PHL100Y1 Lecture Notes - Lecture 2: Lewis Carroll
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The question is whether this reasoning is valid, whether these two premises really do logically entail this conclusion. (make sure to review your definitions on the arguments handout!) For validity, then, it doesn"t matter whether the premises really are true. What matters is what would be the case if they were true. Well, no more vulgar suspense: the lewis carroll argument is not valid. The reason why is that the premises leave open three distinct possibilities: that no professors are vain, that some professors are vain, and that all professors are vain. Thus, the argument"s conclusion which is the first of these three possibilities is not forced on us by its premises. Those premises fail to rule out the other two possibilities. So even if no professors are ignorant and all ignorant people are vain, it could turn out that no professors are vain is false.
