the illusion of superficially contingent a priori knowledge

I suppose the fact that I think it is easier to get examples of deeply contingent a priori knowledge than of superficially contingent a priori knowledge puts me in the minority. Anyway, Hawthorne (in “Deeply Contingent A Priori Knowledge”) cites Evans’ Julius case as a paradigm example of superficially contingent a priori knowledge:

(E) ∃!x(x invented the zip) → Julius invented the zip

(E) is contingent, I presume, because there are worlds in which someone uniquely invented the zip, but it wasn’t Julius. It is, according to Hawthorne, superficially contingent because the name ‘Julius’ has been stipulated to designate the inventor of the zip, so simply understanding the meaning of (E) puts one in a position to recognize that the actual world verifies (E).

The problem is that there are two readings of (E), one on which ‘Julius’ takes narrow scope with respect to the antecedent, and one on which ‘Julius’ takes wide scope over the whole conditional. I contend that only the narrow scope reading is knowable a priori, but the narrow scope reading is necessary, not contingent.

The wide scope reading isn’t knowable a priori because names carry existence presuppositions. Glossing over some important detail, note that, given the details of Evans’ case, ‘Julius’ will bear the same presupposition as the definite noun phrase ‘the inventor of the zip’, namely (EP):

(EP) ∃!x(x invented the zip)

The epistemological principle (AK) tells us why sentence (1)’s content is not knowable a priori.

(AK) For all sentences S and propositions p and q, if S expresses p and presupposes q, p is knowable a priori only if q is knowable a priori.

(1) Julius invented the zip.

(1)’s content isn’t knowable a priori because (1) presupposes the truth of (EP), and (EP)’s content is not knowable a priori.

The natural move here is to embed (1) in a larger sentence in such a way that the larger sentence does not presuppose that (EP) is true. One natural way of doing this is to make (1) the consequent of a conditional whose antecedent entails that (EP) is true, as, e.g., in (E) .

(E) ∃!x(x invented the zip) → Julius invented the zip

This will seem to neutralize (1)’s presupposition, since (PC) is a plausible constraint on the presuppositions of conditionals:

(PC) The presuppositional content of a conditional of the form A C is the conjunction of all of A‘s presuppositions and all of C‘s presuppositions not entailed by A.

Since (EP) is entailed by (E)’s antecedent, according to (PC), (E) will not presuppose the truth of (EP). And this appears to be exactly what’s needed to get us around the objection from (AK).

The appearance is misleading, since (PC) is underspecified; it fails to take account of the relevant scopal facts. Two readings of ‘Julius’ in (E) are possible: a bound (narrow-scope) reading, and a free (wide-scope) reading. Here’s how the free reading will get represented:

(E1) Julius = ιx [∃!y(y invented the zip) → x invented the zip]

(Paraphrased: Julius is the individual such that, if anyone uniquely invented the zip, he did.)

In (E1), the name ‘Julius’ takes wide scope. This prevents the presupposition borne by ‘Julius’ from being neutralized by the antecedent of the conditional, since neutralization of the presuppositions borne by some piece of syntax R by another piece of syntax S is not generally possible when the syntactic scope of R includes S. So while (E1) is plainly contingent, it will still presuppose the truth of (EP) and fail to be knowable a priori, by (AK)’s lights. (It is easy to verify this intuitively; who among us actually thinks the paraphrasal of (E1) is actually knowable a priori??) Anyway, (PC) obviously needs to be revised to account for the possibility of reading (E) in this way, though I won’t actually attempt the revision here.

A bound reading of the name is also possible. It can be represented as follows:

(E2) ∃!x(x invented the zip) → x invented the zip

In other words, we interpret ‘Julius’ as a variable bound by the quantifier in the antecedent of (E2). (We do need to modify our logic somewhat to show how this is possible, since regular existential quantifiers aren’t allowed to do this. This wrinkle isn’t important for our purposes.) What is important is that giving (E) the reading in (E2) is the only way to neutralize the presuppositions of the name ‘Julius’ (or so I maintain; if you disagree, I’d like to hear an argument). Now note that (E2) is obviously a necessary truth. According to (AK), we need to neutralize the presuppositions of ‘Julius’ in order to get something that is knowable a priori. If the only way of neutralizing the presuppositions of ‘Julius’ in (E) is to give (E) the reading in (E2), then it turns out that (E) is in fact not an example of a superficially contingent a priori truth. The possible readings of (E) fall into two categories: necessary a priori, and contingent a posteriori.

[Cross-posted to my blog]

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16 Responses to the illusion of superficially contingent a priori knowledge

  1. Dustin says:

    Hi Nate,

    I think you’re right that the two readings you’ve identified are necessary a priori and contingent a posteriori. But what reason is there to think that either of those readings is the correct reading? It seems to me pretty obvious that neither reading is correct.

