First, logic is the study of the forms of arguments and of the parts of arguments. What exactly do I mean by the phrase form of argument? The basic notion can be introduced with an example. Here’s an example of an argument:
A All humans are mortal. Socrates is human. Therefore, Socrates is mortal.
We can rewrite argument A by putting each sentence on its own line:
B All humans are mortal.
Socrates is human.
Therefore, Socrates is mortal.
Now, to demonstrate the important notion of the form of an argument, I will substitute letters for similar items throughout B, like this:
C All S is P.
a is S.
Therefore, a is P.
All I have done in C is to put "S" for "human" and "humans," "P" for "mortal," and "a" for "Socrates"; and there we have the form of the original argument in A. So argument form C is the form of argument A. And each individual sentence of C is the sentence form of its respective sentence in A. So if you want a definition of "form," you can use this (though it’s not exactly a rigorous definition): The form of an argument is what you get after you replace different words, or sentences, that make up the argument with letters; the letters are called variables. Just like variables can stand for various numbers in math, variables can stand for various words, or sentences, in logic. All right, now argument forms like C are very important in the study of logic. And the parts of argument forms -- by which I mean such sentence forms as the first line -- "All S is P," are equally important. In a logic class you would learn how to determine what the forms of various sentences and arguments are; we do not have time for that, but I think you can at least understand the basic concept of logical form. That’s all I want you to understand right now: what logical form is.
There is a very good reason why attention to argument and sentence forms is important. The reason is this: Form is what makes an argument valid or cogent. That’s very important and it bears repeating: form is important because it determines whether an argument is valid or not, or cogent or not. So next let’s look at part (2) of our definition of "logic," which concerns validity and cogency.
Part (2) says this: logic is the study of the qualities of validity, cogency, and soundness, and strength. Roughly, if an argument is valid or cogent, then the conclusion really does follow from the premises; in other words, if the premises are true, then, it follows that, the conclusion is true; in yet other words, the premises (if true) actually give one good reason for believing the conclusion.
Now, there are two different ways that the conclusion can follow from the premises: the argument can be valid or it can be cogent. Those are the two ways. These are different, and mutually exclusive properties; an argument cannot be both valid and cogent. But if an argument is one or the other, then the conclusion does follow from the premises.
Here then is what "valid" means. I will define and discuss "cogent" later.
An argument is valid if, and only if, when the premises are all true, then the conclusion must be true.
And validity is the property of being valid. Now, validity is a conditional notion. Look at the definition of "valid": it does not say that the premises have to be true. It doesn’t say that the conclusion has to be true. But it does say that if the premises are true, then the conclusion has to be true. As far as validity is concerned the premises might be completely and obviously false! So let me show you an argument that is valid, but which has totally false premises:
D All dogs have eight legs.
The President is a dog.
Therefore, the President has eight legs.
This is, strange to say, a perfectly valid argument. Remember, in logic, "valid" doesn’t mean anything more than what we define to mean. So the fact that an argument is valid, in logic, does not necessarily mean that it is a good argument. In fact, it might be a really bad argument, just like argument D. But argument D is, at least, valid. What does that mean, in this case? Something like this: suppose it were true that all dogs had eight legs; and suppose, just suppose, that the President really were a dog; well, in that absurd imaginary world, the President would have to have eight legs. The conclusion has to be true, if the premises are true. So the argument is valid, even though it has false premises. Not to mention a false conclusion.
But just a bit ago I said that form is what makes an argument valid. But I also said that a valid argument is one where, if the premises are true, then the conclusion must be true -- or here’s a way to put it more briefly: the premises make the conclusion necessary. Now put these two propositions together:
Form makes an argument valid.
If an argument is valid, then the premises make the conclusion necessary.
Putting these two claims together, you can see that
Form makes an argument such that the premises make the conclusion necessary.
Another way of putting this thought is by saying that you can see whether the premises make the conclusion necessary just by looking at the form of the argument. That’s why form is so important. Look, for example, at form C. In fact, any argument that follows the form C is valid: you can see that just by reading C. Now look at D -- it fits that form and is valid. Or to take another example, look at this argument:
E All dogs are canines.
Fido is a dog.
Therefore, Fido is a canine.
And since E follows form C, it’s a valid argument. Its conclusion must be true if its premises are true.
All right, that is enough, I hope, to introduce you to the notion of validity. Validity is a really basic, essential notion in logic, since it is a basic requirement for an argument to be good. But validity by itself isn’t enough to make an argument good.
What more is needed? True premises. So suppose we have a valid argument with true premises. Then, we will say, we have a sound argument. Here’s a definition:
An argument is sound if, and only if, (1) the argument is valid and (2) all of its premises are true.
So suppose we have a sound argument. An excellent example is B. In this case we have an argument where, first, if the premises are all true, then the conclusion must be true; and, second, it so happens that the premises are all true. What follows? That the conclusion must be true. That’s the dandy thing about soundness: if you know an argument is sound, then you know that the conclusion of the argument is true. By definition, all sound arguments have true conclusions. So soundness is a very good quality for an argument to have.
Now, the premises of an argument can give you reason to believe its conclusion, without making the conclusion necessary. Suppose you have an argument in which the premises make the conclusion probably true. That might still be a good argument. Such an argument we call cogent. So here’s a definition of "cogent":
An argument is cogent if, and only if, supposing the premises are all true, then the conclusion is probably (but not necessarily) true.
And cogency is the property of being cogent. Now, exactly what "probably" means is a matter of considerable debate in philosophy. And we simply do not have time to examine that debate right now. Still, you can understand what I mean reasonably well. Here, for example, is a cogent argument:
F There is a barrel jammed full of ordinary marbles, of different colors.
