I am enjoying Trad. Logic overall, but I'm greatly struggling with enthymemes. Although I get the general principles (first, second, third order, etc.), I do not understand how to convert an enthymeme into a syllogism very well. When doing that with a 3rd Order enthymeme, in what order should I place the premises  the order they were given in or the correct order? This affects the order, mood, figure, syllogism name, everything! Thank you so much for clarifying.
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Traditional Logic II, Ch. 6, Day 3
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Jamie,
You want to place them in the correct order. In a third order enthymeme, the conclusion is the missing statement, so you have the two premises. Arrange them in a subprae form, so that you will have a first figure syllogism. You always want to shoot for a subprae, First Figure if you can. If you can't (if, say, it would end up as an AE or something), then look at the mnemonic verse to see what possible syllogism formations it would. This can be done by simply paying attention to where the middle term is (the term that will appear in both statements). Then you can easily identify the minor and major terms and place them properly in the conclusion.
Let's say you have the following third order enthymeme:
There is a fly in my soup
I don't like soup with flies in it
You would put them in logical form first:
This soup is soup that has a fly in it (A statement)
No soup that has flies in it is soup that I like (E statement)
This is currently in praesub form, fourth figure. Let's see if we can put it in the first figure:
No soup that has flies in it is soup that I like (E statement)
This soup is soup that has flies in it (A statement)
Is there an EA syllogism in the first figure? Yes: CELARENT. So let's go with that. In that case, I simply have to identify the minor and major terms and put them in the right order to make my conclusion. We know what the middle term is: "soup that has flies in it". We know that because it appears in both premises. So how do we determine the minor and major terms? Well, we now know which are the minor and major premises (major first, minor second), so all we have to do is see the other term in the major premise (that's the major term) and the other term in the minor premise (that's the minor term). In the first or major premise the other term is "soup I like", so that is the major term. In the second or minor premise the other term is "this soup", so that must be the minor term.
We know that a conclusion consists of the minor term as the subject, and the major term as the predicate. So the subject must be "soup I like" and the predicate must be "this soup". And, further, we know that the conclusion must be an E statement, since the premises are EA, and that if one premise is negative, the conclusion must be negative (one of the rules of validity). So our conclusion will be:
No soup I like is this soup
Or, simply: "I don't like this soup". There we go. Now since there was also a praesub fourth figure AE (CAMENES), you could have left the premises where they were originally. But this won't always be the case.
Note that we had to employ various different things we have learned here, like the order of major and minor premises, and the mnemonic verse, and one of our rules of validity, but that's why all those previous chapters were important, right?
Let me know if this doesn't help.
Martin Cothran
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