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July 09, 2013

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Sprachlogik.blogspot.com

This is fantastic - the criticism of Bennett's Philosophical Guide to Conditionals arguments against the simple theory seems definitely right.

I have a couple of reasons for thinking these truth-conditions aren't quite right as they stand. One seems easy to fix, the other may be more of a problem.

The first is that I think some counterfactuals with nomologically possible antecedents are categorical - that is, require that all A-worlds are C-worlds. (I argue briefly for this here.) But even if that's right, provision can be made for it easily (at the cost of a tiny bit of complexity), and the simple theory can be taken to govern non-categorical cases.

The second worry is about cases where the most relevantly similar A-worlds may be nomologically impossible, even though there there are nomologically possible A-worlds; counterfactuals where the similarity relation is resolved in a way which counts certain things as more important than sameness of law. (I don't think there's any reason to think our relevant-A-world(s)-determining-practices for counterfactuals inherently, i.e. by their very nature, hold laws fixed, even when there are legal A-worlds.)

Such a case might be:

If Einstein had been wrong in paper N, this light would not have bent.

(Suppose Einstein in the actual world stated a law in paper N which actually holds, and which predicted the bending of the light.)

It seems we can naturally understand this as holding fixed what Einstein wrote in N, and having a chance at being true, since the relevant worlds at which what Einstein actually wrote is false would be counterlegal.

But this counterfactual still falls within the intended scope of the simple theory, since there are legal A worlds, namely ones where Einstein wrote something different in paper N. But they are not similar enough in the contextually relevant respect of what Einstein actually wrote. Do you think there might be a problem here? (If there is one, it could perhaps be avoided by more carefully and narrowly delineating the indented scope of the theory.)

- Tristan Haze

tomkow

Tristan,

Thanks very much for your kind remarks. And congratulations on your own splendid blog. It is good to see someone doing philosophy (as opposed to philosophical shmooze) on line.

I'm not sure I understand your first point. I agree that there are some counterfactual statements that require that all the A-worlds be C worlds. That is my analysis of "would have to be" (A>>C) counterfactuals. Perhaps you believe there is a class of counterfactuals which deserve this A>>C analysis but which cannot be heard as synonymous with any "would have to" claim? Do you have examples?

On your second point. I think your counterexample only shows how the vagueness of the counterpart relation can give rise to vagueness in our judgments of similarity. In your story Einstein writes "paper N" in which he says that light will bend. Assuming the light's bending is nomologically necessary, are the closest worlds at which the light does not bend worlds where Einstein was wrong or worlds at which he wrote something different in "paper N".

Here our answer will depend on whether or not we take "saying light bends" as an essential property of paper N. That is, it depends upon whether we are willing to count some other worldly paper as a counterpart of paper N if it advances a contrary thesis. (Compare, "If Woody Allen had written Mien Kampf it wouldn't have been so anti-semitic and would have had more jokes.") And, it seems to me, our willingness on this score will depend greatly on context. If Einstein's acuity is topic of discussion we might suppose that he wouldn't have written "light bends" in a world in which it doesn't. On the other hand if our topic is the accuracy of what Einstein actually wrote we will not treat the contents of paper N as fungible.

But I expect you anticipated this move and framed your example to get round it. Your example is:


(H) If Einstein had been wrong in paper N, this light would not have bent.

I think your thought here was that the Simple Analysis requires the reading under which this is false (because it requires the closest A-worlds to be legal) and yet we are likely to hear (H) as true.

But I don't think this works. The reading under which this sentence is true- and the reading we would normally give it-- is one in which the antecedent entails that Einstein said the light would bend. So it reads as:


(H'') If Einstein had been wrong to say the light would bend, the light would not have bent.

Which seems logically true and so true on any theory of counterfactuals. The reading of (H) under which it is false is, I guess,:


(H*) If Einstein had said something wrong in Paper N (but not about light bending), the light would not have bent.