Without looking, I pulled out 100 marbles from various holes in the lid; 95 of the marbles I pulled out were red.
Therefore, the next marble I pull out, without looking, from another hole in the lid, will be red.
This is, I claim, a cogent argument. That means that if the two premises are true, then probably the conclusion is true; for all I know it doesn’t have to be true. And notice this: maybe I’m lying and there is no barrel, or maybe all of the marbles were blue. But that wouldn’t matter to my claim that the argument is cogent. If the argument is cogent, then supposing the premises to be true, the conclusion is probably true. Like validity, cogency is a conditional property.
And also like validity, the cogency of an argument can be assessed by examining the form of the argument. Consider, for example, the form of argument F -- we might say it basically follows something like this pattern:
G 95% of observed F’s were G.
Therefore, probably, the next F observed will also be G.
I’m saying that practically any argument that follows form G will be cogent. Now, there are some complications that I am ignoring here; for example, suppose we’re working with a deck containing 100 cards, and we know in advance that five of them are special cards called "jesters." All the other cards cards are called "royalty." Then, suppose it’s true that 95% of drawn cards were royalty; well in that case, the five cards that are left are jesters! So in that case the premise would lead you conclude that the next observed card will not be royalty -- exactly the opposite of what argument G would say. If we were studying inductive logic (as you would in Philosophy 150), then we would go into this in more detail. We would talk about background assumptions, about a random sample, having a large enough sample size, and so forth. But for now let’s stick with the simpler story. For simplicity we can say that any argument that follows form G is cogent. Just bear in mind that G is a simplification.
Now just as you added true premises to a valid argument to get soundness, you can add true premises to a cogent argument to get a strong argument. So we can define strength, for arguments, as follows:
An argument is strong if, and only if, the argument is cogent and all of its premises are true.
Similar things to what I said about soundness can be said about strength. If you know an argument is strong, then you know that, if the premises are true, then its conclusion is probably true; and since you do know that its premises are true, then you know that its conclusion is probably true.
Basically, what we mean by "good argument" is simply "sound or strong argument." If you have offered a sound or strong argument in defense of your view -- a philosophical conclusion -- then you have stated a true view, or at least a probably true view. And the premises of your argument support, or, with some sophisticated complications aside, justify your belief in the conclusion. So that’s why good argument are so important: in philosophy, a good argument is the closest thing we have to a guarantee that a belief is true. If you’re armed with a good argument you have helped to justify your belief in the conclusion, and remove doubts about it.
Now we’re ready to understand a very important distinction in philosophy. Namely, the difference between deduction, or deductive logic, and induction, or inductive logic. Here are some definitions:
Deductive logic is the study of arguments that aspire to be, at least, valid.
Induction logic is the study of arguments that aspire to be, at least, cogent.
The reason I have these in terms of what the arguments "aspire" to be is that an argument can be properly the subject of deductive logic even though it’s not valid or cogent; it can be studied by logic even though it fails to be what it aspires to be. Anyway, then, deduction is concerned with validity; induction is concerned with cogency. So in deductive logic you’ll study forms of arguments such that the conclusion must be true if the premises are true; and in inductive logic you’ll study forms of arguments such that the conclusion is probably true if the premises are true. That’s the difference between deduction and induction, and deductive logic and inductive logic.
Now remember that we started this excursion into validity and so forth by way of explaining the definition of "logic" I gave. So let’s get back to that. Logic is the study of what makes something a good argument; but it is also the study of how to tell whether or not an argument is any good. Studying logic is a little like studying medicine. In medical school one studies what makes a person healthy, as well as how to tell whether a person is healthy. In logic and medicine (and many other fields generally), one learns the standards something (such as good arguments and healthy people) must meet, as well as how to tell whether those standards are met in particular cases (of arguments and people, for example).
So now here’s the third part of the definition of "logic": logic is the study of how to construct, identify, interpret, and evaluate various kinds of arguments. Let me just take up each one of these words, "construct," "identify," "interpret," and "evaluate" in turn.
To begin with the construction of arguments. We do all, or at least should, construct arguments for our beliefs. We back up what we say, with reasons. We marshall evidence, state our grounds for belief, and give justifications. Someone who never does these things would be, I think, just irrational and unthinking, but I doubt there is any person here who is so irrational and unthinking that he, or she, never does these things. However that may be, logic is, in part, the study of how to construct one’s own arguments well, so that they display the aforementioned virtues of validity or cogency, and soundness or strength. So logic will help you do what you do already -- only better.
Logic is also the study of how to identify arguments, about a huge variety of different subject matters. This is very important for being able to use logic in everyday life; the first step in assessing the arguments of others is to identify when and where others have made arguments. After all, not all nonfiction writing you come across does contain arguments. So to evaluate a passage from a logical point of view, first you’ve got to learn how to distinguish argumentative prose -- writing containing arguments -- from mere rhetoric, explanations, the giving of examples, and other kinds of nonargumentative prose.
Logic is, finally, the study of how to interpret and evaluate actual, real-life arguments -- arguments of various kinds. In other words, to study logic is, in part, to study how to restate arguments you find in their real-life contexts (once you have found them) in a very clear manner, and then to judge whether those arguments are valid or cogent, first of all, and if so, whether they are also sound or strong.
Learning the construction, identification, interpretation, and evaluation of arguments are all important parts of learning logic, and well worth practicing, but in this course we won’t have time to do that. We will, as is the case with a lot of philosophy, have learn those things by doing. But there is, after all, a great deal that one can learn about logic by doing it.
![[Home]](wikipedia.png)