Thursday, March 12, 2009

Does Science Produce Knowledge?

The following seem to be an inconsistent triad:
  1. The ideal gas law is a paradigm case of scientific knowledge.
  2. All items of knowledge are true propositions.
  3. The correspondence theory of truth.
Since the ideal gas law, taken as a literal statement, either assumes the existence of things that don't exist or doesn't apply to anything and is thus empty, the ideal gas law is cannot be a substantive, literally true proposition. Either we have to deny that this is a major achievement of scientific knowledge, or we have to deny that truth is a necessary condition of knowledge, or we have to deny that an idealized law about non-existent entities is false.

For (1), you could substitute almost any bit of science you like, and it still raises the problem. E.g., Newton's Laws are a paradigm advancement of scientific knowledge. Copernican astronomy is an advance in knowledge over Ptolemaic astronomy. Most of science is either heavily idealized, has been shown to be (strictly speaking) false in the light of more recent theories, or will likely be shown to be false in the light of future theories.

One might consider various realist ways out of the problem. So, structural realists say that there is a certain core of science that is true, and so is knowledge. But then, the problem still applies for most of science. While we think that a certain law counts as knowledge, really only the structure underlying that law does. Other types of realist might argue that science at least gets approximate truth, but this requires that we weaken (2) such that knowledge only requires approximate truth.

How should we get out of this problem? And can you point to anyone who has explicitly wrestled with this issue?


Dan said...

Yes. Galileo wrestles with this issue, and the answer (which I agree with) is that idealized laws are true, in the sense that they correspond to the world. In the Dialogue, Simplicio objects to one of Salviati's arguments:

"[...] these mathematical subtleties are true in the abstract, but when applied, they do not correspond to sensible physical matter" (193).

And again:

"Material spheres are subject to many contingencies to which immaterial [i.e., mathematical] ones are not subjected" (198),

Salviati, the voice of Galileo, replies:

"Oh, I easily grant you all these things, but they are quite irrelevant. [...] It would have been better for you to concede the conclusion, but to do so conditionally; that is, to concede that if there should be any material spheres and planes and if they should be and remain perfect, then they would touch at a single point."

Of course, if we say that the ideal gas law applies conditionally to ideal gases, we are left with the question how that law tells us anything about the real world (as it seems to do). Galileo gives the start of an answer by saying that it is possible to account mathematically for "impediments" and the like. That is to say, when looking at real world objects, we note the differences between them and our ideal objects and then the task is to bear in mind, or even calculate, the effects of those differences (to the extent that this is practical in a given context).

How does a conditional claim say anything about the real world? Here's the beginning of an answer: things in the real world really would behave in the stated way (if the claim is true) in the idealized circumstances. In that way, it is a claim about what exists, not a claim about ideal objects.

That concludes my break from paper-writing. It's a rough answer, but it will have to do.

Dan said...

I want to add to my suggestion at the end that the idealized circumstances need not be stated explicitly, nor need the theorizer even be aware that the real world departs from those ideal conditions. I won't spell this out in detail, but I believe that this allows me to maintain that Newtonian mechanics was true and REMAINS true today, and to view subsequent scientific progress largely as a specification and accounting of "impediments".

Matt Brown said...

Thanks, Dan. This seems cogent, but I think it's going to get us into something weird about the truth-makers of these statements. Some options:

1. Real universals. There is really some object, a universal, in the actual world, but outside of space and time, which makes the ideal laws true, even though it is never active.

2. Possible worlds. While not operative in the actual world, there is some nearby possible world in which the antecendent obtains, and the law obtains. The counterfactual nature of your example seems to support this. Lewisian modal semantic craziness ensues, though. What about the worlds in which the antecedent obtains, and then weird (but possible) things happen, and the law doesn't obtain?

3. Nomological machines. Build one of Nancy's nomological machines, and the laws obtain always (and only) in such machines. This would require that building such a machine would be possible, which it isn't, on the literal interpretation of the ideal gas law.

Per said...

I actually like the two realist answers you suggested. Why not accept one of them. I prefer the claim that the core of science is true, but a lot of the other stuff is not.

Are there unacceptable consequences that result from accepting this (or the other realist option)? You found specific problems with Dan's suggestions, but is your 3 premise puzzle still a puzzle given the realist response about core science? After all, it seems like such a position is consistent with also claiming that most scientific knowledge outside the core of true structural facts, is nonetheless quite probable.

What's the problem here?

Dan said...

I just want to say that I have responses to Matt, but no time to discuss them right now.

Asur said...

From the realist perspective, I don't see any reason to believe that there are any core truths or structural facts immune to possible revision.

The entire edifice seems one of approximation, given that once 'truth' is treated as such knowledge and all the rest must be as well.

I don't see abandonment of certainty in favor of probability as a weakness--rather, it seems to be the source of science's strength; its methodology and a spirit of critical inquiry.

Replacing the notion of binary truth values with one of degrees of truth based on approximation to reality seems the most effective solution to the problem of scientific knowledge.