An Essay Featured in (Re)constructing “A Is A” by O.G. Rose
The Trinitarian and Metageometrical Ontology of Gottfried Leibniz
Considering Geometry & the Interior Life by Anthony Vincent Morley
Anthony Vincent Morley is an incredible and careful scholar who has unlocked the mysteries of “On Analysis Situs” by Gottfried Leibniz. I myself have been unable to penetrate the work, but in his book, Geometry & the Interior Life, Anthony provides profound guidance and insight. The following is entirely thanks to him: anything of value you see, it is because of his blessing.
I
Leibniz frames his analysis in terms of a comparison between ‘magnitude and situation,’ suggesting that ‘as magnitude is to arithmetic, so situation is to geometry,’ and furthermore claims that if we make “situation” and/or geometry ‘the primary element, many things easily become clear, [things which] are more difficult to show through the algebraic calculus.’¹ Leibniz is critical of Cartesian approaches in Geometry and claims that a problem at the foundation of mathematics ‘is a problem of reduction to algebra and induction back to geometry (or situation).’² Critically, we should note that ‘[s]ituation is particular, and therefore contextual, and novel. Unforeseen postulates and assumptions are situational.’³ In other words, situation entails an inherent “one-of-one”-ness we must keep in mind, a reality Leibniz doesn’t think ‘Cartesian approach[es] to mathematics’ can account.⁴
‘Algebra is quantitative and thus, entirely mechanical’ (as we will later explore, the quantitative can efface, per se).⁵ Algebra is in the business of magnitude, which for Leibniz is at best incomplete (regardless its great use). ‘Situation and magnitude seem co-extensive. But there is an inherent difference. Not every magnitude has a situation, but every situation has a magnitude’ (as we will discuss and explain, magnitude entails A and B, as does situation, but situation also include C).⁶ Leibniz suggests that ‘a true analysis of situation’ is yet to be supplied, but more critically it could be that a ‘true analysis is always still to be supplied, because there are always unforeseen postulates and assumptions.’⁷ Situation is always “one-of-one,” as we will explore, and that means analysis must always be live(d) (a C or “third thing” must be practically present).⁸
‘Situation is the ground or measure of magnitude,’ which means geometry grounds algebra.⁹ ‘For Leibniz, [this means] the foundation of mathematics is metaphysical,’ and this is because ‘[s]imilarity is the metaphysical element of situation.’¹⁰ This movie is massive, but thanks to Anthony, it can be grasped clearly. Basically, mathematics or algebra outside of geometry (which is our physical world and spacetime) is a “pure abstraction” and/or “pure thought” (suggesting Hegel) which cannot be realized into actuality, and this is because magnitude always occurs in a situation. And situations are only conceivable and understandable thanks to similarity: because we see patterns and “things like one another,” we can make sense of the world. But there is technically no “similarity” in physical reality (for everything is “one-of-one”), only “difference,” and so “similarity” must be metaphysical. We, a necessary C, make similarity possible (which is to say we make possible the “similar/difference”-process of understanding, as described in “The VORD” by O.G. Rose): if we did not exist, there would (practically, at least) be no metaphysics. As Leibniz has framed it, this would make the (practical) continual existence of mathematics questionable.
Situation is not exclusively metaphysical, for it also entails ‘[the] non-metaphysical element [of] magnitude.’¹¹ Still, for Leibniz, situation entails an inevitable metaphysical dimension of “similarity,” which for Leibniz is the ‘geometric explanation of the philosophical notion of ‘forms’ that begins with Socrates, Plato, and Aristotle’ ’ (the doctrine of analogy found in Aquinas is also relevant, as defended by Leibniz scholar, Austin Farrer).¹² “Equality” and “magnitude” are algebraic, while “similarity” and “form” are geometric. Humans live in geometric realms and know of the algebraic through the geometrical; this being the case, seeing as the geometrical is meaningful in terms of similarity, mathematics is meaningful when it is metaphysical (which is according to “a nonphysical judgment” and/or “judgment which cannot be justified by physical reality,” seeing as physics entails difference).
