1. Are there any shortcuts to remembering these terms and methods?
2. What is a good way of choosing between Venn diagrams and rules as tests for validity?

1. Are there any shortcuts to remembering these terms and methods?

One huge drawback of categorical logic is that it gets top-heavy with special vocabulary and with rules that rely on that vocabulary. If you feel overwhelmed by the initial blitz of detail, take heart: Students of Aristotelian logic have responded that way for over two thousand years--because for at least that long, logicians have been inventing memory aids to keep the elements of logic straight.

You will probably find the logical procedures of Chapter 9 stranger at first sight, and reminiscent of mathematics; but before long you will see that they involve less of this sort of memorization. So Chapter 8 is the one to work on.

What follow are a few tricks for getting a handle on what seem like arbitrary symbols and rules. If they strike you as far-fetched, silly, or harder to remember than the chapter's actual material, please ignore them.

A-, E-, I-, O-claims. The definitions of these terms in "Key Words," above, include suggestions for remembering them.

Converse, obverse, contrapositive. The work here is remembering which operations you may apply to which sorts of claims. No one worries about obversion, because every categorical claim is equivalent to its obverse; learn how to do it and apply it everywhere. You may think of obversion as a way of taking a double negative: Negate the form of the claim (negative to affirmative or affirmative to negative), and then negate its content (with the complementary term, the denial, of the predicate).

Which claims may be converted, and which need contraposition? Both operations involve switching the subject and predicate terms. But that's all you do to an E- or an I-claim, whereas A- and O-claims require that you also replace each term with its complementary term. What is it about A- and O-claims that makes the added step necessary?

E- and I-claims are symmetrical statements, whereas the other two are asymmetrical. "Some bakers are Italians" tells you what "Some Italians are bakers" does (aside from subjective emphasis), so you can trot out those terms in either order. "All bakers are Italians," on the other hand, is saying something about all bakers, and has nothing to say about Italians in general.

The Venn diagram is one way to identify symmetrical statements. In diagrams for E- and I-claims, the only marks within the two circles, whether shading or X, are made in the lens-shaped area between them. You can relabel the two circles and still have the same claim. But A- and O-claims yield diagrams in which all the action happens outside that lens-shaped space.

Here's another way of thinking about it. Some categorical claims can be naturally translated into sentences containing "S and P," but others can't. An E-claim, "No S are P," says, "Nothing is both S and P." The corresponding I-claim, "Some S are P," tells you, "At least one thing is both S and P." By contrast, the O-claim turns into "At least one thing is S and is not P"; the A-claim has no graceful translation into a claim about S and anything else.

This "and" should tip you off. If something is both S and P, it's both P and S. If nothing is both S and P, nothing can be both P and S either. So claims you can restate as being about S and P make equally good sense about P and S; hence they're symmetrical; hence you convert them and don't take the contrapositive.

Distributed terms. Some memorization helps with distributed terms, but a few little tips will help you keep them straight. In the first place, you have noticed that no two types of categorical claims distribute their terms in the same way. If you remember how terms are distributed in two types of claims, you have narrowed down the possibilities for the other two. If you remember three, the fourth type of claim will be the remaining alternative.

The general way to remember distributed terms is this: The subject term of a universal claim (one that doesn't begin with "some") is always distributed, as is the predicate term of a negative claim.

One linguistic sign is the word right before the term. If the word is either "all" or a negation ("no" or "not"), the term is distributed. If the word is "some," the term is not distributed. Some terms have no signs before them, of course: The predicate term of an E-claim is distributed without any linguistic hint. But if you remember "all or none," you will have a signpost marking three out of the four distributed terms that arise.

2. What is a good way of choosing between Venn diagrams and rules as tests for validity?

Don't base your decision on which method is easier to understand, or which method's rules you can absorb faster. Venn diagrams win on both counts; but, while you might decide to use Venn diagrams in all cases, the rules have advantages that don't appear right away.

First of all, the rules are easier to learn than they first appear. Stated in a row, they have an alienating effect: so abstract and so complicated. But once you are familiar with distributed terms you will find yourself looking over syllogisms and quickly spotting their validity or invalidity.

Remember: When you have written a syllogism in standard form, go over it to circle all distributed terms. This will make the application of the second and third rules even faster.

Venn diagrams have the great advantage of resting on an obvious principle: Because the premises of a valid argument make the conclusion true, diagramming the premises should make the conclusion appear. However, this method is often harder to get the hang of than it looks. Before deciding to stay with it, make sure that you feel comfortable with the procedures for diagramming an entire syllogism.

One thing that leads to little errors in the use of Venn diagrams is the crucial difference between their appearance in logic and the appearance you may be familiar with from a math course. When making the diagram of a set in math, you shade in to show that an area is full. When diagramming an A- or E-claim, however, you shade to show that the area is empty.