Supposita

We have been discussing the question of the logical consistency of the orthodox doctrine of the Trinity. Dr. Lukas Novak (Charles University, Prague) has offered a solution to the consistency problem that relies crucially on the notion of a suppositum or supposit. If I have understood him, his suggestion is that there is nothing logically problematic in the suggestion that the individual divine nature has three supposits, The Father, the Son, and the Holy Spirit.

It is worth reminding ourselves that any solution to the consistency problem will depend on one's background logic and general ontology. And the same holds if one decides that the problem is insoluble.

But being none too clear about what a supposit is supposed to be, I asked Novak if he could define the term and how it stands vis-a-vis such terms as 'bare particular' (Gustav Bergmann) and 'thin particular' (David Armstrong). He responded as follows:

Ad 4) X is a suppositum iff X is something endowed with individual nature and suppositality, that is, X is both uninstantiable and incommunicable to a subject (and not a part nor an aggregate).

Ad 5) It is better said that Socrates' humanity inheres in Socrates, who is a suppositum. Suppositum is not a bare or thin particular. If there were bare particulars, they would probably be classified as supposita, but classically supposita are not considered to be "thin" or "bare" – they have their rather "thick" essences or natures de re necessarily. Socrates is identical to Socrates' suppositum. Socrates' humanity inheres in Socrates and is a metaphysical constituent of Socrates. Socrates' humanity plus his suppositality makes up Socrates. Neither Socrates' humanity nor his suppositality are entities in their own right, they are just aspects or metaphysical constituents of Socrates. So I use "inhere" here as _not_ implying any particular kind of distinction between the nature and the suppositum.

I am afraid that this explanation does not clear up the notion of suppositum for me. The definition is tolerably clear if a suppositum is something like a bare or thin particular. But then we are told that supposita are not bare or thin particulars. Why not? Because they have essences (natures) of de re necessity. So far, so good: bare particulars are bare in that there is nothing in the nature of a bare particular to require it to have any particular set of properties. Bare particulars, being mere individuators/differentiators, can combine 'promiscuously' with any set of properties. Not so with supposita on Novak's account. But now Novak makes three claims that I cannot see are consistent:

1. Socrates is identical to Socrates' suppositum.

2. Socrates' humanity is a metaphysical constituent of Socrates.

3. Socrates' humanity plus his suppositality make up Socrates.

One problem concerns the meaning of (3). Does it mean

3*. Socrates' humanity plus his suppositum make up Socrates?

(3*) has a clear meaning but is not consistent with (1) and (2). For if S is identical to his suppositum, then S cannot be identical to S's suppositum + S's humanity. A thing cannot be identical to a proper part of itself.

But it all depends on what we mean by 'identity.' I take identity to be an equivalence relation (i.e., one that is reflexive, symmetrical, transitive) which satisfies the Indiscernibility of Identicals and the Necessity of Identity (Necessarily, for any x, y, if x = y, then necessarily x = y). Perhaps Novak understands something else by 'identity,' or it could be that he accepts what I just wrote but adds to the mix one or more contingent sameness relations. I await his clarification.

Another problem is that 'suppositality' is given a purely negative explanation: It is the feature of being both uninstantiable and incommunicable to a subject. What is it positively? And to what does it apply? Socrates' suppositum? Socrates? Both? The feature does apply to bare particulars, but they are not supposita.

We are told that "Neither Socrates' humanity nor his suppositality are entities in their own right, they are just aspects or metaphysical constituents of Socrates." I find this highly problematic. First let me say that I have no argument with the notion of ordinary concrete particulars being composed of metaphysical, or as I prefer to say, 'ontological' constituents. I make heavy use of them in my book A Paradigm Theory of Existence (Kluwer 2002). But it is difficult to see how a metaphysical constituent could be a mere aspect of the thing of which it is the constituent. It is a bit like saying that the stones of which a stone wall is composed are 'aspects' of the wall. 'Aspect,' I presume, is from ad-spectare, and that suggests that aspects are relative to a viewer or thinker. Perhaps Novak will respond by saying that these aspects are 'amphibious' : theya re both in the mind and in the thing.

Finally, Novak tells us in effect that there is no distinction of any kind between nature and suppositum. I am afraid this makes no sense to me at all. Surely there must be some kind of distinction here! Otherwise, nature = suppositum. If so, in the case of the Trinity, it cannot be that one nature has three distinct supposita. What's worse, if Socrates is identical to Socrates' suppositum, and the latter is identical to his nature, then Socrates ends up an ontologically structureless 'blob' to use a term David Armstrong employs.

Posted

February 1, 2010

Constituent Ontology, Scholasticism New and Old, Trinity and Incarnation

Bill Vallicella

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35 responses to “Supposita”

