Deductive Strength
I. Deductive Strength is a label that we give to arguments that meet two conditions:
For an argument to be deductively strong for a person S, it must be
a) valid
AND
b) it is reasonable for S to believe the premises.
So while validity is an objective property of argument--arguments are either valid or invalid, whether or not S recognizes it--the reasonableness of the premises will, to some extent depend upon the other views that S has, S's background information, S's evidence, and so on.
If the premises are reasonable for S to believe, that means that S thinks they are true. And if the argument is valid, then it is an argument where the truth of the premises would guarantee the truth of the conclusion. So S is rationally committed to accepting the conclusion. The argument supports the conclusion for S.
But if S thinks that one or more of the premises are false, or even if S is not sure and suspends judgment about one or more of the premises, then the argument will not be strong for her. That is, the argument doesn't support the conclusion. The conclusion might be true, and the argument might be valid. It might even have all true premises. But unless S believes all the premises, they won't be adequate support to render the conclusion reasonable.
So consider John who believes, like all of us do, that "If the earth was flat, then ships sailing on the ocean would fall off." And John also believes that, "Ships sailing on the ocean do not fall off." So when John considers this argument:
1. If the earth was flat, then ships sailing on the ocean would fall off.
2. Ships sailing on the ocean do not fall off.
___________________________________
3. Therefore, the earth is not flat.
it is deductively strong. It is valid, and S believes the premises, so the argument supports the conclusion and S should accept it (John does), or S is being irrational.
This argument is also deductively strong for John:
1. If my textbooks and teachers are reliable, then the earth is round.
2. My textbooks and teachers are reliable.
______________________________________
3. Therefore, the earth is round.
This argument is weak for John, however:
1. The United States wins every war it engages in.
2. The United States is engaged in a war in Iraq.
________________________________
3. Therefore, the United States will win the war in Iraq.
John doesn't believe premise 1. Vietnam was a war that the United States engaged in, but did not win. So Vietnam is a counter example to 1. Premise 2 is true. And the conclusion may turn out to be true (John doubts it.) But this argument is not good support for its conclusion.
The same argument could be deductively strong for someone else, however. Suppose that Marion believed premise 1. Suppose that she had received a poor education and lots of people she trusts and believes, and who are normally good sources of information either never mentioned Vietnam, or they were mistaken about Vietnam too. So she believes 1. falsely. And she believes 2. And the argument is valid. So it meets the conditions of deductive validity for Marion. But if Marion were to learn about Vietnam, and become convinced that that was a war that the United States lost, then the argument would be weak for Marion too.
Inductive Strength
II. Inductive Strength: An argument is inductively strong for a person S when it meets three conditions:
For an argument to be inductively strong for S, it must be:
1) cogent
AND
2) the premises are reasonable for S to believe.
AND
3) the argument is not defeated by S's total evidence.
We add condition 3) for inductive strength because at best, cogent arguments would make their conclusions likely to be true if their premises are true. But there could still be a possibility that the premises are true but the conclusion is false. And S might have information that indicates that this is what has happened.
So consider Ellen who has read a New York Times article that cites several reputable studies that have found that most people in her neighborhood in Brooklyn are Democrats. Then Ellen considers her neighbor Amy. She doesn't have any particular reason to doubt that Amy is an exception, or in the non-Democrat minority. So this argument:
1. Most people who live in Brooklyn are Democrats.
2. Amy lives in Brooklyn.
____________________________
3. Therefore, Amy is a Democrat.
is inductively strong for Ellen.
But Michael, who also knows Amy, and who knows that Amy lives in Brooklyn, has listened to lots of anti-Democrat tirades from Amy. He's heard her say that she's a Republican and that she wouldn't be a Democrat if held a gun to her head. And he thinks she's sincere. So the same argument is weak for Michael. Notice that the premises are true and that they are reasonable for Michael to believe; the argument is not weak because he rejects a premise. It is weak because it is defeated by his total evidence.
For our purposes, an argument is defeated only under these circumstances:
An argument is defeated for S if and only if, the argument is cogent, the premises are reasonable for S to believe, but S believes the conclusion is false because it conflicts with S's total background evidence.
In other cases where the argument is ill-formed, or S suspends judgment about one or more premises, or S thinks that one or more of the premises are false, the argument is weak.