[Although this post is a continuation of the post linked below, it is largely self-contained.
https://steemit.com/onemanyproblem/@apollonius/climbing-mount-everest-with-metaphysical-induction-part-1]

Goal and Plan For This Post

The question I have been addressing in the previous three posts is, or are: What is being? Which can also be formulated as What is reality? What is the One (Reality) and the Many (the finite things found in the One)?

In this post, I finish establishing – I firmly believe – that “Reality” comprises the unique, intrinsically and extrinsically infinite, eternal One (or God), under which exists the unique one in which abide all finite things, called “the Totality”. The existence of the Totality and the ordering of the hierarchy of being is thus established: highest in the hierarchy is the One, second is the Totality, third comes the finite unities and relations among these.

The method of argument is the same used in the previous article, where I introduced explicitly the “Principle of Metaphysical Induction”, and I also mentioned its historical origins, discovering what I called “the Principle of Diogenes of Apollonia”, which I expressed in the brief aphorism, “If things are different, then (in some sense) they must be the same (or one)!”.

I shall use the same method of argument which I used to establish the necessary existence of the One, except that I am going to draw out more consequences from the concatenated chain of ascending ones or “Cs” used in that argument – which I shall redevelop here for the sake of the self-containment of this post. I reargue succinctly the existence of the One, then back up and consider the ascending chain of which the One is the highest unity, and establish that the penultimate or second to last C in the chain (immediately before the One in the series) is the unique Totality.

This establishes the fundamental, “skeletal” structure of reality. In upcoming posts, I plan to add the “flesh and sinews” to the skeleton of this hierarchy, by which I mean, the ontology or the being, to fill out this vision of what I think Reality really looks like. I propose this as undiluted realism. I do not believe it is a naive realism (such as Plato’s metaphysical system of substantialized “Ideas”). The argument I propose I believe to be so straightforward and strong as to resist any relativist or skeptic reactionary attempt at deconstruction. I offer this as a challenge in the midst of the topsy turvy relativist milieu to all liberals, communists and nihilists out there. But above all, I offer this post and this developing metaphysical system to truth seekers that cannot abide with putting truth on the same level as falsehood.

But first, a brief and helpful clarification of terminology.

Some Terminology – Degrees of Metaphysical Sameness and of Metaphysical Opposition

Instead of talking about “differences”, “distinctions”, and “diversities”, or for that matter, on the contrary end of the scale, of “oneness”, “unity” and “sameness”, I like to use the catchall terms of “metaphysical opposition” and “metaphysical oneness or sameness”.

In general, “metaphysical opposition” simply means any sort of difference of any degree. I shall often write the opposition between two realities, say, “X” and “Y”, thus: “X – Y”, which may be read, “opposition xy”. Furthermore, “metaphysical oneness/sameness” indicates the opposite of metaphysical opposition. I shall apply these terms elastically and according to the context. Therefore, metaphysical oneness/sameness increases in a subject as metaphysical opposition decreases in the same subject; and vice versa. I shall try to preserve the comparative ordering of degrees as per the following table:

Metaphysical Oneness or Sameness (in decreasing order)
(1) eternal oneness (this oneness is coextensive with its being, e.g., God)
(2) absolute oneness (e.g., this oneness is inseparable from its being, e.g., an amoeba cannot be split; a hand cannot be cut off the arm, without destruction of the member or whole entity)
(3) one, unity, or oneness (anything insofar as resisting division, but may be potentially divisible)
(4) the same or sameness (e.g., siblings belong to the same family, chickens to the same species)
(5) similar or alike (e.g., more extrinsic than being the same: chickens are similar to ducks)

Metaphysical Opposition (in decreasing order)
(1) disparities, incomparable (e.g., the slimy frog in the swamp, the star; or being and non being)
(2) separations, disconnected (e.g., two things separated by space or time, not like whiteness on Socrates)
(3) diversities, divisions (e.g., caviar and chicken feed... very different)
(4) differences (e.g., rooster and hen; note that these could also be called “same” for the species)
(5) distinctions (e.g., said of aspects in a thing; whiteness and roundness in a golf ball)

