Maverick Philosopher

Footnotes to Plato from the foothills of the Superstition Mountains

An Identity Theory of Predication

I will sketch a two-name, quasi-Scholastic, nominalistic/reistic  theory of predication that I believe is quite hopeless. But it may serve as a foil against which and in comparison to which a more plausible theory may be developed.

Suppose it is true that Sam is poor. What are the truth-conditions of 'Sam is poor'?  Rewrite the sentence as 'Sam is a poor individual.' Think of 'Sam' ('S') and ''poor individual' ('P') as names where the first name is proper and the second common. We assume that there are no universals. Accordingly, 'poor' in our original sentence cannot be construed as an abstract substantive, as a proper name for the universal poorness.  It must be construed as a common name for poor individuals.

And because we are assuming that there are no universals, we cannot parse 'Sam is poor' as 'Sam instantiates poorness.' Nor can we take the truth-maker of 'Sam is poor' to be the state of affairs, Sam's being poor.

First idea. 'Sam is a poor individual' is true just in case:

A. For some x, 'S' denotes x and for some x, 'P' denotes x.

This is obviously insufficient since it doesn't guarantee that the item denoted by 'S' is numerically the same as one of the items denoted by 'P.'  While the second two occurrences of 'x' are bound variables, they are not bound by the same quantifier. So we try 

B. For some x, 'S' denotes x and 'P' denotes x.

This is much better. The second and third occurrences of 'x' are bound by the same quantifier. This ensures that the item denoted by 'S' is identical to one of the items denoted by 'P.'  The first item is called 'Sam' and the second we can call 'Poboy.'  Obviously these names denote one and the same item given that our sentence is true.

This yields an identity theory of predication. A simple predicative sentence such as 'Sam is poor' is true just in case the denotatum of the subject term is identical to one of the denotata of the predicate term.  The truth-maker of the sentence is the identity of Sam with Poboy, i.e., the identity of Sam with himself.

Objection 1. Sam might not have been poor.  But it is not the case that Sam might not have been Sam. So the manifestly contingent truth  of 'Sam is poor' cannot be explained in terms of identity. 

Objection 2. That was a modal objection; now for a temporal one. The poor have been known to become rich. Suppose Sam goes from poor to rich.  The identity theory implies that Sam, who was identical to Poboy, ceases to be identical to Poboy and become identical to Richboy.  But surely this is absurd inasmuch as it is equivalent to saying that Sam, who was numerically the same as himself, is now no longer numerically the same as himself.

This is absurd because, if Sam changes in respect of wealth, going from poor to rich, there has to be a self-same substrate of this change. Sam must remain numerically the same through the change. After all, the change is accidental, not substantial. The identity theory of predication, however, cannot accommodate these truisms. For if Sam is poor in virtue of being identical to one of the poor individuals, then he cannot become rich without ceasing to be himself.

Notice how these problems disappear if properties are admitted.  Sam instantiates the property of being poor, but he might not have. Sam instantiates the property of being poor at one time but not at others.

I now invite the Noble Opponent to show how his version of the identity theory circumvents these objections, if it does.  

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22 responses to “An Identity Theory of Predication”

  1. John Avatar
    John

    Here’s a quick, not particularly Scholastic, thought: could the identity theory of predication be saved by adopting perdurantism as a theory about persistence over time?
    Consider your temporal objection to the identity theory: Sam becomes rich. At t1, Sam is identical to Poboy, whereas at t1, Sam is identical to Richboy. Your objection is: “surely this is absurd inasmuch as it is equivalent to saying that Sam, who was numerically the same as himself, is now no longer numerically the same as himself.”
    But now suppose that Sam persists over time by perduring, that is, having temporal parts. Then might we save the identity theory by saying that at t1, Sam’s t1-temporal-part is identical to Poboy, whereas at t2, Sam’s t2-temporal-part is identical to Richboy? It’s true that Sam’s t1-temporal part is not numerically the same as his t2-temporal part, but that’s no objection. Sam is just a cross-temporal whole composed of these different temporal parts, one of which is identical to Poboy, the other of which is identical to Richboy.
    This doesn’t touch your modal objection, but most metaphysicians willing to buy into perdurantism these days are happy to accept counterpart theory as a view about identity across possible worlds. So you could rig up a counterpart-theoretic defense of the identity theory of predication to handle your modal objection.
    I myself am not sympathetic either to perdurantism or counterpart theory. But I think it would be really interesting if they could be used to defend this theory of predication.

    Reply
  2. The Noble Opponent Avatar
    The Noble Opponent

    Equally, ‘some man is poor’ is true when for some x, x instantiates the property of being a man, and x instantiates the property of being poor. Thus a sentence of the form ‘some S is P’ is true just in case any object that instantiates the subject term ‘S’ is identical to any object that instantiates the predicate term ‘P’.
    So I don’t understand why the same objection does not apply to your property theory.

