Most of the arguments philosophers concern themselves with are--or purport to be--deductive arguments. Mathematical proofs are a good example of deductive argument.
Most of the arguments we employ in everyday life are not deductive arguments but rather inductive arguments. Inductive arguments are arguments which do not attempt to establish a thesis conclusively. Rather, they cite evidence which makes the conclusion somewhat reasonable to believe. The methods Sherlock Holmes employed to catch criminals (and which Holmes misleadingly called "deduction") were examples of inductive argument. Other examples of inductive argument include: concluding that it won't snow on June 1st this year, because it hasn't snowed on June 1st for any of the last 100 years; concluding that your friend is jealous because that's the best explanation you can come up with of his behavior, and so on.
It's a controversial and difficult question what qualities make an argument a good inductive argument. Fortunately, we don't need to concern ourselves with that question here. In this class, we're concerned only with deductive arguments.
Philosophers use the following words to describe the qualities that make an
argument a good deductive argument:
Validity is a property of the argument's form. It doesn't matter what the premises and the conclusion actually say. It just matters whether the argument has the right form. So, in particular, a valid argument need not have true premises, nor need it have a true conclusion. The following is a valid argument:
Neither of the premises of this argument is true. Nor is the conclusion. But the premises are of such a form that if they were both true, then the conclusion would also have to be true. Hence the argument is valid.
To tell whether an argument is valid, figure out what the form of the argument is, and then try to think of some other argument of that same form and having true premises but a false conclusion. If you succeed, then every argument of that form must be invalid. A valid form of argument can never lead you from true premises to a false conclusion.
For instance, consider the argument:
This argument is of the form "If P then Q. Q. So P." (If you like, you could say the form is: "If P then not-Q. not-Q. So P." For present purposes, it doesn't matter.) The conclusion of the argument is true. But is it a valid form of argument?
It is not. How can you tell? Because the following argument is of the same form, and it has true premises but a false conclusion:
Since this second argument has true premises and a false conclusion, it must be invalid. And since the first argument has the same form as the second argument (both are of the form "If P then Q. Q. So P."), both arguments must be invalid.
Invalid arguments give us no reason to believe their conclusions. But be careful: The fact that an argument is invalid doesn't mean that the argument's conclusion is false. The conclusion might be true. It's just that the invalid argument doesn't give us any good reason to believe that the conclusion is true.
If you take a class in Formal Logic, you'll study which forms of argument are valid and which are invalid. We won't devote much time to that study in this class. I only want you to learn what the terms "valid" and "invalid" mean, and to be able to recognize a few clear cases of valid and invalid arguments when you see them.
Sometimes an author will not explicitly state all the premises of his argument. This will render his argument invalid as it is written. In such cases we can often "fix up" the argument by supplying the missing premise, assuming that the author meant it all along. For instance, as it stands, the argument:
is invalid. But it's clear how to fix it up. We just need to supply the hidden premise:
You should become adept at filling in such missing premises, so that you can see the underlying form of an argument more clearly.
Sometimes a premise is left out because it is taken to be obvious, as in the engineer argument, and in the exploding car argument. But sometimes the missing premise is very contentious, as in the abortion argument.
Sound ArgumentsAn argument is sound just in case it's valid and all its premises are true.
is an example of a valid argument which is not sound.
We said above that a valid argument can never take you from true premises to a false conclusion. So, if you have a sound argument for a given conclusion, then, since the argument has true premises, and since the argument is valid, and valid arguments can never take you from true premises to a false conclusion, the argument's conclusion must be true. Sound arguments always have true conclusions.
This means that if you read Philosopher X's argument and you disagree with his conclusion, then you're committed to the claim that his argument is unsound. Either X's conclusion does not actually follow from his premises--there is a problem with his reasoning or logic--or at least one of X's premises is false.
When you're doing philosophy, it is never enough simply to say that you disagree with someone's conclusion, or that his conclusion is wrong. If your opponent's conclusion is wrong, then there must be something wrong with his argument, and you need to say what it is.
Persuasive ArgumentsUnfortunately, merely having a sound argument is not yet enough to have the persuasive force of reason on your side. For it might be that your premises are true, but it's hard to recognize that they're true.
Consider the following two arguments:
Both of these arguments have the form "P or Q. not-Q. So P." That's a valid form of argument. So both of these arguments are valid. What's more, at least one of the arguments is sound. If God exists, then all the premises of Argument A are true, and since Argument A is valid, it must also be sound. If God does not exist, then all the premises of Argument B are true, and since Argument B is valid, it must also be sound. Either way, one of the arguments is sound. But we can't tell which of these arguments is sound and which is not. Hence neither argument is very persuasive.
In general, when you're engaging in philosophical debate, you don't just want valid arguments from premises that happen to be true. You want valid arguments from premises that are recognizable as true, or already accepted as true, by all parties to your debate.
Hence, we can introduce a third notion:
A persuasive argument is a valid argument with plausible, or obviously true, or antecedently accepted premises.
These are the sorts of arguments you should try to offer.
ConditionalsA claim of the form "If P then Q" is known as a conditional. P is called the antecedent of the conditional, and Q is called the consequent of the conditional.
In this class, you can take all of the following to be variant ways of saying the same thing:
Now, just because P entails Q, it doesn't follow that Q entails P. However, sometimes it's both the case that P entails Q and also the case that Q entails P. When so, we write it as follows (again, all of these are variant ways of saying the same thing):
For example, being a male parent is both necessary and sufficient for being a father. If you're a father, it's required that you be a male parent. And if you're a male parent, that suffices for you to be father. So we can say that someone is a father if and only if he's a male parent.
ConsistencyWhen a set of propositions cannot all be simultaneously true, we say that the propositions are inconsistent. Here is an example of two inconsistent propositions:
When a set of propositions is not inconsistent, then they're consistent. Note that consistency is no guarantee of truth. It's possible for a set of propositions to be consistent, and yet for some or all of them to be false.
Sometimes we say that a proposition P is incompatible with another proposition Q. This is just another way of saying that the two propositions are inconsistent with each other.
A contradiction is a proposition of the form "P and not-P."
Sometimes it's tricky to see that a set of propositions is inconsistent, or to determine which of them you ought to give up. For instance, the following three propositions all seem somewhat plausible, yet they cannot all three be true, for they're inconsistent with each other:
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Last Modified: 03/26/02
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