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

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.

There is a plausible link between “would”-counterfactuals and “might”-counterfactuals. We can capture it with the following principle:

(M) A counterfactual of the form “If A had been the case, B would have been the case” is assertable just in case “If A had been the case, B might not have been the case” is rejectable (if A is taken to be possible).

On Lewis’s account, there is a straightforward explanation for this: the former “would”-counterfactuals are true just in case the latter “might”-counterfactuals are false. To put it another way, “might”-counterfactuals are duals of the corresponding “would”-counterfactuals.

Now, in order for the phenomenon of reversing Sobel sequences to get off the ground, one really needs the fact that (1) is assertable in the initial context. Given (M), this requires that 

(4) If she had been at the concert, she might not have seen Mick Jagger (because she might have been stuck behind a group of tall people)

can be rejected. But in the circumstances most naturally associated with the example, (4) cannot be rejected. This suggests that (1) wasn’t really assertable in the first place. Perhaps it seemed o.k. to assert it because one did not think of the possibility that she might have got stuck behind tall people. Plausibly, if the standards of assertability are low, a counterfactuals passes these standards if most of the close antecedent-worlds are consequent-worlds. But once certain possibilities are mentioned, the standards of assertability are raised, and beeing close to the truth isn’t good enough any longer. 

Note that the picture changes if (4) can be rejected. Suppose it is known that there weren’t any tall people around at the concert. Then (4) can indeed be rejected and (1) is indeed fully assertable in the initial context. But then it doesn’t seem clear to me that (3) would not be o.k. Perhaps the following utterance would lack a decisive point, but from a semantic perspective it seems fine:

(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 since there weren’t any tall people around at the concert, if she had been at the concert, she would have seen Mick Jagger.

Recently, I have been to the ‘because’-conference in Geneva and the Paris-Arché workshop on Abstract Objects in Paris. You may take a look at some pictures of the two events on this page.

Posted by Benjamin.

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.

The problem I have in mind concerns our credences in sentences like ‘The coin will come down heads’. In most situations, it will be the right thing to think that it is roughly 50% likely that the coin will come down heads. The question is whether Supervaluationism and Relativism can explain this kind of epistemic attitude. The corresponding problem in the case of vagueness would concern our credences in statements about borderline cases. But it is less clear whether we should have definite credences with respect to borderline cases. It may well be that we should simply suspend jugdment (or stick with a coarse grained ordering of likelihoods). So, the problem of our epistemic attitudes with respect to sentences which are neither supertrue nor superfalse is less pressing in the case of vagueness than it is in the case of future contingents. 

Let’s state the case. Consider a convinced indeterminist who is certain that it is a truely chancy matter whether the coin will come down heads or not. Also, he thinks that there is an objective chance of 50% that the coin will come down heads. Since he has no other relevant information about the future, he assings subjective probability 1/2 to this statement. In this situation, this seems to be the right thing to think. Now given supervaluationist’s and relativist’s views about how to evaluate such statements, it is hard to see how this can be explained. For, our indeterminist has only trivial attitudes towards the sentence’s semantic value as described by supervaluationism and relativism: he can be certain that the sentence is neither supertrue nor superfalse, since he is certain that there is both an objective possibility which would verify the sentence and an objective possibility which would falsify it. Consequently, he can be certain that it is neither supertrue nor superfalse that the coin will come down heads. Hence, his credence in this statement does not aim at supertruth (nor at some weighted average between the three values as is obvious from the fact that supertruth and superfalsity get credence 0). So, how can our non-trivial credences in statements about the future be justified within the framework of supervaluationism and relativism?

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.

The Principal Principle can partly be motivated by way of examples. Suppose a fair coin is going to be tossed tomorrow. How likely should we think it to be true that it will come down heads? 1/2, of course. Why? Because its present objective chance of coming down heads is 1/2. The Principal Principal generalises this pattern of reasoning. It states that in the absence of evidence which bears more directly on a proposition A, we should adjust our credence in A to what we take to be the objective chance of A. More precisely, the Principal Principal can be stated as follows:

(The Principal Principle)
Let be any reasonable initial credence function, any
proposition within the domain of objective chances, any time,
and any proposition which is admissible at . Now, let be
the proposition that the objective chance of at is . Then
.

A few remarks may be in order. The reference to times is needed, since objective chances obtain relative to times. Today the chances of the coin coming down heads may be 50%. Tomorrow, after the coin was tossed, the chances will be either 1 or 0, depending on whether it comes down heads or not. Now to the idea of admissible evidence. It requires a great deal of work to specify the admissible propositions. As a first approximation, one can start by saying that information is admissible if it is solely concerned with the history up to time t. For instance, every proposition which is solely about the history up to now will be admissible for the proposition that the coin will come down heads tomorrow. Since the question of which propositions are admissible will not play any role in the argument, I will leave it at that.

