Portal:Logic

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The Logic Portal

  

Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason or principle) is the study of the principles and criteria of valid inference and demonstration.

As a formal science, logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and through the study of arguments in natural language. The field of logic ranges from core topics such as the study of fallacies and paradoxes, to specialized analysis of reasoning using probability and to arguments involving causality. Logic is also commonly used today in argumentation theory. [1]

Traditionally, logic is studied as a branch of philosophy, one part of the classical trivium, which consisted of grammar, logic, and rhetoric. Since the mid-nineteenth century formal logic has been studied in the context of the foundations of mathematics. In 1903 Bertrand Russell and Alfred North Whitehead attempted to establish logic as the cornerstone of mathematics formally with the publication of Principia Mathematica. However, the system of Principia is no longer much used, having been largely supplanted by set theory. The development of formal logic and its implementation in computing machinery is the foundation of computer science.

References

  1. ^ J. Robert Cox and Charles Arthur Willard, eds. Advances in Argumentation Theory and Research, Southern Illinois University Press, 1983 ISBN 0809310503, ISBN-13 978-0809310500
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Or

In logic and mathematics, or, also known as logical disjunction or inclusive disjunction is a logical operator that results in true whenever one or more of its operands are true. In grammar, or is a coordinating conjunction.

Logical disjunction is an operation on two logical values, typically the values of two propositions, that produces a value of false if and only if both of its operands are false. More generally a disjunction is a logical formula that can have one or more literals separated only by ORs. A single literal is often considered to be a degenerate disjunction.

The truth table of p or q:

p q ∨
T T T
T F T
F T T
F F F

The Venn diagram of p or q:


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Logic Lane

A view of Logic Lane toward the High Street from within University College, Oxford.

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Bertrand Arthur William Russell, 3rd Earl Russell OM FRS (18 May 1872 – 2 February 1970), was a British philosopher, logician, mathematician and advocate for social reform.

A prolific writer, he was also a populariser of philosophy and a commentator on a large variety of topics, ranging from very serious issues to those much less so. Continuing a family tradition in political affairs, he was a prominent anti-war activist, championing free trade between nations and anti-imperialism.[1][2]

References

  1. ^ J. Robert Cox and Charles Arthur Willard, eds. Advances in Argumentation Theory and Research, Southern Illinois University Press, 1983 ISBN 0809310503, ISBN-13 978-0809310500
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Great Logicians

 · Aristotle · Boole · Cantor · Carnap · Church · Frege · Gentzen · Gödel · Hilbert · Kripke · Peano · Peirce · Putnam · Quine · Russell · Skolem · Tarski · Turing · Whitehead ·
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Logical Theorem of the month

A \equiv A

— Law of identity An object is always the same as itself
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“ To be is to be the value of a bound variable. ”

W. V. O. Quine

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