    Reply
  3. The Noble Opponent Avatar
    The Noble Opponent

    On the temporal objection, what is the problem meant to be?
    Both ‘was poor’ and ‘is poor’ can be true of one person, no?

    Reply
  4. The Noble Opponent Avatar
    The Noble Opponent

    Also, ‘Sam is poor’ is true if and only if Sam is identical with some poor man, whatever your theory of predication.

    Reply
  5. BV Avatar
    BV

    Hi John,
    Good to hear from you. It’s been a while. Are you still in grad school?
    As you realize, your perdurantist suggestion is not particularly Scholastic. I am not sure, but I don’t think any Scholastic was a perdurantist. I think it was just assumed that primary substances are wholly present at every time at which they exist. I think that is built into the Aristotelian notion of substance with which they operated. I could be wrong, but I don’t think any scholastic at any time ever raised the perdurantism vs. endurantism issue. What we call endurantism was just assumed.
    I invite refutation on this historical point.

    Reply
  6. BV Avatar
    BV

    John,
    We should also note that if Sam is a trans-temporal whole of temporal parts with rich parts following poor parts, then Sam at t1 cannot be identical to a poor temporal part as he would have to be if the truth-maker of ‘Sam is poor’ is the identity of the denotatum of ‘Sam’ with one of the denotata
    of the common name ‘poor individual.’
    If Sam is a whole of temporal parts, then at t1 Sam is not identical to Poboy, but rather has Poboy as a proper part. Identity is an equivalence relation, but *x has y as proper part* is not.

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  7. BV Avatar
    BV

    >>On the temporal objection, what is the problem meant to be?<< At t1 there is Sam and there are poor men. On the above theory, what makes 'Sam is poor' true is the identity of Sam with one of these poor men, call him 'Poboy.' So at t1, Sam = Poboy. At t2, Sam = Richboy (one of the rich men). Now it's a datum, a Moorean fact, that a man can go from poor to rich. But the above theory cannot accommodate this datum. This is because Poboy and Richboy are numerically distinct, which implies that Sam at t1 cannot be numerically identical to Sam at t2. But if you throw off your nominalist/reist straijacket and admit properties, then you can accommodate the datum. You can say that the accidental change from poor to rich is to be understood as Sam's instantiating poorness at t1 but instantiating richness at t2. This allows Sam to remain self-same through the change. But I am not endorsing this theory since it has its own different problems. I am making a negative point: the identity theory of predication I sketched does not hold water. Now tell me: is the theory I sketched the theory you endorse?

    Reply
  8. The Noble Opponent Avatar
    The Noble Opponent

    I still don’t follow why precisely the same objection doesn’t apply to the property theory.
    “At t1 there is Sam and there are poor men.” Likewise, at t1 there is Sam and there are men who possess the property of poorness. Anything you say about the ‘identity theory’ applies to the property theory.
    “On the above theory, what makes ‘Sam is poor’ true is the identity of Sam with one of these poor men”. Likewise, on your property theory what makes ‘Sam is poor’ true is the identity of Sam with one of the men who possess the property of poorness.
    “Poboy and Richboy are numerically distinct, which implies that Sam at t1 cannot be numerically identical to Sam at t2.” But Poboy was Sam, and Richboy is Sam. What’s the problem?
    “You can say that the accidental change from poor to rich is to be understood as Sam’s instantiating poorness at t1 but instantiating richness at t2. This allows Sam to remain self-same through the change.” Likewise, the accidental change from poor to rich is to be understood as Sam’s being denoted by ‘poor’ at t1 but being denoted by ‘rich’at t2. This allows Sam to remain self-same through the change.
    >>Now tell me: is the theory I sketched the theory you endorse?
    I cannot agree to what I do not understand. Your whole account utterly mystifies me.

