• Banno
    23.1k
    There's been some interest in Kripke's article Identity and Necessity

    There's a PDF at
    Identity and necessity, but it's pretty ugly. Someone might like to link to a better version.

    This paper predates the book Naming and Necessity, which has been treated elsewhere on this forum. It covers a similar set of ideas, so one of things we might discuss here is how the book differs from the paper.

    Kripke, at a very young age, developed a formal semantics for modal logic, presenting a completeness theorem. His work on possible world semantics ushered in a period of rapid and varied growth in that area. The present paper and the subsequent book look to the wider philosophical implications of that work.

    The key topic of the paper is 'How are contingent identity statements possible?", or as Kant may have put it, "How are synthetic a priori judgements possible?".

    So there's a start. This thread will be focused on this paper, and posters are asked to stay on-topic and engage with the paper and ideas/arguments therein (it is strongly recommended to read the paper, if you're not already familiar with Kripke's work)
  • Banno
    23.1k
    Here's the formal argument from the first pages.



    What's posited here is that if two things are identical then they are necessarily identical.

    So what? Well, if it is right - and it seems it is - then in no possible world is Clark Kent not Superman. For we know the Kent is Superman, and we can swapping x for Superman and y for Kent, we show that necessarily Kent is Superman.

    But surely it may have turned out that Superman had taken on a different secret identity?

    That's the pull of the argument attributed to David Wiggins.

    (the maths I used, for those wanting to use Mathjax is
    (1)\,(x)(y) [(x=y) \supset (Fx \supset Fy] \\(2)\,(x) \Box (x=x) \\(3)\,(x)(y) (x=y) \supset [ \Box (x=x) \supset \Box [(x=y)] \\ (4)\,(x)(y) [(x=y) \supset \Box [(x=y)]
    )
  • Shawn
    12.6k
    I'm on page 15 out of 30. It's an easy read if you're aquatinted with Naming and Necessity, which you can find here:

    https://thephilosophyforum.com/discussion/4545/naming-and-necessity-reading-group

    https://thephilosophyforum.com/discussion/4857/naming-and-necessity-lecture-three/p1

    Some thoughts about terminology. Kripke introduces the term de re modality, which I think to newcomers can be confusing. Care to address this @Banno?

    Further, on around page 15, Kripke brings up the statement, that the the 37'th president of the United States is non-rigid and Nixon is rigid. This would sound confusing to someone at first. I can attempt answering this on the basis that one doesn't need to invoke their imagination too wildly and simply designate that there could be a possible world where Humphrey won the election, thus it is contingent. However within the reference frame of our world Nixon won the the 37 elections for the president of the United States, making him a rigid designator. It's important to note that the possibility of 37th election of the United States sets up the possibility that out (this is our criteria condition for identity) of two possible candidates one or the other won. So, following from this we can only reference who won based on the feature of the world obeying causality (Kripke relies on a causal theory of reference).

    I'm not sure if this is a good place to start, so please let me know @Banno.

    Edit:

    I would like to reiterate where people go on a wild goose chase, that counterfactuals like Nixon could have lost the binary relation of either winning or losing the presidency or winning it with respect to the causal chain of events in our world, not some other, and hence the status of Nixon being a rigid designator is assigned by our world not any other. That's just one instance where a counterfactual could have arisen given the epistemic criteria that fulfills the condition of him winning or losing the election. Treat everything else as et. cetera.

    And, if it needs to be said in the positive that, yes, the causal chain of events would be the framing relation that allows Nixon to obtain as a rigid designator, in our world.
  • RussellA
    1.6k
    The key topic of the paper is 'How are contingent identity statements possible?", or as Kant may have put it, "How are synthetic a priori judgements possible?"

    Kant's synthetic a priori judgement is more in agreement with a Kripke necessary identity statement than a contingent identity statement, though Kant's synthetic a priori is more about knowledge by acquaintance than Kripke's knowledge by description.

    Contingent identity statements versus Kant's a priori judgements
    Kripke writes in the introduction: "“How are contingent identity statements possible?” This question is phrased by analogy with the way Kant phrased his question “How are synthetic a priori judgments possible?”. However, he later writes: "To state finally what I think, as opposed to what seems to be the case, or what others think, I think that in both cases, the case of names and the case of the theoretical identifications, the identity statements are necessary and not contingent"

    As regards contingent identity statements, such as "Hesperus is Phosphorus", from Hume's principle of constant conjunction, we logically infer that Hesperus is Phosphorus, and therefore is logically contingent rather than logically necessary.

    As regards Kant's synthetic a priori judgement, which is about a priori pure and empirical intuitions, it is not about the identity statement "the postbox is red", rather it is about the identity statement "this is red", and as a priori "knowledge", logically necessary.

    Synthetic a priori judgements
    I've always thought the phrase "synthetic a priori" was wrong, as it mixes two fundamentally different things. To my understanding, within language are synthetic and analytic propositions, some knowledge can be a priori and some a posteriori and within logic is the necessary and contingent. It is as if one said "anger is a heavy thing", not to be understood literally but metaphorically.

