Syllogisms and Figures and Nonsense Pnemonics

I realized that when I ran into baralipton in my OED study that I would be spending some time trying to master the theory of Western logic, in which baralipton is one of the moods in the first figure. I have never been convinced that it is hugely important to study logic, since if you are a clear enough thinker the theory and practice of logic just comes "naturally." On second thought, however, thinking about logical theory may relate to improved argument as thinking about musical theory relates to better compositional ability.

So, this essay lays out some of the traditional terminology of logic, with some clear examples so that we know what we are doing. As with most things in Western intellectual life, it all begins with Aristotle. His brief treatise Prior Analytics sets out some terminology and issues [A humorous Billphorism, number 431, speculates about Aristotle.] His work was taken over by the Stoics and others in late antiquity, but was systematized and expanded in the 13th century, especially by Peter the Spaniard and William of Sherwood in England. I know neither whether the latter ever ventured into the forest or whether Robin Hood and his merry men ever robbed him. After that weak humor, let's begin with the central term: syllogism.

Syllogisms and Figures, First of All

A syllogism is a three-lined series of affirmations where the conclusion follows from the first two statements. The simplest form is:

"1. All humans are mortal;
2. Socrates is a human;
3. Therefore, Socrates is mortal."

I much prefer the three-lined haiku or the five-lined limerick, but today our medicine is logic. So, we have a series of lines like this, which is called a syllogism. The technical definition of a syllogism is "an argument expressed or claimed to be expressible in the form of two propositions called the premisses, containing a common or middle term, with a third proposition called the conclusion." Let's walk through what things are called. This overall type of syllogism is called a "simple" or "categorical" syllogism. The first sentence is the major premiss and the second the minor premiss. The "middle term" ("M") is the identical or linking term in the first and second lines. The subject ("S") is the first term of the conclusion; the predicate ("P") is the second term of the conclusion. So, a simple diagram, from what we know so far, of the syllogism above would be

1. M (humans) -P (mortal); or M-P.
2. S (Socrates)-M (human); or S-M.
3. S (Socrates) -P (mortal); or S-P.

Just to say things again, so that it doesn't confuse, we have "humans," the same word that appears in both the major and minor premise, as the "Middle" term. "Mortal" is the predicate in the conclusion; "Socrates" is the subject in the conclusion.

The two most important things to learn about categorical syllogisms are the moods and figures of the syllogism. Let's begin with a figure, of which there were four in medieval logic (though Aristotle only expressly used the three). A figure is determined by the different positions of the middle term (the word "human/s" above) in the syllogism. If, for example, the M appears as the first term of the major premiss and the second of the minor, like our simple example, it is the "first" figure.

The "second" figure is where M is the predicate of both premisses. It is diagrammed as follows:

"1. P-M;
2. S-M;
3. S-P."

An example of the second figure would be:

"1. All horses (P) have hooves (M);
2. No humans (S) have hooves (M);
3. No humans (S) are horses (P)."

I will get into the types of statements in the premisses (affirmations, negations) when I speak of moods. The third figure is where the middle term is the subject of both premisses:

"1. M-P;
2. M-S;
3. S-P."

An example of this third figure would be:

"1. All fruit is nutritious;
2. All fruit is tasty;
3. Some tasty things are nutritious."

It would take a lot of time to sort out whether a fourth figure was conceived by Aristotle even though he never spoke of it directly, but if we just want to "finish" the nice structure we have been creating, we logically have a "fourth" mood, digrammed as follows:

"1. P-M;
2. M-S;
3. S-P."

Or, giving an example:

"1. All colored flowers are scented;
2. No scented flower grows indoors;
3. No indoor flowers are colored."

Conclusion

If you have these four figures in your mind, you have the basic building blocks for arguments. But until you connect these to the "moods" of each figure, you won't be able to know the full scope of argument. The next essay introduces the "moods," and then, finally, brings you to baralipton and the nonsense...

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