# Philosophy of logic

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Philosophy of logic

Philosophy of logic is the branch of philosophy that is concerned with the 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?

Topics

Truth, Propositions and Meaning

Truth

Tarski's definition of Truth

Logical Truth

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 [Ludwig Wittgenstein, Tractatus Logico-Philosophicus] . 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."

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

The analytic/synthetic distinction

*
* Analytic-synthetic distinction

Propositions

Leibniz's Law

Rationality and Logic

Plato's Beard & The problem of non-being

Vacuous names

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

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

Do predicates have properties?

ense,Reference,Connotation,Denotation,Extension,Intension

The status of the Laws of Logic

Classical Logic

Intuitionism

Realism

The Law of Excluded Middle

Quantum Logic

Quantifiers, Quantification Theory and Identity

Validity, Inference and Entailment

Modality, Intensionality and Propositional Attitude

Counter-factuals

The problem of the material conditional

Psychologism

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

* Logic
* Is logic empirical?

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

* [http://www.rep.routledge.com/article/X046 Routledge Encyclopedia of Philosophy entry]
* [http://www.organelle.org/organelle/glossary/unA.html essay on the nature of logic (from organelle.org)]
* [http://www.rbjones.com/rbjpub/philos/logic/ Philosophy of logic] (from rbjones.com)

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