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April 28th, 2004

Ceteris Paribus Laws

I think the following passage, from John Earman, John Roberts and Sheldon Smith’s paper “Ceteris Paribus Lost” (Erkenntnis 57: 281–301, 2002) is somewhat mistaken.

But the second problem with CP laws, their untestability, is decisive in our view. In order for a hypothesis to be testable, it must lead us to some prediction. The prediction may be statistical in character, and in general it will depend on a set of auxiliary hypotheses. Even when these important qualifications have been added, CP law statements still fail to make any testable predictions. Consider the putative law that CP, all Fs are Gs. The information that x is an F, together with any auxiliary hypotheses you like, fails to entail that x is a G, or even to entail that with probability p, x is a G. For, even given this information, other things could fail to be equal, and we are not even given a way of estimating the probability that they so fail. Two qualifications have to be made. First, our claim is true only if the auxiliary hypotheses don’t entail the prediction all by themselves, in which case the CP law is inessential to the prediction and doesn’t get tested by a check of that prediction. Second, our claim is true only if none of the auxiliary hypotheses is the hypothesis that “other things are equal”, or “there are no interferences”. What if the auxiliaries do include the claim that other things are equal? Then either this auxiliary can be stated in a form that allows us to check whether it is true, or it can’t. If it can, then the original CP law can be turned into a strict law by substituting the testable auxiliary for the CP clause. If it can’t, then the prediction relies on an auxiliary hypothesis that cannot be tested itself. But it is generally, and rightly, presumed that auxiliary hypotheses must be testable in principle if they are to be used in an honest test. Hence, we can’t rely on a putative CP law to make any predictions about what will be observed, or about the probability that something will be observed. If we can’t do that, then it seems that we can’t subject the putative CP law to any kind of empirical test.

They are arguing against the claim that there are any ceteris paribus laws with ineliminable CP clauses. And they claim, plausibly, that if the claim that other things are equal is statable in physical terms then it quite well can be eliminated. So far so good.

The problem is that they leave out a very easy way in which the CP law could be testable without the CP clause being statable in physical terms. Assume that there is a p such that p entails that other things are equal, but is not entailed by it. Now nothing in what has been said about CP clauses rules out this possibility. Indeed, if CP clauses are infinite disjunctions of physical state descriptions, that situation will be easily possible. Then if p is one of the auxiliary hypothesis, the CP law will be testable even though the CP clause cannot be (finitely) stated.

I don’t have any particular fondness for CP laws, but this argument that they are untestable seems to have a hole here. (We’re bracketing questions about the philosophical importance of testability here by the way. I also have no idea whether this point has been made elsewhere in the literature – this is a diary entry not a quasi-publication.)

Posted by Brian Weatherson in Uncategorized

8 Comments »

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8 Responses to “Ceteris Paribus Laws”

  1. Ryan Miller says:

    perhaps i’m missing your point, but it seems to me that your objection is not tenable:

    p must be physical in order to entail physical state descriptions without itself being CP or untestable. now p itself can’t be an infinite disjunction of physical state descriptions or we’ve simply moved the problem one step back. p also must imply an infinite disjunction of physical state descriptions.

    if i’ve understood you correctly and those conditions are accurate, then p is a physical impossibility because chains of physical causation are transmitted by energy and so for p to entail an infinite disjunction of physical descriptions would be for p to cause those states, which would require an infinite amount of energy.

    the only exception would be if the physical state descriptions were systematic, or related to each other in some intelligible way, but empirically this isnt the case: physical antecedents form nonsystematic diverging series.

    therefore it would seem that p is entirely outside of our scientific experience.

  2. Brian Weatherson says:

    Well, I was rather assuming that p could imply the infinite disjunction by simply being one of the disjuncts. If that’s true, then there isn’t a problem here. If it’s not, then there is a problem, but then I really don’t know how to think about disjunctions anymore.