Let me start by pointing to the fact, highlighted in Williamson’s paper, that statements about objective chances do not generate hyperintensional contexts. A sentential operator D is said to be hyperintensional if there are necessarily equivalent sentences A and B such that D(A) is true but D(B) is false. The idea that objective chances do not give rise to hyperintensional contexts can be put like this:

(Objective Chances Are Not Hyperintensional)
If and are necessarily equivalent, then the objective chance
of always equals the objective chance of . More formally, for
all times (where denotes the objective chance distribution
at ):
.

The argument for this thesis is straightforward. Objective chances measure objective possibilities. Thus, the objective chance of a proposition or sentence to be true derives from its modal properties. But if two propositions or sentences are necessarily equivalent, they have the same modal profile and therefore the same modal properties. Hence, the expression of objective chances does not constitute a hyperintensional context.

Subjective probabilities, on the other hand, seem to give rise to hyperintensional contexts. Consider the following example. Suppose a proposition is actually true. Then the proposition is necessarily equivalent to (I use as the ‘actually’-operator). For, if we evaluate at a counterfactual world , will be true at just in case is true at , since is actually true. Now, as an obvious instance of the contingent a priori, we should always be certain about . However, we should not always be certain about any proposition which happens to be true. For instance, we should not be certain that the coin will come down heads tomorrow (even if in fact the coin will come down heads tomorrow). But, of course, we should be certain that the coin will come down heads just in case the coin will actually come down heads. Hence, subjective probabilities constitute a hyperintensional context:

(Subjective Probabilities Are Hyperintensional)
There are necessarily equivalent propositions or sentences and
such that the subjective probability of should not always
equal the subjective probability of . More formally ( being a
reasonable credence function),
.

Of course, this does not hold if one identifies propositions with sets of possible worlds as, for instance, Lewis (1980) did. But the foregoing example shows that this way of individuating propositions is too coarse grained to be sensitive to the distinctive features of our epistemic lifes.
The observation is thus that subjective possibilities measure epistemic possibilities which are, as examples of the contingent a priori and the necessary a posteriori show, incomparable in strength with metaphysical possibilities. Since subjective probabilities fall on the epistemic side of this distinction, it takes no wonder that they give rise to hyperintensional contexts.

Now to the counterexample. Let be the proposition that the coin will come down heads tomorrow, and let be today. As above, is the objective chance distribution at time (and, of course, at the actual world). The crucial observation is that the following two statements are a priori equivalent:

(1) ,
(2) .

To see this, note that the logic of ‘actually’ implies the following theorem:

(3) .

We have already argued for this principle. If is true at the actual world, then is true exactly at the -worlds, and if is false at the actual world, then is true exactly at the -worlds.

From (3), the equivalence of (1) and (2) follows by using the non-hyperintensionality of objective chances. For the direction from (1) to (2): By (3) and the non hyperintensionality, we get that the objective chance of is either the one of or the one of ; since both are the same, (2) follows. For the direction from (2) to (1): By (3) and the non hyperintensionality of objective chances, it follows from (2) that either the objective chance of is or the objective chance of is ; since both disjuncts are equivalent, (1) follows.

Now, the Principal Principle makes the following prediction:

(4) .

But this is wrong. We should assign credence to no matter what, since we can always be certain that the coin will land heads just in case it will actually land heads. Hence, there seems to be a counterexample to the Principal Principle.

One may think that conditionalizing on should undermine our certainty in . Even though I do not take this idea to be a live option (we should always be certain about a logical truth such as !), one can demonstrate the coherency of the epistemic state described by

(5) .

relative to the coherency of another state. Clearly, the following epistemic state is rational:

(6) .

My thinking that the objective chance of the coin landing heads is should not undermine my certainty that the coin will land heads just in case it will actually land heads. However, since is a priori equivalent to (as we have seen in arguing for the equivalence of (1) and (2) above), (6) is a rational epistemic state just in case (5) is. So, we have shown the relative coherency of an epistemic state described by (5): it is coherent just in case (6) desribes a coherent state. So, there is a counterexample to the Principle Principal if (6) is correct. And, as I have argued, (6) is correct.

What is the source of the counterexample to the Principal Principal? An answer suggests itself: the counterexample derives from the fact that subjective chances are hyperintensional whereas objective chances are not.

We proudly present: The “official” theme song of our project. The German band Einstürzende Neubauten wrote a ‘because’-theme. You can listen to it on this page (unfortunately, there is only a German version; indeed, an English translation would presumably corrupt the metrics).

Finally, the threat that philosophy poses to the people has been realized. Henceforth, metaphysical content will rank beside violence, depiction of sexual congress or nudity, etc. as a danger for the welfare of children.

You don’t think so? Then read the New York Times’s review of Coppola’s new movie “Youth Without Youth”.

The new journal Semantics & Pragmatics is now accepting submissions. The journal, editetd by Kai von Fintel and David Beaver, is peer-reviewed and open access and has managed to assemble a very impressive team. You can find the journal’s website here and the editors’ blog here. Good luck S&P!

