ABSTRACT
In the preceding chapter it was shown that all propositions imply an obverse the terms of which are related to the terms of the original as S—P̄ to S—P, and that some propositions have a converse, the terms of which are related to those of the original as P—S to S—P. Let us now consider in a purely abstract manner what other implications are conceivable involving the terms of a given proposition and their contradictories. The terms in question will be four in number, namely S, P, S̄, P̄, of which S and P represent the subject and predicate of the given proposition. Let us omit merely tautological statements, such as S is S, or S is not S̄, and self-contradictory statements like S is not S, or S is S̄. We are then left with the following conceivable combinations of terms for conceivable additional eductions, namely, P − S ¯ , P ¯ − S , P ¯ − S ¯ , S ¯ − P , S ¯ − P ¯ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429054389/44a8c165-1c30-4594-8b98-e9b9085dd2d8/content/inq_chapter6_53_1.tif"/> . If we add to these the original S—P, the obverse S—P̄, and the converse P—S, we obtain the following table of conceivable combinations of terms of propositions in relation to any given proposition. As there can be no harm in christening these various conceivable 54combinations before studying them more closely, names are added in all cases.
S—P original proposition.
S—P̄ obverse.
P—S converse.
P—S̄ obverted converse.
P̄—S contrapositive.
P̄—S̄ obverted contrapositive.
S̄—P inverse.
S̄—P̄ obverted inverse.
