Do Counterfactuals Violate Modus Ponens?

9 08 2008

There has been an intensive debate about whether modus ponens fails for indicative conditionals. Less attention has been paid to the question of whether similar examples can be constructed for counterfactuals as well. This is insofar surprising as McGee claimed that the Import/Export principle (which leads to the counterexamples for indicatives) holds also for counterfactuals. So, are there counterexamples to modus ponens for counterfactuals?

Let us recall the setting of McGee’s counterexample. There are three candidates for the 1980 election: the two republicans Reagan and Anderson, and the democrat Carter. The polls see Carter far behind Reagan, with Anderson a distant third. Prima facie, McGee’s counterexample can go counterfactual. Suppose I know about the polls but do not receive any relevant information afterwards, perhaps because I go on a safari trip or because I just don’t care. After the time of the election I consider the following argument:

(1) If a republican had won, then if it had not been Reagan, it would have been Anderson.

(2) A republican won.

(3) Therefore, if Reagan had not won, it would have been Anderson.

Given the polls, I will find the premises highly probable although I will dissent from the conclusion. This comes as a surprise: if an inference is classically valid, the uncertainty of the conclusion cannot exceed the sum of the uncertainties of the premises. This puts pressure on the validity of modus ponens for right-nested counterfactuals.

Posted by Moritz.

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And Yet They Exist.

13 06 2008

Finally, biology proved a philosophical theory: Fictional Realism was right all along (or, at least, nearly right).

“Might”-Counterfactuals and Reversed Sobel Sequences

19 05 2008

To which extent are counterfactuals context-dependent? Lewis suggested that we can do without a systematic dependence on context by combining an invariant similarity relation with a variably strict analysis of counterfactuals. Recently, this approach has been challenged partly by drawing attention to the phenomenon of reversed Sobel sequences: sometimes it seems as if the order in which two counterfactuals are uttered makes for a difference in truth-value. Philosophers who take this phenomenon to be semantic in nature have reacted to it by allowing the similarity relation to vary from context to context (for instance, have a look at von Fintel’s semantics for counterfactuals, which you can find here). In this note, I’d like to challenge the semantic analysis of reversed Sobel sequences by arguing that it does not square well with a plausible link between “would”-counterfactuals and “might”-counterfactuals.

Here is the phenomenon. In an initial context, the counterfactual

(1) If she had been at the concert, she would have seen Mick Jagger

may be truly asserted, or so it is assumed. Subsequently, the counterfactual

(2) If she had been at the concert and got stuck behind a group of tall people, she would not have seen Mick Jagger

may be accepted, too. All this is to be expected on Lewis’s account: strengthening the antecedent is not a valid rule of inference. But now suppose that (1) and (2) are uttered in reversed order: it seems that asserting (1) after (2) is not o.k. There is something odd about saying

(3) If she had been at the concert and got stuck behind a group of tall people, she would not have seen Mick Jagger, but if she had been at the concert, she would have seen Mick Jagger.

So, can the order in which these counterfactuals are uttered affect their truth-values?

 Posted by Moritz.

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A Problem for Supervaluationism and Relativism?

31 01 2008

Supervaluationism and Relativism are popular accounts of future contingents. Even though they differ quite radically, they agree, at least in their most common forms, in how they evaluate present utterances about the future. For instance, consider the sentence A = ‘The coin will come down heads’ as it is evaluated from the present time t. Both the supervaluationist and the relativist will say: A is (a) supertrue at t/(with respect to t) just in case there is no objective chance at t that A is false, (b) superfalse at t/(with respect to t) just in case there is no objective chance at t that A is true, (c) neither supertrue nor superfalse otherwise. 

In general, supervaluationism and relativism seem to fare better as accounts of future contingents than as theories of vagueness, since there is no equivalent of the problem of higher-order vagueness for future contingents. In this note, I will try to challenge this assumption by pointing to a problem which seems to arise for supervaluationism and relativism with respect to future contingents without being as problematic in the case of vagueness. 

Posted by Moritz. Read the rest of this entry »

A Counterexample to the Principal Principle

25 01 2008

In his paper ‘A Subjectivist’s Guide to Objective Chance’, Lewis proposes an intimate connection between subjective probabilities and objective chances: the Principal Principle. In Lewis’s eyes, this principle captures almost all there is to know about our conception of objective chances.

In a forthcoming paper entitled ‘Knowledge and Objective Chance’, Hawthorne and Lasonen mention in passing a counterexample to the Principal Principle (a draft of which you can find here). Essentially, they think that instances of the contingent a priori provide a source of potential counterexamples. This idea stands in an interesting relation to a recent paper of Williamson (‘Indicative versus Subjunctive, Congruential versus Non-Hyperintensional Contexts’), in which the modal status of statements involving objective and subjective probabilities is discussed (a draft of which you can find there). It seems to me that Williamson’s considerations may provide a deeper reason to explain why we should not expect something like the Principal Principle to hold. In the following note, I will present a structurally similar counterexample by way of relating it to Williamson’s claims about the modal nature of the two kinds of probability.

Posted by Moritz.

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Schlick’s Chair

27 11 2007

I just stumbled across the following passage from Moritz Schlick’s “Form and Content” (1932):

I might use a chair in my room, for instance, as a means of saying anything I like. All I need to do is to select a number of different positions of the chair in the room and agree that each one shall correspond to a letter of the alphabet. By this agreement I shall have constructed a new language which will consist in changing the position of the chair; and by moving it about in the room I shall be able to express all the plays of Shakespeare with the same perfection as the best of the printed editions. (p. 288)

It is quite amusing to picture Schlick wildly moving his chair around his office to “read”, say, a passage from Macbeth. I wonder whether Carnap would have stayed and “listened”. On a more serious note, though, Schlick seems to be quite wrong when he says that he has created a new language. But what has he done? In a way, I guess, he has created, not a new language, but merely a new set of letters. His chair’s standing in the relevant position stands to the letter A as, e.g., “A”, “A” and “A” stand to it.

Posted by Miguel.

Can Truth Conditional Semantics Explain Linguistic Competence?

24 11 2007

[The issue of this post has been discussed by Jeff Speaks in a recent paper here. Hence, even though I am setting things up in a different manner and with a different target, I am not claiming originality on the main point. Speaks’ point deserves reiteration since it raises a challenge that has not been sufficiently addressed by proponents of truth conditional semantics. Another sidenote: a more precise title for this post would be: “Can TCS explain *the possibility of* linguistic competence?”. But it just looked too awful with such a long heading…]

Natural languages are infinite. Human beings are finite. Yet humans are competent with natural languages. A finite being cannot learn, one by one, what each of the infinitely many expressions of a language means. How is it possible that a finite being acquires competence with an infinite language? The task of answering this question is one of the central themes that drive the truth conditional project. Hence, if it turned out that truth conditional semantics (TCS) cannot provide a satisfying answer that should be worrisome to the Davidsonian. This post is about whether the Davidsonian should be worried. In the end, I believe, she should. Read the rest of this entry »