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Derivation vs. Generic Theories – part 4: Problems for a Derivation View (JT)

Q stunned

“You were filming that?”

In the last post, I explained that for Athanasius’s version of the derivation view, when the Father generates the Son, the Father shares his substance with the Son. That means, I took it, that the Father himself becomes a constituent in the Son, similar to the way that a lump of bronze is a constituent in a bronze statue.

One of the things Athanasius wants to do with this idea is explain how the Son is divine/God. The basic idea is that the Father shares his substance, i.e., Divinity, with the Son, and so the Father shares his properties with the Son. That is, to put it the other way around, the Son inherits properties from the Father. This is supposed to account for how the Son gets divine properties. However, this is where we start to run into problems.

Suppose, for example, we said that the Son inherits all the Father’s properties. If that’s the case, then for any property the Father has, the Son will inherit it and therefore have that property too.

This might be desirable for all the divine properties like omniscience, omnipotence, and so forth because we might want to say that the Son is all those things. But what about the Father’s property of begetting the Son? Consider an argument given by Richard Cross:

  1. The Son inherits all the Father’s properties =df for any F,
    if the Father is F, the Son is F.
  2. The Father begets the Son.
  3. Therefore the Son begets the Son.

Is this feasible? Well, not if we assume that begetting is an irreflexive relation. If begetting (or, more generally, production) is irreflexive, then nothing can beget itself:

(T2) For any x, it is impossible for x to beget x.

If that’s right, then T2 contradicts (3), so we have a problem. Of course, we might reject T2, but that doesn’t necessarily get us out of hot water. After all, we might just reformulate (1) – (3) like this:

  1. The Son inherits all the Father’s properties =df for any F, if the Father is F, the Son is F.
  2. The Father is unbegotten.
  3. Therefore the Son is unbegotten.

But (3) contradicts the original claim T1: the Son is begotten by the Father. So we’re still in trouble. We might point out that being unbegotten is not a genuine property, but rather only a logical negation. Even so, if (1) and (2) are true, it’s hard to see how (3) wouldn’t follow, irrespective of whether or not negative properties (like being unbegotten) are real, extramental properties. At the very least, then, we have a logical problem to solve.

The most obvious way to escape such problems is to deny (1): the Son does not inherit all the Father’s properties. Instead, we might say that the Son inherits some of the Father’s properties, but not all of them. In particular, we might say that the Son inherits the Father’s divine properties, but no other properties:

(T3) The Son inherits the Father’s divine properties =df for any F that belongs to the Father, the Son is F iff F is a divine property.

Nonetheless, it’s not clear to me that T3 is compatible with DV. If the Son inherits only some but not all the Father’s properties, what determines which properties the Son inherits? How could that be explained without resorting to ad hoc strategies?

One might say that Divinity is identical to the Father’s substance, but the Father’s substance is not identical to the Father (the Father has his own property or properties that his substance/Divinity does not). That way, when the Father shares his substance with the Son, he’s only sharing Divinity and not his whole self. Then the Son would only inherit divine properties, not the Father’s personal property or properties.

However, that more or less commits one to a generic view, not a derivation view. In the next post, I’ll turn to the generic view.

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18 thoughts on “Derivation vs. Generic Theories – part 4: Problems for a Derivation View (JT)”

  1. Pingback: trinities - Derivation vs. Generic Theories – part 5: The Generic View (JT)

  2. Hi Aurelius — Interesting thoughts. I’m sure one could work out a derivation view with some form of relative identity. Mike Rea’s paper ‘Relative Identity and the Doctrine of the Trinity’ might be helpful there. Anybody have any thoughts on that?

    I suppose I would still ask a similar question: If we say x and y are the same F but not G, I would assume this to be taken as sortal-relative. So F and S are the same God, but not the same person. Still, what determines that x and y share F but not G? If it’s possible for x to give F to or share F with y, but the same is not possible for G, then F and G must be distinct (or at least it’s hard to see how they wouldn’t be distinct), in which case x wouldn’t be simple.

    As for each person having exactly similar but distinct sets of properties, I must admit that when I very carefully read the bits where Athanasius actually tries to explain how F and S are the same ‘essence/ousia’, it’s very hard to tell whether he means same in kind or same in number. But I think you’ve hit the question right on the money: if it’s same in kind, wouldn’t that be tritheism? I suppose it depends on how we count ‘gods’.