    Reply
  9. John Avatar
    John

    Hi Bill,
    It has indeed been a long time! Dissertations have a tendency to take over one’s life, as you well know. Happily, it’s finished, and I have my Ph.D. now. Unhappily, I am suffering through the various indignities of the job market.
    Anyhow, as for the historical point, I completely agree. No Scholastic that I am aware of is a perdurantist, and they would all agree that change of any sort requires a persisting substratum. (Although – and this is purely speculative, as I don’t know nearly enough about it – there are apparently some reasons to think Peter Abelard might’ve been a mereological essentialist of a certain kind, and would’ve treated ordinary objects as entia successiva. So the theoretical resources for a kind of Scholastic perdurantism might have been available.)
    I had been thinking, however, that the identity theory of predication discussed here was offered not primarily as a historical curiosity, but a candidate for truth. So even if no Scholastic would’ve endorsed perdurantism, it remains an interesting question whether perdurantism can rescue the theory.
    Turning to your worry about the view I propose, I think perhaps we need to be more careful in formulating the view. Here is the suggestion (and, for the sake of simplicity, I will suppose that there are just two times, t1 and t2). We start with two entities, Sam-at-t1 and Sam-at-t2. Together, these compose Sam. (I hope the order of presentation isn’t misleading. We could as easily start with Sam and divide him into his temporal parts.) Thus, Sam-at-t1 is a proper temporal part of Sam. Likewise for Sam-at-t2. Now, composition is not identity, so – as you rightly point out – Sam is not identical either to Sam-at-t1 or Sam-at-t2, but instead has these as proper temporal parts. But the theory I was suggesting is that it is *Sam-at-t1* that is identical to Poboy, and it is *Sam-at-t2* that is identical to Richboy. Thus, Sam has both Poboy and Richboy as proper temporal parts, for each of these is identical to one of Sam’s proper temporal parts.
    In other words, I think your objection can be addressed by being careful to distinguish phrases like ‘at t1 Sam’ and ‘Sam-at-t1’. The latter is a proper name for a temporal part of Sam, but the former is not. So it’s quite correct to say that “at t1 Sam is not identical to Poboy”, but it doesn’t follow that “Sam-at-t1 is not identical to Poboy”.
    Hopefully this is a bit clearer.

    Reply
  10. The Noble Opponent Avatar
    The Noble Opponent

    >>Poboy and Richboy are numerically distinct,
    No. ‘Poboy’ is a name given to Sam when he was poor. ‘Richboy’ is a name given to the same person after he became rich. So Poboy and Richboy are not numerically distinct. They are one and the same person.
    Note also that while Poboy was once poor, he is so no longer.

    Reply
  11. The Noble Opponent Avatar
    The Noble Opponent

    >>It must be construed as a common name for poor individuals.
    Perhaps this is the key to my puzzlement. I think you are assuming that a common name rigidly designates, i.e. if it is a name for n individuals in this possible world, then it designates the same n individuals in every possible world, and every possible time.
    I.e. you are assuming that if ‘poor’ designated Sam at t1, then equally it must designate Sam now, at t2. Who would hold such a theory?

    Reply
  12. David Brightly Avatar
    David Brightly

    Bill, Why do you say that Poboy and Richboy are numerically distinct? Do you see the denotations of ‘poor’ and ‘rich’ as fixed and exclusive, perhaps? But can’t the denotations change so that something denoted by ‘poor’ at t1 can be denoted by ‘rich’ at t2?

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  13. BV Avatar
    BV

    Opponent @ 2:14:
    >>I still don’t follow why precisely the same objection doesn’t apply to the property theory.
    “At t1 there is Sam and there are poor men.” Likewise, at t1 there is Sam and there are men who possess the property of poorness. Anything you say about the ‘identity theory’ applies to the property theory.<< You are just not getting it. First of all, we are both assuming that Sam persists by enduring, not be perduring. John can explain this if it needs explaining. It is a datum that Sam undergoes what scholastics call an accidental as opposed to a substantial change: Sam goes from being poor to being rich. Now suppose that there are properties and that they are universals. Suppose that one of them is poorness. Now it is obvious that Sam is not identical to poorness. It is rather the case that Sam instantiates poorness at t1 but no longer instantiates it at t2 when he is rich. You understand, of course, that identity is an equivalence relation and that instantiation is not. But you don't like properties. So you say that 'Sam is poor' is true in virtue of Sam's identity with exactly one of the poor concrete particulars denoted by the predicate 'poor' construed as a common name. I introduce 'Poboy' as the proper name of this concrete particular. So your theory boils down to this. Sam is poor at t1 in virtue of Sam's identity with Poboy at t1. But Sam = Poboy. So Sam is poor at t1 in virtue of Sam's identity with himself at t1. It follows from this that Sam cannot undergo an accidental change from poor to rich. Why not? Because if he did he would not longer be numerically self-same. Why not? Because if Sam = Poboy, then Sam = Poboy at every time at which Sam/Poboy exists. It cannot be that a = b now but not at every time at which a/b exists. But it can easily be the case that a is F now but not at every time at which a exists given that F-ness is an accidental property of a. Capiche?

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  14. Opponent Avatar
    Opponent

    >>So Sam is poor at t1 in virtue of Sam’s identity with himself at t1.
    No. Who is saying this?
    >>You are just not getting it.
    No.