‘Similarity is the first property of situation,’ and yet everything in the world is different.¹³ On what grounds then can things be similar if they are not the same? Well, thanks to a judgment, which is made possible by human consciousness. We cannot observe consciousness itself in physical reality (not even neurons solve “the hard problem”), only through it, and in this way, consciousness is “metaphysical” (even if it ultimately has a physical origin thanks to some emergence, as considered in “The VORD” by O.G. Rose). By extension, judgement is metaphysical, and since mathematics in “situation” ultimately requires judgment, mathematics is ultimately metaphysical or else it is meaningless.¹⁴ If math means something to us, it is not merely math.
In this judgment being “nonphysical,” there is a technical sense in which it cannot correspond with reality, even if the judgment is somehow and mysteriously correct and true (this brings both Gödel and Hegel to mind). This being the case, how can we have faith in this judgment? Well, the answer might simply be because we do: we have faith in it because we have faith in it (perhaps because it has somehow “worked” for us). What is “metaphysical” is that which we must relate to by “faith,” precisely because it lacks physical reality by which we can trust the judgment in terms of its “correspondence” to actuality. This doesn’t mean necessarily that God Exists or that theology is valid (those are different lines of inquiry), only that what Leibniz argues must bring about ‘[a] harmony of reason and faith.’¹⁵ To quote Anthony at length:
‘Man will always differentiate between things with observation. And that is desirable so that we have a good quality of experience. But if we are unable to see the supremely beautiful quality that weaves the many distinct things together, then there is no longer any ground or foundation by which to differential things. And in that case, all things become the worst kind of minutiae and tedium […] The notion of similarity then, is what grounds differentiation in reason itself; it is the harmony of reason and faith.’¹⁶
If math is meaningful, it is metaphysical, and that means reason and faith are working together.¹⁷ If there was no similarity, we could not reason — reality would be too chaotic and dissimilar to find any patterns — and yet similarity is a metaphysical judgment we can only trust in, for “similarity” lacks correspondence in physicality. That doesn’t mean “similarity is an illusion,” but it does mean “similarity” suggests something “out of this world,” per se.
II
Judgment is metaphysical because judgment inherently requires similarity (and thus situation). To quote Anthony extensively:
‘I am not listening to Beethoven’s 7th Symphony right now, but I internally conceive the possibility that I could be listening to Beethoven’s 7th Symphony right now. And hence, I can act in such a manner that brings it about that I am actually listening to Beethoven’s 7th Symphony right now. As I internally conceive of my present self and my future self as simultaneous, so I conceive of the whole sequence of causal relations in the external material world that could bring about the actual simultaneity of my present self and future self. And then I act upon those external material conditions one by one, to bring about the actual simultaneity. I causally affect the conditions of the external world and they mutually, causally affect me. The mutual harmony or similarity between these brings about their coincidence.’¹⁸
“Similarity” is thanks to an internal condition being “laid” on physical reality or “brought about”: since there is no “similarity” or “correspondence” in reality to itself, if two things are “brought into harmony or similarity,” it is thanks to human consciousness and judgment. Potential is “similar” to actuality, and potential independent of actuality can only be conceived in the human mind. I consider a potential, and then I can act in a way that brings about “something similar” in actuality. Likewise, I can consider two entities “similar,” and so put them in a bowl together (say an apple and an orange). But aren’t apples and organs actually “similar?” They both consist of natural sugars, can be eaten — what do I mean “similarity” isn’t found in actuality? Well, why should we think something is “similar” just because it has sugar in it? Do the two entities have the exact same sugars in them? If not (which they cannot), what do we mean when we say they are “similar?” It’s a judgment, right or wrong (maps can be useful even though not territories), and that means it’s metaphysical.