  3. I am not sure I (explicitly) finished my thoughts. So, to continue . . .

    In the first case, if P1 = P2 relative to X then it is impossible that X have P1 and not also have P2. However, if P1 =/ P2 relative to Y then it is possible that Y have P1 and not have P2. Thus, relative identity might allow us to say that there is an X such that X is simple and has both P1 and P2 and there is a Y such that Y is constituted of X and Y has P1, yet lacks P2.

    In the case of the Trinity, could we not say that the Father has both P1 and P2 and that relative to him P1 and P2 are identical and that the Son is constituted of the Father, yet the Son only has P1 and that this is possible because relative to the Son P1 and P2 are not identical?

    In the second case, Y is constituted of X, yet each is identical to their own set of properties and it is the case that some of their properties are qualitatively identical to each other. Thus, it is no contradiction to say that X = P and Y = P, yet X =/ Y; for technically X = P and Y = P*. For example, we may say that the substance (S) that constitutes Athena is it’s bronzeness (B) or S = B and that Athena, the statue that is constituted of S, is its bronzeness or A = B. Yet A =/ S; for technically what is really being said is that S = B and A = B*. In other words, despite appearances, there are two lumps of bronze that occupy the same space, namely, B and B*.

    So, perhaps, this can apply to the Trinity. Could we not say that the Father (F) is identical to his divine substance (D) and the Son (S), who is constituted of the Father, is identical to his divine substance (D*). Thus there are two overlapping divine substance that are qualitatively identical. Doesn’t this allow the Father to be the source of the Son’s divinity (i.e., the Son is begotten of the Father) and, yet, also make them one in essence (homoousios)?

    It also seems to me that both of the view above would qualify as derivation views. What do you think?

    p.s., Is any of this making sense or are you all shaking your heads and saying “What is he talking about?” In other words, am I in way over my head here?

  4. JT:

    Very good question! Here are my thoughts.

    Suppose, for the sake of simplicity, that there exists some thing X such that X is simple and has only two properties P1 and P2 (ignore, for the moment, that existence and simplicity might be two additional properties). In this case, P1 = P2 and P2 = P1. The question is then: Does it now follow that if Y is constituted of X then Y also has P1 and P2 such that P1 = P2 and P2 = P1? I am not exactly sure. But I have my doubts. I think this would only follow if we were to say that X = Y and Y = X. But that is not what the derivationist (constitutionalist?) says. So, perhaps there is a way for Y to be constituted of X where X is simple, yet Y does not have every property that X has.

    One solution that comes to mind is to use the concept of relative identity. In this case, we might be able to say that P1 = P2 relative to X, yet P1 =/ P2 relative Y. For instance, suppose John (J) is a passenger on a Delta flight from Denver to France (P1) and then from France to Denver (P2). From John’s perspective J = P1 and J = P2 therefore, P1 = P2. However, when Delta is adding up the number of total yearly passengers P1 =/ P2. Can we solve the derivation dilemma in the same way? Truthfully, I am not sure. But it might be fruitful to try.

    Another way to solve the derivation dilemma might be for the derivationist to deny that when they say that Y is constituted of X where X has P and, thus, so too does Y that they are saying that X and Y share the numerically same property of P. Perhaps the derivationist could say that X has its own P and Y has its own P. So, for instance, the substance that constitutes Athena has its own property of “being bronze” (B1) – and is, perhaps, identical to its own bronzeness – and Athena, the statue that is constituted of the substance, has her own property of “being bronze” (B2) – and, again, is, perhaps, identical to her own bronzeness – yet B1 and B2 are not numerically the same. Put more simply, perhaps all the derivationist has to say is that when Y is constituted of X such that X and Y have the “same” P the term “same” should be taken to denote qualitative sameness and not quantitative sameness. I think the problem with this approach, however, is that it might lead to tritheism when applied to the Trinity.

    Have these options been pursued by anyone? Have they been critiqued? What do you think?

  5. I left out the consequent of the last sentence of my 1st paragraph.. so, Alkibidy is less properly human than Socrates, even though Alkibidy does many human actions.

  6. One thing that comes to mind re: DV is to ask what is ‘more properly’ supposed to mean? Is this like saying, Socrates is more properly a human being, than his pet-dog Alkibidy. We could look at Alkibidy as less properly human in the sense that technically he isn’t a human being, however b/c he’s such a clever dog, he opens doors, fetches the new-paper-scroll, eats at the table with Socrates, and many other human like things.

    Clearly this sense of ‘more properly’ is not the right one. But what is the sense?

