Take the following Pairs of Premisses:—
“None of my boys are conceited;
None of my girls are greedy”.
“None of my boys are clever;
None but a clever boy could solve this problem”.
“None of my boys are learned;
Some of my boys are not choristers”.
(This last Proposition is, in my system, an affirmative one, since I should read it “are not-choristers”; but, in dealing with “The Logicians,” I may fairly treat it as a negative one, since they would read it “are-not choristers”.)
If you, dear Reader, declare, after full consideration of these Pairs of Premisses, that you cannot deduce a Conclusion from any of them——why, all I can say is that, like the Duke in Patience, you “will have to be contented with our heart-felt sympathy”! [See [Note (C), p. 196].]
[§ 5.]
Euler’s Method of Diagrams.
Diagrams seem to have been used, at first, to represent Propositions only. In Euler’s well-known Circles, each was supposed to contain a class, and the Diagram consisted of two circles, which exhibited the relations, as to inclusion and exclusion, existing between the two Classes.