If meaningful, potential is always coordinated into actuality, which means a consciousnesses judges the best way to bring potential into actuality, which is to say the best way to realize ‘[an] organic harmony between the unity of internal simultaneity and the variegation of external world.’¹⁹ If there were no “internal lives,” there would be no such coordination, and that means “meaningful situation” would be impossible. If mathematics isn’t irrelevant, there must be ‘a relation between situation and intellect’; otherwise, distinction is impossible (“A is B,” a supposed “mistake” that is nevertheless possible because we are ontologically A/B, which here can be said to mean we are “(meta)physical”).²⁰
Two things ‘are similar which cannot be distinguished when observed in isolation,’ and quantity requires things to be ‘actually present together’ or some “third thing” to be ‘applied to [them]’ (say memory).²¹ We determine “similarity” because we see “something” across things (a “quality”) which strikes us as “reason to think” there is a pattern, though ultimately this is a “metaphysical judgment” (seeing as reality is composed only of difference). Patterns are metaphysical, as is the act of seeing them. ‘[Sameness] is not observable,’ which is to say it ‘is entirely real in the intellect only,’ and the same logic applies to “similarity” and “patterns.”²² This is because we decide such things ‘based on whether they incline towards or away from the general [sameness],’ a state intellect must be “toward” and yet that cannot be found in the materiality which requires it to be sensible.²³
Leibniz shows that “similarity” and “equivalence” cannot be identical, that there must be a ‘quality or proportion that is irreducible to equality,’ and that is supplied by metaphysical means.²⁴ ‘Similarity is a self-grounding axiom that has irreducible qualitative proportionality between the internal and external.’²⁵ Ultimately, this means ‘that Cartesian mathematical equality is merely a special case of Leibnizian congruence […] and that there are proportions that are not reducible to equality.’²⁶
III
The more similar two entities are, the more they will seem “the same” when we see them apart, which is to say ‘things are similar which cannot be distinguished when observed in isolation from each other.’²⁷ In other words, to the degree I am able to recognize B as “not A” when I see B apart from A is to the degree B isn’t similar to A, which is to say A and B are similar to the degree I think they are “the same” when they are apart. Funny enough, if I think B and A are “the same,” I don’t think anything is “apart at all”; instead, I think A and B are the same thing, which would mean there aren’t multiple entities which can be separated. We cannot say A and B “aren’t the same” unless we see them together, and yet the very act of seeing “two things together” would verify that A and B weren’t the same: the act needed to verify the equivalence of A and B would be the act which verified the impossibility of that equivalence being a “total equalization,” a paradoxical situation that’s very existence suggests the impossibility of equality. Equivalence or “sameness” can only be “observed” in a context which unveils equality’s impossibility, which is to say the moment “equality” is observed, it is negated into “equivalence.”²⁸ (All understanding entails a kind of Hegelian negation/sublimation — a strange l act, but one to be expected if we are ontologically A/B.)
“Sameness” is impossible, technically (which would be to say all “sameness” is a possible effacement), but here’s the thing: when A and B are apart, if I’m experiencing A, I easily don’t know B exists, as the same applies when I’m experiencing B apart from A. “Sameness” as possible effacement requires there to be multiple things being the same, and if I don’t know there are “multiple things,” I cannot realize the risk of “sameness” as present (only mentally and logically recognize the error). I would have to experience A and B apart and know they were distinct, all while then bringing them in memory together into a “mental situation” according to which I can realize they are “similar but not the same.” In other words, to use a temple example like what Leibniz himself uses, if I experienced temple A in Rome, then experienced identical temple B in Russia, I could “know” the temples were distinct because of their locations and “bring them together” into “a mental situation” in my memory to “observe” them as distinct. However, notice the role that I myself, as an observer, play in this formulation: I can “bring together” A and B to make it clear that A ≠ B, suggesting a “Schrödinger-esq” role for the observer (though we will not stress that association in this particular work). If there was no observer, for all “practical purposes,” A would be B.
