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Thursday, November 30, 2006

Modal Adverbials

It seems that it should be possible to treat 'actually' as the modal adverbial 'in @', where '@' is a term for the actual world. Moreover, if terms have a primary intension in addition to a secondary intension, in Chalmers' sense, one should expect that non-actual scenarios verify '@' (just as some non-actual scenarios verify 'Hesperus is not Venus'). But these two positions appear to be inconsistent.

Suppose, for reductio, that for any given scenario S, S verifies '@' as it occurs in 'in @'. Then it is true at the actual world, that there is no scenario at which 'p iff in @, p' fails to obtain. So, 'p iff in @, p' is a priori. But the same holds regardless of which world the utterer occupies. So, at w2, it is true that there is no scenario (accessible from there, as it were) in which 'p iff in @, p' fails to obtain. And at w3, it is true that there is no scenario at which 'p iff in @, p' fails to obtain, and so on. So, 'p iff in @, p' is necessarily a priori. Now, this much still seems obvious to me.

But then Chalmers dropped the bomb: 'necessarily, it is a priori that (p iff in @, p)' entails 'necessarily, (p iff in @, p)'. But 'necessarily' operates on the secondary intension of the operand sentence. Since at any world the referent of '@' is the world of utterance, it is not necessary that (p iff in @, p). So, it is not necessarily a priori that (p iff in @,p).

But then it is and isn't necessarily a priori that (p iff in @, p). Contradiction. By reductio, it is not the case that for any given scenario S, S verifies '@'. So, 'in @' cannot have a primary intension, and so, given 2Dism 'actually' cannot be treated as a modal adverbial.

Now, I don't really believe the conclusion of this argument yet. So I am left to wonder whether it is sound, and if not, why I fail to see where it goes wrong.

16 comments:

Mike said...

But the same holds regardless of which world the utterer occupies. So, at w2, it is true that there is no scenario (accessible from there, as it were) in which 'p iff in @, p' fails to obtain. And at w3, it is true that there is no scenario at which 'p iff in @, p' fails to obtain, and so on. So, 'p iff in @, p' is necessarily a priori.

Hi Brit! I think I'm not following this part of the argument. Take the statement 'I am here now' or 'this stick is one metre'. Both are contingent, certainly. Both seem to be a priori. But no matter what world the utterer occupies, these are a priori. But it can't follow that they are necessarily a priori, since they are clearly contingent. So I must be missing something in your argument.

Brit Brogaard said...

Hi Mike! Yes, 'I am here now' and other contingent statements which are a priori are not necessarily a priori, for given normal modal logic and the facticity of 'it is a priori that', 'necessarily, it is a priori that p' entails 'necesssarily, p'.

And I am assuming the same holds for 'p iff actually p'.

But (and this was the core of the argument) it seems that for this very reason, one cannot treat 'actually' as the modal adverbial 'in @', and also hold that terms have a primary and a (distinct) secondary intension. For '@' is a term. By supposition, its primary intension is distinct from its secondary intension. How can it be distinct? Well, the secondary intension of '@', for any world of evaluation, is the world of utterance. So, the primary intension of '@' must be, for each world of evaluation, the world of evaluation. But then in all possible scenarios, 'p iff actually, p' is true (as the world is the world of evaluation not the world of utterance). But then, by definition, 'p iff actually p' is a priori. Since this argument holds for any world you may happen to be located in, we get: 'necessarily, it is a priori that p'.

Therein lies the contradiction (this plus what you observed earlier). And since we have a contradiction, we have a reason to deny that '@' has a primary and a secondary intension. But then, if two-dimensionalism is true, 'actually' is not a modal adverbial.

QED

Mike said...

Brit, thanks! You say,

But then, by definition, 'p iff actually p' is a priori. Since this argument holds for any world you may happen to be located in, we get: 'necessarily, it is a priori that p'.

But 'p iff. actually p' (= q) is a priori in every world considered as actual, right? Considered counterfactually, there are worlds in which p holds, but in which p does not hold actually (i.e., in our world). So I guess I'm wondering why we don't get that it's a priori that it's a priori that q rather than that it's necessary that its a priori that q. That is, I know not only that q is true without knowing what world I am in (or any facts about that world) I also know that q is a priori true without knowing what world I am in (or any facts about that world).

Anonymous said...

what does the @ symbol mean here Brit?

djc said...

Hi Berit,

This is a nice issue (it's closely related to the "nesting argument" presented by Josh Dever in his comment on Scott Soames' book). To start with, it's worth noting that you can generate a version of the problem independently of two-dimensionalism, arising for any view that believes in the contingent a priori. One way to put it is that the following three claims are inconsistent, where N and A are necessity and apriority operators: (i) Ap -> NAp (ii) N(Ap -> p) (iii) Ap & ~Np. There's an initial plausibility in the claim that (i) and (ii) hold for any p, and (iii) holds for any contingent a priori p -- e.g. q if actually q.