Note that this terminology I intend to apply elastically, and according to context. Note also that the senses of oneness/sameness and of opposition given in the table overlap: things that are similar are also distinct, or different. I find the use of “metaphysical opposition” or “metaphysical sameness” useful. The other terms in the table often are too specific, whereas these two terms are general. In developing this metaphysical system, I find I often need to have terms that are absolutely general, and therefore applicable to all being, not just to being within a certain type or genus.

Establishing the Essential Characteristics of the Totality

From the previous post: Reviewing the argument for the existence of the One

I recover the argument from the previous post. Here goes...

I took any two concrete realities, labeled them “X” and “Y”, and saw that the metaphysical opposition between X and Y (denoted, “X–Y”) required for the resolution of their opposition – by the Principle of Metaphysical Induction – the preexistence of a common sameness between X and Y. Otherwise, X and Y would each be notionally isolated in incomparable, solipsistic universes, eternally separated from one another, which of course is absurd. Empowered by the Principle of Metaphysical Induction, which asserts that if X and Y are in opposition, then there must preexist a common sameness between them in which their opposition resolves, I was compelled to assert the preexistence of a common sameness, “C(1)”, by which the opposition between X and Y (“X–Y”), could exist despite their mutual opposition.

Hence X–Y implied a preexisting C(1). Now either C(1) was bounded by another being or not. If not bounded, C(1) would be unlimited, therefore infinite and God, and my argument attempting to establish the existence of God, the One, would be done.

So I supposed that C(1) was bounded by some other being, which I’ll call here “X(1)”. From the opposition, C(1)–X(1), I induced the preexistence of C(2). Reiterating the process, if C(2) is unbounded, C(2) is the One and God, and I have finished my argument.

So I supposed again that C(2) was bounded by some being X(2), with the opposition C(2)–X(2) inducing the preexistence of C(3), which if not God and unbounded, must be bounded by some other being, X(3)..., and so on.

And by this reiterative process, I built up, from the original opposition of two real, actually existing things, X–Y, a series of ascending, concatenated unities: C(1), C(2), C(3),..., C(n+1),... (where “n” is a counting number); that resolved the oppositions X–Y, C(1)–X(1), C(2)–X(2), C(3)–X(3),..., C(n)–X(n),...

And I asked the obvious question: Does this ascending concatenated series of unities ever arrive at a final C(z), z being a determined counting number?

If there is no highest member of this ascending chain of Cs, and therefore no highest counting number z, such that C(z) is the One, then the whole chain vanishes, and perforce, X–Y would also vanish; except that it is a fact of experience, and cannot be equated with a “non fact”. That would be contradictory, and is impossible.

Perforce, there necessarily must preexist a oneness C(z) with finite counting number z to sustain the existence of X–Y and the whole chain.

Thus, C(z) is the highest and last member of the series, and I identified it with the One, and God. I also drew out a list explicitly articulating 8 essential properties for all the Cs in the series, not least of which was and is that remarkable and essential property of being that is transcendence. All of these properties the reader may wish to review here:

https://steemit.com/onemanyproblem/@apollonius/climbing-mount-everest-with-metaphysical-induction-part-1

The Existence of “the Totality” and Some of Its Essential Characteristics.

A slight expansion of the terminology regarding boundedness and unboundedness is helpful for the following considerations regarding “C(z-1)”, soon to be called “the Totality”.

Definition of external or extrinsic boundedness. Let “R” be any finite reality. R is externally or extrinsically bounded means that there exists a finite reality, say “S”, that does not depend on R for its existence, and is at least partially independent of R. R is externally or extrinsically unbounded if no such S exists. Note that R and S may vary in the degree of metaphysical opposition between them, as articulated in the table of terminology given above.

