Thursday, July 9, 2009

Is truth explanatory?

Rorty (in Lepore, ed., Truth and Interpretation, 1986) claims that the concept of truth does not enter into explanations. Suppose, however, that I observe physicians and magicians attempting to cure diseases. I notice that the physicians are often successful, while the magicians are no more successful than chance. Moreover, suppose that I know nothing about the actual disciplines of medicine and magic. I might, nonetheless, form the explanatory hypothesis that:

  1. Physicians are more effective at healing because their beliefs about the causes of diseases are more often true than those of the magicians.

Rorty considers simpler versions of this sort of explanation (he considers the case of a person getting a destination because he knows where it is), and thinks that those are only "promissory notes for explanations", and that the full explanation will say what the contents of the beliefs are, without the need to refer to truth. Thus, Rorty thinks that (1) is enthymematic (that much is obvious—there is a lot of background assumed in (1)), and indeed enthymematic for an explanation that makes no reference to truth. Presumably this expanded explanation is something like this:

  1. Physicians are more effective at healing because physician A believes that gout is caused by elevated levels of uric acid, and gout is caused by elevated levels of uric acid, and physician B believes that ..., and ..., and magician X believes that gout is caused by demons, but gout is not caused by demons, ..., and 'A, B, ...' is a list of most physicians, while 'X, Y, ...' is a list of most magicians.

It is a mistake, however, to take (1) to be enthymematic for (2). One reason is that the inference to (1) was an instance of inference to best explanation, and was an inference that one could make without anything like the sort of information involved in (2). A different reason for this is that we lose important explanatory information in passing from (1) to (2). We miss the regularity about physicians' and magicians' beliefs that is expressed by (1), a regularity that is not merely coincidental but itself explained, e.g., by the physicians' employment of the scientific method and the magicians' adherence to a secrecy that makes intersubjective testing impossible.

To take (1) to be enthymematic for (2) would be relevantly like replacing the explanation:

  1. About half of the coins I tossed landed heads because the outcomes of the throws are independent random variables, with probability 1/2 of landing heads, and hence it is statistically likely that approximately half of the coins I tossed land heads,
  1. About half of the coins I tossed landed heads, because six is about half of ten, and coin 1 landed heads, coin 2 landed heads, coin 3 landed tails, coin 4 landed tails, coin 5 landed heads, coin 6 landed heads, coin 7 landed heads, coin 8 landed heads, coin 9 landed tails and coin 10 landed tails.
First, one can know (3) without knowing anything like the kinds of details in (4), and make an explanatory inference to (3) without making any explanatory inference to (4). Second, (3) contains additional information—information about the statistical facts. Claim (4) is compatible with it just being a coincidence that about half of the coins landed heads, just as claim (2) is compatible with it just being a coincidence that the doctors are better at treating disease, while (1) and (3) are explanatorily richer, making it clear that we are not dealing with mere coincidence.

The point has been made, in a somewhat different way, by Hartry Field. And Kitcher has run a similar argument, too. There is nothing original about the basic argument, but I think the comparison to (3) and (4) is illuminating.

Corollary: Truth enters into explanation of physical facts. But if it enters into explanation of physical facts, then either naturalism is false, or truth is a natural property. The prospects for seeing truth as a natural property are poor—that is something we see from the literature on truth, as well as from the fact that if truth were a natural property, then presumably a liar sentence could be formulated in the (first-order? I think so!) language of science. Hence naturalism is false.


Heath White said...


Suppose Rorty offers the following gloss:

Physicians are more effective at healing than magicians because, typically, what physicians believe to be the causes of illness are the causes of illness, while typically, what magicians believe to be the causes of illness are not the causes of illness.

Does that capture everything?

Alexander R Pruss said...

Yes, at the cost of a concept of reference (we're talking about what causes their beliefs refer to). But reference and truths are in central cases interdefinable. Thus, "R" refers to something whose name is "N" iff it is true that "x is an R". And "S" is true iff "The number 1 if S and the number 0 otherwise" refers to 1.

Alexander R Pruss said...

