Maverick Philosopher

Footnotes to Plato from the foothills of the Superstition Mountains

Of Birth and Barcan

The Opponent writes,

"Death is not an end to existence, but the process of becoming non-concrete. Birth is the making concrete of something that has existed since the beginning of time and will exist until the end of time." (Reina Hayaki)

This is one way of interpreting the Barcan formula (possibly for some x Fx implies for some x possibly Fx).  If the formula is true, there are no ‘contingent objects’, i.e. no objects that exist in some worlds but not others.

My position is that there are contingent entities (as well as contingent identities). I imagine you will be less sympathetic to this, however. Interested in your thoughts.

The Opponent is misrepresenting Professor Hayaki's view.  On a careful reading of her article, the quotation above is not her view but expresses a temporal analog of the modal view of Linsky and Zalta that she is opposing.

Barcan Contrapositive T-ShirtBe that as it may.  Let's consider the Barcan formula by itself.

The formula is that Possibly, something is F implies Something is possibly F.  The modality in question is 'broadly logical' in Plantinga's sense.  Some call it 'metaphysical.'   

By my modal intuitions, the formula is false.  A trio of  'possible' counterexamples.

A. Sally wants a baby.  But there is no actual baby such that Sally wants it.  Sally wants to have a baby, i.e, give birth to a baby, her own baby, one that does not yet exist.  What Sally wants is possible. So, possibly, some baby is such that Sally wants it.  But it doesn't follow that some actual baby is possibly such that Sally wants it. For every actual baby is such that Sally does not want it.

B. It is possible that there be a sinless man.  But it does not follow that one of the men who exist is possibly sinless.  

 

C. Possibly, some sloop satisfies Ortcutt's exacting specifications.  (It is possible that there be such a sloop.)  But it doesn't follow that some existing sloop (without modifications) is possibly such as to satisfy Ortcutt's exacting specifications.  For it could be that every sloop that exists fails to satisfy our man.

I am assuming actualism: there are no merely possible objects.  The truth of Possibly, something is F does not commit us to the existence of a merely possible individual that is F. 'Possibly, something is a matter transmitter,' for example, does not commit us to the existence of a merely possible matter transmitter.  I should think it commits us only to the existence of a conjunctive property that is possibly instantiated.

The Barcan formula may hold for necessary beings such as the number 7.  But it fails for contingent beings.

Of course I hold that there are contingent beings.  Whether there are contingent identities is another topic entirely.  One topic at a time. 

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Bill Vallicella

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18 responses to “Of Birth and Barcan”

  1. Astute opponent Avatar
    Astute opponent

    I did not mean to misrepresent Hayaki. The passage I quote, which is her paraphrase of the Linsky / Zalta position, is immediately followed by ‘I find this account highly counter-intuitive’, and she later argues that the real problem is fictional characters such as Sherlock Holmes. ‘If the character of Sherlock Holmes were a necessary existent, Conan Doyle could not have created it; it would simply have been discovered, in the way that a mathematical proof might be discovered’ (here she is paraphrasing Amie Thomasson, but with approval this time).
    I think your second counterexample may work for different reasons than non-existence. Buridan discusses ‘I promise you a horse’. This is not equivalent to ‘I promise you Alfie or I promise you Billie or etc’, but rather to ‘I promise you Alfie or Billie or etc’. I.e. it is not the non-existence of the promised horse that is the problem. I grant that ‘Sally wants a baby’ involves the non-existence of the wanted baby, but the similarity to ‘Sally wants a husband’ suggests that existence is not the reason. I agree with the other examples.
    The reason I said ‘I imagine you will be less sympathetic’ is ‘Death is not an end to existence, but the process of becoming non-concrete’. I thought you were sympathetic to the idea of a soul with an identity separate from the body, which can be separated from the body while retaining that identity. Where the soul exists before birth is more of a mystery, but wouldn’t the proposition that Bill Vallicella’s soul does not yet exist have been true 100,000 years ago? Generally, just as the Barcan formula implies that the domain of quantification cannot grow, doesn’t it imply that the domain of souls cannot grow?