Yes, I can know mentally that “sameness is impossible,” but I cannot know A and B are “only similar” (and not “the same”) unless I know about both A and B. If I only know about A and never hear about B, or if I were to encounter A, forget about it, and then encounter B, I could practically end up treating A and B “as if” they were the same without realizing I made this mistake. But this suggests something important: in order to grasp that A and B aren’t the same (which in that very act actually proves “similarity/difference”), a third thing is needed, which in this case is memory (as found in me).²⁹ If no “third thing” was ever introduced, we could never practically recognize that A and B weren’t the same, only similar/difference. Again, mentally knowing that “sameness was impossible” wouldn’t be of any use to us, because without “a third thing,” we could never remember encountering, seeing, etc. A and B as distinct to thus realize they weren’t the same. In other words, there is nothing “in” A and B themselves which can practically verify their distinction: A and B require something “outside themselves” which in the temple example is us (and our memory)
A geometric point in spacetime that makes it possible for A and B to be observed together is itself a “third thing” (which we can associate with what Leibniz calls “situation”). Leibniz also discusses “magnitude” as a potential “quality” which could help us define A and B as distinct, and the same logic applies to memory (as I myself as an observer make possible). But the point is that a “third thing” (which we will call C) is needed beyond A and B for A to be recognized as A for B to be recognized as B. Without C, A must practically be B and B must practically be A: for all “practical purposes,” C is why “A = A” and “B = B”; if there was no C, “A = B” (but not as Hegelian difference). Considering this, distinction is only possible where A, B, and C are present (trinitarian): if there was no C, “A = B,” which is (the effacing contradiction) of “sameness.” This is “sameness” as effacement.
(Before moving forward, please note that the use of “A = B” in this context is different from the Hegelian “A/B” I discuss elsewhere. Yes, Hegel’s notion can be written as “A = B,” but I try to avoid that in favor of “A/B,” which alludes to “On ‘A Is A’ ” by O.G. Rose. Now that we’ve brought up Hegel though, let’s focus in on this issue of “contradiction.” C is why we don’t have to live with a “practical contradiction,” but if we recognize the role of C, we can “imagine” removing C, and thus imagine “A = B.” And this is perhaps what we always do when we make a contradiction, for contradictions in one sense don’t exist. When we commit or think a contradiction, we must be “toward “nonexistence,” which would be “nonexistence” (an effacement). This is a “pure thought,” as described in “Hegel and the Ontological Implications of ‘Pure Thought’ About What’s Not There” by O.G. Rose, and for Hegel it is “contradiction” which shows that there is reason to think humans are able to meaningfully define themselves in terms of “creation” outside of “causation” (as hopefully the paper explains). Humans can ponder what isn’t in the world while in the world, which in this context means humans are capable of “thinking ‘as if’ C didn’t exist.” All Hegelian “pure thought” is a consideration of A and/or B without some C.)
IV
Are all Cs equal? The C of “spacetime” seems different from the C of “memory,” for example: if there was no spacetime, then nothing would exist (as far as we know), but if there was no memory, A and B could still exist, just never be recognized (as real). A very fair point, but at least regarding human beings, there is no “meaningful” distinction in this context between the “practical” and the “technical”: for us, the loss of a given C can be like the loss of every C (I’m tempted to say that the loss of “any C is like the loss of every C,” but I’m not sure if I can make that claim). If there was no memory, then for humans there “might as well” not be any spacetime, as if there wasn’t any spacetime, there “might as well” not be any memory. A, B, and C must all be “in” and “of” spacetime to interact, but while A and B could represent two identical but distinct temples, C would be the field on which the two could be built alongside one another (for example). A geometrical point outside of A and B must exist if A and B are to be recognized as distinct, which is to say that A and B require C to avoid being an effacement.
