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- Consequentia_mirabilis abstract "Consequentia mirabilis (Latin for "admirable consequence"), also known as Clavius's Law, is used in traditional and classical logic to establish the truth of a proposition from the inconsistency of its negation. It is thus similar to reductio ad absurdum, but it can prove a proposition true using just its negation. It states that if a proposition is a consequence of its negation, then it is true, for consistency. It can thus be demonstrated without using any other principle, but that of consistency.In formal notation:which is equivalent to .Consequentia mirabilis was a pattern of argument popular in 17th century Europe that first appeared in a fragment of Aristotle's Protrepticus: "If we ought to philosophise, then we ought to philosophise; and if we ought not to philosophise, then we ought to philosophise (i.e. in order to justify this view); in any case, therefore, we ought to philosophise."The most famous example is perhaps the Cartesian cogito ergo sum: Even if one can question the validity of the thinking, no one can deny that they are thinking.".
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- Consequentia_mirabilis wikiPageRevisionID "567868115".
- Consequentia_mirabilis hasPhotoCollection Consequentia_mirabilis.
- Consequentia_mirabilis subject Category:Latin_logical_phrases.
- Consequentia_mirabilis subject Category:Theorems_in_propositional_logic.
- Consequentia_mirabilis type Abstraction100002137.
- Consequentia_mirabilis type Communication100033020.
- Consequentia_mirabilis type Message106598915.
- Consequentia_mirabilis type Proposition106750804.
- Consequentia_mirabilis type Statement106722453.
- Consequentia_mirabilis type Theorem106752293.
- Consequentia_mirabilis type TheoremsInPropositionalLogic.
- Consequentia_mirabilis comment "Consequentia mirabilis (Latin for "admirable consequence"), also known as Clavius's Law, is used in traditional and classical logic to establish the truth of a proposition from the inconsistency of its negation. It is thus similar to reductio ad absurdum, but it can prove a proposition true using just its negation. It states that if a proposition is a consequence of its negation, then it is true, for consistency.".
- Consequentia_mirabilis label "Consequentia mirabilis".
- Consequentia_mirabilis label "Consequentia mirabilis".
- Consequentia_mirabilis label "Consequentia mirabilis".
- Consequentia_mirabilis label "Consequentia mirabilis".
- Consequentia_mirabilis label "Закон Клавия".
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