| 词条 | Dictum de omni et nullo |
| 释义 |
In Aristotelian logic, dictum de omni et nullo (Latin: "the maxim of all and none") is the principle that whatever is affirmed or denied of a whole kind K may be affirmed or denied (respectively) of any subkind of K. This principle is fundamental to syllogistic logic in the sense that all valid syllogistic argument forms are reducible to applications of the two constituent principles dictum de omni and dictum de nullo.[1] Dictum de omniDictum de omni (sometimes misinterpreted as universal instantiation) is the principle that whatever is universally affirmed of a kind is affirmable as well for any subkind of that kind. Example:
Premise (1) states that "dog" is a subkind of the kind "mammal". Premise (2) is a (universal affirmative) claim about the kind "mammal". Statement (3) concludes that what is true of the kind "mammal" is true of the subkind "dog". Dictum de nulloDictum de nullo is the related principle that whatever is denied of a kind is likewise denied of any subkind of that kind. Example:
Premise (1) states that "dog" is a subkind of the kind "mammal". Premise (4) is a (universal negative) claim about the kind "mammal". Statement (5) concludes that what is denied of the kind "mammal" is denied of the subkind "dog". Each of these two principles is an instance of a valid argument form known as universal hypothetical syllogism in first-order predicate logic. In Aristotelean syllogistic, they correspond respectively to the two argument forms, Barbara and Celarent. See also
References
Notes1. ^{{cite book|author=John Stuart Mill|title=System of Logic Ratiocinative and Inductive: Being a Connected View of the Principles of Evidence and the Methods of Scientific Investigation|url=https://books.google.com/books?id=cL-0QxoZZAIC&pg=PA114|accessdate=6 March 2011|date=15 January 2001|publisher=Elibron.com|isbn=978-1-4021-8157-3|page=114}} External links
4 : Latin logical phrases|Arguments|Term logic|Inference |
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