Tooley’s Laws of Nature and Counterfactual Support

In “The Nature of Laws”, Michael Tooley argues that some proper subclass of the nomological truths are laws of nature, since laws should support counterfactuals and not all nomological truths do that.

He says, “If one says that all nomological statements support counterfactuals, and that it is a nomological truth that all salt when both in water and near gold dissolves, one will be forced to accept [that if this piece of salt were in water and were not dissolving, it would not be in the vicinity of a piece of gold], whereas it is clear that there is good reason not to accept [that].”  (Last line in first paragraph of section 3.)

I take it that he is using the following argument (reconstructed from the first paragraph of section 3) to show this:

  1. Suppose it is a law that all salt, when in water, dissolves.
  2. Nomological truths are true generalizations of the form (x)(Fx -> Gx).
  3. Then it is a nomological truth that all salt, when in water, dissolves (since laws are true).
  4. Then it must be a nomological truth that all salt, when in water and near gold, dissolves in water.
  5. So, it must also be a nomological truth that (L5) all salt that is in water and doesn’t dissolve isn’t near gold.  (This just follows from messing around with the material conditional in the generalization.)
  6. Laws support counterfactuals.  For example, the law in (1) supports the counterfactual that if some salt were in water, it would dissolve.
  7. Suppose, for reductio, that the derived nomological truth L5  is a supports counterfactuals.
  8. That (C8) if this piece of salt were in water and were not dissolving, it would not be in the vicinity of a piece of gold would be a counterfactual supported by L5.
  9. If a nomological truth supports a counterfactual, then the counterfactual is true.
  10. C8 is true.
  11. “It is clear that there is good reason not to accept” C8.  -><-
  12. L5 does not support counterfactuals.
  13. Some nomological truths do not support counterfactuals.
  14. Some nomological truths are not expressed by laws (since laws support counterfactuals by 6).

I think that this argument is valid: 14 depends on 13 and 6.  13 depends on 12.  12 depends on 7-11 (the reductio argument).  1,2,4, and 6 are premises.  3 follows from 2 and 1.  5 depends on 4.

You might think this argument is not sound, though.  3 claims that in the actual world, it is true that all salt dissolves in water.  10 asserts that if this piece of salt were in water and were not dissolving, it would not be in the vicinity of a piece of gold.  On first glance, you may treat this as a material or indicative conditional and think it claims that if this piece of salt is in water and not dissolving then such-and-such.  Of course, if 10 did say this, there would be contradiction between the antecedent of C8 and 3.   But! 10 does not say this, it merely asserts the counterfactual conditional if this piece of salt WERE in water and WERE not dissolving, it would not be in the vicinity of a piece of gold. So no funny business is going on there.

All of this a bit confusing though when all the details of the motivation are included.  I think that some of the lines of the argument are not strictly needed, and that it can be expressed more succinctly as follows:

  1. It is a nomological truth that all salt that is in water and doesn’t dissolve isn’t near gold.  (This was the old line 5.)
  2. Laws support counterfactuals.
  3. Suppose, for reductio, that the nomological truth in 1 supports counterfactuals.
  4. That (C) if this piece of salt were in water and were not dissolving, it would not be in the vicinity of a piece of gold would be a counterfactual supported by L5.
  5. If a nomological truth supports a counterfactual, then the counterfactual is true.
  6. C is true.
  7. It is clear that there is good reason not to accept C.  -><-
  8. The nomological truth in 1 does not support counterfactuals, by reductio.
  9. Some nomological truths do not support counterfactuals, by construction.
  10. Some nomological truths are not expressed by laws.

This reconstruction appears to be both valid and sound to me.  But, when it’s put in this shorter form, it seems like Tooley’s argument is somehow less profound.  Here, the point seems to be that nomological truths that are apparently candidates for laws entail truths that are not candidates for laws.  Since if a nomological truth entails a truth then that truth is itself nomological, some nomological truths are not laws.

This seems much less significant than it should.  For instance, either I am typing now or I am not is entailed by all salt dissolves in water, but it at least appears to me that either I am typing now or I am not is obviously not a candidate for a law of nature.  This is an obvious point, and we don’t need all that business about counterfactuals to show it.

Maybe I am missing a subtlety of the argument?  I have posted the argument below.  What do you think?

Thanks to J. Dmitri Gallow and Gordon Belot for helping me think about or inspiring me to think about these issues, but none of the faults/problems here are theirs.

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4 Responses to Tooley’s Laws of Nature and Counterfactual Support

  1. dtlocke says:

    Perhaps the interesting result is supposed to be that both of the following claims are true.

    1. All laws support counterfactuals.
    2. Some statements that are entailed by laws do not support counterfactuals.

    It seems to me that this could be an interesting result, depending on what one means by “supports counterfactuals”. Anyone who’s interested might want to check out Marc Lange’s book “Laws in Scientific Practice” where he spends at least a chapter pulling apart the several things one might mean when one says that laws “support counterfactuals”.

  2. Alex S. says:

    Hi Daniel,

    Nice post; I agree with what Dustin says, too.

    Two quick comments. First, Tooley’s argument seems to be double-pronged. Not only does he purport to show that, if (the deductive closure of) nomological truths were all laws, then not only the link between laws and counterfactuals but also the link between laws and causal statements would be broken. But I take it that you’re ignoring that second component of the argument.

    Second, I don’t think that Tooley needs premise 11 (premise 7 in your second reconstruction) in order for the argument to have force. All Tooley needs is the premise that *it is not clear whether* C is true, and the premise that, if C were a law, then it *would* be clear whether C were true. The former premise seems much more plausible, and the latter premise is not obviously false either (though perhaps too vague for positive assent).

  3. Thanks for the comments guys and thanks for the pointer Dustin. I think both of your comments are probably right.

  4. […] on Laws of Nature and Counterfactual Support So I was looking over Dan’s reconstruction of Tooley’s argument below, and I’m still somewhat worried about its […]

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