    I suppose you’ll repsond by asking me to produce a reading that is a priori contingent. Well, what do you count as ‘a reading’? Do I need to offer a sentence in some recognized formal (or formal + English) language?

    Moreover, I take it as initially quite plausible that (E) is contingent a priori. Supposing you agree with this, isn’t the burden on YOU to provide some reason to think that one of the readings you produced is the right one? Supposing you don’t agree with this, how would you react to your argument if you were me–i.e., if you did agree with this?

    All that said, I really do think your argument is interesting and clever. I’m just trying to assess what sort of convincing force it should have for someone in my shoes.

  2. nate charlow says:

    Hi Dustin. Thanks for your comment. Can you tell me a bit more about the reading you have in mind for (E)? I’m having a hard time here, since I think (E1) and (E2) exhaust the possible readings for (E). It would help if you could give an LF rendering of what you have in mind, but it isn’t strictly necessary.

    To put the argument a bit differently (i.e., without using the scope stuff), two readings are linguistically possible for ‘Julius’: a bound reading, and an unbound (free) reading. No matter how you represent the bound reading, it will be necessary.

    As to the free reading, there will be a sense in which any sentence which contains a free occurrence of a proper name “N” is saying something about N. So there is a sense in which the free reading of (E) is saying something about the bearer of the name “Julius”. Since we can’t know anything about Julius a priori, we can’t know the free reading of (E) a priori.

  3. Dustin says:

    Hi Nate,

    I think that some sort of ‘free’ reading of ‘Julius’ is the right one. And I disagree that it follows from this alone that (E) is saying something about Julius. Rather, I think that IF there exists a unique inventor of the zip, then, yes, (E) is saying something about Julius. However, if there does not exist a unique inventor of the zip, then, no (E) is not saying something about Julius. That is, whether (E) is saying something about Julius depends on whether there exists a unique inventor of the zip.

    So does your argument go through on the assumption that there is a unique inventor of the zip? Well, you just asserted that nothing can be known a priori about Julius. Why should we believe that? It seems perfectly plausible to me that I know (E) a priori and that if there exists a unique inventor of the zip then knowing (E) is knowing something about Julius. Thus, if there exists a unique inventor of the zip, then I know something a priori about Julius. Now, supposing there does not exist a unique inventor of the zip, it follows that I don’t know anything a priori about Julius. But it doesn’t follow that I don’t know (E) a priori.

    So why think that (E) is a priori contingent? Well, again, I just find that really, really plausible–i.e., it seems to me both that I know, without doing any empirical work, that (E) and that if might not have been that (E).

    But you seem to be insisting on an argument where we give a ‘reading’ (whatever that amounts to) of (E). OK, I’ll play along. Haven’t people suggested a ‘dthat’ reading of (E)? I.e,

    (E3) ∃!x(x invented the zip) → dthat[the unique inventor of the zip] invented the zip

    Isn’t (E3) both a plausible reading of (E) and a priori contingent?

  4. nate charlow says:

    Dustin,

    Take a context C in which there is a unique inventor of the zip. In C, you agree, (E) says something about Julius. What does it say about him? Presumably that he (uniquely, though this isn’t important) satisfies the following open formula: ∃!y(y invented the zip) → x invented the zip. In other words, in C, (E)’s content is given by (E1), which you agreed is not knowable a priori. (I think this sort of exportation is generally fine. Ignoring intensional contexts, given a formula F containing a singular expression a, to find out what F says about a’s referent, replace a with a free variable and say that a’s referent satisfies the result.)

    The ‘dthat’ reading doesn’t, as far as I can tell, help things. It’s still saying something about the unique inventor of the zip. So you can do the same exportation move and arrive at a reading of (E3) that doesn’t seem intuitively knowable a priori. Likewise for (E4), which also has a contingent reading:

    (E4) ∃!x(x invented the zip) → the unique inventor of the zip invented the zip

    I’m curious to know what you think about (AK). You’ve committed yourself to denying it, but doesn’t it strike you as at least somewhat intuitively compelling?

  5. Dustin says:

    Nate,

    RE: “I’m curious to know what you think about (AK). You’ve committed yourself to denying it…”

    Why? I deny that (E) presupposes (EP). Doesn’t that allow me to accept (AK)? Well, perhaps it’s better we ignore this issue for now. Let’s focus on the following.

    RE: “Take a context C in which there is a unique inventor of the zip. In C, you agree, (E) says something about Julius. What does it say about him? Presumably that he (uniquely, though this isn’t important) satisfies the following open formula: ∃!y(y invented the zip) → x invented the zip. In other words, in C, (E)’s content is given by (E1), which you agreed is not knowable a priori.”