    "Synthetic a priori" means no more than humans are born with certain innate abilities, such as the innate ability to be able to distinguish between a loud and quiet noise, something hot and something cold, etc. Children don't need to go to school to be able to distinguish between a sweet and sour taste, as this is instinctive.

    The term a priori knowledge is not correct either, in that humans don't have a knowledge of the colour red before seeing it for the first time, but they do have the ability to see the colour red before ever seeing it for the first time. As an analogy, a wine glass passively shatters when the frequency of an opera singer's voice matches the natural resonant frequency of the wine glass, it is not the case that the wine glass is an active participant.

    The term "synthetic a priori" should be understood as an idiomatic expression rather than as a literal guide to Kant's doctrine of "transcendental idealism".

    Better copy of Identity and Necessity
    There is a web site, but one needs to sign in through your library.
    https://academic.oup.com/book/36436/chapter/320710138

    Anyway, I have to go now to see what Santa Claus has left under the tree.
  • litewave
    797
    What's posited here is that if two things are identical then they are necessarily identical.Banno

    Right, and our spacetime is necessarily what it is and could not have been different. Bye bye free will?
  • Shawn
    12.6k
    As regards contingent identity statements, such as "Hesperus is Phosphorus", from Hume's principle of constant conjunction, we logically infer that Hesperus is Phosphorus, and therefore is logically contingent rather than logically necessary.RussellA

    Sorry, but if you read the paper, Kripke posits the logicality on the empirical finding that Hesperus is Phosphorus. It's only a contingent identity statement upon observation that would allow us to conclude that it is Venus, in fact. Hence it is de facto a synthetic a priori upon examination via observation.
  • Shawn
    12.6k
    Right, and our spacetime is necessarily what it is and could not have been different. Bye bye free will?litewave

    Could you elaborate?
  • Mww
    4.5k
    The term "synthetic a priori" should be understood as an idiomatic expression rather than as a literal guide to Kant's doctrine of "transcendental idealism".RussellA

    Kantian transcendental idealism, not needing any inverted commas, is predicate on the possibility of synthetic a priori relations, and cannot stand without them, so must be understood as a literal guide to it, whether or not one regards the philosophy itself as legitimate.

    In Kant, identity is the ground for truth in analytic judgements, which are never contingent. Synthetic judgements do not rely on identity, and the truth of them relies on the relation between its conceptions, hence is contingent. Kripke wants to unite the contingent with identity, which Kant deemed, if not impossible, then at least logically insufficient in regard to a brand new philosophy.

    So maybe Kant’s term isn’t a mere idiom after all. Which is neither here nor there with respect to the thread.
  • litewave
    797
    Could you elaborate?Shawn

    Does Kripke believe that it is possible for us to act differently than we actually act? It seems he doesn't, because our actions are parts of spacetime and spacetime is necessarily identical to itself, which means it cannot be different than it is and so our actions cannot be different than they are.
  • Shawn
    12.6k
    That's the pull of the argument attributed to David Wiggins.Banno

    Could you provide that argument? I'm reading the paper again and see that Wiggins argument seems to point out the fact that sometimes we refer to the same object with two different proper names. But, he (Kripke) goes on to say that we discover these truths after observation, as in the case of Hesperus and Phosphorus being Venus.
  • Shawn
    12.6k


    I would argue that that is too strictly a transcendental argument. Every day we make choices where seemingly we could have done something otherwise. Even taking your argument to the extreme, there could be a possible world where causality would have allowed for a different event cone to allow a counterfactual to arise.
  • litewave
    797
    Every day we make choices where seemingly we could have done something otherwise.Shawn

    Yes, seemingly.

    Even taking your argument to the extreme, there could be a possible world where causality would have allowed for a different event cone to allow a counterfactual to arise.Shawn

    Quantum-mechanical indeterminacy could do that. But a world with a different outcome of a quantum measurement would be a different world, with a different identity, than our world. And I cannot be in both worlds, if by "I" we understand someone who is conscious of being only in one world. The "I" in the different world would be my copy, a counterpart.
  • Shawn
    12.6k
    But a world with a different outcome of a quantum measurement would be a different world, with a different identity, than our world.litewave

    Yes, a world which is called a possible world ...

    And I cannot be in both worlds, if by "I" we understand someone who is conscious of being only in one world. The "I" in the different world would be my copy, a counterpart.litewave

    The issue of personal identity is somewhat justified by the fact that my identity is consistent with the world that my personal I obeys causality in. The degree to which I have influence over the causal chain of events culminating in my identity is not a philosophical question, in my opinion.
  • Shawn
    12.6k
    Anyways, since the issue raised by @litewave often crops up in these discussions, here's a link. Fraught with controversy, I believe:

    https://plato.stanford.edu/entries/identity-transworld/
  • Banno
    23.1k
    ...de re modality...Shawn

    Yeah, it's an important, but fraught, distinction. I suspect focusing on it will cause yet more confusion. It's a distinction that is important because of ambiguities in natural languages, that simply do not carry over to formal modal languages.