    The point is that the infinite disjunction can be true while precisely one of its disjuncts is true, so since the others are false nothing has to cause them.

  3. Ryan Miller says:

    ok, i think i read your comment a bit more carefully now, so backing up a step:

    you’re clearly correct that only one of the physical state descriptions needs to be correct in order to satisfy the infinite disjunction (or i dont understand infinite disjunctions either).

    the trick, however, seems to be that in order for p to imply that all other things are equal, the state described by p has to take account of all factors that need to exist in order for the original claim to be true. these factors, however, empirically form a nonsystematic infinitely divergent series, so p must either fail to include some factors or p must not be an empirical claim.

  4. Brian Weatherson says:

    Well maybe, but there’s a giant premise there that Earman et al don’t go close to defending, and prima facie doesn’t look true. Namely, that no proposition has all of the following three properties.

    First, it is both sufficient for other things to count as equal.

    Second, it is logically possible. (We need this because contradictions satisfy the other two clauses.)

    Third, it is finitely statable in physical language.

    The proposition that other things are equal satisfies the first and maybe the second but not the third. What I don’t really see is why a very strong statement like “There are no other impinging forces” couldn’t satisfy all three, even if the CP clause was infinite. In other words, even if some of the disjuncts are themselves going to be infinite, which I agree they could well be, some of the extreme cases will be finite, and that’s sufficient for testability in principle.

  5. Ryan Miller says:

    absolutely correct, and i cant say as i read the original article, just your comments, so i cant speak to its relevance for their position. i know the premise i’m using here (that you state pretty well) is defended by Bernard Lonergan and Patrick Byrne among others, I would tend to think that an example like ‘no other impinging forces’ makes a distinction between forces and the absence of forces which doesnt hold in a world of general relativity, but i’d need to do more research to back that up. thanks for clearing things up.

  6. Nospam says:

    Let me see if this helps Earman, Roberts, and Smith:

    Take a CP law like ‘If OTE [other things equal] then Q.’ Suppose that P implies OTE (e.g. by being one of its disjuncts). Then, OTE can be written as “P or OTE2” where OTE2 is an infinite disjunction consisting of the other disjuncts of OTE (whatever they are). So, the very same law can be written as: If P or OTE2 then Q. But, this is equivalent to: If P then Q and if OTE2 then Q. One can test the first conjunct, but ERS can claim that one has done nothing at all to test the second conjunct by testing the first. So, one does not really get at a claim that is testable but not stateable since the unstateable part has eluded testing and only the stateable part has been tested.

  7. Nospam says:

    Let me see if this helps Earman, Roberts, and Smith:

    Take a CP law like ‘If OTE [other things equal] then Q.’ Suppose that P implies OTE (e.g. by being one of its disjuncts). Then, OTE can be written as “P or OTE2” where OTE2 is an infinite disjunction consisting of the other disjuncts of OTE (whatever they are). So, the very same law can be written as: If P or OTE2 then Q. But, this is equivalent to: If P then Q and if OTE2 then Q. One can test the first conjunct, but ERS can claim that one has done nothing at all to test the second conjunct by testing the first. So, one does not really get at a claim that is testable but not stateable since the unstateable part has eluded testing and only the stateable part has been tested.

  8. Nospam says:

    Let me see if this helps Earman, Roberts, and Smith:

    Take a CP law like ‘If OTE [other things equal] then Q.’ Suppose that P implies OTE (e.g. by being one of its disjuncts). Then, OTE can be written as “P or OTE2” where OTE2 is an infinite disjunction consisting of the other disjuncts of OTE (whatever they are). So, the very same law can be written as: If P or OTE2 then Q. But, this is equivalent to: If P then Q and if OTE2 then Q. One can test the first conjunct, but ERS can claim that one has done nothing at all to test the second conjunct by testing the first. So, one does not really get at a claim that is testable but not stateable since the unstateable part has eluded testing and only the stateable part has been tested.