    Be that as it may, it doesn’t follow that if (E1) is not a priori then (E) is not a priori. Indeed, what (E) says about Julius in C is that Julius is the x such that ∃!y(y invented the zip) → x invented the zip. But it doesn’t follow from this that (E) is epistemically equivalent to ‘Julius = ιx [∃!y(y invented the zip) → x invented the zip]’. The sentence used to say what a sentence says about an individual O is not generally epistemically equivalent to the original sentence. Consider

    (I) I am posting a comment.

    In the present context, this sentence says something about Dustin–namely, that Dustin is posting a comment. So

    (I1) Dustin is posting a comment.

    gives the content of (I) relative to our context. But clearly (I) and (I1) are not epistemically equivalent.

  6. nate charlow says:

    Dustin,

    I get confused when we start to take sentences (rather than their contents) as the objects of epistemically evaluable attitudes. The basic question is whether a proposition is knowable a priori for some individual. If we need to bring sentences into the mix, here is how I would do it: two sentences S1 and S2 are epistemically equivalent for some individual A iff an utterance by A of S1 and S2 (in a standard context) would express the same proposition. So (I) and (I1) are epistemically equivalent for you, but not for me. Likewise for (I2) and (I3):

    (I2) I exist.
    (I3) Dustin exists.

    For an individual B who goes through the stipulative procedure described by Evans, an utterance by B of (E) and (E1) would express identical propositions, so (E) and (E1) are epistemically equivalent for B. I haven’t thought about any of that before, so it might be hopelessly confused (if so, I hope you’ll set me right).

    I do want to note that your argument has changed in an important way from the beginning of this discussion. I think you now agree that, if we fix the context in the required way (by making it a context in which there is a unique inventor of the zip), the right reading of (E) is the one given in (E1). Originally, you thought it was important to deny this (in order to save (E) as an example of the contingent a priori). Now it seems that you don’t, and I’m not quite sure why.

  7. Shen-yi Liao says:

    Nate:

    (I2) I exist.
    (I3) Dustin exists.

    I, as somewhat of a centered worlds advocate, don’t think they express the same proposition, nor are they always epistemically equivalent. For them to be epistemically equivalent, i’d have to believe something like ‘I am Dustin’. And I would trace the differences to the propositions they express.

    I am not sure about the relevance of this distinction to the rest of your argument though.

  8. Dustin says:

    RE: “I do want to note that your argument has changed in an important way from the beginning of this discussion. I think you now agree that, if we fix the context in the required way… the right reading of (E) is the one given in (E1). Originally, you thought it was important to deny this”

    Certainly not. I still maintain that (E1) is not the correct reading of (E). This is perfectly compatible with (E1) giving the ‘content’ of (E). This is even compatible with (E) and (E1) expressing the same proposition (if that’s something different from ‘giving the content’). I have understood all along that, when epistemic issues are at stake, two sentences need to be epistemically equivalent if one is to be a ‘correct reading’ of the other.

    RE: “two sentences S1 and S2 are epistemically equivalent for some individual A iff an utterance by A of S1 and S2 (in a standard context) would express the same proposition.”

    This cannot be right. I take it that

    (P) Hesperus is Phosphorous
    (H) Hesperus is Hesperus

    express the same proposition (when uttered by me, in this context). But they are clearly not epistemically equivalent–that is, one has epistemic properties that the other lacks. This too is why the issue cannot be “whether a proposition is knowable a priori for some individual”. Propositions do not have such properties simplicter–they have them relative to sentences that express them (or thoughts that express them, or modes of presentation, or Kaplanian characters, or some such thing).

    RE: “For an individual B who goes through the stipulative procedure described by Evans, an utterance by B of (E) and (E1) would express identical propositions, so (E) and (E1) are epistemically equivalent for B.”

    I agree that in such a context, (E) and (E1) express the same proposition when uttered by B. But, again, it does not follow that they are epistemically equivalent for B.

  9. Dustin says:

    RE: Sam’s comment.

    Just so my cards are on the table, I disagree with Sam in that I think that

    (I2) I exist.
    (I3) Dustin exists.

    do indeed express the same proposition when uttered by me (in contexts where ‘Dustin’ refers to me and not, say, D Tuck). But again I disagree with you, Nate, in that I deny that it follows from this that (I2) and (I3) are epistemically equivalent.

  10. nate charlow says:

    Dustin,

    Sorry, I was being careless about terminology. I actually meant to focus on a more restricted notion of epistemic equivalence, namely the kind that’s relevant to this discussion — apriority/aposteriority. To be explicit, I meant to make the claim that a sentence can be known to be true a priori by A iff any sentence that expresses the same proposition in A’s mouth can be known to be true a priori. (P) and (H) don’t falsity this claim, since neither sentence is knowable a priori. If the claim is right, and if (E1) expresses a proposition that is not knowable a priori, and if (E) expresses the very same proposition, then (E) cannot be known to be true a priori.