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  2. BV Avatar
    BV

    Of course you didn’t intend to misrepresent Hayaki, but what you wrote misrepresented her. Another interesting example of how speaker’s meaning and sentence meaning can diverge.
    But doesn’t this make sense: Sally wants a husband, but there is no man alive such that Sally wants him to be her husband. Sally may be on a quixotic quest for Mr Right.
    Yes, the Barcan formula seems to imply that the domain of quantification cannot grow. This is presumably because nothing comes into existence on a possibilist scheme. This would seem to hold for Platonic souls as well: they pre-exist and post-exist their embodiment, and there are all the souls there might have been. Each then is a necessary being, and the domain of souls cannot grow.
    But this is all very murky to me, and I am still several hours away from holiday cheer.

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  3. Astute opponent Avatar
    Astute opponent

    >>This would seem to hold for Platonic souls as well: they pre-exist and post-exist their embodiment, and there are all the souls there might have been. Each then is a necessary being, and the domain of souls cannot grow.
    Right.
    Happy Christmas.

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  4. BV Avatar
    BV

    Same to you, old friend.
    It’s raining cats and dogs here this Christmas Eve. 40 more minutes of work and then I’ll pour myself a drink.

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  5. Astute opponent Avatar
    Astute opponent

    We didn’t get the Boulevardier this year, what with getting ingredients and all. Meanwhile I hope you enjoy this Western Christmas song. I have a soft spot for this music, as you may know.
    My Christmas present was Swinburne’s The Christian God where he questions the necessity of ‘Hesperus = Phosphorus’, so I am also checking out Kripke Naming and Necessity Lecture III (pp. 106 ff, 1981 edition if you have it) which has all the arguments quod sic. Particularly compelling is the argument on p.109.

    We have concluded that an identity statement between names, when true at all, is necessarily true, even though one may not know it a priori. Suppose we identify Hesperus as a certain star seen in the evening and Phosphorus as a certain star, or a certain heavenly body, seen in the morning; then there may be possible worlds in which two different planets would have been seen in just those positions in the evening and morning. However, at least one of them, and maybe both, would not have been Hesperus, and then that would not have been a situation in which Hesperus was not Phosphorus. It might have been a situation in which the planet seen in this position in the evening was not the planet seen in this position in the morning; but that is not a situation in which Hesperus was not Phosphorus. It might also, if people gave the names ‘Hesperus’ and ‘Phosphorus’ to these planets, be a situation in which some planet other than Hesperus was called ‘Hesperus’. But even so, it would not be a situation in which Hesperus itself was not Phosphorus.

    I have a follow up question, but interested if you find Kripke’s argument good.

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  6. BV Avatar
    BV

    I enjoyed the song very much and will try to remember it for next Xmas. One of these Sat. nights I will finish a post in which I ask about cultural appropriation, e.g., people who can’t rope and ride singing about being a cowboy, well-off whites singing the songs of blacks who were down and out when the white boys and girls never were, a middle-class English kid like Eric Clapton mastering the blues idiom of Robert Johnson, et al.

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  7. BV Avatar
    BV

    So does Swinburne reject a Millian theory of names? If ‘Hesperus’ and ‘Phosphorus’ refer directly and not via senses, then ‘Hesperus = Phosphorus’ if true has the logical form: a = a. And that must be true in every world in which a exists, and in that sense is necessarily true.
    Is this valid?
    Sam believes that Hesperus is F
    Hesperus = Phosphorus
    Ergo
    Sam believes that Phosphorus is F.
    Not valid. But the following is:
    Hesperus is such that Sam believes of it that it is F
    Hesperus = Phosphorus
    Ergo
    Phosphorus is such that Sam believes of it that it is F.
    Are we back to the problems that a Kripkean semantics has with belief?
    I am inclined to say that we don’t get at things in thought or language directly but only via senses and descriptions. Or if you insist that we do get at things directly, then those things are incomplete objects. A complete object is never given in its completeness to thought or perception.
    Our minds are finite and that finitude needs philosophical accounting.
    The man coming down the street, in reality, is infinitely propertied; but what I see is an item that is indeterminate in many respects.

