Proof vs. Justification

I would like to try to clarify a crucial point that came up in class today. Consider the following argument for an anti-Thalean conclusion:

1. Water is H2O.
2. Some things are not H2O.
3. Therefore, (1) and (2). (from 1,2 by Conjunction)
4. If (3), then not everything is water.
5. Therefore, not everything is water. (from 3,4 by Modus Ponens)

(1-5) is a valid argument. Its premises are plausible--we do not have good reason to doubt them. So we are plausibly justified in believing that they are true. But since the argument is valid, we are plausibly justified in believing that the conclusion is true as well. So barring a good argument that one of the premises in (1-5) is false, we are plausibly justified in accepting the conclusion. So we should accept the conclusion.

My point in class is that, though I believe the foregoing is correct, we should not believe either (a) that (1-5) is a *proof* of its conclusion, in the mathematical or strictly logical sense, or (b) that the argument is no good unless Thales (or a Thalean) would be *forced* to accept all of its premises. Anyone can be so stubborn so as to resist a premise. But they are not playing the same game we are. The game is not to force others to believe so and so; rather, it is to figure out what we are plausibly justified in believing, given our evidence.

Some further comments are in order.

First, even if we accept (1-5), we are not entitled to *ignore* those who do not. Recall that it's plausible to accept the premises in (1-5) provided we lack good reasons to doubt them. Now if Thales, or a Thalean, comes along and gives a valid argument for the conclusion that some premise in (1-5) is false, and backs up the premises with reasons, then we no longer lack good reasons to doubt the premise. Thus, we should either no longer accept the premise in question or we should find what is wrong with the objection to it. A nice thing about validity is that we know that if the conclusion of the objection is false, one of the premises must be false as well. Takeaway point: THe goal of rational inquiry is to determine what is most plausible. The goal is not to make those who disagree cry "Uncle".

Second, different people are justified in believing different things. You have a justified belief about the color of your underwear, and I do not have a similarly justified belief, since you have evidence about the color of your underwear that I lack. What is reasonable to believe is what is best supported by your evidence. That evidence is different for different people. So two people can reasonably believe different things. But when the question is important for rational inquiry, our goal is to find out what is correct. The best way to proceed in figuring out what is correct is to consider arguments. Those for whom the evidence supports answer A should give their reasons (arguments) for thinking that A is the case. Those for whom the evidence supports answer B should give their reasons (arguments) for thinking B is the case. If it cannot be the case that both A and B are correct, the arguments will help us sort out whether it is more plausible that A is the case or that B is the case. Takeaway point: Rational inquiry is about sharing evidence to better justify our beliefs in answers to the questions that we are interested in (be they scientific, philosophical, or what have you).

Third (and finally!), given the above, it is hopefully clear that the following objection is no good:

Argument A does not prove its conclusion. Therefore, argument A is no good.

In the mathematical/logical sense of "proof", there is precious little that can be proven. (This is so despite the fact that infinitely many propositions can be proven in the strict mathematical/logical sense! What I mean is that few of the conclusions that we encounter on a day to day basis or in science or philosophy admit of anything like mathematical/logical proof.) In the strict sense of "proof", no one can prove that you have a face or that the sun will come out tomorrow. But that no one can prove such things is pretty clearly a poor reason for you to believe that you have no face and that the sun will not come out tomorrow.

I apologize about the length of this post; I think these issues are of vital importance, however. While the picture of rational inquiry I have outlined might be wrong in detail, and is certainly debatable (recall that we can rationally inquire about rational inquiry itself!), I believe it is substantially correct. Please feel free to comment about any aspect that you agree with/disagree with/find unclear/etc.