Tuesday, February 21, 2006
A note on "All bachelors are men."
All bachelors are men. This is an analytic truth, and therefore its negation is self-contradictory. Palmer does not show the reasoning, however. Here it is.
If not all bachelors are men, then some bachelors are not men. But since bachelor means unmarried man, we can substitute "unmarried man" for "bachelor." In doing so, we obtain: Not all unmarried men are men. But an unmarried man is a man. Thus we obtain "Not all men are men", wich is self-contradictory. (This note is intended to clarify Palmer's page 179, in which an intermediary step of the reasoning is omitted.)
If not all bachelors are men, then some bachelors are not men. But since bachelor means unmarried man, we can substitute "unmarried man" for "bachelor." In doing so, we obtain: Not all unmarried men are men. But an unmarried man is a man. Thus we obtain "Not all men are men", wich is self-contradictory. (This note is intended to clarify Palmer's page 179, in which an intermediary step of the reasoning is omitted.)
# posted by Michael @ 10:21 PM 
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I was wondering how a mathematical question is analytic because you have to experience it in order to know that 2 + 2 = 4. Would that not be synthetical? Or am I just confused on what analytic means?
Sara Hope
Sara Hope
# posted by 
: 8:10 PM, March 01, 2006
: 8:10 PM, March 01, 2006
Sara, you are not "just" confused, but rather justly so. Notice that on page 179 Palmer gives as an example of an analytic proposition (according to Leibniz) the proposition 3 + 2 = 5. And yet on page 210 that "Kant also claimed that mathematics belonged in the category of the synthetic a priori." So we must conclude that in Kant's view 3 + 2 = 5 was NOT an analytic proposition. Thus we have an important difference in the thinking of Leibniz and Kant here. Palmer also attributes to Hume the opinion that 3 + 2 is a relation of ideas (i.e., in Kant's lingo, analytic), on p. 199. Thus your confusion is well founded! So perhaps it would be best to begin your statement about such questions on the midterm by identifying which philosopher you are following, even if the question does not do so.
As for the substantive question of who is right, I'll have to leave that till later, Sara.
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As for the substantive question of who is right, I'll have to leave that till later, Sara.
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