On reflection it looks like the best thing to do is to deny (i). In cases where p is contingent a priori, p is not necessarily a priori, because apriority requires truth. Now, you give an argument in your post that 'p iff in @, p' is necessarily a priori. My reaction to this argument is related to that of Mike above. Prima facie, your argument seems to establish that an utterance of 'p iff in @, p' in any world expresses a priori knowledge. But this doesn't entail that 'p iff in @, p' as uttered in our world is necessarily a priori. I suspect that you intend the argument to involve more than this, but maybe you can fill in the details?

The precise 2Dist treatment of the case will depend on the 2Dist semantics of apriority ascriptions and their embedding in modal contexts. I currently favor an approach where A and N are both operators on propositions and where propositions are 2D structured entities involving both the primary intensions and the extension of the relevant parts. Then utterances of 'p iff in @, p' will express different propositions at different worlds. One can then make a case that each proposition is a priori at its own world but not at other worlds (it's not true at other worlds, and indeed not even entertainable at other worlds), so the entailment above will not go through.

This does involve one wrinkle. This treatment requires that for a proposition to be a priori at a world, it doesn't suffice that it has a necessary primary intension (otherwise the propositions above would be a priori at all worlds). It is also required that the proposition be entertainable at that world (which requires an appropriate relationship between primary intensions and extensions). Of course at the world of utterance, this requirement will always be satisfied.

Brit Brogaard said...

Mike: Regardless of which world I happen to be uttering the sentence 'it is a priori that (p iff actually, p)' at, 'it is a priori that (p iff actually p)' is true (given the above assumptions about the primary intension of '@' being the world of evaluation and not the world of utterance). Does that make sense?

Adam: Good question. I am assuming that '@' is a term. So, in the Kripkean sense, it refers directly to the world of utterance (the actual world). But in the Fregean sense, it refers directly to the world of evaluation (the world considered as actual).

Brit Brogaard said...

Dave and Mike: let me try to fill in the details (without moving on to the new account offered by David). No, of course, you are right. I cannot equate the world of evaluation and the world of utterance. But let us begin backwards (as it were). "Necessarily, it is a priori that (p iff actually p)". Whether this latter claim is true depends (among other things) on what 'necessarily' operates on. It seems plausible that it operates on secondary intension. Then 'necessarily, it is a priori that (p iff actually p)' is true iff at every world, the secondary intension of 'it is a priori that (p iff actually p)' is true. But then what does it take for the secondary intension of 'it is a priori that (p iff actually p)' to be true at every world? Well, 'p iff actually p' must be verified (true) at every scenario accessible from the world in question. But (by supposition), 'p iff actually p' *is* verified by every scenario. For, the primary intension of 'actually' (= 'in @') is (by supposition), for each scneario, the world of the scenario in question. So, 'necessarily, it is a priori that (p iff actually p)' is true.

Now, as for the other part of the post. Dave, you say:

"Then utterances of 'p iff in @, p' will express different propositions at different worlds. One can then make a case that each proposition is a priori at its own world but not at other worlds" ---

but consider one such utterance of 'p iff in @, p'. It is arguable that if the proposition expressed is a priori at its own world, then that is (partially) in virtue of it being true at every scenario (accessible from there). But this fact (= its apriority) should hold for any world at which this proposition is evaluated. so, how do you prevent the proposition from being necessarily a priori?

Here is another way to put it. Begin with 'necessarily it is a priori that (p iff actually p)', as uttered at one particular world, for instance, the actual. Then 'necessarily' needs to operate on something (secondary intension) and so, if 'it is a priori that (p iff actually p)' is false at some world (as it must be if it is not necessary), then there is some world where 'it is a priori that (p iff actually p)' is false. But what would be an example of that? You might say: 'an example of this would be a world where p's truth-value in @ is not entertainable". But doesn't that presuppose that 'actually' operates only on secondary intension and so always takes us back to @? For if 'actually' has a primary intension (as distinct from its secondary intension), and 'actually' always takes us back to the scenario of evaluation, then there cannot be a world where 'it is a priori that p iff actually p' is false.

But, now, suppose you are happy to grant that 'actually' operates only on secondary intension. Then it is not clear that you can account for the truth of 'it is a priori that (p iff actually p)'. For if 'actually' really does operate on secondary intension, then it cannot be the case that 'p iff actually p' is true at EVERY scenario accessible from the world of utterance. For p may have one truth-value at a given scenario and another at the actual world.

djc said...