Michael Sullivan

February 1, 2010

Two definitions of “supposit”:
1) From Roy Deferrari’s “Latin-English Dictionary of St Thomas Aquinas”: “(2) That which underlies all the accidents of a thing, i.e. the individual substance of a certain kind which is the subject of existence and all accidental modifications which constitute the individual, synonym of hypostasis, subjectum, and substantia . . . – Kinds of suppositum in this sense are (a) suppositum aeternum seu increatum and suppositum temporale seu creatum, the eternal or increated and the temporal or created individual substance. – (b) suppositum completum ultima completione, the individual substance of highest completion . . .”
2) From Allan Wolter’s Scotistic glossary: “The general name for a being that is per se in the third sense defined by Scotus. If the suppositum is of a rational or intellectual nature, it is called a person. Suppositum is a close Latin parallel to hypostasis, the term Greek theologians use to designate a divine person in the Trinity . . . Because of their interest in explaining the union of Christ’s human nature and his divinity in the person of the Word, theologians were forced to develop some clear idea of what constituted a person, be he human, angelic, or divine. In this connection they went on to determine the analogue of person in a nonrational subsistent, and retained “suppositum” as a general designation for any full subsistent individual, be it rational or not. Boethius had defined a person as “an individual substance of a rational nature”. Those who accepted this definition pointed out that “substance” was not to be taken in a categorial sense but as equivalent to a distinct subsistent, in the sense that Scotus seeks to clarify in discussing the various meanings of subsistent or per se being. Others stressed that “rational” was equivalent to “intellectual” in its most general sense, vis., as applicable also to the divine nature as well as to one which reasoned in the discursive manner characteristic of humans. Others, who unlike Scotus made matter the basis for individuality, had to qualify the term “individual”. Richard of St Victor called attention to what seemed to be an even more serious drawback of the Boethian definition, namely, that, according to it, the divine nature itself would be a person in its own right. Hence he suggested an alternate definition, viz., that a person is “the incommunicable exisetence of an intellectual nature”. “Existence” here seems to be simply the abstract form for “the existent” or “the subsistent”. It implies that the subject characterized by it has substantial being (esse) in a transcendental or non-categorial sense, and that this being is complete and individual. It also connotes, says Richard, that this existent has this being in virtue of some property that indicates something of its origins, that is to say, it has this being of itself, or by creation, or by propogation, etc. In God the divine nature itself has such “existentia”, for it has substantial being of itself. Now the three divine persons share this “existentia” commonly and hence indistinguishably, but each person also has his own incommunicable existence in virtue of which he is a discrete and unique individual. It is this incommunicable “existentia” in the divine intellectual nature that best defines what a divine person is. And more generally, it is the incommunicable existence of any intellectual nature that commonly defines a person, be he divine, angelic, or human. On this Richardian definition, which Scotus accepts and develops, a suppositum would seem to be the incommunicable existence of any nature, and a person would be an intellectual suppositum.”

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Michael Sullivan

February 1, 2010

As I hope these references make clear, it’s not at all the case in traditional scholastic terminology that “nature=supposit” absolutely, whether “nature” is taken as a universal, a common nature, or even just an abstract noun. What “suppositality”, as Dr Novak calls it, is for Socrates will obviously depend on one’s theory of individuation.
It should also be clear that “supposit” is almost the inverse of the “bare particular”, since Socrates’ supposit contains all of his essential and individuating factors (I’m hesitant to use the word “properties”, since this is taken in different senses by scholastic and contemporary analytic thinkers). I don’t think there’s any room for “bare particularity” in most scholastic metaphysics, except perhaps (in some thinkers) for pure unformed matter, which is generally assumed not to exist.

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aresh v.

February 2, 2010

In short:
– Suppositum = incommunicable existence of any nature
– Person = incommunicable existence of an intellectual nature
– Divine Person = incommunicable existence of an intellectual and divine nature
– God = communicable existence of an intellectual and divine nature
Is that right?

Reply
Vlastimil Vohánka

February 2, 2010

Bill and Lukas,
Bill wrote here, in the main text:
“I take identity to be an equivalence relation (i.e., one that is reflexive, symmetrical, transitive) which satisfies the Indiscernibility of Identicals and the Necessity of Identity (Necessarily, for any x, y, if x = y, then necessarily x = y). Perhaps Novak understands something else by ‘identity,’ or it could be that he accepts what I just wrote but adds to the mix one or more contingent sameness relations. I await his clarification.”
Bill also wrote to Peter Lupu in a comment to a thread responding to Michael’s e-mail:
“We must try to solve the problem without falling into heresy (Arianism, Sabellianism, etc.)and also without abandoning standard logic, where standard logic requires absolute identity (as opposed to sortal-relative identity).”
Lukas just does not share Bill’s 2nd goal: cf. Lukas’s last comment to the same thread. I guess Bill takes the talk of relative, sortal identity as untelligible. Similarly Lukas WRT the talk of absolute identity. Identity is, in Lukas’s view, relative to a sortal concept. Absolute identity is ill-defined. Maybe analogically to the way time and moral value are relative — to reference frame; and to person, time, goals, etc., respectively — at least according to many people.
—————-
Maybe Lukas would rather say that “identity” is just ambiguous. Here I wonder whether this is the same position as claiming that the concept of identity is relative to a sortal concept. ?
—————-
I noticed that Lukas’s strategy is repeatedly a one of disambiguation. He disambiguates: “God” (divine nature vs divine person vs divine substantial being), “substance” (substantial being vs suppositum), “identity” (of beings vs of supposita), “entity” (being vs suppositum). In this respect, Lukas, although a relative trinitarian, agrees with the positive mysterian James Anderson: trinitarian mysteries are “MACRUEs”: that is, merely apparent contradictions resulting from unarticulated equivocations.