Leibniz focuses on the topic of “magnitude” to make this point, suggesting that two identical triangles which only differed in terms of magnitude would requires a “third thing” to be defined apart. He writes that ‘magnitude can be known only by observing together either both triangles at the same time or each with some other unit of measure,’ which again means a “third thing” is required.³⁰ Basically (as far as I can tell), Leibniz argues that mathematics which doesn’t entail “a third thing” is purely abstract and risks meaninglessness, because it would necessarily treat A and B as practically identical, which would be an effacement. This problematic mathematics he associates with ‘algebraic calculus,’ while calling his work ‘Analysis Situs’ (“analysis of situation”).³¹ This ‘calculus of situation […] will contain a supplement to sensory imagination and perfect it,’ Leibniz tells us, and ‘have applications hitherto unknown not only in geometry but also in the invention of machines and in the descriptions of the mechanisms of nature.’³² Leibniz is after practical mathematics, and he believes that requires “a trinitarian structure” missing from mathematics at the time of his work.³³
What is not practically possible is what is practically impossible, and seeing as humans are stuck in “practice,” it is critical for Leibniz that we introduce a “calculus of situation” that helps mathematics align with the human condition. But once we do that, strangely, many “primary pillars” come into question, mainly “equality” and “quantity.” We’ve already explored equality, suggesting “sameness” is also an effacement, which would suggest that “2 + 2 = 4,” precisely in entailing an “=,” cannot refer to the realm of situation, which is arguably the realm of human reality. This would mean mathematics is “a map but not a territory,” which is bizarre, because mathematics works so well that it seems like it must be discovered versus created, and indeed, mathematics can still prove invaluable thanks to its coherence, even if ultimately it doesn’t fully correspond with the human condition. What kind of mathematics is possible without equalization? Well, that seems to be the angle Leibniz wants to undertake, a place where a unique “unity of human knowledge” might be possible, as Maria Rosa Antognazza argues was Leibniz’s dream — I will leave it to others to explore this landscape.³⁴
“Quantity” is the only pillar of mathematics which Leibniz draws into question, which is to say “counting” — hard to get more basic than that, suggesting how strange a “mathematics without counting” would be (perhaps Leibniz makes all mathematics geometrical?).³⁵ Paradoxically, quantity can only be determined in a situation which verifies there is only one. When I see A and B together, since they don’t efface, they must be distinct, which means they are both “one-of-one” (only seemingly identical). I can only say there are “two, three, four, etc.” of something that is identical: the moment difference is introduced, I cannot technically say there are “two, three, four, etc. things” — there is only one. Every point of spacetime is occupied by a single thing that alone can occupy that point of spacetime, and that means “sameness” doesn’t exist. “Sameness” is only possible outside of situation, which is to say outside of spacetime, which is to say “sameness” and “equality” only occur in algebraic mathematics, logic, and similar fields. There is no “=” (equal sign) in reality, per se, only similarities which must be “similarities/differences” (which Leibniz seems to call “congruence”) (all of this brings to mind what Alex Ebert says regarding how mathematics today is debating the use of “equality” in favor of “equivalence”). Quantity beyond “one” is always an abstraction, a technical error, despite its use (like a map). And arguably the word “quantity” doesn’t have any practical meaning if we can only ever count to “one,” so it would seem the term “quantity” is always an effacement when autonomous. Quantity only exists in abstraction (not that abstraction is never extremely useful or important).
How many As exist in the world can only be determined to the degree I gather together all the As in the world in one place at one time (into “the same situation”), the very act of which would show that only one A actually exists while all the other “As” are actually each distinct (B, C, D, E, F….). Sameness is always one-ness (“one-of-one”-ness), and similarity is always harmony (of “similar-enough differences”). For a Christian like Leibniz, this move is critical, for if “sameness” never exists across things (in situation), then we cannot be quick to argue that its heresy to say, “The persons of ‘The Trinity’ aren’t the same, only similar.” Yes, the persons of “The Trinity” have “one essence” (“the same essence”), but the persons themselves are not “the same,” for that would be an effacement. “The Trinity” is three similar persons with an essence that is “one and the same.”
If “sameness” that isn’t effacement is always “one-ness,” then the “The Trinity” can, in this way, logically be “the same and yet different,” but only in situation (which is perhaps why we can say ‘with Dr. De Risi that the late Leibniz is moving towards a form of phenomenology’).³⁶ For Leibniz, “The Trinity” has seemed like a contradiction because it has been considered mainly in terms of “algebraic calculus,” which for Leibniz has been a mistake. The brain though practically must be “toward” the world in terms of abstraction in order to function — if it took in everything as a “one-of-one,” we’d be paralyzed — so it’s understandable why this mistake has been made (the brain is a frenemy, as I like to say). But this is a mistake we should overcome if we are to ever understand the inescapability and necessity of metaphysics, which is to say if we are ever approach reality.
