·-------· |(.)| | |---|---| | | | ·-------· Hence these three Propositions are equivalent. [In the "books" example, these Propositions would be (1) "Some old English books exist; (2) Some old books are English; (3) Some English books are old".] The two equivalent Propositions, "Some x are y" and "Some y are x", are said to be '=Converse=' to each other; and the Process, of changing one into the other, is called '=Converting=', or '=Conversion='. [For example, if we were told to convert the Proposition "Some apples are not ripe," we should first choose our Univ. (say "fruit"), and then complete the Proposition, by supplying the Substantive "fruit" in the Predicate, so that it would be "Some apples are not-ripe fruit"; and we should then convert it by interchanging its Terms, so that it would be "Some not-ripe fruit are apples".] pg032 Similarly we may represent the three similar Trios of equivalent Propositions; the whole Set of _four_ Trios being as follows:-- (1) "Some xy exist" = "Some x are y" = "Some y are x". (2) "Some xy' exist" = "Some x are y'" = "Some y' are x". (3) "Some x'y exist" = "Some x' are y" = "Some y are x'". (4) "Some x'y' exist" = "Some x' are y'" = "Some y' are x'". Let us take, next, the Proposition "No x are y". This tell us that no Thing, in the _North_ Half, is also in the _West_ Half. Hence there is _nothing_ in the space _common_ to them, that is, in the _North-West Cell_. Hence the North-West Cell is _empty_. And this we can represent by placing a _Grey_ Counter in it. ·-------· |( )| | |---|---| | | | ·-------· [In the "books" example, this Proposition would be "No old books are English".] Similarly we may represent the three similar Propositions "No x are y'", and "No x' are y", and "No x' are y'". [The Reader should make out all these for himself. In the "books" example, these three Propositions would be "No old books are foreign", &c.] Let us take, next, the Proposition "No y are x". This tells us that no Thing, in the _West_ Half, is also in the _North_ Half. Hence there is _nothing_ in the space _common_ to them, that is, in the _North-West Cell_. That is, the North-West Cell is _empty_. And this we can represent by placing a _Grey_ Counter in it. ·-------· |( )| | |---|---| | | | ·-------· [In the "books" example, this Proposition would be "No English books are old".] Similarly we may represent the three similar Propositions "No y are x'", "No y' are x", and "No y' are x'".