    We could say ‘more properly’ means:

    DV.1: The Son’s being identical with the divine essence is (causally) dependent on the Father’s being identical with the divine essence.

    I’m sure there are various other ways we could take ‘more properly’, any other suggestions?

  7. Hi Aurelius —

    One could (and probably should) say something like T3*. I’m just not sure it’s enough to get past the problem. If D = F, and if F is simple, then all of F’s properties will be identical to each other. So if the Son inherits one property from the Father, by transitivity he’d have to inherit them all.

    On the other hand, I take your point that I spoke too quickly. Actually, I go back and forth on whether or not DV and T3 are compatible. I’ve phrased DV like this:

    (DV) Divinity belongs more properly to the Father than to the Son.

    Richard Cross formulates it like this:

    (DV*) Divinity is identical to the Father in a way it’s not identical to the Son.

    DV* is stronger than DV, and DV* seems incompatible with T3 since DV* seems to encourage the disjunction that either (i) we say D = F and get a derivation view, or (ii) we deny D = F and get a generic view.

    However, DV allows that D is not = F, and yet D can still belong to the Father more than the Son. I think that if one took DV, then one could probably work T3 and T3* into their perspective much more easily.

    What do you think?

  8. Hi Scott,

    I just had the old spiritual classics portion plus the Spade. I wasn’t aware of the paternoster volume. Did a philosopher do the paternoster one? If not, experience suggests that it may not be precise enough for philosophical purposes… Maybe you should send a proposal to Hackett or someone, then revise iff you get a book offer you want?

  9. Correction:

    So, we might have to make a distinction between logically generated properties of the second person of the Trinity AND received properties of the second person of the Trinity.

  10. JT:

    You state:

    “Nonetheless, it’s not clear to me that T3 is compatible with DV. If the Son inherits only some but not all the Father’s properties, what determines which properties the Son inherits? How could that be explained without resorting to ad hoc strategies?”

    Why can’t the derivationist accept something like:

    (T3*) For any F such F belongs to the Father, the Son has F iff the Son’s having F does not entail a contradiction.

    Of course, this is a bit vague. But I don’t think its ad hoc. And this would rule out the Son having properties like “being the Father”, “Generating the Son”, “being numerically identical to the Divine substance” and so forth.

    On a different note, I wanted to get all of your opinions on something.

    I was watching a show the other day (I think it was Matlock . . . mmmm hotdogs) and one of the characters said something that sparked my theological mind. In the story a Father was trying his best to love his Son; however, the Son would have nothing to do with him. Tired and frustrated, the Father at one point stated “He is no Son of mine . . . He’s not my Son.”

    This got me thinking about this post. It seems that the views of the Trinity that you are discussing here (or that I have read about) have the Son being the Son because and only because he is (somehow) “of” the Father. But the above got me wondering if the Son’s being the Son not only has to do with the fact that he is “of” the Father, but also that he receives something from the Father. So, I wonder if the (T3) should look something more like this:

    (T3**) For any F such that F belongs to the Father, the Son has F iff (1) the Son receive F and (2) the Son’s receiving F does not entail a contradiction.

    I don’t think this work for all Fs, however; for there seem to be Fs such that the Son would have them of logical necessity (e.g., being constituted of the Father). So, we might have to make a distinction between logically generated properties of the second person of the Trinity is received properties of the second person of the Trinity. With this distinction in hand we could say that it is only in virtue of the received properties that the second person of the Trinity becomes the Son and not in virtue of the logically generated properties.

    Well . . . I hope that made sense.

  11. Dale,

    Which translation do you have? The one forthcoming by Paternoster Press? I don’t know of any other translation of R.’s de Trin., i.e. books 1 thru 6. PV Spade’s website has a trans. of book 1, and book 3 is in the western spiritual classics vol. of R.’s. Bernd Goehring and I were thinking of typing out our own trans. of the whole De Trin. sometime soon; but if the Paternoster trans. is good, we may not. In any case, there are some tough passages to translation. the French trans. fudges a few lines; of course the ‘few lines’ are not easy in latin!

    As an aside, near the end of Bk. 4 R. posits this amazing illustration of point he is trying to make of the skin of a (human) person blown up with as many angels as possible inside of it. Something like a balloon-person–those of us reading this had a big laugh about the idea of publishing a trans. of De Trin. complete with pen & ink drawings of R.’s illustrations for points he tries to make.

    In any case, R. is suggestive indeed–esp. since he doesn’t employ much Aristotelian phil. vocabulary– he’s working with the same sort of notions that Anselm had.