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  8. Astute opponent Avatar
    Astute opponent

    >>If ‘Hesperus’ and ‘Phosphorus’ refer directly and not via senses
    I appreciate that but Kripke’s argument stands on its own without that assumption, at least not explicity. Here it is again:

    Suppose we identify Hesperus as a certain star seen in the evening and Phosphorus as a certain star, or a certain heavenly body, seen in the morning; then there may be possible worlds in which two different planets would have been seen in just those positions in the evening and morning. However, at least one of them, and maybe both, would not have been Hesperus, and then that would not have been a situation in which Hesperus was not Phosphorus. It might have been a situation in which the planet seen in this position in the evening was not the planet seen in this position in the morning; but that is not a situation in which Hesperus was not Phosphorus. It might also, if people gave the names ‘Hesperus’ and ‘Phosphorus’ to these planets, be a situation in which some planet other than Hesperus was called ‘Hesperus’. But even so, it would not be a situation in which Hesperus itself was not Phosphorus.

    What is the argument and what are the implicit assumptions, and what does it prove? That’s what I am grappling with.

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  9. BV Avatar
    BV

    This passage is extremely poorly written. (The lectures were actually spoken, and Kripke didn’t bother to re-write obscure passages.) But what Kripke is saying is as follows.
    1. In the actual world A, we use ‘Hesperus’ to refer to a certain bright object in the evening sky and ‘Phosphorus’ to refer to a certain bright object in the morning sky.
    2. In the actual world A, it is discovered that these bright objects are the same object, the planet Venus. So we say, ‘Hesperus is Phophorus.’
    3. There is a merely possible world W in which two different objects, call them Shesperous and Shposphorus, appear in the same positions as Hesperus and Phosphorus appear in the actual world.
    4. In W it remains true that Hesperus is Phosphorus.
    5. If the people in W use ‘Hesperus’ and ‘Phosphorus’ to refer to Shesperous and Shposphorus, the fact remains that Hesperus is Phosphorus.
    Therefore,
    6. ‘Hesperus is Phosphorus’ is true in every possible world in which Venus exists. And the same goes for ‘Shesperus’ and ‘Shposphorus.’ This is because names are rigid designators: their reference does not vary from world to world as it would if the reference of the names were routed through sense.
    >>Kripke’s argument stands on its own without that assumption,<< I think that is false. Kripke needs the assumption that names are rigid designators the reference of which is not determined by whatever happens to satisfy a description that encapsulates the meaning of the name. The meaning is the referent. Names are tags as far as reference is concerned. The passage is not so much an argument for the necessity of identity, as an elaboration of what follows from it.

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  10. Astute opponent Avatar
    Astute opponent

    >>Kripke needs the assumption that names are rigid designators the reference of which is not determined by whatever happens to satisfy a description that encapsulates the meaning of the name.
    Right. More later.

    Reply
  11. BV Avatar
    BV

    So did I explain the cryptic/Kriptic passage to your satisfaction?

    Reply
  12. Astute opponent Avatar
    Astute opponent

    >>So did I explain the cryptic/Kriptic passage to your satisfaction?
    The particular passage: yes, and thanks. The whole argument of which that is a part, no. I have now mislaid my copy, but it begins around p. 107 at the start of ch. 3, with all the ‘identity schmidentity’ stuff. My problem is that identity statements are in my view contingent, whether flanked by proper names or descriptions or anything else. E.g. the statement ‘Nabu-sharrussu-ukin is the same person as Nebo-sarsekim’ is contingent, for it is far from certain that the person mentioned in Jer 39:3, NIV is the same as the person mentioned in a certain clay tablet identified by Michael Jursa. And I think we can agree that proper names such as these are rigid designators in some sense. But if Kripke is correct, this means the identity statement is either true, in which case necessarily true, or false, in which case necessarily false, and so in neither case contingent. This is somewhat problematic.

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  13. BV Avatar
    BV

    Can you give me some more examples, examples that don’t presuppose your level of Biblical expertise?

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  14. Astute opponent Avatar
    Astute opponent

    The classic example, and one on which much thought has been expended and much ink has been spilt on the question of whether Shakespeare was the same person as Edward de Vere. This doesn’t work so well for me because ‘Shakespeare’ probably just means ‘the man who wrote the plays with the name ‘Shakespeare’ on them’, hence it is a definite description. What works for me are examples where each name occurs in only one source, and where the mention is brief. It is hard to find examples outside ancient texts. This works for Nebo-sarsekim. Jeremiah 39:3

    Then all the officials of the king of Babylon came and took seats in the Middle Gate: Nergal-Sharezer of Samgar, Nebo-Sarsekim a chief officer, Nergal-Sharezer a high official and all the other officials of the king of Babylon.