Posted by Miguel.

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. 28

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.

[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.

Let us start by considering, with respect to some infinite language L, the following question:

Q How can a finite being acquire competence with L?

Competence with a language L relies on (or arises from, or consists in) knowing what the expressions of L mean. If we could specify a finite set of knowable propositions P = {that p1, … that pn} such that knowing that (p1 & … that pn) was (in some sense) sufficient for knowing, of every expression of L, what it means, we would be in a position to answer Q: a finite being can acquire competence with L by coming to know P. This has explanatory value since P itself is finite.

Suppose, though, that P had the following feature: if someone X is competent with the infinite language L*, then knowing P is, for X, sufficient to understand L. If, however, X does not understand L*, then P will be of no help to her in coming to know L. Suppose someone suggested providing an answer to Q based on P. A rather natural response to such an attempt seems to be this: You have explained how a finite being X can come to know L given that X already has knowledge of some other infinite language L*. But the interesting question was precisely how it is possible that X has knowledge of an infinite language. So maybe you have answered Q, but this only shows that Q was a bad way of phrasing the question. We are really interested, not in Q, but in:

Q* How can there be an infinite language with which a finite being is competent?

To answer Q* we must not presuppose competence with any infinite language. If TCS can only answer questions of the Q-kind, but not Q*, it falls short of explaining a fact which is frequently alluded to in order to motivate the whole enterprise: the fact that finite beings understand infinite languages. Can current TCS-approaches provide an answer to Q*? I will try to show that the one developed by Ernie Lepore and Kirk Ludwig (L&L) in their recent book “Donald Davidson’s Truth Theoretic Semantics” cannot. (References are to this book.)

Terminology: A truth-theory for a language L given in a metalanguage L* is interpretive iff all of its axioms are interpretive. An axiom for an L-expression E is interpretive if it uses an L*-expression E* synonymous with E to state satisfaction / reference conditions (e.g., an interpretive axiom for the German “ist rot” given in English will use “is red” rather than “is red and self identical”). (See 85-89 for a more rigorous account). A T-sentence “S is true iff p” is interpretive iff S and “p” have the same meaning. A canonical proof procedure is a syntactical procedure that yields only interpretive T-sentences.

Suppose that for some language L we had both an interpretive truth theory T given in a language L* and a canonical proof procedure. According to L&L, we can now give a theory of meaning TM for L. TM contains the following axioms (60; I ignore context sensitivity):

[1] Every instance of the following schema is true:
S in L means that p iff it is canonically provable on the basis of the axioms of an interpretive truth theory TT for L that S is true in L iff p.

[2] T is an interpretive truth theory for L whose axioms are …

[3] Axiom … of T means that … (for each axiom).

[4] A canonical proof in T is …

(Replace dots appropriately.) Is TM of any help in answering Q*? That is, do the axioms of TM taken together express some finite set of propositions P such that knowing P would be sufficient to understand some infinite language without thereby presupposing competence with some infinite language?

If X knows everything that TM states, X will be in a position to infer, for every S of L meaning that p, that “S is true in L iff p” is a canonical theorem of an interpretive truth theory for L. ([2] provides the axioms and tells her that they form such a theory, while [4] provides a canonical proof procedure and states that it is such a procedure.) But X’s knowledge that “S is true in L iff p” is such-and-such is simply knowledge about a linguistic item. If you don’t understand German, then knowing that a theory T has “Schnee ist weiß” as a theorem will not be sufficient to know that it is provable on the basis of T that snow is white. Likewise, if X does not understand “S is true in L iff p”, then knowing that it is a canonical theorem of T will not be sufficient for X to know that it is canonically provable from T that S is true in L iff p. But then (even given that X understands the schema in [1]) she will be in no position to infer that S means in L that p. Hence, if X is not competent with L*, knowing that [1], [2] and [4] will be of no help in coming to understand L. This leaves [3].

But how could [3] help? It would help if the following was the case: if you have a set of sentences S (e.g. the axioms of T) and are able to apply certain syntactical transformation rules to them (e.g. the canonical proof procedure), then telling you what the sentences in S mean will ensure that you know the meaning of the derived sentences. Given this, TM would indeed provide an answer to Q*. But of course, this is simply false. (In fact, if it were the case, it would be quite incomprehensible what we needed the whole theory-of-meaning-thing for to begin with. If telling X what the axioms of a truth theory mean was sufficient to ensure that she understood all the theorems, then telling X what the axioms of a truth theory in L* for a language L mean would be sufficient to ensure that she is competent with an infinite language at least as strong in expressive power as L.)

Theories along the lines of TM cannot provide an answer to Q*. L&L seem to be content with this. They write:

This should not come as a surprise. For there is no question of a standpoint for understanding meaning that is outside of language altogether. (9)

I am not sure that they fully appreciate the point, and in any case, I am sure I do not fully understand their reply. But since this is already a somewhat lengthy post, discussion of their reaction will have to wait.

Posted by Miguel.