Wikipedia:Reference desk/Archives/Mathematics/2017 May 12

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May 12

Translation of categorical propositions in predicate expressions

I remember reading in some elementary source/textbook on logic that when categorical propositions are translated in predicate logic expressions, some of the features of these type of propositions are lost. The source does not specify which are those lost features. Can someone help to an answer to this question of lost features? Thanks.--82.137.13.223 (talk) 23:21, 12 May 2017 (UTC)

Without seeing exactly what was in the other source it's hard to say for sure, but it might be that categorical propositions make a distinction between subject and predicate which is sometimes lost when you convert to predicate logic. For example the proposition "Some S are P" is logically equivalent to "Some P are S" even though the roles of subject and predicate are reversed. --RDBury (talk) 21:36, 13 May 2017 (UTC)

Some formulae for transcription are given in the logic textbook, = meaning translation:

a)SaP =$\forall x$ (Sx →Px)

b)SeP =$\forall x$ (Sx → ~ Px)

c)SiP =$\exists {x}$(Sx&Px)

d)SoP =$\exists {x}$(Sx&~Px)

The translation done with the four mentioned formulae use the implication for the universal quantifier and the conjunction for the existential quantifier.

Then the following sentences are given saying: As any other form of translation, the previous formulae are not a perfect translation; categorical propositions have a series of peculiarities which disappear by translating them in predicate logic expressions. As a consequence, not all which holds for categorical propositions also holds for corresponding predicate logic formulae. Nevertheless, the mentioned formulae allow a satisfactory translation in order to use the methods of predicate logic to test the validity of categorical propositions inferences, especially in the case of polysyllogisms for which the Venn diagram method is more difficult.(This is all what is said in the textbook).--82.79.114.201 (talk) 23:44, 14 May 2017 (UTC)

Some hint occurred to me reading the above answer that perhaps the lost features involve the relations encountered in the square of opposition and the obversion?!? Any other thoughts?--82.137.9.192 (talk) 23:56, 14 May 2017 (UTC)