"x is an R" should read "N is an R". Or maybe just "R" or "the R". Anyway, it's the other direction that is relevant--defining truth via reference.

Heath White said...

Sorry, Alex, I'm not following the bit about the cost of the concept of reference. Are you making an argument like this?

1. If the truth of the belief that N is F does not explain anything, then the reference of the belief (perhaps via some mental 'N') does not explain anything.

2. The efficacy of beliefs is explained by their reference, e.g. to the causes of illness.

3. Therefore the efficacy of beliefs is explained by their truth.

I would agree with the general point that what we say about truth, and what we say about reference, stand or fall more or less together.

Alexander R Pruss said...

On reflection, I am making a more roundabout point. Anybody who for grand philosophical reasons (e.g., ones tied to anti-realism or to physicalism) rejects the idea that the truth of sentences is explanatory will have exactly the same grand philosophical reasons for rejecting the idea that the reference of definite descriptions is explanatory. So while your proposed explanation would let Rorty keep the point that truth is not explanatory, it would be at the expense of holding that reference is explanatory, which is just as problematic for him.

Your explanation makes use of this ternary relation: x believes of y that it is an F (e.g., Jones believes of uric acid buildup (a quasi-natural kind) that it is a cause of gout, while Smith believes of the northeastern foot imp (a supernatural kind) that it is a cause of gout). But what is it to believe of y that it is an F? It seems that it is to have a belief of the form "... is an F", where the subexpression "..." in fact refers to y. (There is also the issue of reference to F. In the above, I was careful with regard to use/mention of y, but I was not careful with regard to use/mention of F.) We may not be happy with this linguistic take on beliefs, but at least to a first approximation it seems right.

Alexander R Pruss said...

It looks like my (3) and (4) example is basically the same as Kitcher's Fischer's law example.

Here is a further thought for why (1) is to be preferred to (2) or at least not reduced to (2). There are cases where you can explain a phenomenon based on a specific set of laws L1, L2 and L3, and where you can instead explain the phenomenon based on law L*, where L* is more general than the conjunction of L1, L2 and L3, in the sense that the conjunction of L1, L2 and L3 entails L*, but L* does not entail all the three more specific laws. For instance, one might explain something in terms of details of the dynamical forces between molecules (L1, L2 and L3), or, more generally, in terms of the second law of thermodynamics (L*).

In such a case, there is something to be said for the L*-based explanation, because it is more robust (it will hold in some worlds where L* holds, but where the more specific laws are different; e.g., the second law of thermodynamics is compatible with many laws about the interactions of microparticles). In any case, whether the L*-based explanation is superior to the L1, L2 and L3 based explanation or not (there are purposes which are better served by the explanation in terms of more specific laws), nonetheless the L*-based explanation is typically seen by working scientists as a genuine and illuminating explanation.

Now, Rorty (and Horwich and others) will say that what explains the physicians' success and the magician's failure is that certain biomedical laws L1, L2 and L3 (actually, a lot more than three hold), and that the physicians have such-and-such beliefs, and the magicians have such-and-such beliefs, and from all this mess it follows that the physicians succeed and the magicians fail. But the explanation in terms of the higher likelihood of the truth of the beliefs arrived at using the scientific method is more robust because it holds not just in our world, but also in worlds where the specific biomedical laws and biomedically relevant non-nomic facts (such as that there is 21% oxygen in Earth's air) are different. The explanation works in all worlds in which the basic laws are sufficiently nice ("sufficiently nice" is a cool term of art that we mathematicians use--e.g., a function is "sufficiently nice" provided that it has all the desirable properties, like continuity, differentiability or integrability that are required to make the requisite theorems go through) that induction works. This seems relevantly like an explanation in terms of the second law of thermodynamics, or in terms of the law of conservation of energy.

(I myself don't think higher level law explanations are necessarily better, or even independent of the lower level ones, so for me the argument is weaker. But in the case at hand, the robustness encompasses not just variation in laws, but variation in particular facts.)

This isn't particularly original--a number of authors have tried to get at this robustness.