But this reading seems to me be precluded for Gricean reasons. I have very hard time imagining any context in which (H) should be read as (H*) because I can't imagine what the speaker might be attempting to communicate.

In any case the Simple Theory does not entail anything about how we should disambiguate a sentence 'A>C' when 'A' is genuinely ambiguous between an interpretation which is nomologically possible and another that is not. The Simple Theory, as it stands, doesn't account for the truth conditions of counterfactuals with contra-legal antecedents, but it doesn't require that we pretend they don't exist.

I agree that we do need an account of counterfactuals with contra-legal antecedants. I explicitly left them off the table in this post because I think we need first to get clearer about laws.

I'll be offering a new theory of laws in my next post.

Tristan Haze

Hi Terrance,

Thanks for the response. I will try to clarify both points.

'I agree that there are some counterfactual statements that require that all the A-worlds be C worlds. That is my analysis of "would have to be" (A>>C) counterfactuals. Perhaps you believe there is a class of counterfactuals which deserve this A>>C analysis but which cannot be heard as synonymous with any "would have to" claim? Do you have examples?'

I don't think this succeeds in avoiding the counterexample. That a counterfactual with a legal antecedent of this sort can be paraphrased as a 'would have to be' conditional, and that you have another analysis for those, doesn't change the fact that it still falls under the scope of the Simple Theory as stated here, and that that theory seems to assign the wrong meaning. It should be easy to fix this by restricting the scope of the theory.

A similar point applies regarding my second counterexample (which you call (H)) as you construe it. But I intended it somewhat differently (which I wasn't clear about).

The idea was roughly this (it's inspired by my cartoon understanding of the confirmation of relativity, but let's just treat it as a fiction): Einstein asserted a law in paper N which actually holds, and which, together with the facts of some experimental setup E, predicts that some light will bend.

Now, it seems to me we can evaluate counterfactuals where the relevant closest A-worlds are worlds where the law doesn't hold, for example ones with the antecedent '~L' (where L is the law in question). As you say, 'we do need an account of counterfactuals with contra-legal anteced[e]nts'. So far, no problem for the Simple Theory.

But my idea is that there are counterfactuals whose antecedents are legal, but where the similarity relation is contextually understood in such a way that the closest relevant A-worlds are counter-legal. The idea was that with (H), both what Einstein wrote and the experimental setup was supposed to be held fixed (i.e. match in these respects required for close similarity), but not the actual laws of nature.

For a given counterfactual and contextual understanding of it, call the 'focus set' the set of A-worlds at which C is required, by the counterfactual, to be true. (This of course assumes that a theory with broadly Lewisian/strict-implication outlines is basically right.)

The special property this example was designed to have is thus: having a legal antecedent, yet being legitimately and naturally understandable such that its focus set contains counter-legal worlds.

If there are counterfactuals with that property, that's a problem for the Simple Theory as stated, since is says that 'A > C iff C is true at the legal [my emphasis] A-worlds that most resemble a at TA'.

Their having legal antecedents puts them in the scope of your theory as stated, but the presence of counter-legal worlds in their focus sets (on the relevant understandings of them) conflicts with it.

Tristan Haze

I've turned this into a post: http://sprachlogik.blogspot.com/2013/07/a-problem-for-simple-theory-of.html

Vivek Iyer

Great post. It would be interesting to hear more about the adaptive pressures on Lewis's evolving idea in this respect.
I have a sort of hazy memory that there was the problem of every counterfactual having a 'smaller' counterfactual that could be its truthmaker.
Also no biological life could exist if 'it is a logical truth that any two worlds governed by the same deterministic laws that are different at any time must be different at every prior time'
Did that motivate Lewis's 'miracles'?
Perhaps something like evidentiary decision theory (which gives wiggle room for backward causation without the difficulty posed by the impossibility of establishing an entropic arrow for time for Stalnaker-Lewis) better captures the 'folk' understanding of counter-factuals?

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