Logic Tutorial, Part 2.
Formal Logic

(c) 2017 by Barton Paul Levenson

The basic premise of logic is that contradictions are impossible. We all know situations where they exist--John is both "Marsha's husband" and "Betty's father" without being two different people--but I mean an "absolute contradiction" or "contradiction in terms." An example of a contradiction:

2 + 2 = both 4 and 7.

This is wrong because it implies a contradiction--the sum of two and two cannot be both four and seven, because four is not seven, and seven is not four. Either 2 + 2 = 4, or 2 + 2 = 7, but they can't both be true.

Given this, one can construct an elaborate system of logic. I like to phrase arguments in a particular form called a "syllogism." Syllogisms have three parts:

1. A major premise that states a general situation.
2. A minor premise that cites a specific instance.
3. A conclusion implied by the premises.

In addition, the premises (parts 1 and 2 above) must share a common term. For instance:

The logic here is perfect, and the syllogism is therefore constructed correctly. The argument is valid, meaning the conclusion follows logically from the premises. Nonetheless, this is a bad argument, because the major premise is false. A single contrary case, known to be true, can replace the minor premise to show how false the major premise is:

Once again, the logic is correct, but the conclusion is false because the major premise is false. Both premises must be true and the logic must be valid in order to reliably reach a true conclusion.

An argument with good logic is valid.

An argument with good logic and true premises is sound.

Valid arguments are good, but sound arguments are even better. Keep this in mind: Just because something is logical doesn't mean it's true. If one or more premises are false, the conclusion will likely be false as well, even if the logic is flawless. People often say a position on some issue is "irrational" or "illogical" because they disagree with it, dislike it, or think it false. That is not what those words mean.

Note, and this is very important, that you cannot find truth by logic alone. Logic only finds new premises from old premises. If your original premises are false, your conclusion will usually be false, no matter how good your logic.

Let me rephrase that, and display it separately, because it's very, very important:

If one or more of your premises is false, your conclusion will usually be false, even if your logic is perfect.

Douglas Adams, in The Hitchhiker's Guide to the Galaxy (1979), introduced a computer called Deep Thought. When it was first briefly turned on it started from "I think, therefore I am" and deduced the existence of rice pudding and income tax before it could be shut off again. This is cute, but probably not possible.

Most arguments in speech and in writing are not phrased as syllogisms. It's a good discipline to translate an argument into a syllogism before you analyze it. That makes it much easier to pick out the flaws, if any.