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- Problem_of_multiple_generality abstract "The problem of multiple generality names a failure in traditional logic to describe certain intuitively valid inferences. For example, it is intuitively clear that if:Some cat is feared by every mousethen it follows logically that:All mice are afraid of at least one catThe syntax of traditional logic (TL) permits exactly four sentence types: "All As are Bs", "No As are Bs", "Some As are Bs" and "Some As are not Bs". Each type is a quantified sentence containing exactly one quantifier. Since the sentences above each contain two quantifiers ('some' and 'every' in the first sentence and 'all' and 'at least one' in the second sentence), they cannot be adequately represented in TL. The best TL can do is to incorporate the second quantifier from each sentence into the second term, thus rendering the artificial-sounding terms 'feared-by-every-mouse' and 'afraid-of-at-least-one-cat'. This in effect "buries" these quantifiers, which are essential to the inference's validity, within the hyphenated terms. Hence the sentence "Some cat is feared by every mouse" is alloted the same logical form as the sentence "Some cat is hungry". And so the logical form in TL is:Some As are BsAll Cs are Dswhich is clearly invalid.The first logical calculus capable of dealing with such inferences was Gottlob Frege's Begriffsschrift, the ancestor of modern predicate logic, which dealt with quantifiers by means of variable bindings. Modestly, Frege did not argue that his logic was more expressive than extant logical calculi, but commentators on Frege's logic regard this as one of his key achievements.Using modern predicate calculus, we quickly discover that the statement is ambiguous.Some cat is feared by every mousecould mean (Some cat is feared) by every mouse, i.e.For every mouse m, there exists a cat c, such that c is feared by m,in which case the conclusion is trivial.But it could also mean Some cat is (feared by every mouse), i.e.There exists one cat c, such that for every mouse m, c is feared by m.This example illustrates the importance of specifying the scope of quantifiers as for all and there exists.".
- Problem_of_multiple_generality wikiPageID "931381".
- Problem_of_multiple_generality wikiPageRevisionID "598728887".
- Problem_of_multiple_generality hasPhotoCollection Problem_of_multiple_generality.
- Problem_of_multiple_generality subject Category:Term_logic.
- Problem_of_multiple_generality comment "The problem of multiple generality names a failure in traditional logic to describe certain intuitively valid inferences. For example, it is intuitively clear that if:Some cat is feared by every mousethen it follows logically that:All mice are afraid of at least one catThe syntax of traditional logic (TL) permits exactly four sentence types: "All As are Bs", "No As are Bs", "Some As are Bs" and "Some As are not Bs". Each type is a quantified sentence containing exactly one quantifier.".
- Problem_of_multiple_generality label "Problem of multiple generality".
- Problem_of_multiple_generality label "Problema da generalidade múltipla".
- Problem_of_multiple_generality label "多重普遍性问题".
- Problem_of_multiple_generality sameAs Problema_da_generalidade_múltipla.
- Problem_of_multiple_generality sameAs m.03r39j.
- Problem_of_multiple_generality sameAs Q7246960.
- Problem_of_multiple_generality sameAs Q7246960.
- Problem_of_multiple_generality wasDerivedFrom Problem_of_multiple_generality?oldid=598728887.
- Problem_of_multiple_generality isPrimaryTopicOf Problem_of_multiple_generality.