    To resist this argument, you need to deny that epistemic status (a priori vs. a posteriori) is wholly a function of the proposition expressed. So (E) and (E1) may express the same proposition, but (E) may be a priori though (E1) is not. This makes a priority extremely fine-grained, in a rather bizarre way. On your view, one way to make a sentence fail to be a priori is to move a proper name of a concrete individual to topic position (since this is basically all that’s been done in (E1) vis-a-vis (E)). I find that extremely odd, but I don’t have any way to argue you out of your view.

  11. dtlocke says:

    Nate,

    RE: “On your view, one way to make a sentence fail to be a priori is to move a proper name of a concrete individual to topic position (since this is basically all that’s been done in (E1) vis-a-vis (E)). I find that extremely odd”

    That assumes that what goes for ‘Julius’ goes for all proper names. And, it wouldn’t be odd at all if ‘Julius’ had certain properties that ‘ordinary’ proper names lack, since it’s not clear that ordinary proper names have the descriptive content associated with ‘Julius’.

    RE: “To resist this argument, you need to deny that epistemic status (a priori vs. a posteriori) is wholly a function of the proposition expressed.”

    That’s what I’ve already been doing.

    RE: “I actually meant to focus on a more restricted notion of epistemic equivalence, namely the kind that’s relevant to this discussion — apriority/aposteriority.”

    “I meant to make the claim that a sentence can be known to be true a priori by A iff any sentence that expresses the same proposition in A’s mouth can be known to be true a priori. (P) and (H) don’t falsity this claim, since neither sentence is knowable a priori.”

    How about

    (W1) Everything that is water is H20.
    (W2) Everything that is water is water.

    Of, if you accept (I2) as a priori, how about

    (I4) I am me.
    (I5) I am Dustin

    I do want to note that your argument has changed in an important way from your last comment. You appealed to a principle, which I counterexampled. Now you’ve offered a new principle, to which I have offered a new counterexample. Haha, jk. But seriously, there is something important to note here. The falsity of the general principle

    (Nate 1) Sentences that express the same proposition are epistemically equivalent.

    does cast the more specific principle

    (Nate 2) Sentences that express the same proposition are epistemically equivalent with respect to aprioricity.

    into considerable doubt. For why would be expect such sentence to always be equivalent with respect to a prioricity if they are not generally epistemically equivalent?

  12. dtlocke says:

    Oh, and no comment on my post?

    Weak.

  13. nate charlow says:

    “And, it wouldn’t be odd at all if ‘Julius’ had certain properties that ‘ordinary’ proper names lack, since it’s not clear that ordinary proper names have the descriptive content associated with ‘Julius’.”

    I can rephrase in terms of descriptions. On your view, one way to make a sentence fail to be a priori is to move a definite description (receiving an unbound interpretation) to topic position. That’s just as odd. If the relevant expression receives the same semantic treatment in both topic and non-topic position (and it will), why would the bare movement to topic position affect the epistemic status of the sentence?

    (Nate 2) is supported by a lack of counterexamples. (W1) and (W2) are not counterexamples because I don’t think they express the same proposition. Both (I4) and (I5) seem plausibly a priori.

    P.S. I read your post but I don’t think I’m qualified to comment on it. Sorry.

  14. Dustin says:

    RE: “Why would the bare movement to topic position [of Julius] affect the epistemic status of the sentence?”

    I don’t know. Presupposition reinstatement?

    RE: “(W1) and (W2) are not counterexamples because I don’t think they express the same proposition.”

    On what view of propositions? On the standard unstructured view of propistions, these express the same proposition (since they are true at all and only the same worlds). On the stanard structured view of propositions, these express the same proposition (because the property of being water = the property of being H20).

    RE: “Both (I4) and (I5) seem plausible a priori.”

    Did I forget to tell you that I forgot my name is ‘Dustin’? I came to use the name ‘Dustin’ only by reading the comments posted on this blog.

  15. nate charlow says:

    The movement to topic position doesn’t affect the presupposition borne by the expression (on an unbound interpretation). It bears the same presupposition in non-topic position. The only way to neutralize the presupposition, as far as I can tell, is to give it a bound reading.

    I know how I would defend (nate2) — roughly, I would argue that ‘water’ and ‘H2O’ carry different presuppositions, and that ensures that (w1) and (w2) express different propositions, on the view of presupposition that I accept — but it would be too controversial to be worth airing here. Really I don’t even need (nate2), since your view about the effects of movement to topic position are so strange.

  16. Dustin says:

    “Really I don’t even need (nate2), since your view about the effects of movement to topic position are so strange.”

    Sticks and stones may break my bones, but incredulous stares…

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