Reply
Lukas Novak

February 2, 2010

Dear dr. Vallicella,
I am afraid that a satisfactory explication of the scholastic ontology and semantics would amount to a book, therefore what I am going to write must be necessarily fragmentary and sketchy. Many times I am writing something that would require further qualification, which however would require another 3-4 paragraphs of explanation, so I refrain from it. I assume that any point can be further developed or clarified in case you ask for it.
One way how to relate the notion of a bare particular and a suppositum is this: in the analytic cocneption a bare particular is both a “suppositator” (rather than “individuator”) and a suppositum. The classical doctrine distinguishes betwen the principle – the “suppositator” or suppositality, that which “formally” makes something a suppositum but is NOT itself a suppositum – and the principiatum – the resulting suppositum.
Thus we have Socrates, who is a man, an individual, and a suppositum. All these characteristics of Socrates must be somehow principled within Socrates. The principle of his being a man is his specific nature. The principle of his being this individual man is his individual nature (which is made up of his specific nature and his individual difference, socrateity, which is the ultimate principle of his individuality as such). The principle of his being a suppositum is his suppositality.
Thus: (3*) is false, since suppositality is not, in all respects, the same thing as a suppositum (see below).
Now the crucial thing: The entire scholastic ontology, semantics and logic presupposes that there is a kind of parts which _are_ really identical to their wholes. These are the “metaphysical parts” (MP) or “gradus metaphysicales”. Note that “real identy” does not imply “numerical identity” here (which can be described by means of the axioms of identity common in the modern logic). Numerical identity/distinction presupposes numerical unity, but MP as such typically lack numerical unity. MP can be distinct from each other, but the distinction is of some lesser kind, as not to make them distinct individual beings. In other words: individual beings have a fine inner structure, a structure of various facets or aspects independently conceivable, but not capable of independent existence. Note that real identity does not imply interchangeability in any context, since words and concepts can refer to one MP with exclusion of the others, despite the real identity of them. We can say that Socrates is human due to his humanity and that he is individual due to his individual difference, and although both Socrates’ humanity and individual difference are really identical to Socrates, they are not interchangeable in the aforementioned sentences salva veritate.
Why do we insist that the MP are really identical with the individual they constitute and with each other? It is an implication of taking as face value these two things:
1) the common nouns in language stand for THE SAME THINGS as individual nouns: I can refer to Socrates as Socrates, but also as a man, or an animal, etc. I can address him “Hey, Socrates!”, but also “Hey, man!”. This suggests that the common terms like “man” etc. can signify something identical to Socrates (and not, e.g. some set, or some abstract entity, etc.).
2) The common nouns can be predicated of individuals via identity: when we are saying that “Socrates is a man”, we mean that. We mean that Socrates IS a man – not that he just partakes on humanity, or that he exemplifies humanity, but very simply he just IS a man. The predicate “man” reveals something of the very identity of Socrates himself, something of his inner constitution. We cannot say that the property “man” is a part of Socrates which is different from Socrates, like e.g. Socrates’ hand is different from Socrates, because in that case we could not say that socrates IS a man, just like we cannot say that Socrates is his hand.
Of course, there is an elaborated theory behind these bold statements, which it is hard to sum up in few lines. If I may dare another self-promotion, perhaps some additional explanation here can be helpful:
http://www.skaut.org/ln/docs/univocity.pdf
Now: specific nature, individuality and suppositality are all kinds of such metaphysical parts. They contribute jointly to the inner constitution of a supposit, each in its own way. A supposit is the wholly completed substantial item – while by “completed” is meant that any other additional properties come to it as something extrinsic and really distinct, that is, as accidental forms which are individual being with acidental natures of their own.
The metaphysical parts can be conceived “in concreto”, that is, as immersed in and identified with the suppositum they constitute. The resulting concrete concepts like “man”, “animal”, “individual”, “suppositum” denote or stand for (the latin term is “supponere”, “supposit for”) the suppositum itself and can be predicated of it via identity.
Or they can be conceived in abstracto (“humanity”, “animality”, “individuality”), that is, prescinding from the suppositum. This way they are conceived as quasi-forms that inhere in or communicate themselves to the suppositum. Even suppositality itself can be conceived in this abstract way, as a quasi-form that makes the suppositum precisely a suppositum.
Now you ask: what is the suppositality positively? Well, to speak the truth, I am not sure. There are several theories which I can list, but I cannot choose one of them because I am personally not very sure concerning some more basic questions, like the nature of distinction between esse and essentia.
1) Scotists: It is a mere negation of actual and aptitudinal inherence in a supposit; no positive entity but mere lack of certain capability.
2) Majority-Thomists: it is a positive substantial mode, the last determination in the line of essence which completes and “seals” it. It comes before the existence (or “esse”).
3) Minority-Thomists: the role of suppositality is played by the “esse” itself. Perhaps you may like this position… 🙂
4) Suarezians: like in the majority-Thomists, it is a positive substantial mode over and above individual nature; but since suarezians identify esse and essentia, they must say that it comes “after” the esse.
So my position is: I know there must be something that plays the role of suppositality, but I am not sure what it is. If the ontology of modes can be clarified, then I should say it is a mode, either in the Suarezian or Thomist way. But I know what it DOES, and that is enough 🙂
To conclude: Socrates is really identical to all his metaphysical parts or constituents, but that does not mean identical in every way, that there is no distinction whatsoever. There are less-than-real distinctions between his metaphysical parts (the precise kind of these distinctions need not be specified, it is a matter of dispute among the schools), and so Socrates is not a structureless blob.
But he is not an aggregate of really distinct beings with their own esences, like a stone-wall or a wood, or a family. In addition, Socrates does have really distinct integral parts, that is, parts of his extension (arms, legs, fingers…). But Socrates is not _essentially_ composed of them, because his extension is an accidental form really distinct from Socrates (i.e. a distinct being with a distinct essence of its own). Thus Socrates is having hands and feet only accidentally, in principle, he can lose these parts and remain the same individual.
Regards,
Lukas

Reply
Bill Vallicella

February 2, 2010

Vlastimil writes, “Identity is, in Lukas’s view, relative to a sortal concept. Absolute identity is ill-defined.”
Is this what it comes down to, then? A fight over the nature of identity?
For now, what I would like you, Vlastimil, to do is give me a nice clear example of a true sentence that is of the form *x is the same F as y but not the same G.* You understand that this challenge cannot be met by adducing the sentence, ‘The Father is the same God as the Son but not the same Person.’ I need a mundane example from our ordinary experience.
Don’t throw any texts or links at me, or appeal to any authority. Just give me one of more examples. If identity is sortal-relative, then I think the consistency problem is solved.
I put this challenge to Peter Lupu and he referred me to a water example. But ‘water’ is a mass term, not a sortal. So please note that the substituends of ‘x’ and ‘y’ must be proper names and the substiuends of ‘F’ and ‘G’ must be sortals.
Good luck!

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Vlastimil Vohánka

February 2, 2010

Hey, Bill, I can’t. (Is not that similar to asking for some ordinary experience object which would be absolutely simple in order to admit the epistemic possibility of the doctrine of divine simplicity?)
Suppose no one can. But what exactly does it mean for the epistemic possibility of the relative Trinity?

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Bill Vallicella

February 2, 2010

V writes: >>(Is not that similar to asking for some ordinary experience object which would be absolutely simple in order to admit the epistemic possibility of the doctrine of divine simplicity?)<< No, because identity is a pervasive structure of all of reality. If you say that identity is sortal-relative, you mean that to hold across the board. It would be absurd and ad hoc to say that identity is absolute in all cases except that of the Trinity where it is relative.

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Vlastimil Vohánka

February 2, 2010

The analogy is not ruled out: say that sortal-relative identity is pervasive, but simplicity (unity) too. We do not experience sortal-relative identity cases when *x is the same F as y but not the same G*, but we do not experience absolutely simple objects either.

