principle of explosion

Antinomy (Greek αντι-, against, plus νομος, law, literally, the mutual incompatibility, real or apparent, of two laws) is a term used in logic and epistemology, which, loosely, means a paradox or unresolvable contradiction. The term acquired a special significance in the philosophy of Immanuel Kant, who used it to describe the equally rational but contradictory results of applying to the universe of pure thought the categories or criteria of understanding proper to the universe of sensible perception or experience (phe ...

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In logic, the law of noncontradiction judges as false any proposition P asserting that both proposition Q and its denial, proposition not-Q, are true at the same time and "in the same respect". In the words of Aristotle, "One cannot say of something that it is and that it is not in the same respect and at the same time." More tersely, for any proposition P, it is not both the case that P and not-P. Symbolically, this is expressed as Bivalence and related laws examines how the law of non-contradiction is related to similar laws, such as the ...

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Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of arguments, although the exact definition of logic is a matter of controversy among philosophers. However the subject is grounded, the task of the logician is the same: to advance an account of valid and fallacious inference to allow ...

Including:

• Logic - Nature of logic
• Logic - Informal formal and symbolic logic
• Logic - Rival conceptions of logic
• Logic - History of logic
• Logic - Relation to other sciences
• Logic - Deductive and inductive reasoning
• Logic - Topics in logic
• Logic - Syllogistic logic
• Logic - Predicate logic
• Logic - Modal logic
• Logic - Deduction and reasoning
• Logic - Mathematical logic
• Logic - Philosophical logic
• Logic - Logic and computation
• Logic - Controversies in logic
• Logic - Bivalence and the law of the excluded middle
• Logic - Implication: strict or material?
• Logic - Tolerating the impossible
• Logic - Is logic empirical?

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Because of its fundamental role in philosophy, the nature of logic has been the object of intense dispute: it is not possible clearly to delineate the bounds of logic in terms acceptable to all rival viewpoints. Despite that controversy, the study of logic has been very coherent and technically grounded. In this article, we first characterise logic by introducing fundamental ideas about form, then by outlining some schools of thought, as well as by giving a brief overview of logic's history, an account of its relationship to other sciences, and finally, an exposition of some of logic's essential concepts. Logic - I ...

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Logic, Logic - Nature of logic, Logic - Informal formal and symbolic logic, Logic - Rival conceptions of logic, Logic - History of logic, Logic - Relation to other sciences, Logic - Deductive and inductive reasoning, Logic - Topics in logic, Logic - Syllogistic logic, Logic - Predicate logic, Logic - Modal logic, Logic - Deduction and reasoning, Logic - Mathematical logic, Logic - Philosophical logic, Logic - Logic and computation, Logic - Controversies in logic, Logic - Bivalence and the law of the excluded middle, Logic - Implication: strict or material?, Logic - Tolerating the impossible, Logic - Is logic empirical?

Read more here: » Logic: Encyclopedia II - Logic - Nature of logic

Because of its fundamental role in philosophy, the nature of logic has been the object of intense disputation; and it is not possible to give a clear delineation of the bounds of logic in terms acceptable to all rival viewpoints. Nonetheless, the study of logic has, despite this controversy, been very coherent and technically grounded. Here we characterise logic, first by introducing the fundamental ideas about form and then by outlining some of the different schools of thought as well as giving a brief overview of its history, an account of its relationship to other sciences, and--finally--an expositi ...

See also:

Logic, Logic - Nature of logic, Logic - Informal formal and symbolic logic, Logic - Rival conceptions of logic, Logic - History of logic, Logic - Relation to other sciences, Logic - Deductive and inductive reasoning, Logic - Topics in logic, Logic - Syllogistic logic, Logic - Predicate logic, Logic - Modal logic, Logic - Deduction and reasoning, Logic - Mathematical logic, Logic - Philosophical logic, Logic - Logic and computation, Logic - Controversies in logic, Logic - Bivalence and the law of the excluded middle, Logic - Implication: strict or material?, Logic - Tolerating the impossible, Logic - Is logic empirical?

Read more here: » Logic: Encyclopedia II - Logic - Nature of logic

There are several motivations for paraconsistent logic, all of which arise out of a dissatisfaction with the consistency of classical logic, which seems to lead to results which are counterintuitive. Paraconsistent logic can be used in modelling belief systems which are inconsistent, and yet from which not anything can be inferred. In standard logics, care has to be taken to not allow such statements as the liar paradox to be formed; paraconsistent logics can be much simplified in that they do not have to excise such statements (thoug ...

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Paraconsistent logic, Paraconsistent logic - Motivations, Paraconsistent logic - Problems, Paraconsistent logic - Approaches, Paraconsistent logic - Sources

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In classical logic, a set of sentence, Λ, is said to be negation inconsistent if and for some sentence P. In classical logic, any sentence within the language of the logic can be derived from a negation inconsistent set. A similar model theoretic property holds for classical logic. This is called the principle of explosion, since a single inconsistency ensures that inference can go in any arbitrary direction. Classical logic, intuitionistic logic, and indeed most other logics suffer from this problem. Paraconsistent logics were developed to avoid ...

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Paraconsistent logic, Paraconsistent logic - Motivations, Paraconsistent logic - Problems, Paraconsistent logic - Approaches, Paraconsistent logic - Sources

Read more here: » Paraconsistent logic: Encyclopedia II - Paraconsistent logic - Problems

Throughout history, there has been interest in distinguishing good from bad arguments, and so logic has been studied in some more or less familiar form. Aristotelian logic has principally been concerned with teaching good argument, and is still taught with that end today, while in mathematical logic and analytical philosophy much greater emphasis is placed on logic as an object of study in its own right, and so l ...

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Logic, Logic - Nature of logic, Logic - Informal formal and symbolic logic, Logic - Rival conceptions of logic, Logic - History of logic, Logic - Relation to other sciences, Logic - Deductive and inductive reasoning, Logic - Topics in logic, Logic - Syllogistic logic, Logic - Predicate logic, Logic - Modal logic, Logic - Deduction and reasoning, Logic - Mathematical logic, Logic - Philosophical logic, Logic - Logic and computation, Logic - Controversies in logic, Logic - Bivalence and the law of the excluded middle, Logic - Implication: strict or material?, Logic - Tolerating the impossible, Logic - Is logic empirical?

Read more here: » Logic: Encyclopedia II - Logic - Topics in logic

Just as we have seen there is disagreement over what logic is about, so there is disagreement about what logical truths there are. Logic - Bivalence and the law of the excluded middle. Main article: classical logic The logics discussed above are all "bivalent" or "two-valued"; that is, they are most naturally understood as dividing propositions into the true and the false propositions. Systems which rej ...

See also:

Logic, Logic - Nature of logic, Logic - Informal formal and symbolic logic, Logic - Rival conceptions of logic, Logic - History of logic, Logic - Relation to other sciences, Logic - Deductive and inductive reasoning, Logic - Topics in logic, Logic - Syllogistic logic, Logic - Predicate logic, Logic - Modal logic, Logic - Deduction and reasoning, Logic - Mathematical logic, Logic - Philosophical logic, Logic - Logic and computation, Logic - Controversies in logic, Logic - Bivalence and the law of the excluded middle, Logic - Implication: strict or material?, Logic - Tolerating the impossible, Logic - Is logic empirical?

Read more here: » Logic: Encyclopedia II - Logic - Controversies in logic