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"Hesperus (the evening star) is Phosphorus (the morning star)" is one of Kripke's examples of necessary aposteriori, statements that are true necessarily if true at all, even if their truth can only be established empirically. Since this is a path from is to ought there is a catch. According to Kripke (in Soames's phrasing), "being non-identical is a relation that holds essentially of any pair it relates. So, we know apriori that if any objects... stand in this relation, then they have, or stand in, them in any genuinely possible circumstance in which they exist". "Water is H20" necessarily for the same reason, although here identity is applied not to singular objects but to "natural kind" of objects.

I understand the reasoning, what I do not understand is what drives it. What makes some properties/relations essential and others not? what do we gain by attaching "essential" to them, and "necessarily" to statements? For example, is "inertial mass=gravitational mass" necessarily? Like Hesperus and Phosphorus they appear in two ostensibly different situations, when measuring inertia and attractive force respectively, however every measurement to date produced identical results. It is as empirically solid as the identity of Venus's manifestations, and a postulate of general relativity. But is it necessary? and what does that mean in practice? What about "green is extended" that Quine puzzled over, certainly every manifestation of green we met or imagined was extended in space?

Generally, when we discover some persistent empirical coincidence, how are we to decide if it is necessary or just true? I can think of two possible approaches, a testing principle or a guiding principle, perhaps their is a third or they can be mixed.

1) Testing: necessity is relative to a set of presuppositions to be tested. We heuristically designate some relations as essential, and see what distribution of necessities/contingents obtains, then we test if it works. Obviously we can not test it directly, since possible worlds are empirically inaccessible, but perhaps attaching modal logic to scientific theories may prove fruitful/unhelpful in some ways. This is not the impression I get from Kripke, he seems to envision some absolute intuitions about essential and necessary, but were there any concrete proposals for testing them, from others perhaps?

2) Guiding: there is some methodological principle or a speculative model about how the world works that motivate essentialness. Perhaps, not a cut and dry prescription but solid enough to specify broad classes of properties/relations as definitely essential, and others as definitely not. If so, what is this principle, and why is it plausible?

Conifold
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    Are you intending to ask this only in the context of Kripke? –  Aug 20 '15 at 23:32
  • @jobermark Not really. The problem with necessity goes at least as far back as Hume's criticism of causality, and is a variation on the circularity of reasoning problem explained in Quine's criticism of analyticity. Solutions proposed by Kant and Carnap respectively, did not work out. I am not sure Kripke himself is that interested in philosophical foundations of modal logic, but his views are popular, so perhaps others are. – Conifold Aug 22 '15 at 19:44

2 Answers2

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I guess I would go with at testing procedure -- consistency with a stated or implied theory.

Necessity is a modality -- the collection of 'must' statements, construed as rigidly as possible.

Instead of Kripke's semantics, consider an older (and better) way of looking at modals.

Modal assertions are incomplete statements that gain meaning only when an appropriate context is affixed. So necessity is dictated by what part of your reality is considered accidental, and what part is considered 'the context in which you are operating'.

A necessity statement gains meaning only when a global theory is attached. At that point the consequences of the theory are necessary, anything that does not violate it is possible, and everything else is just true or false.

This style of modal reasoning is most obvious in the modality of obligation. Every 'should' statement only has implications when an ethics is attached. By the ethics of Aristotle we should not kill our parents. By the ethics of Manson we probably should.

A similar relativism applies to 'essence'. Pick your paradigm, and its basic terms dictate what is essential. For biology, acidity is an accident; for basic chemistry it may be essential; for physics, it is emergent.

To the motivating statement by Kripke, any modern mathematician must consider it childish.

There is no 'essentially essential', there is always an equivalence relation: a definition of 'essential' which eliminates all other details and establishes the context in which one is working. In a broader context, the things we consider different are really the same, in a narrower context, we can look inside our equivalence classes and study the structure of the isomorphisms hiding information from us.

