the application of formal logical techniques to philosophical problems.^{[citation needed]}

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

Introduction

This article makes use the following terms and concepts:

• Type-token distinction
• Use–mention distinction

Truth

Aristotle 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^[2]

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^[3]

(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, Statements, Proposition.

Tarski's definition of Truth

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.^[4]
• Logical truths are those necessary truths that are necessarily true owing to the meaning of their logical constants only.^[5]
• 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 &c.).

• 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]

Are Logical Truths a priori or a posteriori knowledge? Synthetic or Analytic?

Ludwig Wittgenstein said that a logical truth was a statement which is true in all possible worlds^[6]. This is contrasted with synthetic claim (or fact) which is only true in this world as it has historically unfolded.

Some argue that a "proposition" such as “If p and q, then p.” and the proposition “All husbands are married.” are logical truths because they are "analytic"^[7] true, i.e. because of their meanings and not because of any facts of the world, i.e they are not synthetic.

See

• Is logic empirical?
• Willard Van Orman Quine: Rejection of the analytic-synthetic distinction
• Analytic-synthetic distinction

Paradox

Meaning and reference

Names and descriptions

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
• Representationalism
• 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

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)

References

Important figures

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

Philosophers of logic

Literature

• 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.
• Sainsbury, Mark, 2001. Logical Forms: An Introduction to Philosophical Logic. 2nd ed. Oxford: Blackwell. ISBN 0-631-21679-0.
• McGinn, Colin. 2000. Logical Properties: Identity, Existence, Predication, Necessity, Truth. Oxford: Oxford University Press. ISBN 0-19-926263-2.
• Wolfram, Sybil, 1989. Philosophical Logic: An Introduction. London: Routledge. 290 pages. ISBN 0415023181, 9780415023184
• Journal of Philosophical Logic, Springer SBM
• Fisher J, On the Philosophy of Logic, Thomson Wadworth, 2008, ISBN 13 978-0-495-00888-0
• Strawson, PF (1967). Philosophical Logic. OUP. 
• Kneale, W&M (1962). The development of logic. Oxford. 
• Quine, Willard Van Orman (1970). Philosophy Of Logic. Prentice Hall: New JerseyUSA.. 

External links

• Routledge Encyclopedia of Philosophy entry
• essay on the nature of logic (from organelle.org)
• Philosophy of logic (from rbjones.com)