: Symbolic Logic by Carroll Lewis - Logic Symbolic and mathematical Philosophy

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These matters are as follows:--

And so, with regard to the question whether a Proposition is or is not to be understood as asserting the existence of its Subject, I maintain that every writer may adopt his own rule, provided of course that it is consistent with itself and with the accepted facts of Logic.

"All m are x; All m are y. .'. Some y are x". pg169 This they would interpret as follows:--

"If there were any m in existence, all of them would be x; If there were any m in existence, all of them would be y. .'. If there were any y in existence, some of them would be x".

"Taking S, M, P, as the minor, middle, and major terms respectively, the conclusion will imply that, if there is an S, there is some P. Will the premisses also imply this? If so, then the syllogism is valid; but not otherwise.

"The conclusion implies that if S exists P exists; but, consistently with the premisses, S may be existent while M and P are both non-existent. An implication is, therefore, contained in the conclusion, which is not justified by the premisses."

Let us suppose that a Boys' School has been set up, with the following system of Rules:--

"All boys in the First Class are to do French, Greek, and Latin. All in the Second Class are to do Greek only. All in the Third Class are to do Latin only."

"If there were any boys doing French, all of them would be doing Greek; If there were any boys doing French, all of them would be doing Latin."

And the Conclusion, according to "The Logicians" would be

"If there were any boys doing Latin, some of them would be doing Greek."

Some further remarks on this subject will be found in Note , at p. 196.

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