  • I don't understand the downvote, one way or another modal logic is relative to its presuppositions, and will be tested by practice or lack thereof. However, relativism by itself is barren, I am interested in general ways of deciding on essence and necessity given a global theory. This was exactly Carnap's sticking point with analyticity according to Quine: how does one go about defining analyticity relative to a framework generally, rather than postulating analytic parts ad hoc case by case. – Conifold Aug 22 '15 at 19:34
  • The problem is that Wittgenstein is not wrong. The usefulness of language itself is relative to a set of purposes. Any notion of necessity really does depend on the context established by that set of purposes. Attempts to evade that just result it a lot of circular hand-waving.

    At the same time, I don't see where acknowledging the primacy of context results in anything ad-hoc.

     –  Aug 22 '15 at 20:09
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Are you reading Naming and Necessity or the paper Identity and Necessity?

If you're just looking at N&N, then I encourage you to look at the paper, because Kripke there gives a pretty slick argument for the necessity of identity that is perfectly straightforward.

It starts from Leibniz's Law, which Kripke (plausibly) takes a kind of implicit definition of the very notion of identity:

(1) for all x, y (if x = y, then (if Fx, then Fy)) [premise]

The only other premise we need is the perfectly obvious truth that:

(2) for all x, it is necessarily the case that x = x. [premise]

The clever trick is that we instantiate (1) with the property of being necessarily identical to x for the dummy predicate F to obtain:

(3) for all x, y (if x = y, then (if necessarily x = x, then necessarily x = y)). [from 1, by universal instantiation.]

And now, we universal instantiate (3) to get:

(4) if x = y, then necessarily x = y [universal instantiation (3)]

and then:

(5) necessarily x = y [from 2, 4, modus ponens].

that's the argument that identity is necessary. Now the other philosophical question is what does the necessity of identity show us? That question is much more open ended and difficult to answer. Certainly the immediate consequence of Kripke's argument was to pose some difficulties for physicalist philosophers of mind in the 60s (who thought that the mind = the brain's activity, but that this was merely contingent. NOTE this isn't an argument against physicalism, just one particular flavor of it popular in the 50s-60s.)

The issue about "essentialism" is somewhat different. Kripke also believes that the names of natural kind terms are "rigid designators", which refer to the same kind necessarily. Whether Kripke is right that natural kinds terms are rigid designators is a separate issue from the question whether identity is necessary or contingent.

  • I also strongly recommend Jeff Speaks's lecture notes on Kripke: http://www3.nd.edu/~jspeaks/courses/2011-12/83104/handouts/kripke-lecture-2.pdf –  Aug 20 '15 at 23:23
  • also, for an alternate way of trying to make contingent identity possible, see the famous paper "contingent identity" by allan gibbered http://philpapers.org/rec/GIBCI –  Aug 20 '15 at 23:27
  • This is in no way an answer to the question. –  Aug 20 '15 at 23:32
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    @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 '15 at 23:34
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    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 '15 at 23:44
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    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 '15 at 23:45
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    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 '15 at 23:47
  • Then OP should make a separate question asking that. –  Aug 20 '15 at 23:48
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    No. You should read the whole question, and address his entire concern. –  Aug 20 '15 at 23:48
  • Let us continue this discussion in chat. –  Aug 20 '15 at 23:49
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    How is (2) different from (2'): For all x: x=x. What is the inclusion (introduction?) of the word "necessarily" adding to the statement? – Dave Aug 21 '15 at 18:34
  • @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 22 '15 at 01:16
  • Doesn't the "for all x" clause already cover the idea that "x has to be ..."? – Dave Aug 22 '15 at 16:22
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    @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 '15 at 17:27
  • 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 '15 at 17:30
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    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) – Conifold Aug 22 '15 at 19:18
  • 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 '15 at 20:33
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    @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 23 '15 at 11:50
  • @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 '15 at 11:54
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    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? – Conifold Aug 25 '15 at 01:56
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    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 '15 at 13:27
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    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)" http://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. – Conifold Aug 27 '15 at 00:34
  • 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. – sdenham Aug 02 '19 at 20:28