Logic in an Argument

People cringe when one talks about using "logic". This is sad, and kind of odd, since logic is quite common - that is, used by everyone all the time - and even untrained people can be very logical. Long ago, there was a term for this: "common sense". One of the most wonderful of the powers of common sense is to have a basic and reliable awareness of what things are logical.

But people think logic is very tech and get scared. Logic is of course very high tech, if applied in it full rigor - computers work because of, or rather are physical implementations of, pure logic, sometimes called "propositional calculus", which sounds very hard, but is quite simple: there are just a handful of things to deal with, some of which feel like math, but are lots easier than almost any math you've seen, since there are only two numbers, zero and one (also called "false" and "true") and a very few operations: AND, OR, NOT, and a couple of extensions, like "IMPLIES" and "IF-AND-ONLY-IF", and the famous "XOR" we talked about some time ago. I cannot give you the whole thing today, but it would not take you long to grasp. It's also fun.

Then there's the other part, called "predicate calculus", which is the main technique used in the formal arguments we are talking about at present. These are built on top of the propositional calculus, but we add two new ideas, called the "universal" and the "particular" statements, both of which can take an affirmative or a negative form. So there are four versions of these, named for the first four vowels. Each uses "variables" like x, y, z - or you can think of them as "pronouns" - when we actually do stuff, we fill in some actual words for the x, y, and z. Here they are:

A: All x are y.
E: No x is y.
I: Some x is y.
O: Some x is not y.

Now that we have these statement forms, we can make the grand traditional and classical form of logic, which is called the "syllogism" and is the starting point for all formal argument. The syllogism is simply three statements: two premises and a conclusion. As Shallo says in Scholastic Philosophy: "A syllogism is an argumentation consisting of three explicit propositions so connected with each other that one of them necessarily follows from the other two." That is, whenever we know both of the two premise statements are true, the conclusion MUST be true.

Here's an example, the first of all syllogisms, the form which is called "BARBARA" (Yes they all have names, some very curious words, but I have no time to go into them just now.)

MINOR premise: All "M" are "S".
MAJOR premise: All "P" are "M".
CONCLUSION: so All "P" are "S".

It does not matter what you put in for the three "variables": every time you assume the premises as I have stated them here, the above conclusion MUST follow. You can get some odd things depending on what you put in, and you can even make up fantasies - but the truth remains. That's what logic means. It's a way of checking that you are talking sensibly, and accurately.

It does NOT - repeat - does NOT tell you that the PREMISE statements are true!

It does NOT - repeat - does NOT tell you that the true statements apply to reality.

Logic simply says that the form of the argument is correct.

Huh? What good is that?

Well, here's what Chesterton said, and we ought to have it at our fingertips as we proceed, since it summarizes our tool, in both its power and its weakness:

Logic and truth, as a matter of fact, have very little to do with each other. Logic is concerned merely with the fidelity and accuracy with which a certain process is performed, a process which can be performed with any materials, with any assumption. You can be as logical about griffins and basilisks as about sheep and pigs. On the assumption that a man has two ears, it is good logic that three men have six ears, but on the assumption that a man has four ears, it is equally good logic that three men have twelve. And the power of seeing how many ears the average man, as a fact, possesses, the power of counting a gentleman’s ears accurately and without mathematical confusion, is not a logical thing but a primary and direct experience, like a physical sense, like a religious vision. The power of counting ears may be limited by a blow on the head; it may be disturbed and even augmented by two bottles of champagne; but it cannot be affected by argument. Logic has again and again been expended, and expended most brilliantly and effectively, on things that do not exist at all. There is far more logic, more sustained consistency of the mind, in the science of heraldry than in the science of biology... There is more logic in Alice in Wonderland than in the Statute Book or the Blue Book. The relations of logic to truth depend, then, not upon its perfection as logic, but upon certain pre-logical faculties and certain pre-logical discoveries, upon the possession of those faculties, upon the power of making those discoveries. If a man starts with certain assumptions, he may be a good logician and a good citizen, a wise man, a successful figure. If he starts with certain other assumptions, he may be an equally good logician and a bankrupt, a criminal, a raving lunatic. Logic, then, is not necessarily an instrument for finding truth; on the contrary, truth is necessarily an instrument for using logic - for using it, that is, for the discovery of further truth and for the profit of humanity. Briefly, you can only find truth with logic if you have already found truth without it.
[GKC Daily News Feb 25, 1905 quoted in The Man Who Was Orthodox]

And there you have it. Let us say it again, and burn it into our thoughts, and keep it with us: You can only find truth with logic if you have already found truth without it.

But we will need logic: we need the syllogism. If we are going to argue, and not have it degenerate into a quarrel, or a boxing match, we need to have some rigorous form. (Hey - even boxing matches have a form, and rules!) Next time we'll see the form, and then the fun will begin.