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Bill Vallicella

February 2, 2010

Addendum:
‘x is the same F as y but not the same G.’ One might say that this is trivially satisfied by ‘Fido is the same dog as Rover but not the same cat.’ Fido and Rover are not the same cat because they are not cats at all. So, to give my challenge a sharper formulation, you must find a true substitution-instance of this schema:
x is the same F as y but x and y are different Gs.
Good luck!

Reply
Bill Vallicella

February 2, 2010

Very bad analogy, Vlastimil!
There is only one absolutely simple entity, God. Absolute simplicity entails, among other things, no real distinction between essence and existence. In God they are one, but not in me or my desk.
But identity, as I said, is all-pervasive.

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Bill Vallicella

February 2, 2010

‘Tim’s car and Tom’s car are the same model but different cars.’ This is not an instance of the relative identity schema because ‘model’ is adjectival; it is not a sortal.

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aresh v.

February 2, 2010

Dr. Jackyll and Mr. Hyde are the same man but different persons.
Maybe here “person” is taken as in “personality”

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Vlastimil

February 3, 2010

Bill, I am not sure what is and is not a sortal.
Even if sortal identity is not so pervasive as identity in your sense, do I (or you) need to have an example of the kind you’ve wanted in order to entertain the proposition that “the Father is the same God as the Son but the Father and the Son are different persons”? Can’t Lukas’s explications (+ his new scheme http://www.skaut.org/ln/docs/trinity.pdf ) do?
———
Aresh, I guess Bill would say “personality” is not a sortal. And Lukas, if you tried to apply to the Trinity, that persons are not personalities.

Reply
Bill Vallicella

February 3, 2010

Aresh,
That is a good prima facie example. Jekyll and Hyde are the same man, but not the same person. But this is plausible only if by ‘person’ we mean personality. But then there is no support for the relative identity thesis. See David Wiggins, Sameness and Substance, pp. 36-37.

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Bill Vallicella

February 3, 2010

V,
Sortals are such words as ‘man,’ ‘dog,’ ‘apple,’ ‘ash tray,’ etc. The contrast with mass terms such as ‘water,’ ‘beer,’ ‘furniture.’ Sortals are count-nouns. I can ask how many ash trays are on your desk but not how many furnitures are in your apartment.
As for you other question, if there is no clear example of sortal-relative (as opposed to absolute) identity, then one cannot take the Trinitarian formulations as examples of relative identity claims.

Reply
Lukas Novak

February 3, 2010

Regarding identity:
No, I don’t think that “identity is relative to a sortal concept, absolute identity is ill-defined.” I just think that there are many kinds of identity. And, obviously, it is not the case that God’s simplicity is to be understood so that absolutely everything in God is identical in the strongest way to anything else in God.
Saying that each Person is really identical to God does not exclude some weaker non-ientity between the dividne essence and the three distinct personalities/suppositalities. Traditionally this disticntion is called “virtual”; precise interpretations vary among the Schools, but this need not bother us here too much.
Now see: The identity invoked in saying “Father is identical to God” cannot be numerical identity of any kind, because that identity can only obtain between items possessing the same kind of numerical unity. But this precisely is not the case here, for God has the unity of individuality whereas Father has the unity of a suppositum.
The identity in question can be called “essential identity”, meaning “not having distinct essences”.
Now take the classical objection:
(1) Any two items identified to something third are identified among themselves.
(2) Father and Son are identified to God.

Reply
Bill Vallicella

February 3, 2010

Lukas,
This may indeed be the crux: “The entire scholastic ontology, semantics and logic presupposes that there is a kind of parts which _are_ really identical to their wholes.”
If you mean proper parts, then I am afraid that makes no sense, at least not to me. A proper part of a whole W is a part of W that is not identical to W. Thus the following strikes me as a flat contradiction:
Socrates’ humanity is a proper metaphysical part of Socrates & Socrates’ humanity is identical to Socrates.
Do you have an argument for the existence of metaophysical parts that have the curious property you ascribe to them? Please be brief.

Reply
Vlastimil Vohánka

February 3, 2010

Bill,
I do not know clearly what you mean by absolute numerical identity as opposed to sortal identity.
Lukas,
I do not know exactly how your claim that “there are many kinds of (numerical) identity” differs from the clam that “(numerical) identity is relative to a sortal.”
The sortals you used: “being” and “supposit” — hence different counting questions: 1. how many beings?, 2. how many supposits? The answers in the case of God-the Holy Trinity: 1 being, 3 supposits. Does not that suggest that numerical identity, used in counting, is sortal?
Excuse my incompetence.

Reply
Lukas Novak

February 3, 2010

Dr. Vallicella,
if “proper part” is defined as you say, while “identical” meaning “really identical”, then metaphysical parts are not proper parts, clearly.
The argument, well: we conceive Socrates in various ways. We conceive him as a man, as an animal, as a substance. All these concepts are truly predicable of Socrates. In the predication of the kind “Socrates is a man” the subject concept refers to certain part of reality and the predicate concept expresses in its comprehension our cognition of that part of reality. By saying “S is P” we mean that the reality referred to is such as we conceive it in the predicate, or that what we conceive by means of the predicate is the same that really exists. Truth means that this purported adequation, viz. of that which is conceived to that which is, is successful.
From that follows that if it is true that Socrates is a man, an animal, a substance, then what is conceived by these concepts is something that is identical to Socrates. But clearly “substance” or “animal” does not express fully what Socrates is. Therefore, it expresses that just partially. It expresses but a part of what Socrates is. But if we can express different parts or aspects of what Socrates is, then there must be some thus expressible or conceivable parts in Socrates in the first place. Nevertheless all these are something that Socrates IS, for by conceiving “man” we do conceive (beside others) Socrates. So they are parts but they are identical to Socrates. Q.E.D.

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Vlastimil Vohánka

February 3, 2010

Addendum
If I say “A is numerically identical to B,” Lukas and his scholastic colleagues will say that NUMERICAL identity is (1) used for counting and (2) ambigous BTW at least:
(a) A and B are to be counted as 1 being; and
(b) A and B are to be counted as 1 supposit.
Relative identity theories, it seems to me, essentially claim that when one is confronted with the sentence like “Saul is numerically identical to Paul,” the sentence is ambiguous BTW
Saul and Paul are to be counted as one:
… human,
… person,
… apostle,
… animal,
… being,
… supposit,
etc.
Is not, then, Lukas’s position the one of relative (sortal) numerical identity? If not, I’m conceptually puzzled (which would not puzzle me), and I wonder where Lukas would situate himself in the SEP classification of the theories of the Trinity: http://plato.stanford.edu/entries/trinity/

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Vlastimil Vohánka

February 3, 2010

Aresh, it seems I was wrong. “Personality” is a sortal and Bill seems to thinks so. Yet, as I and Lukas suggested, and as Bill said, too, it is doubtful that persons are personalities.
Bill, could you sum up how that entails, according to Wiggins, that there is no support for the relative (numerical) identity thesis?

Reply
Jan

February 3, 2010

Gentlemen,
Not being qualified, I have not yet taken part in the Trinity discussion. I have followed it carefully though. Here is something that might be useful.
Objects having proper parts being identical to themselves is a common occurrence in mathematics. With regards to the set – subset example, it has been said:
“none of the subsets is absolutely identical to the superset”
But this is false in the category of sets. In this category identity is bijectivity! In abstract set theory members of a set are formal objects.
One can produce a plethora of similar examples. Line segment [0, 2] is identical to segments [0, 1] and [1, 2] in the category of topological spaces or manifolds. For a topologist, a square and a circle are identical, are completely the same. For a differential geometrist, who is concerned with stuff like curvature, they are not. One might argue: “you’re just playing with words, they are obviously not really identical. Here, look at the picture: one has edges, and the other does not”. But the blots of ink this person has produced are not the square and the circle. They are physical objects, and as such are obviously different, being composed of different atoms.
‘Real identity’ is a trivial concept. A thing is ‘really identical’ only to itself. Large part of the Trinity discussion has been about establishing in what category ‘is identical’ is to be understood.
I do not fully understand what is going on here. It seems to me that while ‘circle’ is an ideal, there still are second order ideals that are contained in it.

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Vlastimil Vohánka

February 3, 2010

Lukas,
Identity BTW Socrates and his MP’s is not relative to a sortal concept, but NUMERICAL identity is — right?
———
Jan,
I suspect “real identity” means something very different for you and the scholastics.

Reply
Lukas Novak

February 3, 2010
Vlasta,
Regarding my place in the classification of trinitarian theories in the SEP: frankly, it seems to me that the traditional orthodox position (which I hope I maintain :-)) is not listed. It is located somewhere under the “Latin trinitarianism”, but none of the modern attempts to capture it seems to do justice to it.
I would like to seize the opportunity to say a few words concerning the “trinitarian metatheories”. It seems to me that the distinction between “mysterianism” and “intelligibilism” is not clearly made – for I don’t know whither I belong! I believe that the orthodox position to which I try to adhere is this:
1. The doctrie of the Trinity (T) cannot be discovered by natural reasoning.
2. T, once revealed, can be undersood, that is, the notions used to express it do have certain meaning. (so – intelligibilism?)
3. T, once understood, cannot be shown to be against reason in the sense that no contradiction can be derived from it, and all objections can be solved.
4. HOWEVER: T cannot be comprehended, that is, although the concepts used to express it have SOME intelligible content, they i) do not express all there is to say about Trinity (very, very far from that), and ii) even that which they do express cannot be by us fully comprehended, that is, their content cannot be fully analysed so that all the conceptual notes are distinguished.
5. Therefore, T cannot be proved to be consistent or it cannot be shown “how” it is consistent. (so – mysterianism?)
The problem of the mysterianism-intelligibilism distinction seems to be that it neglects the alternative that T can be intelligible and defendable against charges of inconsistency, and yet not demonstrable to be consistent and not fully comprehensible.
Regarding identity: Having given some thought to your question, I think that it may be that my “different kinds of identity” thesis is equivalent to certain version of “relative identity” thesis. But certainly not to “sortal relativity” thesis (SRT).
The concept of identity is derived from the concept of unity. Therefore, different kinds of identities go with different kinds of unities. Now when the critic of the SRT writes that

Given that we have succeeded in picking out something by the use of “a” and in picking out something by the use of “b” it surely is a complete determinate proposition that a = b […]

it is true, but the problem is: how do we know exactly what to “pick out” by “a” and “b”? For example: what is picked up by “humanity in Socrates”? Is it just exactly that which is formally signified by the term? Or anything that goes necessarily with it? Exactly speaking, we need to specify whether we pick out all that is formally identical to the humanity in Socrates, or all that is really identical to it, etc. So the truth of absolute identity statements is given by what we pick out, but what we pick out depends on our criteria of identity; and our criteria of identity, arguably, are based on certain notion of unity.
So to say that there are various kinds of identity perhaps can be read so that identity is relative to – but to what? Not to sortals, because different kinds of unities are not distinguished according to sortals; all sortals are, traditionally speaking, concrete essential predicables (man, animal, substance…) which semantically function so that they “pick out” the entire suppositum of the given sort (I would not classify “person” or “individual” as sortals. But I sure about the exact nominal definition of “sortal”). Therefore with regard to these true sortals identity is absolute, or (in my terms), they determine the kind of identity to be understood as numerical identity of supposita. Normally we just deal with this kindof identity. But sometimes we need to count not supposita, but natures, or metaphysical parts, or species, or something else. In that case we need to specify our criteria of identity of these items, and correspondingly various different kinds of stronger or weaker identity. The semantics of our terms is often less defined in these “philosophical” cases, and so we either have to specify what is “included” in the item “picked out” – from the “relative identity” point of view -; or alternatively, we must specify which kind of identity are we talking about – the “kinds of identity” point of view.
Reply
Vlastimil Vohánka

February 4, 2010

Lukas,
Dale Tuggy, the author of the SEP entry on the Trinity, comments on your theory and classifies it here: http://trinities.org/blog/archives/1447

Reply
aresh v.

February 5, 2010

Lukas,
Thanks a lot for your abundant explanations (and also for the scheme of the trinity). Here my comments:
I agree with all the perplexities expressed by Bill so far. But now let’s assume for a moment that your (orthodox) ontological framework
is acceptable, what could we infer to be true according to it?
– That all 7 sentences which compose the minimal trinitarian doctrine are at the same time true consistently
– But there is also an 8th sentence which can be correctly and consistently inferred to be true with the 7 sentences (always within your ontological framework), namely that:
8) There are 3 gods
Which is what monotheism should avoid, I guess! For even though you keep insisting that there is only one instance of the divine nature ‘Godhead’, however that statement goes along with considering ‘God’ as something asymmetrically predicable and inhering to supposita as all property instances are. But supposita are as many as suppositalities!
The ambiguity we see about the numerical identity, arises only if we use this framework of yours to confound us about the normal way we count things. In fact your insistent “But there is only ONE instance of Godhead!” which is intended to recall us that we always have to count “God” as an instance of a given property, is:
– not only uncommon in our ordinary view: we usually don’t count ‘instances’ of properties, just supposita (have you ever heard someone asking you, “can you kindly tell me how many instances of properties you count in my car?! I’m afraid there is someone missing!”). At most we can count properties as long as we are comparing supposita.
– but, I guess, also against the assumptions of the other 2 major monotheistic religions, Islam and Hebraism (try to expose your ontological framework in detail to a jewish or a muslim and then ask them at once “how many Gods are are?” and see if they reply “I believe there is only one God precisely because there is only one instance of Godhead, no matter how many supposita of divine nature there are!!!”)
Please let me know what you think. Thanks again!

Reply
Lukas Novak

February 5, 2010

Aresh,
I think that you are right! If you mean “There are three Gods” in the sense “there are three supposits of whom each is God”, then this is true and orthodox! It is really as simple as that. This is what the orthodox doctrine really means.
Now why do all the theologians reject the statement “There are three gods” as heretical, you ask? This requires a bit of explanation.
The concrete common nouns like “man”, “animal” are normally used to refer to supposita, but they refer to them by means of expressing their essential nature. From this it comes that when used in plural, they signify both plurality of the supposita AND multiplication of the natures. In ordinary discourse we never have the reason to distinguish these two aspects, because they come always together. This is also the reason why the languages did not develop any systematic means to make this distinction. We only can avoid pluralisation of the essential noun by saying for example “three of whom each is a man” instead of “three men”.
Therefore, according to this common pattern in language, when one says “three Gods”, it is regularly understood as “three supposita, each of them having a distinct instance of divine nature”. The noun “God” primarily signifies divine essence and only through that essence refers to its bearer. Therefore the plural of that noun naturally suggests multiplication of the essence inthe first place. This is the reason why the expression “three Gods” is banned from theological speech.
But as long as you always understand the phrase “three Gods” with the reservation that you ONLY inted to multiply the supposita, that is, you intedn nothing more by it than “three (supposita), each of them being God”, then, as far as the intended meaning goes, it is entirely OK from the doctrinal point of view.
Alternatively, you can decide that you will set up the semantics of “God” not according to the supposita, but according to the individual natures. In that case, the concrete term “God” will refer to the entire Trinity indiscriminatedly (for as a concrete term it captures the essence together with any suppositality that goes with it). But then you must only say “there is but one God” but not “there is but one that is God” – because only the first phrase can be understood to count the natures whereas the other clearly counts supposita.
(The third option, to let the term refer to the essence as abstracted from the three suppositalities, is probably unsubstantiated, since we already have the abstract term “divinity” or “Godhead” for that and it there is no reason to let a concrete term supposit as though it were an abstract one.)
So to your objections I would reply:
1) We usually count supposita, but we pick them out by means of terms which express properties, and therefore we understand the pluralization to affect both supposia and their natures. Besides, in case of accidental forms, we only count the “instances of properties”, because they have no suppositality. For example, in “John succeeded in concealing but two of his three vices” we count the individual instances of John’s vices (not vices in general as universal properties – for John certainly did not conceal universals).
2) Of course that the doctrine of Trinity is against the assumptions of the non-trinitary religions. How could we expect that they would ever accept any trinitarian doctrine whatsoever? They clearly believe that monotheism requires belief in just one divine suppositum. There can never be a reconciliation until one of the parties gives up its faith.
3) So far I have very much emphasised the plurality of the persons. But note that the “suppositalities” are not thought of as some absolute entities added over and above the divine essence and making composition with it. They are thought of as mere relative entities, relations of origin. The distinction of the persons consists only in the fact that Father has his essence as “unbegotten”, the Son has the same essence from the Father, and the Holy Ghost has it from the Father and Son jointly. These relations of origin are real (independent from our thought), therefore also the distinction of the Persons is real; but from certain point of view there is nothing more than the divine essence related to itself in various ways. Or better said: what is there are the three Persons (for existence and operation is properly ascribed to the suppositum, not its nature), but the three Persons are only distinguished in the way they posses their common essence. They do not posses anything else than the essence by means of which they could differ. Their difference is real but only relative.
Best regards,
Lukas

Reply
aresh v.

February 6, 2010

Lukas,
The load of your ontological commitments is getting heavier and heavier:
– There are 3 Persons which share the same instance of divine nature (while for all other kind of supposita, there are as many instances of a given property as supposita)
– Each person has 2 real natures: one absolute and simple (the divine nature) and the other relative (the essence corresponding respectively to Father, Son and Holy Ghost). These natures must be real and distinct (because the essence of father is distinct both from the essence of God and at the same time from each essence of the other 2 Persons due to its relativity) but at the same time be joint with God (in a way that must not imply that God is composed of the other Persons’ individual natures, because that would imply God to be not simple). And finally to enlighten this very puzzling way of establishing distinctions and relations, you use the notion of “aspect” in an ontological and vague way even though this notion is epistemical.
– Each Person as a suppositum is relatively identical to God as suppositum proper constituent
– (I would also add a further inconsistency:) when we say that a property is universal, we mean BY DEFINITION that this property CAN be multi-exemplified (that is e.g. there is one red apple on my table now but it’s possible that there could have been 3 red apples instead). Now you hold that Godhead is a universal but by necessity there is only one instance of it: that is, there could have not been more instances of Godhead. But that contradicts the notion of universal which implies the possibility of many instances.
– Finally according to all these commitmens one must use the term “monotheism” differently from the other 2 major monotheistic religions. And count things in a different way from what we usually do. Therefore WE (atheist, muslim, jewish and ordinary people ignorant about scholastic notions) are the ones supposed to adjust to the orthodox scholastic terminology, because WE are using the language ambiguously (?!), even though we would need the orthodox scholastic terminology only to support the idea that trinitarinism is consistent (assumed but not conceded that it is), and for nothing else!
If my reading is correct, then it’s also clear why your account of the trinity waves between 2 different uses of “is” in the sentence “The Son is God”: the absolute identity is recalled to surreptitiously scale the notion of “God” to the status of a suppositum (so that we all would be compelled to count it as we usually do with supposita; otherwise the ordinary view wouldn’t take it seriously to change/revise terminology in case the uniqueness of God amounted just to a uniqueness of a property instance!) and the relation of constitution (because at the same time you want to explicitelly maintain that “God” is not a suppositum but the instance of “Godhead”). From these 2 incompatible needs pops up the inconsistent idea of a relative identity involving a Person and God (in “the Son is God”), the whole and its proper part!
If you have any further comments on that, please let me know. Thanks

Reply
Lukas Novak

February 8, 2010

Aresh,
– I don’t know from what of what I have said you derive that “Each person has 2 real natures: one absolute and simple (the divine nature) and the other relative (the essence corresponding respectively to Father, Son and Holy Ghost)…” etc. I have always consistently repeated that there is just one nature in God. I am puzzled.
– When you say “further inconsistency” – which were the previous ones? I have thought that an inconsistency consists in both asserting and denying the same proposition.
– If the other 2 monotheistic religions interpret “monotheism” as implying “just one divine suppositum”, then yes, I am using it in a different sense. But this should not be a real problem, should it? We can always agree on nominal definitions.
– You write:

And count things in a different way from what we usually do. Therefore WE (atheist, muslim, jewish and ordinary people ignorant about scholastic notions) are the ones supposed to adjust to the orthodox scholastic terminology, because WE are using the language ambiguously (?!), even though we would need the orthodox scholastic terminology only to support the idea that trinitarinism is consistent (assumed but not conceded that it is), and for nothing else!”

No, I count ordinary things precisely as everyone else. But the criteria how to count ordinary things are ambiguous when it comes to God. Yes, you atheists and muslim are supposed to adjust to the orthodox trinitarian (not terminolgy, that is conventional, but) conceptual apparatus, as long as you wish to comment on or discus the supposed problems of the orthodox trinitarian doctrine. Or else you never actually get at discussing the doctrine but insist on discussing something else.
If you want to discuss the coherence of quantum mechanics, you are of course supposed to adopt the conceptual framework of quantum mechanics. If you insisted on applying newtonian concepts on the theory, not only would your charges of contradiction be unjustified but you would in fact never succeed in discussing quantum meachanics at all.
You don’t need the scholastic conceptual framework to support the idea that trinitarianism is consistent. You need it to be able to actually state orthodox trinitarianism.
I am afraid I do not understand your last point: could you rephrase, please? In “The Son is God” the “is” is an “is” of predication.

Reply
Lukas Novak

February 8, 2010

Another explanation of “suppositum” from the Neo-Thomist classic, Joseph Gredt, Elementa philosophiae Aristotelico-Thomisticae (my translation):

A singular substance that is complete according to its species, perfect in its substantiality and absolutely incommunicable is also called a “suppositum” (hypostasis). A suppositum of rational nature is called a “person” (prosopon). In all created things there is a distinction between the suppositum and the singular nature or quiddity or substantial essence; for no created being (ens) is its own existence (esse), but is composed of essence and existence (esse). Therefore there can never be indentity between the whole existing in reality and the singular substantial essence. The essence has the character of “that by means of which” (“quo”), whereas solely the suppositum has the character of “that which” (“quod”). Since suppositum is that which is, it is also that which operates; while nature is that by means of which the suppositum operates. Hence the axiom: operations belong to the supposita (actiones sunt suppositorum). Therefore, anything that is predicated of a thing accidentally, is predicated not according to the nature or quiddity, but according to the suppositum, insofar as subsistence, being the form of a suppositum, on the one hand makes the nature incommunicable in relation to anything that is outside the essence of the thing, but on the other hand integrates the substantial nature as a subject of everything that comes to it accidentally.

Reply
aresh v.

February 9, 2010

Lukas,
First of all, thanks a lot for your patience 🙂
– I’m sorry for this terrible misunderstanding regarding the double nature, so just forget it… nevertheless there is something still to be clarified: you say “Persons are only distinguished in the way they posses their common essence”. The only way I would think a suppositum possesses its essence, is only by means of the relation of “inherence”. Now you are pointing out there are 3 different ways which respectively each Person possesses its nature, do you mean that also the notion of “inherence” is ambiguous?
– I was referring to the identity between “the Son is God” that is between the WHOLE suppositum and its ontological PROPER PART… but after reading your reply I guess this is another ambiguity hinging on a different conceptual framework: in fact you consider the subject as referring to a suppositum part not to the whole suppositum (“the subject concept refers to certain part of reality”) while I don’t.
– You didn’t rebut to my objection regarding the notion of “universal”, which I would like to hear, if it were possible
– I think I could summarize my comments like this: 1) To prove the consistency of the Athenasian Creed we have to adopt an ontological framework (developed by the scholastic ortodoxy) based on conceptual assumptions either inconsistent or ad hoc (they look designed to accommodate our ordinary view to the christian conception of God) 2) the ambiguity of our ordinary language shows up only if we assume that the ontological framework formulated by the ortodoxy is valid (and this is something that should be proved). 3) All your distinctions wouldn’t change the fact that WITHIN the orthodox framework we could truly state “there are 3 Gods” even though orthodox conventions don’t allow that, because their main concern is to highlight the truth about God’s uniqueness at any rate against any suspicion of polytheism. But I’m afraid that goes far beyond linguistic ambiguities arising from different ontologies and harmless convention issues as you suggest.
– As regards the comparison to physics paradigms and how we can assess the validity of an ontological paradigm objectively, I would emphasize that one can prove the explanatory power of physical theories by resorting to criteria like predictability and productivity which don’t seem applicable to formal ontology. So the only criteria we have are consistency, economy and comprehensiveness.
cheers

Reply
aresh v.

February 9, 2010

Lukas,
First of all, thanks a lot for your patience 🙂
– I’m sorry for this embarrassing misunderstanding on the double nature of the Persons, so please just forget it… nevertheless there is something still to be clarified: you say “Persons are only distinguished in the way they posses their common essence”. The only way I would think a suppositum possesses its essence, is only by means of the relation of “inherence”. Now you are pointing out there are 3 different ways which respectively each Person possesses its nature, do you mean that also the notion of “inherence” is ambiguous?
– I was referring to the identity between “the Son is God” that is between the WHOLE suppositum and its ontological PROPER PART… but after reading your reply I guess this is another ambiguity hinging on a different conceptual framework because you read the subject as referring to a part not the whole suppositum (“the subject concept refers to certain part of reality”).
– You didn’t rebut to my objection regarding the notion of “universal”, which I would like to hear, if it were possible
– I think I could summarize my comments like this: 1) To prove the consistency of the Athenasian Creed we have to adopt an ontological framework (developed by the scholastic ortodoxy) based on conceptual assumptions either inconsistent or ad hoc (they look designed to accommodate our ordinary view to the christian conception of God) 2) the ambiguity of our ordinary language shows up only if we assume that the ontological framework formulated by the ortodoxy is valid (as regards the comparison to physics paradigms, their explanatory power can be proved by resorting to criteria like predictability and productivity which don’t seem applicable to formal ontology; so the only criteria we have, are consistency, economy and comprehensiveness) 3) From your ontological framework, one could still state “there are 3 Gods” even though orthodox terminological conventions don’t allow that, because their main concern is to highlight the truth about God’s uniqueness at any rate against any suspicion of polytheism; and I’m afraid that goes far beyond linguistic ambiguities arising from different ontologies as you suggest (by the way, see how flexible are your terminological conventions in the case of “The man Jesus does not exist necessarily”, where “The man Jesus” is supposed to refer to the whole suppositum while you understand “does not exist necessarily” as implicitely involving Jesus’s divine nature (?!))
Regards

Reply
Lukas Novak

February 13, 2010
Aresh,
Absolutely no need to apologise. I apologise for my sarcastic tone – it was not intended, it just happens to me sometimes that trying to be succint I sound rude, without intention…
Regarding “inherence”: I don’t think that “inherence” is ambiguous, it is just universal. There can be various kinds of inherence, all satisfying the single meaning of “inherence”. Just like there are various kinds of animals all satisfying the single definition of “animal”.
Regarding the reference of a subject: by “part of the reality” I did not mean “part of the suppositum”. I just meant the part of all the reality all around us. A suppositum can be such a part. Concrete substantial terms usually refer to supposita as wholes. So you first undestood correctly.
Regarding “universal”: “God” or “Godhead” is not universal in the sense that it is multiply instantiable. It is universal in the sense that the concept of God or Godhead does not explicitly contain individuality and uninstantiability. It is only after long and careful analysis that we come to know that there can be just one instance of God / Godhead. The question whether there are more instances of God is not answered in semantics but in philosophy. Besides, even in case of “individual” concepts like “God” there still is a distinctin betwen God and the concept of God. And we can say that God is an instance of the concept of God.
Regarding your summary:
1. I am not trying to prove consistency. I am trying to rebut individual objections that are raised against it. I do not thing it is possible to prove consistency of the doctrine – see my reply to Vlastimil here:
  http://maverickphilosopher.typepad.com/maverick_philosopher/2010/02/materialist-mysterianism.html
  I deny that my ontological assumptions are inconsistent. They may be “ad hoc” in the sense that they are only applicable to God. This is not something that should make us wonder, rather it would be quite suspect if God could be completely squeezed into the conceptual boxes taken from His creation. But as regards the distinction between natura and suppositum, although it perhaps was motivated primarily theologically, it certainly has brought also better philosophical insights (it has, for example, gradually helped to clarify the various confused meanings of “substance”).
2. I agree – but note that the trinitarian doctrine is not a “theory” in the sense of modern empirical theories. A theory in the modern sense is produced in order to explain phenomena; therefore it can never be proved as true, and therefore the various possible theories must be evaluated against certain criteria, like explanatory power. The trinitarian doctrine is not construed in order to explain some phenomena. It is just conceptual articulation and development of the revealed truth. Comprehensiveness and economy are irrelevant.
3. I can state “there are 3 Gods” only given that “3 Gods” is understood in a very non-standard way. I don’t understand your remark concerning my “terminological flexibility”. I insist that concrete nouns refer to the supposita; the suppositum involves, of course, the nature(s) that constitute(s) it.
Reply
peterlupu

February 13, 2010

Jan,
Sorry, I did not notice your post previously.
In the mathematical cases you site do we really have the violation of absolute identity or do we have isomorphism?
e.g., “Line segment [0, 2] is identical to segments [0, 1] and [1, 2] in the category of topological spaces or manifolds. For a topologist, a square and a circle are identical, are completely the same.”
Are the line segments [0,2], [0,1] numerically identical or are they isomorphic in topological spaces? Doesn’t the former line segment have a property lacking in the later (e.g., one has limit 2 whereas the other 1)? Again, can’t we say that the square and the circle are isomorphic in topological space rather than identical?
Of course, much will depend upon whether in such cases we can distinguish isomorphism vs. numerical identity. Perhaps, the two collapse in topological spaces or manifolds. If they do in these cases, I suppose we can say that the notion of an individual object becomes murky in topology and, hence, the strongest equivalence relation that is applicable (i.e., a relation which is transitive, reflexive, and symmetrical) is isomorphism and not absolute identity. But this would mean that this relation is not sensitive enough to discriminate within topological spaces between otherwise clearly different objects: e.g., circle vs. a square.
This is interesting. Thanks.

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Supposita

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