*This post is quite compressed and relies on things explained in the previous posts on the task of linking necessity to apriority, as well as alluding to my account of necessity as expressed in my PhD thesis. In a future post, I intend to explain and explore what these developments mean for my account of necessity.*

There has recently appeared an unpublished manuscript on PhilPapers (PDF available here at time of writing) which contains even stronger counterexamples to both Casullo's and my proposed link between necessity and apriority. It is by Margot Strohminger and Yuhani Yli-Vakkuri.

Strohminger & Yli-Vakkuri argue that Kipper's examples are contentious, relying on dubitable assumptions about natural kind terms and perhaps even embracing what they call 'Chalmersian two-dimensionalist ideology'. They provide even simpler examples of propositions whose general modal status cannot be known

*a priori*(and, relevantly for me, these examples also don't seem to be

*implied*by propositions whose general modal status can be known

*a priori*). For example:

Bob Dylan is at least as tall as Robert Zimmerman.This is necessary, since Bob Dylan

*is*Robert Zimmerman. But for all we can know

*a priori*, Dylan and Zimmerman are distinct, in which case this proposition would not be necessary, but contingent.

But hold on a minute! My link appeals to implication, and I said that the example above isn't implied by a proposition whose general modal status is knowable

*a priori*. But can't we say that it is implied by 'Bob Dylan is Robert Zimmerman', which we can know

*a priori*to be necessary? Yes, we can - although here we need a notion of implication which takes into account the meaning of 'is at least as tall as' - or at least the fact that it's a certain kind of comparative expression - rather than just the meanings of subject-neutral particles like 'or', 'all' and 'some'. So, from the point of view of disproving Casullo's proposed link, this example may be the best available so, but from the point of view of disproving my proposed implication-involving link, Kipper's natural kind examples may still have an edge.

It seems to be a very exciting time to be thinking about these issues! So far, in this post and the last, I've been talking about how these examples affect my proposed link between necessity and apriority. But the situation is more serious than that for me. The centrepiece of my PhD thesis was an account of the conditions under which a proposition is necessarily true (I've blogged about this account quite a bit here). And these developments, as far as I can tell, may well show that account to be false. This is very momentous for me, as I worked on that account for several years and considered it to be maybe my best bit of work.

I can't believe I didn't think of the example above in connection with my account! I even considered a very similar example when making a side point about using my notion of a genuine counterfactual scenario description (used in my account of necessity) to arrive at a definition of rigid designation which is in some ways more fundamental than the Kripkean one.

Stay tuned for more on whether and how these developments affect my account of necessity, and what can be done about it if they do.

I thought we went through this with your "Hesperus - Phosphorous" example in "On negation and necessities about concrete existence".

ReplyDeleteAny statement of equivalence (a=b), where the referent of the first term is x1, and the referent of the second term is x1 (i.e., where the two terms are referentially identical) is necessarily true, since it expresses an automorphism. We could add that the property wrt which the equivalence holds must be an appropriate one. "just as tall as" or the weaker "at least as tall as" will do as equivalence relation significances. Whether what is described in the statement exists out there in the world does not enter in to the judgment. "Given name - nom de guerre" may be risky, so 'Morning Star' - 'Evening Star' might be better (at least as big as").

JPL (the modality fan)

Pardon the late reply.

DeleteNo, 'Hesperus is Phosphorus' doesn't pose the same difficulty because it can be known a priori to be either necessarily true or necessarily false. The point of the Strohminger/Yli-Vakkuri example is that it is not like that, and nor is it implied by a proposition which is like that (at least not on an austere formal view of implication).

Thanks for the reply! I may not be connecting yet with what you’re trying to do, but I think I’m getting a better idea of it reading your recent posts and the intro of your diss. Let me just try to indicate why I find sentences like “Bob Dylan is (at least) as tall as Robert Zimmerman” interesting, coming at the problem as a linguistic semanticist.

ReplyDeleteWe can imagine an alternative history of science where the celestial object called “the morning star” is not known to be one and the same object as what is called “the evening star”. Nevertheless, scientists are able to measure the objects with exactness, and they determine that “the morning star is as big as the evening star”. In more exact terms,

1. “the morning star is equivalent in circumference to the evening star”.

This is regarded as a curious but solid empirical fact, and scientists wonder whether there is any reason why this is so. By and by, scientists discover that

2. the object they call “the morning star” is identical to the object they call “the evening star”, i.e., that they are referring to one and only one object with these two expressions.

They at once have an explanation for the empirical fact expressed in (1), but this sentence now expresses a necessary truth, and a true discovery about the world that exists independently, etc. Although previously (1) expressed an empirical truth, now (1) expresses a necessary truth, the necessity of which no longer depends on the relation to the world, but only on the fact that it is an instance of the logical form called “automorphism”. We no longer need to actually measure the object; if the order of discovery had been different, we could have saved ourselves the trouble. The objects could later turn out to be illusions, but as long as the measurements remain valid, (1) is still true in both senses.

(1) Expresses the equivalence relation between the objects referred to by the expressions “morning star” and “evening star”, and (2) expresses the fact that reference using these two expressions is to only one object. Therefore (1) is an instance of the rule I expressed in my above note as

3. “Any statement of equivalence (a=b), where the referent of the first term is x1, and the referent of the second term is x1 (i.e., where the two terms are referentially identical), is necessarily true, since it expresses an automorphism.”

So (1) is necessarily true because it is an instance of the automorphism principle, that any object is equivalent to itself wrt all possible properties. (Sometimes this is called the principle of “identity”, but I prefer the term “automorphism” here.) And one and the same sentence (1), uttered at t1 before the discovery and at t2 after the discovery, has two different meanings (in my terminology, two different propositions), both true of the world (which hasn’t changed), but different, since at t2 it includes the understanding that reference is to one object and not two. “Hesperus is Phosphorus” is true because of presupposed (“relatively a priori”) facts of the language system, but does not express an equivalence relation; the truth of (1) depends upon the fact that, given the linguistic facts, it is an instance of the automorphism principle, and upon that alone. A statement of the automorphism principle in a formal language context would be necessarily true presumably because of its axiomatic position, and it’s this statement that would have a priori status and ultimately confer that status on instances of it. The question of what makes the general principle of automorphism necessarily true is interesting and can be pursued by metamathematical analysis. (I don’t like the idea of resting with “self- evident truth”.)

I haven’t been able to address your particular concerns, but your posts made me consider this interesting case, so thanks!.

JPL

I might add that the case of "Bob Dylan is (at least ) as tall as Robert Zimmerman" is slightly different, because ordinary language usage can be inexact and crude, and because the property wrt which the equivalence relation is expressed as holding may not be an appropriate one. If the expression of referential identity ("Bob Dylan is Robert Zimmerman") is true, then a comparison wrt an intrinsic property (e.g., "Robert Zimmerman is as talented as Bob Dylan") would be necessarily true, but a comparison using an extrinsic property (e.g., "Robert Zimmerman is as famous as Bob Dylan") may not be true. If we, e.g., say that,

ReplyDelete4. Barry Humphries is (at least) as big as Dame Edna":

even though it's true that

5. Dame Edna is Barry Humphries,

(4) may nevertheless be false, since Dame Edna may in fact have a little more padding than Humphries. We may not want to say that (5) implies (4), since we may want to say that a more precise description would recognize two different objects, the man and the character, and thus that the principle of automorphism does not apply.

Again, I'm not sure if this is relevant to your concerns; I simply found this case interesting in various ways.

JPL