# 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

## 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[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:

### 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

## Other topics

### Important figures

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

## 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

## Sources

• 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