    The de dicto interpretation has a wide scope for the modal operator:

    The discussion on p.164 is to the effect that if we can have necessary properties for individuals then (1) must hold; that (1) says the same as that F(x), even if F is (x)(x=x).

    So that page is mostly a justification for the soundness of the argument (1-4).
  • Banno
    23.1k
    For the rest, small steps. I would like to look a the paper with care, rather than moving ahed too quickly, or jumping to Kant or to the mind-body problem.
  • litewave
    797
    Yes, a world which is called a possible world ...Shawn

    But the actual world is still necessarily identical to itself and therefore cannot be something different than it is. My actions in a merely possible world may be different than my actions in the actual world but my actions in the actual world cannot be different than my actions in the actual world.
  • Banno
    23.1k
    , The issue addressed int he article is, how best are we to talk about necessity and identity? The article seeks to sort out the many confusions by looking at how we might pars natural languages in in a possible world semantics.

    This is germane to issues of free will and so on, but in a way logically precedes it. That is, we ought work out how best to talk about such issues prior to addressing them. Work out the grammar before we engage in the conversation.

    All this by way of requesting that we stick to the text for now, rather than wander off on a tangent.
  • frank
    14.5k


    In the early part he's basically explaining the problems with looking at proper names as descriptions.

    We learn empirically that Hesperus is Phosphorus. This couldn't be so if those two words were descriptions.
  • Banno
    23.1k
    We learn empirically that Hesperus is Phosphorus. This couldn't be so if those two words were descriptions.frank

    But we did learn that the star we see in the morning is the same as the star we see in the evening - they are both Venus.

    So we can learn that two descriptions are of the same individual.

    Now, necessarily, Hesperus is Phosphorus. But is is necessary that the morning star is the evening star?
  • Shawn
    12.6k


    If you really need a physical grounding for entertaining the notion of possible worlds, then assume the many worlds interpretation...AND there's no issue with things being deterministic given the MWI. You can still have counterparts and alternate versions of you.
  • Shawn
    12.6k
    The discussion on p.164 is to the effect that if we can have necessary properties for individuals then (1) must hold; that (1) says the same as that F(x), even if F is (x)(x=x).

    So that page is mostly a justification for the soundness of the argument (1-4).
    Banno

    The discussion on pg. 164 in N&N?
  • Banno
    23.1k
    No, in Identity and Necessity
  • Metaphysician Undercover
    12.3k
    Kripke wants to unite the contingent with identity...Mww
    That's what I would call a category mistake.
  • Shawn
    12.6k
    No, in Identity and NecessityBanno

    Oh, okay.

    The discussion on p.164 is to the effect that if we can have necessary properties for individuals then (1) must hold; that (1) says the same as that F(x), even if F is (x)(x=x).Banno

    I think it's important to make a distinction here about properties of objects and properties of individuals. Would it be accurate to label descriptions as also constituting properties also?
  • Banno
    23.1k


    Hmm. Individuals as in individual constants... a,b,c...

    and properties of individuals as in fa, fb, ga...

    Descriptions are presumably formula that pick out at least one individual. "The man who invented bifocals" would be something like "The x such that x is a man and x invented bifocals".
  • Banno
    23.1k
    Much of the next page is concerned with examples of two descriptions of the same individual.

    Let's look at "the author of Hamlet", "H". This picks out one individual. "The author of Hamlet might not have written Hamlet" has ambiguous parsings.

    It might be that Shakespeare did not write Hamlet; that the individual who did write Hamlet might possibly have not written Hamlet. Roughy


    It could not have been that the person who wrote Hamlet, whoever that was, did not write Hamlet; it is not possible that the person who wrote Hamlet did nto write Hamlet.



    The ambiguity dissipates because the scope of the existential and modal quantifiers is explicit.
  • Banno
    23.1k
    And hence to Russell's solution to the apparent problem of substituting descriptions not argument (1-4). The argument seem to be something like that, if P is being the first post master and B being the inventor of bifocals, our conclusion is something like



    "...here, x and y are both Benjamin Franklin, and it can certainly be necessary that Benjamin Franklin is identical with himself" p.166

    So descriptions will not result in the sort of paradox Wiggins seems to have had in mind.

    That's my reading to bottom of p.166. Kripke then passes on to proper names.
  • Shawn
    12.6k
    The ambiguity dissipates because the scope of the existential and modal quantifiers is explicit.Banno

    Can you elaborate about the scope? There is a large footnote about this in the text.
  • Banno
    23.1k
    Note 5? Seems to be about the differences in how the formula are to be written rather than anything of direct import.

    Quine had issues with extensionally opaque contexts, including modal considerations. Seems he wouldn't allow them as knowledge claims. He wouldn't have accepted , it seems.

    Not in the scope of my thinking.
  • Shawn
    12.6k
    Note 5?Banno

    Note 4.
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