    Reply
  15. Opponent Avatar
    Opponent

    Trying again.
    (1) Sam is poor at t1 iff Sam is identical with some poor person at t1
    (2) Sam is poor at t1 iff Sam is self-identical at t1
    (1) is self-evidently true. For it cannot be true that Sam is poor, but not identical with some poor person. Nor can it be that false Sam is poor, but true that he is identical with some poor person.
    But (2) is false. Sam is necessarily self-identical, but not necessarily poor. Therefore (2) does not follow from (1), for a false statement cannot follow from a true one.
    The fallacy is in assuming that being identical with some poor person is the same fact as being identical with oneself.

    Reply
  16. BV Avatar
    BV

    Question for John:
    Do you understand my Objection 2? Do you agree with it? How would you explain it?

    Reply
  17. arash Avatar
    arash

    I have a question: how can the nominalist explain that “Poboy was Sam, and Richboy is Sam” is not simply matter of switching names over time but indeed a substantial change?

    Reply
  18. The Noble Opponent Avatar
    The Noble Opponent

    >>I have a question: how can the nominalist explain that “Poboy was Sam, and Richboy is Sam” is not simply matter of switching names over time but indeed a substantial change?
    Change from poor to rich is an accidental, not a substantial change. The statement ‘Poboy was Sam, and Richboy is Sam’ does not describe any kind of change. ‘Poboy was poor, and Poboy is rich’ describes an accidental change, because ‘is poor’ adds information that is not given by a proper name alone. John Stuart Mill said that common names are ‘connotative’ i.e. descriptive whereas proper names are simply marks, like a cross upon a door. I suspect this is what Bill is missing.
    Bill, I suggest you look at section §5 of book I, chapter i of A System of Logic. I am surprised you have not come across this before – it used to be a part of most undergraduate courses in logic and scientific method. You know, connotation denotation etc. Mill lifted the whole idea from Ockham.

    Reply
  19. BV Avatar
    BV

    Thanks for responding to arash.

    Reply
  20. arash Avatar
    arash

    >> Change from poor to rich is an accidental, not a substantial change. The statement ‘Poboy was Sam, and Richboy is Sam’ does not describe any kind of change. ‘Poboy was poor, and Poboy is rich’ describes an accidental change, because ‘is poor’ adds information that is not given by a proper name alone.
    Thanks for your answer and correction. My use of the term “substantial” was indeed misleading with respect to your philosophical jargon. Actually what I meant by “substantial” in that sentence was simply an alternative maybe loose way to say “related to the thing” or “in re”. Sorry for the misunderstanding.
    But pls let me rephrase my question according to your hints: how can a nominalist explain that in the past Poboy was identical with Sam, and in the present Richboy is identical with Sam, in a way that doesn’t imply accidental change in re nor any arbitrary naming convention change?

    Reply
  21. Opponent Avatar
    Opponent

    >> how can a nominalist explain that in the past Poboy was identical with Sam, and in the present Richboy is identical with Sam, in a way that doesn’t imply accidental change in re nor any arbitrary naming convention change?
    I don’t understand the question. ‘Poboy’ and ‘Richboy’ are proper names. Once you have dubbed an object with a proper name, the name sticks, is rigid. So once we have agreed to call this poor man ‘Poboy’, he remains Poboy, even if he becomes rich.
    Could we have a proper name that refers the object only if the object satisfies certain conditions, say being poor? In that case the statement ‘Poboy is not poor’ would not make any sense, because ‘Poboy’ would fail to have a reference, would be an empty name.
    But I am not sure I understand your question.

    Reply
  22. arash Avatar
    arash

    >> But I am not sure I understand your question.
    Thanks for your answer. Concerning your doubts, I would like to stress in that example (*) we have three names indeed: namely “Poboy”, “Richboy” and “Sam”.
    In the past “Poboy” and “Sam” were coreferring to numerically the same individual, and in the present “Sam” and “Richboy” are coreferring to numerically the same individual.
    From that example two questions arise: firstly, are the name “Sam” in the past usage and the name “Sam” in the present usage coreferring to numerically the same individual? Secondly, are “Poboy” in the past and “Richboy” in the present usage coreferring to numerically the same individual?
    It seems to me that the answer to the first question is yes , and to the second one it’s no. It follows to me that Sam has switched nicknames: from “Poboy” to “Richboy”. Therefore if you agree on that, I’m still wondering how you would explain this name change without supporting the distinction between substance and accident, individual and properties (or at least this is how I understood your position from your exchange with Bill).
    Anyway I guess you are giving an answer also to my question while commenting in another post: http://maverickphilosopher.typepad.com/maverick_philosopher/2017/02/a-thomist-analysis-of-change.html
    where, by the way, you seem to accept the distinction between indidual and properties: “Of course, one and the same thing can have different properties at different times”. So I’ll follow your answers from there if you don’t mind.
    (*)
    >> in the past Poboy was identical with Sam, and in the present Richboy is identical with Sam,

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