Timeline for Why is Hesperus necessarily Phosphorus?
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| Aug 2, 2019 at 20:28 | comment | added | sdenham | I cannot argue "let x = 'Phosphorus'; let y = 'water'; therefore (from 5): necessarily, 'Phosphorus' = 'water'" can I? I guess the argument is that if x and y are at all identical, they are necessarily so? But then I don't see how I could say that it is possible that x and y are identical (or do I need an epistemic modal logic for that?) Furthermore, AFAIK and per @jobermark, the identity of Hesperus and Phosphorus is established only through astronomy, and so is nominally falsifiable, even if that is implausible? I think there's a possible world where they are different. | |
| Aug 27, 2015 at 0:34 | comment | added | Conifold | Aside from controversial alethic/epistemic distinction, in "non-epistemic forms of necessity...for a proposition to be necessary is for its truth to be, in a certain sense, particularly firm, secure, inexorable or unshakable in a wholly objective way. A necessary truth could not easily have been false (it could less easily have been false than a contingent truth)" plato.stanford.edu/entries/modality-varieties/#StrModRea Necessity ascribed to identities indiscriminately has no modal force, it is a decoration, and can not capture the sense in which necessity of identities is nontrivial. | |
| Aug 25, 2015 at 13:27 | comment | added | user5172 | Two things: One--necessity here is alethic, not epistemic. Saying: "necessarily p" doesn't mean "i am certain that p." (you can make an epistemic modal logic, but that's a different issue.) Second: sure, you can treat proper names as just disguised definite descriptions--that position is called descriptivism and it originated with Russell. Identities between definite descriptions are non-rigid (Kripke agrees!), so if names are just definite descriptions, the argument for the necessity of identity won't go through. But descriptivism has it's own theoretical costs. | |
| Aug 25, 2015 at 1:56 | comment | added | Conifold | So if I understand you correctly names are turned into rigid designators to get a system that validates Leibniz's law, which in particular makes identities necessary. That's all there is to it? And the kind of necessity it produces is a trivial one, in the sense that it does not express any degree of certainty in the identity, they are all trivially necessary, and the issue is shifted from necessity to truth. How is one better off than interpreting Hesperus and Phosphorus as Russell's descriptions, and dispensing with rigid designation altogether, along with Leibniz's law? | |
| Aug 23, 2015 at 11:54 | comment | added | user5172 | @jobermark The statement of Leibniz's Law I've given above is the standard formulation found in any introductory text of first-order logic. It's not itself a first order formula, of course, but that's no problem. (There's also obviously no problem with universal quantification over properties in second-order logic. Consider the sentence: "For all P, for all x (Px or not Px)". That's just a statement of bivalence. | |
| Aug 23, 2015 at 11:50 | comment | added | user5172 | @Conifold, "Case in point: F="appears in the evening" is true of Hesperus but not Phosphorus." False. it is true of Phosphorus that it appears in the evening. (Even if nobody knows that H=P, anything that is true of H is true of P.) "To save it descriptors have to be essential". I don't know what a "descriptor" is? A proper name? A definite description? Nobody has a problem with identities between definite descriptions being contingent. But "hesperus" is not a definite description; it's a proper name and proper names designate their referents rigidly (i.e. across worlds.) | |
| Aug 22, 2015 at 20:33 | comment | added | user9166 | So, the F's have to range over something. You can't quantify over all possible properties without paradox. Welcome to reality. If you arrange for proper logic otherwise, the domain of relevant F's just becomes a very indirect way of phrasing for my 'global theory' that establishes necessity. | |
