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

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

Contents

Introduction

This article makes use the following terms and concepts:

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?

Main article: Truthbearer
See also: Sentence, Statements, Proposition.

Tarski's definition of Truth

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:

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

Issues that arise include:

Main articles: necessary truth, logical truth, validity (logic), Corresponding conditional (logic), logical consequence, entailment, and Analytic-synthetic distinction

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

Main articles: Truth and Validity

Paradox

Main article: Paradox

Meaning and reference

See

Names and descriptions

Formal and material consequence

Logical constants and connectives

Main articles: Logical constant and Logical connective

Quantifiers and quantificational theory

Main article: Quantifiers

Modal logic

Main article: Modal logic

Deviant logics

Main article: Deviant logic

Classical v. non-classical logics

Main article: Classical logic

Philosophical theories of logic

Other Topics

See also

Resources

References

  1. ^ Audi, Robert, ed (1999). The Cambridge Dictionary of Philosophy (2nd ed.). CUP. 
  2. ^ Aristotle, Metaphysics,Books Γ, Δ, Ε 2nd edition 1011b25 (1993) trans Kirwan,: OUP
  3. ^ name="Strawson 1952" Strawson, P.F. (1952). Introduction to Logical Theory. Methuen: London. pp. 3. 
  4. ^ Wolfram (1989) p. 80
  5. ^ Wolfram (1989), p.273
  6. ^ Ludwig Wittgenstein, Tractatus Logico-Philosophicus
  7. ^ See Analytic-synthetic distinction

Important figures

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

Philosophers of logic

Literature

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