Distribution

[EddyBlouin]

Dear Mr. Cothran,

I’m still working my way through your first formal logic book and enjoying it. However, I've run into a problem. In the chapter 8 discussion of distribution you show that “I” statements are undistributed and I don’t understand this because of one of the examples that you use.
You illustrate your first example, “some dogs are vicious things”, with a Euler diagram having two overlapping circles. The intersection of the two circles is shaded. This makes sense to me since not all vicious things are dogs. Your next example is “some men are carpenters.” Again you show how this works with two overlapping circles. The overlapping section is shaded representing “some men are carpenters” but in this diagram the section of the carpenter’s circle outside of the shaded region is dotted to show “that there are no carpenters who are not men.”
 Why wouldn’t the carpenters’ circle be entirely within Man’s circle if there are no carpenters who aren’t men?
 If there are no carpenters who are not men then all carpenters are men and so the statement “some men are carpenters” appears to use the term carpenters universally. And if so then it is distributed Is this true? If not then why not?

Thank you for your time,

JCEB

[Anonymous]

Dear JCEB:

Let me answer your two questions:

Why wouldn’t the carpenters’ circle be entirely within Man’s circle if there are no carpenters who aren’t men?

It would get confusing in actual practice, since, if you did it this way, you would not be able to distinguish between a graph representing the statement "All carpenters are men" and "Some carpenters are men."

I often ask my students to tell me what statement a graph represents. If the graphs representing A statements and I statements were similar, they would not be able to tell me correctly which statements were represented by the graph.

In addition, the graph is supposed to give the viewer some accurate graphical picture of the meaning of the statement it represents. Even though the statement, "Some men are carpenters" has the same extension as the statement, "All carpenters are men" (in other words, the two statements apply to the actual circustances in the same way), that doesn't mean it should be shown graphically the same way.

I have made this statement many times, and I'll say it again: In order to properly understand logic, you have to understand the distinction between comprehension and extension. I have felt this distinction so important that I have put the chapter on this distinction in both Traditional Logic I and in my Material Logic text. Modern logicians ignore this distinction, which is why they make many of the key mistakes they do. It is this distinction which is at the heart of your question.

Extension has to do with how a concept applies to a real thing in the world. When Aristotle used the term "featherless biped" as a tongue-in-cheek definition of man, he was playing off of this confusion between extension and comprehension. Just looking at thing from the perspective of extension, featherless biped means the same thing as man because every case of a featherless biped is a case of a man and every case of a man is a case of a featherless biped. In other words, the two terms have the same extension. But do they really mean the same thing? Obviously not.

When we look at what something means, we look not only at its extension (what thing or state of affairs it applies to), but its comprehension (in other words, its intelligible content).

Your question asks why we can't use the same graph for "Some men are carpenters" as we use for the statement, "All carpenters are men." And the answer is that we don't mean the same thing when we make these two statements, even though, in the real world, they work out to the same thing. In other words, they may have the same extension, but they don't have the same comprehension.

It would make it seem that we really mean the same thing when we make these two statements, when, in fact, we do not.

If there are no carpenters who are not men then all carpenters are men and so the statement “some men are carpenters” appears to use the term carpenters universally. And if so, then it is distributed. Is this true? If not then why not?

No. It is not distributed. Once again, the distinction between extension and comprehension is being confused. Just because the extension of the term carpenters happens to fit within the extension of the term men, it does not follow that we mean the same thing when we make these two statements, since they do not have the same comprehension.

Another way to say this would be to say that the statements "Some men are carpenters" and "All carpenters are men" accidentally apply to the same situation, but not essentially.

I hope this helps.

Martin Cothran