The branch of philosophy that studies the principles of valid inference: what makes one claim follow from another, and what distinguishes a sound argument from a merely persuasive one. Aristotle's Organon, especially the Prior Analytics, set out the theory of the syllogism and dominated logical study in the West for roughly two thousand years, until the nineteenth and early twentieth century work of Boole, Frege, and Russell reconstructed logic on a formal, symbolic footing and connected it to the foundations of mathematics. Logic underlies every other branch of philosophy in a specific sense: metaphysics, epistemology, and ethics all proceed by argument, and logic is the study of what makes an argument good independently of its subject matter.
Facts
Central QuestionWhat makes an inference valid: what relation must hold between premises and a conclusion for the conclusion to follow of necessity? 1 Key DebateWhether classical logic's own laws, bivalence and the law of excluded middle among them, are fixed and universal or genuinely open to revision: intuitionistic, many-valued, and paraconsistent logics have all been proposed as legitimate rivals to the classical system rather than as mere curiosities, reopening whether logic is discovered whole or built to purpose. 1 Disputed
Key DebateLogical pluralism versus logical monism: whether classical logic is the single correct account of valid inference, or whether distinct logics, classical, intuitionistic, relevance and paraconsistent among them, can each be correct for different subject matters or purposes. 1 JC Beall and Greg Restall's defense of logical pluralism reopened a question earlier logicians treated as closed in favor of classical logic alone. Logic
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Source Stanford Encyclopedia of Philosophy
Source Stanford Encyclopedia of Philosophy
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Source Stanford Encyclopedia of Philosophy
Hegel's Science of Logic (1812 to 1816) recasts logic itself as a dialectical development of categories, the branch his method is most directly at home in.
The School of Names (Mingjia) is centrally concerned with logic, language and paradox (Gongsun Long's "White Horse" and "Hard and White" paradoxes), placing it in Logic.
Source Stanford Encyclopedia of Philosophy
Source Zeno's Paradoxes (Wikipedia)
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1. Stanford Encyclopedia of Philosophy
Stanford University, Center for the Study of Language and Informationentry: Classical Logic
Typically, a logic consists of a formal or informal language together with a deductive system and/or a model theoretic semantics.
s.v. Classical Logic
Typically, a logic consists of a formal or informal language together with a deductive system and/or a model-theoretic semantics. The language has components that correspond to a part of a natural language like English or Greek.
s.v. Paraconsistent Logic
A logical consequence relation is explosive if according to it any arbitrary contradiction A, not-A entails any arbitrary conclusion B (ex contradictione quodlibet (ECQ)). Classical logic, and most standard non-classical logics too such as intuitionist logic, are explosive.
s.v. Logical Pluralism
Logical pluralism is the view that there is more than one correct logic. Logics are theories of validity: they tell us which argument forms are valid. Different logics disagree about which forms are valid.
- Includes: Aristotle
- Associated With: Aristotle, entry: Aristotle's Logic
- Associated With: Ludwig Wittgenstein, entry: Wittgenstein
View the Source Zeno's Paradoxes (Wikipedia)
WikipediaIncludes: Zeno's Paradoxes, Lead sectionQuote, Includes: Zeno's Paradoxes, Lead section
These paradoxes have stirred extensive philosophical and mathematical discussion throughout history.
Frequently Asked Questions
Is classical logic the one correct logic, or can more than one logic be correct?
Logical monists hold that classical logic is the single correct account of valid inference, while logical pluralists hold that distinct logics, including intuitionistic, relevance and paraconsistent logic, can each be correct for different purposes.
Logical monists hold that classical logic is the single correct account of what makes an inference valid. Logical pluralists disagree, holding that distinct logics, including classical, intuitionistic, relevance and paraconsistent logic, can each be correct for different subject matters or purposes. The dispute reaches down to classical logic's own laws, such as bivalence and the law of excluded middle: intuitionistic, many-valued and paraconsistent logics have all been proposed as legitimate rivals rather than mere curiosities, reopening whether logic is discovered whole or built to purpose.
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