Hi Berit,

Re the first part: this is related to the "wrinkle" mentioned above. For the reasons given there, it is not necessary that a proposition (of the relevant 2D sort) is a priori iff it is true at all scenarios. Rather, this thesis is itself contingent a priori!

Re the second part: I think that 'actually' in effect leaves primary intension unchanged and operates on secondary intension in the obvious way. 'p iff actually p' will still be true at every scenario, as the primary intension of 'actually p' is the same as that of 'p'.

Mike said...

Hey Brit!

Begin with 'necessarily it is a priori that (p iff actually p)', as uttered at one particular world, for instance, the actual. Then 'necessarily' needs to operate on something (secondary intension) and so, if 'it is a priori that (p iff actually p)' is false at some world (as it must be if it is not necessary), then there is some world where 'it is a priori that (p iff actually p)' is false. But what would be an example of that? You might say: 'an example of this would be a world where p's truth-value in @ is not entertainable".

Maybe I'm missing your larger point since I'm tempted to offer this sort of example. Trivially, 'p iff. actually p' is not a priori true in any world w in which it is not true. Since we are focused on the secondary intension of 'p iff. actually p', we need some world w considered counterfactually in which 'p' is true and 'actually p' is false. That is, we need some possible, non-actual proposition p. Take any one. I think that's consistent with saying the primary intension of 'p iff. actually p' is true in every world. Maybe another way to put it is that the secondary intension of 'it is a priori that p iff. actually p' differs from the primay intension of 'p iff. actually p'.

Brit Brogaard said...

Hi Dave and Mike:
Dave, you said:

"I think that 'actually' in effect leaves primary intension unchanged and operates on secondary intension in the obvious way. 'p iff actually p' will still be true at every scenario, as the primary intension of 'actually p' is the same as that of 'p'."

Some apparent counterexamples ('epistemic possibility' is meant to be 'epistemic possibility' in your sense):

(1) It is epistemically possible that (actually, I am not in a world in which this sentence was uttered). ---- FALSE

But if 'p' and 'actually p' have the same primary intension, they are intersubstitutable in epistemic environments; so, we get:

(2) It is epistemically possible that (I am not in a world in which this sentence was uttered). ---- TRUE.

Likewise,

(3) It is epistemically possible that in every world, Julius (if he exists) is the actual inventor of the zip. --- true

(4) It is epistemically possible that in every world, Julius (if he exists) is the inventor of the zip --- false

(5) It is epistemically impossible that (actually, Hesperus is not Phosphorus). --- true

(6) It is epistemically impossible that (Hesperus is not Phosphorus). --- false

In other words, we should be able to attach "it is epistemically possible that" to any actual truth, for epistemic possibility ought to satisfy the T-theorem. ("Any actual truth is conceivable"). But then how can 'actually p' and 'p' have the same primary intension?

Mike, you said:

"Trivially, 'p iff. actually p' is not a priori true in any world w in which it is not true. Since we are focused on the secondary intension of 'p iff. actually p', we need some world w considered counterfactually in which 'p' is true and 'actually p' is false. That is, we need some possible, non-actual proposition p. Take any one. I think that's consistent with saying the primary intension of 'p iff. actually p' is true in every world. Maybe another way to put it is that the secondary intension of 'it is a priori that p iff. actually p' differs from the primay intension of 'p iff. actually p'."

But I was assuming that 'it is a priori that' operates on primary intension regardless of how it is embedded. Otherwise, the embedding operator will be monstrous (in Kaplan's sense). So, setting aside the entertainability maneuvre Dave employs, if Dave is right that 'p' and 'actually p' have the same primary intension, then it becomes hard to see how there could be a world where 'it is a priori that (p iff actually p)' fails to be true. After all, there is no world where 'it is a priori that (p iff p)' fails to be true.

djc said...

Hi Berit,

I think (3) and (4) aren't a counterexample to the claim: in (3) 'actually' is embedded in a modal context, so its operating on secondary intension can percolate into a difference in truth-value.

As for (1)/(2) and (5)/(6), I think that the members of each pair have the same truth-value. The latter pair is easier to analyze, because it avoids distracting issues about whether the utterance of sentences is a priori. Here I think both (5) and (6) are false. 'Actually, Hesperus is Phosphorus' doesn't express a priori knowledge -- it is only knowable a posteriori. One can also see this by noting that 'H=P' is not a priori, that 'H=P iff actually (H=P)' is a priori, and that apriority is closed under a priori equivalence.

So 'Actually (H!=P)' is epistemically possible. Correspondingly, it is true in all scenarios where 'H!=P' is true. Here it worth remembering that although 'Actually S' is true in any world iff it's true in the world of utterance, it's not the case that 'Actually S' is true in any scenario if it's true in th scenario of utterance.

Mike said...

