Concept
Non-classical logic
Overview
Non-classical logics (sometimes alternative logics) are formal systems that differ in a significant way from standard logical systems such as propositional and predicate logic. There are several ways in which this is commonly the case, including by way of extensions, deviations, and variations. The aim of these departures is to make it possible to construct different models of logical consequence and logical truth.
Philosophical logic is understood to encompass and focus on non-classical logics, although the term has other meanings as well. In addition, some parts of theoretical computer science can be thought of as using non-classical reasoning, although this varies according to the subject area. For example, the basic boolean functions (e.g. AND, OR, NOT, etc) in computer science are very much classical in nature, as is clearly the case given that they can be fully described by classical truth tables. However, in contrast, some computerized proof methods may not use classical logic in the reasoning process.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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A book without content is, as every one knows, not a book with empty leaves, but one of which the content is as good as none. We shall find as the last result on closer analysis, that by what is called content an educated mind means nothing but the presence and power of thought. But this is to admit that thoughts are not empty forms without affinity to their content, and that in other spheres as well as in art the…
Georg Wilhelm Friedrich Hegel, The Logic of Hegel
States what Non-classical logic is; the author is tied to Non-classical logic in the knowledge graph.
In the third place, we shall limit ourselves to the particular consideration of the principle itself. Each principle has reigned for a certain time, and when the whole system of the world has been explained from this special form, it is called a philosophical system. Its whole theory has certainly to be learned, but as long as the principle is abstract it is not sufficient to embrace the forms belonging to our…
Georg Wilhelm Friedrich Hegel, Hegel's Lectures on the History of Philosophy
States what Non-classical logic is; the author is tied to Non-classical logic in the knowledge graph.
From the proposition, Some A is not B, we can not even infer that some B is not A; though some men are not Englishmen, it does not follow that some Englishmen are not men. The only mode usually recognized of converting a particular negative proposition, is in the form, Some A is not B, therefore something which is not B is A; and this is termed conversion by contraposition. In this case, however, the predicate and…
John Stuart Mill, A System of Logic, Ratiocinative and Inductive
States what Non-classical logic is.
Related ideas
- First-order logic
- Georg Wilhelm Friedrich Hegel
- Negation
- Truth value
- Kurt Gödel
- Law of excluded middle
- Logical conjunction
- Propositional logic
- Marxism
- Automated theorem proving
- Truth table
- Subset
- Philosophical logic
- Jan Łukasiewicz
- Theorem
- Susan Haack
- Theoretical computer science
- Modal logic
- Logical consequence
- Formal system
- Logical truth
- Well-formed formula
- Logical constant
- Computer science
Opposing perspectives
- Law of identity
- Intuitionistic logic
- Relevance logic
- Reflexive relation
- Three-valued logic
- Non-monotonic logic
- Logical consequence
- Double negation
- Many-valued logic
- Paraconsistent logic
- Logic
- Fuzzy logic
- Linear logic
- Dialetheism
- De Morgan's laws
- Quantum logic
- Dynamic semantics
- Schrödinger logic
- Idempotence
- Dialectical logic
- Computability logic
Place in the tradition
Part of Outline of philosophy.
Narrower topics: