OK, I came up with a description of the relations of the Trinity that seems to have each being identical to God without being identical to each other, and there's not an apparent contradiction in all of it, either. However, I also came up with a quasi-mysterianist level of analysis to add on to the core picture, so I will note that I do not want to claim that I have a special, clear, intuitive understanding of how the Trinity exists as the One God, only that I seem to have found a consistent "grammar" for referring to these concepts and terms.
Alright, the prologion here is a denial of the doctrine of divine simplicity. First, simplicity is not the same as unity, neither objective indivisibility. Because God is eternal and does not intrinsically change, His objective "parts" cannot be divided. Although it is possible to focus on different "facts about God," so to say, and therefore God is not absolutely simple as such, nevertheless this is not the same as to say that God could "in principle" be broken up into pieces. Secondly, the "reason" for the doctrine of divine simplicity is that (A) God is a se, (B) if a being were "complex" then it would "depend on" its parts, so (C) because God does not depend on anything in order to exist, He is not dependent on His parts. However, the entire train of logic (A)-(B)-(C) is complex: it makes God's aseity depend on His simplicity, it would seem, which is self-contradictory. Accordingly, it is unnecessary for God to be absolutely simple in order to be indivisible, the Most High, etc. (Moreover, in some instances we would speak more of the parts depending on the whole or the relation of dependence being internalized, e.g. as with absolute space; saying that God depends upon God would not be to objectively deny His aseity.)
So, the next step is to take the relation of identity as a multiplicity, namely all things have (i) a general identity, (ii) a particular identity, and (iii) a haecceitic identity. This corresponds to the difference between saying, "A god," "The god," and, "This god." Put another way, we are speaking of identity under logical conjunction (A ^ A), logical negation (~(A ^ ~A)), and logical disjunction (A v ~A). The "A" is the same in each case, but each logical function relates A's identity in a different way. (A corollary would be the principle of the difference of identity, as in, "An absence is different from a contrary," where absences and contraries are the different forms of difference per se, and threefold as such.)
Now, let's suppose that persons are unique. That is, the haecceity of a personal being is a person. There is nothing, it seems to me, stopping God's general and particular identities from having a haecceity each of their own, along with His absolute haecceity. (The haecceity of His absolute haecceity is the same as the absolute one.) So, God has three haecceities, and as He is a personal being, so He is tripersonal. Moreover, each haecceity corresponds to a form of His divine identity, so each is God in such a way.
Supposing that the divine essence (the one divine nature and the three Persons) is the unified set of the above-listed five facts (of His three forms of identity and His three haecceities, one of the latter of which is absolutely identical to one of His forms of identity), I think we can also render the description of the Incarnation intelligible. My "diagram" would tend to look like the following:
The idea is that Jesus Christ's human nature is threefold, and He has a haecceity, which is His person, and that His human person corresponds to the haecceity of His divine particularity (the Second Person of the Trinity). So He is adjoined to each nature (divine and human) without fusing each nature into one, or melting the human one into His divine one. In fact, if particular identity overall is identity under negation, then the appearance of contradiction in Christ's dual natures is actually just a symbol of the law of noncontradiction itself (so that His divine nature is A by itself and His human nature, here, is A under the two instances of the negation operator "~").
Quasi-mysterianism
Before congratulating myself on unlocking the secrets of the divine essence, I would like to point out that the above, besides being very abstract, and possibly not even true, is also incomplete for the following reason. First, we can imagine truth as a relation from a total (unitary) assertoric function, to a fact.* But the relation of a subject to a predicate, and of the truth predicate to its assertoric subjects, is also a way to assert the form of truth. And with hypothetical/conditional assertions, we have entire unit-assertions as it goes predicated of each other:
*I think this is what Descartes meant when he spoke of the law of noncontradiction as depending on the will of God. For let us suppose that contradictions can only arise in systems where truth is divisible into subjects and the predicates that are true of them. Assuming the unity (and with Descartes the at least relative simplicity) of the divine nature, however, God's judgment that A is true is not a matter of God predicating some P of some S. But without differences in predicates, God's truth would not "run the risk" of involving contradictory (or even contrary) predicates. Had God created the world where the judgments of created beings were as indivisible as His are (on this account), the law of noncontradiction would not, thereby, have applied to it.
QED...
Alright, the prologion here is a denial of the doctrine of divine simplicity. First, simplicity is not the same as unity, neither objective indivisibility. Because God is eternal and does not intrinsically change, His objective "parts" cannot be divided. Although it is possible to focus on different "facts about God," so to say, and therefore God is not absolutely simple as such, nevertheless this is not the same as to say that God could "in principle" be broken up into pieces. Secondly, the "reason" for the doctrine of divine simplicity is that (A) God is a se, (B) if a being were "complex" then it would "depend on" its parts, so (C) because God does not depend on anything in order to exist, He is not dependent on His parts. However, the entire train of logic (A)-(B)-(C) is complex: it makes God's aseity depend on His simplicity, it would seem, which is self-contradictory. Accordingly, it is unnecessary for God to be absolutely simple in order to be indivisible, the Most High, etc. (Moreover, in some instances we would speak more of the parts depending on the whole or the relation of dependence being internalized, e.g. as with absolute space; saying that God depends upon God would not be to objectively deny His aseity.)
So, the next step is to take the relation of identity as a multiplicity, namely all things have (i) a general identity, (ii) a particular identity, and (iii) a haecceitic identity. This corresponds to the difference between saying, "A god," "The god," and, "This god." Put another way, we are speaking of identity under logical conjunction (A ^ A), logical negation (~(A ^ ~A)), and logical disjunction (A v ~A). The "A" is the same in each case, but each logical function relates A's identity in a different way. (A corollary would be the principle of the difference of identity, as in, "An absence is different from a contrary," where absences and contraries are the different forms of difference per se, and threefold as such.)
Now, let's suppose that persons are unique. That is, the haecceity of a personal being is a person. There is nothing, it seems to me, stopping God's general and particular identities from having a haecceity each of their own, along with His absolute haecceity. (The haecceity of His absolute haecceity is the same as the absolute one.) So, God has three haecceities, and as He is a personal being, so He is tripersonal. Moreover, each haecceity corresponds to a form of His divine identity, so each is God in such a way.
Supposing that the divine essence (the one divine nature and the three Persons) is the unified set of the above-listed five facts (of His three forms of identity and His three haecceities, one of the latter of which is absolutely identical to one of His forms of identity), I think we can also render the description of the Incarnation intelligible. My "diagram" would tend to look like the following:
DGI .................
DPI ........... HGI
DHI ........... HPI
DGIh .......< HHI
DPIh > .............
DPI ........... HGI
DHI ........... HPI
DGIh .......< HHI
DPIh > .............
The idea is that Jesus Christ's human nature is threefold, and He has a haecceity, which is His person, and that His human person corresponds to the haecceity of His divine particularity (the Second Person of the Trinity). So He is adjoined to each nature (divine and human) without fusing each nature into one, or melting the human one into His divine one. In fact, if particular identity overall is identity under negation, then the appearance of contradiction in Christ's dual natures is actually just a symbol of the law of noncontradiction itself (so that His divine nature is A by itself and His human nature, here, is A under the two instances of the negation operator "~").
Quasi-mysterianism
Before congratulating myself on unlocking the secrets of the divine essence, I would like to point out that the above, besides being very abstract, and possibly not even true, is also incomplete for the following reason. First, we can imagine truth as a relation from a total (unitary) assertoric function, to a fact.* But the relation of a subject to a predicate, and of the truth predicate to its assertoric subjects, is also a way to assert the form of truth. And with hypothetical/conditional assertions, we have entire unit-assertions as it goes predicated of each other:
A --> F
(S + P) --> F
A + A --> F / (S + P) + (S + P) --> F
Now, the disquotational scheme is the complete form of the truth predicate in itself:(S + P) --> F
A + A --> F / (S + P) + (S + P) --> F
"S is P," is true if and only if S is P.
So, either truth is as such three-dimensional, or we are only aware of three dimensions of truth (three internal relations of the truth function). At any rate, the appearance of a contradiction in the logic of the Trinity and the Incarnation is an illusion, because the divine essence is infinite, wherefore It either relates to the perfect form of truth (given the three dimensions) or what is for us incomprehensible, namely an infinite number of truth dimensions. Either way, the "predication" of the three Persons, to each other and to the one divine nature, or of the Person of Christ to His divine and human natures, is a higher-dimensional truth function than is standard predication, and so the assumption that statements of the divine essence are true or false in the "usual way" is misplaced.
*I think this is what Descartes meant when he spoke of the law of noncontradiction as depending on the will of God. For let us suppose that contradictions can only arise in systems where truth is divisible into subjects and the predicates that are true of them. Assuming the unity (and with Descartes the at least relative simplicity) of the divine nature, however, God's judgment that A is true is not a matter of God predicating some P of some S. But without differences in predicates, God's truth would not "run the risk" of involving contradictory (or even contrary) predicates. Had God created the world where the judgments of created beings were as indivisible as His are (on this account), the law of noncontradiction would not, thereby, have applied to it.
QED...
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