    That’s absolutely all we have. The other reference is the Nebo-Sarsekim Tablet

    [Regarding] 1.5 minas (0.75 kg) of gold, the property of Nabu-sharrussu-ukin, the chief eunuch, which he sent via Arad-Banitu the eunuch to [the temple] Esangila: Arad-Banitu has delivered [it] to Esangila. In the presence of Bel-usat, son of Alpaya, the royal bodyguard, [and of] Nadin, son of Marduk-zer-ibni. Month XI, day 18, year 10 [of] Nebuchadnezzar, king of Babylon.

    You don’t need any Biblical expertise to get your head round that part. Now it seems to that both names are rigid designators. We could suppose, e.g. (1) that in some possible world Nebo-Sarsekim had not achieved the rank of chief officer under the king of Babylon, and (2) that Nabu-sharrussu-ukin had never donated gold to the temple of Esangila. But the statement ‘Nebo-sarsekim was Nabu-sharrussu-ukin’ is clearly contingent.
    Also, the statement ‘there is no conclusive evidence that Nebo-sarsekim was Nabu-sharrussu-ukin’ seems to be true, whereas the statement ‘there is no conclusive evidence that Nebo-sarsekim was Nebo-sarsekim’ seems to be false. Yet we wouldn’t conclude from this that they must be different people. Clearly they could be the same, even though we can’t substitute one name for the other salva veritate. Note also this is not an epistemic matter or necessarily one connected with belief. The fact that there is no evidence, or no strong evidence, is unconnected with any beliefs we may have.

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  15. BV Avatar
    BV

    >>But the statement ‘Nebo-sarsekim was Nabu-sharrussu-ukin’ is clearly contingent.<< I am having a hard time understanding this. A rigid designator is a term that designates the same object in every possible world in which it exists. Now of course the object designated in your example is contingent. But that's not the issue. The question is whether the identity statement, if true, is true in all the same possible worlds. Now it has to be if the names are rigid designators. If it is true that Nebo = Nabu, then in every world in which both exist, they are the same individual. So the identity is necessary. If you hold that names are rigid designators, then you cannot hold that the identity is contingent. So I must be missing something.

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  16. Astute opponent Avatar
    Astute opponent

    >>If you hold that names are rigid designators, then you cannot hold that the identity is contingent.
    Then we must drop the assumption that names are rigid designators, at least in the sense that you defined rigid designation (‘designates the same object in every possible world in which it exists’).
    I stand by my claim that ‘there is no conclusive evidence that Nebo-sarsekim was Nabu-sharrussu-ukin’. I also claim that, since it is undeniable that Nebo is or was himself, it is false that ‘there is no conclusive evidence that Nebo-sarsekim was Nebo-sarsekim’.If you deny this and accept the second as true, you must also accept that there is conclusive evidence that Nebo-sarsekim was Nabu-sharrussu-ukin.

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  17. BV Avatar
    BV

    My definition is Kripke’s own and is standard in the literature. The df I gave is of weak rigidity. There is also strong rigidity. A term is strongly rigid just in case it designates the same object in every world, full stop. Names of necessary beings are strongly rigid if they are rigid.
    You said: >>Now it seems to that both names are rigid designators.<< Are you now retracting that? Or are you not clear about what a rigid designator is? I also get the sense that you are conflating epistemological with logical/metaphysical issues. I grant that there is no concl. evidence that Nebo = Nabu. But that is an epistemological point. I don't understand your last paragraph.

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  18. Astute opponent Avatar
    Astute opponent

    OK spelling it out.
    (A) there is no conclusive evidence that Nebo was Nabu
    (B) there is no conclusive evidence that Nebo was Nebo
    Do you see that sentences (A) and (B) are identical except for the substitution of ‘Nebo’ for ‘Nabu’? Then there are three possibilities.
    (1) The statements above have different truth values, and thus we reject substitutivity.
    (2) We accept substitutivity, and so accept they are both true or false together. Then if both true, we have to reject that there is any evidence for the principle of identity, A=A.
    (3) If both false, we concede there is conclusive evidence that Nebo was Nabu.
    You objected that (A) is epistemological. How is that relevant? There are only three possibilities. Either the statements have different truth values, or the same. If the same, then either both true, or both false. None of these are without difficulty.
    I reject substitutivity. On the meaning of ‘rigid designation’, can we set that aside for now.

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