Philosophy of logic

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This article is about philosophy of logic not philosophical logic.

Philosophy of logic is the branch of philosophy that is concerned with scope and nature of logic. Some fundamental questions with which it is concerned are:

• Is there only one "true" logic, or are many logics equally correct?
• Is it possible to have genuine disagreements about whether a logical principle (such as the law of excluded middle) is correct?
• What makes an expression a logical constant?
• What are the proper accounts of logical consequence, quantification, and other logical concepts?
• What is the scope of logic (e.g., does it encompass mathematics)?
• Is second-order logic really logic?
• Is logic a matter of convention?
• Is logic empirical?
• What is the nature of logical necessity?
• What is the relationship between the verbal rules of logic and the mental ability to reason logically?

Contents 1 Topics 1.1 Truth, Propositions and Meaning 1.1.1 Truth 1.1.1.1 Tarski's definition of Truth 1.1.2 Logical Truth 1.1.2.1 Are Logical Truths a priori or a posteriori knowledge? Synthetic or Analytic 1.1.3 The analytic/synthetic distinction 1.1.4 Propositions 1.2 Leibniz's Law 1.3 Rationality and Logic 1.4 Plato's Beard & The problem of non-being 1.5 Vacuous names 1.6 Do unicorns have horns and did Hamlet see a real ghost? 1.7 Does the square root of minus one have the same ontological status at the square root of two 1.8 Do predicates have properties? 1.9 Sense,Reference,Connotation,Denotation,Extension,Intension 1.10 The status of the Laws of Logic 1.11 Classical Logic 1.12 Intuitionism 1.13 Realism 1.14 The Law of Excluded Middle 1.15 Quantum Logic 1.16 Quantifiers, Quantification Theory and Identity 1.17 Validity, Inference and Entailment 1.18 Modality, Intensionality and Propositional Attitude 1.19 Counter-factuals 1.20 The problem of the material conditional 1.21 Psychologism 2 Important figures 3 See also 4 Resources 5 References 6 External links

[edit] Topics

[edit] Truth, Propositions and Meaning

[edit] Truth

[edit] Tarski's definition of Truth

[edit] Logical Truth

See also Proposition

Main article: Validity

What is and is not considered a logical truth (also called an analytic truth or a necessary truth) has been a matter for clarification, even up to the early part of the 20th Century.

A logical truth was considered by Ludwig Wittgenstein to be a statement which is true in all possible worlds^[1]. This is contrasted with synthetic claim (or fact) which is only true in this world as it has historically unfolded.

Later, with the rise of formal logic a logical truth was considered to be a statement which is true under all possible interpretations.

Logical truths are necessarily true. A proposition such as “If p and q, then p.” and the proposition “All husbands are married.” are considered to be logical truths because they are true because of their meanings and not because of any facts of the world. They are such that they could not be untrue.

Logic is concerned with the patterns in reason that can help tell us if a proposition is true or not. However, logic does not deal with truth in the absolute sense, as for instance a metaphysician does. Logicians use formal languages to express the truths which they are concerned with, and as such there is only truth under some interpretation or truth within some logical system.

[edit] Are Logical Truths a priori or a posteriori knowledge? Synthetic or Analytic

See also Is logic empirical?

[edit] The analytic/synthetic distinction

see also

• Willard Van Orman Quine: Rejection of the analytic-synthetic distinction
• Analytic-synthetic distinction

[edit] Propositions

see also Willard Van Orman Quine, Proposition

[edit] Leibniz's Law

see also Identity of indiscernibles

[edit] Rationality and Logic

[edit] Plato's Beard & The problem of non-being

[edit] Vacuous names

[edit] Do unicorns have horns and did Hamlet see a real ghost?

[edit] Does the square root of minus one have the same ontological status at the square root of two

[edit] Do predicates have properties?

See also Second-order logic

[edit] Sense,Reference,Connotation,Denotation,Extension,Intension

[edit] The status of the Laws of Logic

[edit] Classical Logic

[edit] Intuitionism

[edit] Realism

see also Platonic realism, Philosophical realism

[edit] The Law of Excluded Middle

see also Law of excluded middle

[edit] Quantum Logic

[edit] Quantifiers, Quantification Theory and Identity

[edit] Validity, Inference and Entailment

[edit] Modality, Intensionality and Propositional Attitude

[edit] Counter-factuals

[edit] The problem of the material conditional

see also Material conditional

[edit] Psychologism

[edit] Important figures

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

Aristotle George Boole George Boolos Rudolf Carnap Alonzo Church Augustus De Morgan W V Quine

Michael Dummett Gottlob Frege Kurt Gödel Georg Hegel Immanuel Kant Gottfried Leibniz David Lewis Wittgenstein

John Stuart Mill Charles Peirce Alvin Plantinga Arthur Prior Willard Van Orman Quine Bertrand Russell Alfred Tarski

[edit] See also

• Logic
• Is logic empirical?

[edit] 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)

[edit] References

[edit] External links

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

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