Classical mathematics (original) (raw)
In the foundations of mathematics, classical mathematics refers generally to the mainstream approach to mathematics, which is based on classical logic and ZFC set theory. It stands in contrast to other types of mathematics such as constructive mathematics or predicative mathematics. In practice, the most common non-classical systems are used in constructive mathematics.
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| dbo:abstract | In the foundations of mathematics, classical mathematics refers generally to the mainstream approach to mathematics, which is based on classical logic and ZFC set theory. It stands in contrast to other types of mathematics such as constructive mathematics or predicative mathematics. In practice, the most common non-classical systems are used in constructive mathematics. Classical mathematics is sometimes attacked on philosophical grounds, due to constructivist and other objections to the logic, set theory, etc., chosen as its foundations, such as have been expressed by L. E. J. Brouwer. Almost all mathematics, however, is done in the classical tradition, or in ways compatible with it. Defenders of classical mathematics, such as David Hilbert, have argued that it is easier to work in, and is most fruitful; although they acknowledge non-classical mathematics has at times led to fruitful results that classical mathematics could not (or could not so easily) attain, they argue that on the whole, it is the other way round. (en) En fondements des mathématiques, les mathématiques classiques se réfèrent généralement à l'approche traditionnelle des mathématiques, qui est basée sur la logique classique et la théorie des ensembles ZFC. Il s'oppose à d'autres types de mathématiques tels que les mathématiques constructives ou les mathématiques prédicatives. En pratique, les systèmes non-classiques les plus courants sont utilisés en mathématiques constructives. Les mathématiques classiques sont parfois critiqués sur ses bases philosophiques, dues à des objections constructivistes et autres à la logique, théorie des ensembles, etc., choisies comme fondations, comme l'a exprimé L. E. J. Brouwer. Les défenseurs des mathématiques classiques, tels que David Hilbert, ont soutenu qu'il est plus facile et fécond de travailler avec l'infini que sans, mais reconnaissent que les mathématiques non classiques ont parfois abouti à des résultats importants que les mathématiques classiques n'auraient pas pu (ou ne pouvaient pas si facilement) atteindre. (fr) |
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| rdfs:comment | In the foundations of mathematics, classical mathematics refers generally to the mainstream approach to mathematics, which is based on classical logic and ZFC set theory. It stands in contrast to other types of mathematics such as constructive mathematics or predicative mathematics. In practice, the most common non-classical systems are used in constructive mathematics. (en) En fondements des mathématiques, les mathématiques classiques se réfèrent généralement à l'approche traditionnelle des mathématiques, qui est basée sur la logique classique et la théorie des ensembles ZFC. Il s'oppose à d'autres types de mathématiques tels que les mathématiques constructives ou les mathématiques prédicatives. En pratique, les systèmes non-classiques les plus courants sont utilisés en mathématiques constructives. (fr) |
| rdfs:label | Classical mathematics (en) Mathématiques classiques (fr) |
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