  12. JT – yeah, Athanasius’ theology seems to turn into dead ends every which way. I guess this is way the medievals felt the need to keep the metaphysical flames burning.

    On Clarke, I will do a series of postings at some future date. He’s badly neglected by recent theologians, written off as being an “Arian”. But in his day he was read by friend and foe alike, and had a huge influence on 18th c. English and American thinking on the Trinity. His views on the Bible are quite interesting, in my view.

  13. Scott – this is fascinating. Would you be willing to slightly fill out your comment here into a full blown post? All I’ll say for now is that it’s a puzzler how a being could have the property of aseity *in any sense* because of another being. Perhaps we need to float a real definition. In my office, I think I’ve got something on this by recent phil theol guys.

    I’ve got a copy of the (I think only) translation of Richard, and have been meaning to read it. Maybe you could do a post or even a series on Richard, maybe after JT is finished?

  14. Oh, and of course a big looming question is this: can Athanasius explain how the Son ‘inherits’ divine properties from the Father without collapsing into sabellianism? If d=s, then we get sabellianism. But if d is not = s, then divine properties belong, strictly speaking, to d, not s, so in what sense could s ‘inherit’ or ‘share’ d’s properties?

  15. Dale —

    Yep, I agree. If one wants to say f shares d with s, then if d=f, f must share his whole self. If one wants to say f shares d with s but f does not share his whole self with s, then one must deny that d=f. And that’s basically just the generic view. On the generic view, f only shares d with s, he doesn’t share his whole self. For generic people, d is a common constituent shared equally by all three persons but belonging properly to none more than the others. For derivation people, d=f, so f is the constituent that’s shared by s and h.

    PS. I’d love to hear more about Samuel Clarke, btw!

    PPS. I wish I knew what’s in her arms there. Whatever it is, it doesn’t bode well for Q’s moral character…

  16. Dale,

    I don’t remember if I’ve mentioned Richard St. Victor’s view on this… it is not yet clear to me just what he means, but nonetheless he says:

    1. Some divine properties are substantial: one substantial property is aseity.

    2. Some divine properties are ‘originative’ (my word for his ‘ex-sistere’ ordinary language phil.)
    – there are three sets of originative properties:
    (i) being not from another and originative of another,
    (ii) being from another and originative of another, and (iii) being from another and not originative of another.

    3. All divine persons are/have 1.
    4. The Father is/has (i).
    5. The Son is/has (ii).
    6. The Holy Spirit is/has (iii).

    So Richard would say all divine persons have aseity substance-wise: no other _substance_ is the cause or origin of the substance that constitutes each divine person. But 2 divine persons are from another _person_ (and with the filioque, Richard is emphatic that the HS is from F and S).

    person =df an incommunicable (non-shareable) existent of a rational nature.

    So, Richard thinks 1 is a communicable (shareable) property, but denies that e.g. (i) is a communicable property.

    So the question then is this: is ‘aseity’ a shareable property? Richard answers ‘yes’ … Clarke says ‘no’. Richard says ‘yes’ on the basis of his understanding of what a substance is (which I don’t yet ‘get’).

  17. Another good post, JT.

    What the heck is in Cptn Janeway’s arms there?

    OK, real comments. “Begetting” whatever it’s supposed to be, must be a dependence or origination relation. Whatever it is, it would in some sense explain the product or offspring. Even if you get all mysterious and say we can’t conceive it, if we didn’t grasp that much, it just would fit to use words like “begetting” and “generating” for it. So, it looks like it’s got to be irreflexive.

    Some day I’ll post on Samuel Clarke on this. He’s a non-Arian subordinationist, inspired by some of the early Fathers, and by (as he saw it) the bankruptcy of scholastic “Latin” theories. From memory, I believe he says that s inherets all the Father’s properties but aseity. Clarke just accepts that this makes the Son not as great as the Father. It seems to me that any derivation view is going to be somehow subordinationistic, unless it is inconsistent.

    Re: the move in your second to last paragraph. If f=d, then sharing d is sharing f. I don’t see any room, then, for saying that “when the Father shares his substance with the Son, he’s only sharing Divinity and not his whole self.” Do you?

    It looks to me like on the view you’re exploring, we’ll have to deny f=d, because you want there to be more to f than there is to d. But then, in sharing d with s, how does f thereby *himself* become a constituent of s? At most, it looks like f by generating would bring it about that d is now also a component of s.

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