V
But why all this focus on “the problem of similarity” (which leads into “the problem of sameness”)? If A and B are clearly distinct, say if A was a cat while B was a table, surely “similarity” isn’t involved at all. It would seem that way, but even if we judge A and B as distinct, we are saying, “They are similar enough to something for me to judge A and B as more different than similar.” Similarity is always involved where there is comprehension and situation: I cannot escape the principle. Thus, to discuss similarity is to discuss all acts of comprehension and judgment: it inescapably involves the intellect, and that means “similarity” always entails “metaphysics,” solidifying Leibniz’s point.
Judgement cannot occur where there is “absolute asymmetry,” for there isn’t even enough coherence to what I am experiencing to begin any kind of thought about it. To recognize a “cat,” I have to judge that the atoms which compose the cat are “harmonized enough” for x to be a cat before judging and contrasting the cat against a dog. “A thing to itself” entails coherence and “harmony” with itself, or otherwise it is not that thing. Where there are “things,” there are judgments, so the logic that is being described “between A and B” applies just as well regarding “A to itself,” for A is composed of a multitude. Someone who calls me, “John,” must see enough “similarity” between the hand attached to my arm and the words coming out of my mouth to think these entities all somehow “compose John” — why the person so judges all this to compose me as “John” is a mysterious question that is not easy to answer (so it goes if a person sees something in a store that they think I would like because it “suits John,” or if someone hears me say something that “is not like me,” etc.). The person judges “a C” between several things that turns them into “parts of a whole” (“a concert”), and that whole is me or “John.” I am composed of multitudes, and yet those who encounter me “judge” these multitudes as making me. Many parts, one essence — trinitarian.
The logic explored between A and B applies just as well regarding A to itself; this being the case, everything that is comprehendible is “trinitarian.” Even if I judge that A and B “are different,” this act itself suggests enough similarity present in A itself and in B itself to make this judgment. If I say, “That bookcase isn’t identical with the wall it is against,” I can only say this because the parts of the bookcase are “similar enough” to come together “as a bookcase,” etc., and because both the bookcase and wall are composed of shapes and colors (both are physical) — similarity is present. If A and B were “totally different,” I couldn’t compare them (“pure difference,” like “sameness,” is an effacement).
And yet, all that said, A and B are different — nothing in reality is identical — and so there is a real sense in which reality is “absolute asymmetry.” To unify the “brown” of the bookcase with the “white” of the wall “as color” is itself an abstraction, as is claiming both have “shapes”: in reality, there is only impressions and scenes and a “present moment” which isn’t linked with anything else (all “linking” is thanks to memory). All “similarity” results from judgement and the intellect (a “third thing”), and the intellect is metaphysical (even if it emerged from the physical). Doesn’t that mean that all “similarity” comes from the intellect? That the world is comprehensible because of something “in the world but not of it?” Well, yes — even if materiality to itself (or “the ontic”) is fundamentally complete and physical somehow (which I am not claiming), for Leibniz, meaningful materiality is fundamentally “(in)complete” and “(meta)physical.” To use Hegel’s language from the paper “Absolute Knowing” by O.G. Rose, we can that “The Truth” could be complete, but not “The Absolute.” We are an essential part of “The Absolute,” for it is “everything that is the case plus us” (to play off Wittgenstein).
In conclusion, whether we are believers or not, the “mental mode” of the Christian Trinity provides a way to understand how ontological reality does indeed seem to entail a “trinitarian structure.” We require A, B, and C to avoid any possibility of ontological effacement, and if that possibility existed, contradiction could exist, and that would seemingly tear apart the fabric of reality. If two entities could come into existence which were actually “the same,” then reality would break its own rules, and it’s hard to say what that would mean. If reality could practically “break its own rules” (even if not technically), that too seems problematic. On these grounds, there is reason to think there is truth to the analysis we find in Leibniz.
