[Home]DefinitionOfLogic

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Today weíre going to study a subdiscipline of philosophy called logic. This is basically the study of argument -- by which we mean, not angry disagreements or fisticuffs, but instead the giving of reasons to believe things. So recall from last time the definition of "argument":

An argument is a set of statements, one of which (the conclusion), it is said or implied, follows from the others (the premises).

Itís extremely important in this class that you understand what arguments are, and that you distinguish them from other things. To give an argument is to give evidence, and then draw a conclusion from it; it is to give reasons to believe something, and then to state the belief. The statements that give expression to the evidence, or the reasons, are all called the premises. The thing one argues for is called the conclusion. You can think of a whole argument as a set of statements, comprising premise or premises, and the conclusion.

Now, there are other kinds of sets of statements besides arguments, such as explanations. Logic does not, or not primarily, concern itself with explanations. For example, suppose I offer an explanation for why there are tides: I talk about the gravitational effect of the moon and the sun on the oceans, and so on. Now, that isnít an argument. It is an explanation. In that case, Iím explaining why there are tides. Iím not trying to convince you that there are tides. We have already agreed that there are tides. The question the explanation answers is why there are.

On the other hand, suppose I argue for the following claim: "God exists." In other words, "God exists" is the conclusion of an argument I make. In that case I am not explaining why there is a God. If I tried to explain why there is a God, I would be assuming that there is a God. But if what Iím doing is arguing for the existence of God, then Iím not assuming that he exists; rather, Iím trying to convince you, or a skeptic anyway, that God exists.

So I think you can see the difference between an argument and an explanation. On the one hand, the function or purpose of an argument is to convince people who might be doubting the conclusion. On the other hand, the function or purpose of an explanation is to give the cause of some phenomenon which we observe, or are willing to assume actually occurs. To put it even more briefly, the purpose of an argument is to persuade, while the purpose of an explanation is to explain.

Just as a hammer is the tool of the carpenterís trade, an argument is the tool of the philosopherís trade. And, as I said last time, it shouldnít be too hard to see why philosophers work so much with arguments: philosophers carry to heroic lengths the human tendency to doubt sometimes the deepest, most fundamental of our beliefs. Because they want to overcome all of these doubts, they offer and examine arguments for various claims: the arguments are supposed to be what will rid us of the doubts. If we accept what we know is an excellent argument for a conclusion, and weíve refuted all the plausible arguments against that conclusion, then weíre very well-positioned to say that we know that the conclusion is true. Arguments, then, have the potential to give us knowledge and to rid us of doubts; thatís why arguments are so important.

But just as there are good and bad hammers, there are good and bad arguments. In fact, I imagine that there are a lot more bad arguments in the world than there are bad hammers. Let me give you an example of a bad argument. Suppose I wanted to argue for the claim that all killing is wrong. And suppose I was giving this argument to a bunch of people who supported the death penalty: they think that some killing is fine, as punishment of the worst murderers, say. So I argue as follows:

If one should never do X, all X is wrong. (X can be any action.)

One should absolutely never kill.

Therefore, all killing is wrong.

Would the supporters of the death penalty be impressed by this argument? Of course they wouldnít. They would say, "Youíre begging the question. In your argument, you say that one should absolutely never kill. But to prove that youíd have to prove that all killing is wrong -- which is what youíre trying to argue for. We disagree with your conclusion: we think that some killing is not wrong. And so of course we are going to disagree with your premise, that one should absolutely never kill. No indeed, in some cases one actually should kill: itís our grim duty, an unfortunately necessary part of justice."

So you can see that my argument just isnít going to work against those people. In it, I presuppose the conclusion: in other words, one of the premises assumes that the conclusion is true. This is an error in arguing. The kind of error has a name: begging the question. If my argument begs the question then in my argument I assume the very thing that Iím trying to argue for. Of course an argument that begs the question wonít, or shouldnít, convince anyone: if I assume what Iím arguing for, anyone who assumes differently will be unimpressed.

Begging the question is one of the ways that arguments can go wrong. There are many, many other ways; and those most common ways that arguments can go wrong are called fallacies. So begging the question is one kind of fallacy. You should make sure that you are not committing any fallacies yourself, when you argue.

Let me give you another example of a fallacy. Suppose I argue like this:

Ted is a good tennis player.

Therefore, Ted is good -- a morally good person.

Here the problem is that the word "good" has different meanings, which is to say that it is an ambiguous word. In the premise, we say that Ted is good at some particular activity, in this case tennis. But in the conclusion we say that Ted is a morally good person. Those are clearly two different senses of the word "good." And so of course the premise might be true, while the conclusion would still be false: Ted might be the best tennis player in the world, but a rotten person morally speaking. Appropriately, since it plays on an ambiguity, this sort of fallacy is called the fallacy of ambiguity.

Now youíre just going to have to trust me that there are zillions of other fallacies. Whole books have been written cataloging fallacies -- all the different kinds of ways that arguments can go wrong. Today weíre going to be less ambitious: weíre going to outline, in broad generalities, how arguments can go right. In other words, Iím going to introduce you to the study of good arguments, non-fallacious arguments -- which is to say that Iím going to introduce you to logic.

Here is a definition of "logic":

Logic is the study of good arguments and definitions; in particular, it is the study of (1) forms of arguments and their parts, (2) the qualities (of arguments) of validity, cogency, and soundness, (3) how to construct, identify, interpret, and evaluate various kinds of arguments, and (4) how to construct and evaluate definitions.

Traditional treatments of logic have included discussion of not just arguments, but the varieties and standards of definitions, as well. And the way Iíll present it, logic will include discussion of both arguments and definitions.

I want to introduce you to some of the most fundamental logical concepts, for two reasons. The first is that logic is one of the basic branches of philosophy, and so if Iím going to introduce you to all, or almost all, of the basic branches of philosophy, Iíd better introduce you to logic. The second reason is practical: namely, logic will help you understand better the rest of philosophy. So it also has practical value.

There is a good reason why logic will help you understand the rest of philosophy. I said last time that it is doubt about the meaning and justification of certain fundamental beliefs that motivates us to do philosophy. Well, very often to extricate us from these doubts what are needed are definitions that explain the meaning of our basic concepts, and arguments to justify, or give reasons for, various beliefs that weíre not quite sure about. Logic states the standards of good definitions and good arguments: it gives us the tools to see whether various proposed definitions, or arguments, are any good or not. It helps us to avoid fallacies.

So letís go back to the definition of "logic" I gave, and examine its various parts, leaving aside part (4), about definitions, for now.

Logic, like mathematics and physics, has a theoretical part and an applied part. Parts (1) and (2) of the definition together describe the theoretical part of logic, and (3) describes the applied part. And just as a nonmathematician learning physics should study mathematics in order to use or apply mathematics well, a nonlogician in any task that requires reasoning, such as confirming rational beliefs, should study logic to learn how to use or apply logic well. Moreover, like mathematics and physics (and many other things), you have to do quite a bit of practice if you want to gain any facility in using logic. Logic is a bit unlike other parts of philosophy in that way: in studying books in other areas of philosophy, such as ethics and metaphysics, youíll rarely see problems at the end of the chapter. But you might very well do problems in logic, in order to learn how to use logic. (Of course, thatís not to say that practice, of various sorts, would not help one to learn other areas of philosophy better. Itís just that the practice would be practice thinking the problems through.)


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Last edited February 2, 2001 11:34 am by PhillipHankins (diff)
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