Hi Brit,

I had in mind only that the secondary intension of 'p iff. actually p' is false in some world, w. If that proposition in false in w, then that proposition is not known a priori in w. That seems to follow trivially, no? If that's so, then it is not necessary that it's a priori that (p iff. actually p). I realize that you think this conclusion is mistaken. But here's why I think it's right. Consider the secondary intension of 'p iff. p'. Isn't it just the same proposition as the primary intension of 'p iff. p'? It seems to be. If so, then 'it's a priori that' operates on it's primary intension iff. it operates on it's secondary intension. After all, they're the same proposition. But then, unlike the case with 'p iff. actually p', it's necessary that it's a priori that (p iff. p). So the suggestion is that in cases where it is necessary that it is a priori that P, 'it's a priori that' operates on the primary intension of P iff. it operates on the secondary intension of P (since in those cases the primary intension just is the secondary intension). Does that make better sense? In any case, that was the idea. Maybe there's a counterexample to that suggestion.

Brit Brogaard said...

Hi Mike and Dave,
-- One last attempt at an objection :
1) It is a priori that ((actually p) iff p) (DC's theory)

2) It is a priori that actually ((actually p) iff p) (DC's theory)

3) So, outermost operator always determines which intension of 'actually' to "look at" . (Reasonable Generalization)

4) So, outermost operator determines which intension to "look at", for any embedded operator (reasonable generalization, as operators should be treated the same in this respect)

5) So, in "Necessarily, it is a priori that actually p iff p", 'necessarily' determines which intension of the rest to look at, for 'a priori' and 'actually': secondary intension. So, this automatically fails.

Now the objections:
6) 'it is epistemically possible that in every world, Julius (if he exists) is the actual inventor of the zip' --- Outermost operator determines which intension to look at for any embedded operators. So, this is equivalent to 'it is epistemically possible that in every world, Julius (if he exists) is the inventor of the zip'

7) the T-theorem for epistemic possibility/necessity fails. For 'it is a priori that (necessarily (p iff actually p)' is true (if outtermost operator determines intension for the rest). But 'necessarily, p iff actually p' is false. "It is a priori that" is a monster, Kaplan's sense.

You might object that 'it is a priori that ' cannot shift the intension to look at for 'necessarily' but then that should aply in the case of 'actually' too (as both are alethic operators when unembedded)

Or you might object that it is not the outermost operator that determines which intension to look at, for embedded operators, but then in line 1, "it is a priori that" cannot determine which intension 'actually' should "look at". And so 'actually p' and 'p' do not have the same primary intension.

On my preferred (and controversial) view, 'it is a priori that (p iff actually p)' is simply false, because embedded operators simply operate on whatever they always operate on. So, 'it is a priori that' operates on primary intension, but it is not a monster (in Kaplan's sense), So, 'actually' still operates on secondary intension. And so, the above is false.

Mike, you said: "I had in mind only that the secondary intension of 'p iff. actually p' is false in some world, w. If that proposition in false in w, then that proposition is not known a priori in w. That seems to follow trivially, no? "

Yes, but not if 'actually p' and 'p' have the same primary intension and 'it is a priori that' operates on primary intension.

For then it is not false (for, on the (a) view I disagree with, "p iff actually p" becomes equivalent to 'p iff p' when embedded under "it is a priori known that" -- and the latter operator appears in your explanation.)

djc said...

Hi Berit,

I think (4) is right if read as saying that the outermost operator determines which intension(s) of the immediately embedded sentence to look at. That's obviously right if the operator operates directly on the intensions of the immediately embedded sentence.

But in any case, I think (6) doesn't follow from (4). The outermost operator here determines that one should look at the primary intension of the immediately embedded sentences 'Necessarily Julius is the actual inventor' and 'Necessarily Julius is the inventor'. But these in fact have different primary intensions: the former is true at all scenarios, the latter is false at all scenarios. Of course the deeply embedded expressions 'the inventor' and 'the actual inventor' have the same primary intensions. But the relevant point is that their difference in secondary intension, once embedded in a modal operator, makes a difference to the primary intension of the relevant modal sentence (which is itself the sentence immediately embedded in the epistemic operator).

Same goes for (7). 'Necessarily (p if actually p)' has a primary intension false at all worlds, so embedding it in 'It is a priori that...' yields a falsehood. As in the previous case, 'p' and 'actually p' differ only in secondary intension, but this difference affects the primary intension of the modal sentences that they're embedded in.

These cases bring out that one shouldn't read (4) as applying to any embedded expression, including deeply embedded expressions. It just applies to immediately embedded expressions.

Brit Brogaard said...

Thanks Dave, Mike and Adam for your helpful comments!

Mike said...

Brit, really interesting post and thread! Mini-seminar in 2D!