| Aug 22, 2015 at 19:18 | comment | added | Conifold | Leibniz's "law", a.k.a. substitutivity of identity, is obviously false when x and y are descriptors, and they always are when identity is asserted non-trivially. Case in point: F="appears in the evening" is true of Hesperus but not Phosphorus. To save it descriptors have to be essential, but reducing essentialness of identity to essentialness of properties tells us nothing about the origin of essentialness, or of necessity. "Slick argument" long predates Kripke, Quine mentions it in Reference and Modality (sec. 3) after making exactly this point, and it is unsound or vacuous (Kripke's version) | |
| Aug 22, 2015 at 17:30 | comment | added | user5172 | Let's take an example. Choose as our domain of discourse a barrel full of apples. Suppose it's true that they're all ripe. Then it is true that "for every x, x is ripe." But that's quite different than saying that the apples have to be ripe. It is possible for an apple to exist without being ripe; we could have had some immature apples or some rotten apples in our domain of discourse even though in fact that didn't happen. Now contrast that with, "for all x, necessarily every x is x." This sentence says that every apple in the barrel had to be the same as itself, which seems plausible. | |
| Aug 22, 2015 at 17:27 | comment | added | user5172 | @Dave no, "for all x Fx" just says, "for every item in the domain of discourse, that item is an F." which is quite different than "it is necessarily the case that for every item in the domain of discourse, that item is an F" or "for every item in the domain of discourse, that item is necessarily an F." (There are two different sentences here with two importantly different meanings--because modal logic is simply far more complicated than ordinary first-order logic.) | |
| Aug 22, 2015 at 16:22 | comment | added | Dave | Doesn't the "for all x" clause already cover the idea that "x has to be ..."? | |
| Aug 22, 2015 at 1:16 | comment | added | user5172 | @Dave what it is adding is modality, i.e. modifying the way the assertion is being made. "x is an F" just says that it happens to be a matter of fact that x is an F. "x is necessarily F" says that x has to be F. making mathematically precise that sense of "has to" is what the modal logic is about. (there's different senses of "have to" and correspondingly different modal logics, by the way. the sense of "have to" involved in one's "having to" obey the moral law is quite different than the sense of have to in "everything has to be the same as itself." | |
| Aug 21, 2015 at 18:34 | comment | added | Dave | How is (2) different from (2'): For all x: x=x. What is the inclusion (introduction?) of the word "necessarily" adding to the statement? | |
| Aug 20, 2015 at 23:49 | comment | added | user5172 | Let us continue this discussion in chat. | |
| Aug 20, 2015 at 23:48 | comment | added | user9166 | No. You should read the whole question, and address his entire concern. | |
| Aug 20, 2015 at 23:48 | comment | added | user5172 | Then OP should make a separate question asking that. | |
| Aug 20, 2015 at 23:47 | comment | added | user9166 | The question, it seems obvious is "Generally, when we discover some persistent empirical coincidence, how are we to decide if it is necessary or just true?" | |
| Aug 20, 2015 at 23:45 | comment | added | user5172 | It isn't an astronomy question, it's a question about the logic of the identity relation--is that relation a contingent relation or a necessary one? Kripke's answer is "necessary" for the reason given above. | |
| Aug 20, 2015 at 23:44 | comment | added | user9166 | If that is the question, it is an astronomy question, and this is still not an answer. The title is not the question. | |
| Aug 20, 2015 at 23:34 | comment | added | user5172 | @jobermark The question is "Why is Hesperus necessarily Phosophorus", let x = "Hesperus", y = "Phospohorus" The stuff about essentialism is a confusion on the OPs part. | |
| Aug 20, 2015 at 23:32 | comment | added | user9166 | This is in no way an answer to the question. | |
| Aug 20, 2015 at 23:27 | comment | added | user5172 | also, for an alternate way of trying to make contingent identity possible, see the famous paper "contingent identity" by allan gibbered philpapers.org/rec/GIBCI | |
| Aug 20, 2015 at 23:23 | comment | added | user5172 | I also strongly recommend Jeff Speaks's lecture notes on Kripke: www3.nd.edu/~jspeaks/courses/2011-12/83104/handouts/… | |
| Aug 20, 2015 at 23:22 | history | answered | user5172 | CC BY-SA 3.0 |