We are in debt to Anthony Vincent Morley for writing such an extraordinary text on Leibniz, one that unlocks philosophical and theological mysteries that not even Bertrand Russel could penetrate. For what he has accomplished, I can think of no better Leibniz scholar than Mr. Anthony Morley — he has forever shaped my thinking.
.
.
.
Notes
¹From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 26.
²From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 27.
³From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 27.
⁴From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 28.
⁵From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 28.
⁶From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 33–34.
⁷From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 37.
⁸Frankly, understanding Leibniz with Anthony’s guidance, I cannot help but see him arguing for Gödel’s “Incompleteness Theorem” centuries in advance. Gödel’s argument cannot be addressed in algebra, only in geometry, and that’s because we and our ability to observe our geometrical.
⁹From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 42.
¹⁰From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 43.
¹¹From Geometry & the Interior Life by Anthony Vincent Morley, page 43. Please note this suggests situation is “(meta)physical,” per se, which would make it “like us” (as described in The Philosophy of Glimpses) and “incarnate.”
¹²From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 43.
¹³From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 49.
¹⁴Why is algebra devoid of geometry so appealing? Well, perhaps it is because ‘similarity can never be ‘proven,’ [which is to say] [i]t can never be proven that two moments observed in isolation are indistinguishable,’ precisely because “moments” cannot be collected, brought next to one another, and compared like apples.(A) We are hungry for proof and certainty (a Freudian dream, perhaps), and algebra can provide us with proof, while what Leibniz only offers us an “open loop” and “incompleteness” that we must actively fill with judgment. Our brains do not naturally like “activity”; our “frenemy” brains want inaction and rest, to be existentially eased.
A. From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 52.
¹⁵From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 53.
¹⁶From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 53.
¹⁷As a theist, Leibniz has thus made a move to suggest the work of the theologian is not any different from any thinker where judgment is involved, as judgment must be if similarity is involved. That doesn’t mean Christianity is true, but it does mean we cannot be quick to suggest theology is uniquely problematically. However, Leibniz has not yet provided “reason to think” that reality in its ontology “points toward” a particularly Christian God or any God at all. That is another move which he will make next.
¹⁸From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy:57.
¹⁹From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 58.
²⁰From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 62.
²¹From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 70.
²²From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 73.
²³From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 74.
²⁴From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 79.
²⁵From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 81.
²⁶From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 82.
²⁷From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 5.
²⁸Perhaps we could say “The Trinity” is “abstractly” One and “practically” Three (a single essence of three people).
²⁹When we compare things as “similar,” we suggest an “equality” between them, and Leibniz refers to ‘the combination of equality and similarity [as] congruence[].’ It is perhaps the case that what Leibniz means by “congruence” I signify with “similarity/difference.”
³⁰From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 7.
³¹From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 8.
³²From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 9.
³³The very fact this is the case is evidence to Leibniz that the universe is made in “the image and likeness” of a Trinitarian God, especially if math is discovered versus created, but that is another topic for another time, one which Anthony explores brilliantly. This also suggests that Hegel’s “pure thought” could be an act that treats the universe “as if” God Doesn’t Exist, yet this act makes us capable of creation versus mere causality, suggesting that we ourselves become “god-like.” Perhaps God humbly steps aside when we “purely think,” like a gentleperson or lover.
³⁴See page 15 of Geometry & the Interior Life by Anthony Vincent Morley for more. Please note that the Christian God is incarnate, so God can only be found in “situation”: the metaphysical is incarnated in the physical. According to Anthony on page 18, ‘[t]he analysis situs is essentially a metageometrical demonstration of the metaphysical principles established by St. Thomas Aquinas’; to accomplish this goal, Leibniz must bring mathematics into “the incarnate realm,” which would be “situation.”
³⁵Please note that if we can’t really count, we can’t really say “The Trinity” is a contradiction.
³⁶From Geometry & the Interior Life by Anthony Vincent Morley, Early Draft Copy: 20.
.
.
.
For more, please visit O.G. Rose.com. Also, please subscribe to our YouTube channel and follow us on Instagram, Anchor, and Facebook.