Definition of internal or intrinsic boundedness. Let “R” be any finite reality. R is internally or intrinsically bounded means that there exists a reality, say “S”, that depends for its being on R, but it is not R; S can be said to be “contained” in R. Note that R and S may vary in the degree of metaphysical sameness or oneness, as articulated in the table of terminology above.

With this clarification of terminology, I obtain this first result for C(z-1).

T1': C(z-1) has no external or extrinsic bound, a bound independent of its being. So it is externally unbounded and infinite. Furthermore, C(z-1) is internally and intrinsically bounded, and therefore, internally finite.

Argument for T1'. By the construction of the series, I can assert that there is nothing to bound C(z-1) externally: if there were, this outward bound would continue the series beyond the One. This external bound would have been labeled “X(z)” of the series, and C(z) would no longer be the last in the ascending series, but rather C(z+1), or possibly another later addition, contradicting that C(z) is the last member and is the One, and God, which we know from earlier results to be internally and externally infinite.

In other words, if there were an exterior bound on C(z-1), it would require the lengthening of the series of Cs, which is contradictory. So there cannot be an exterior bound on C(z-1).

Furthermore, and also by the construction of the ascending series of Cs, C(z-1) is internally bounded by realities within it (that depend on it); for example, both X and Y, the opposition of which resolves in C(1) and the other higher Cs in the series, depend on C(z-1) for their existence, and constitute internal or intrinsic bounds for C(z-1). So C(z-1) is internally bounded and finite.

This concludes the argument for T1'.

It is clear that C(z-1) must contain all finite realities, otherwise it would be externally finite, contradicting T1', an observation sufficient to establish T2'.

T2': C(z-1) contains all the finite realities that exist.

Henceforth, I call C(z-1), “Totality”, because it is a totality containing all the finite realities that exist. It is easy to see that this is a unique and only totality containing all finite realities.

T3': C(z-1) is unique: it is the only Totality containing all finite beings. It is THE Totality (“T”).

Argument for T3'. This follows immediately from T2', that is, from the absolute universality of C(z-1) over all finite realities. If there were a second totality, this would contradict C(z-1)’s absolute universality, depriving it of some of its finite beings. Therefore, there is only one totality under the One containing all finite beings, and I am justified in calling C(z-1), the Totality (of finite beings). This concludes the argument for T3'.

I rewrite the foregoing results for C(z-1), replacing “C(z-1)” with “the Totality” or “T”.

T1: The Totality (T) has no external or extrinsic bound, i.e., a bound independent of its being. So it is externally unbounded and infinite. Furthermore, T is internally and intrinsically bounded, and therefore, internally and intrinsically finite.

T2: The Totality contains all the finite realities that exist.

T3: The Totality is unique: it is the only Totality containing all finite beings. It is THE Totality.

It bears mentioning that any totality, in general, is a more or less extrinsically knit plurality. A substance is not rightly called a totality, but rather a whole, or a one. Moreover, the One is not a totality because it is intrinsically infinite: any aspects it might have must be one with the One, that is, coextensive and infinite with the One. What I am calling “the Totality” is very particular among realities, for as we shall see, its essential cohesiveness is as that of a substance. I am making a concession to its phenomenological dimension in calling it by that name. We experience “the Totality” as a whole bunch of substances and their relations jumbling together. Ontologically and henologically, the Totality is a powerfully cohesive one, as I hope to show in what follows.

Essential Characteristics of the Totality’s Oneness.

I know that finite beings do not and cannot exist without the Totality. I wonder: can the Totality exist without finite beings? Of course, if a chicken, existing within the Totality (it cannot exist outside it) dies, it does not seem that the Totality is any the worse for it. The remnants of the chicken pass to being food or fertilizer, other things in the Totality. Its passing does not appear to produce a “hole” of non being opened up inside of the Totality – which would be a contradictory clash between the nothingness of a “metaphysical hole” and the fullness of being of the Totality. Think of it: if the chicken’s dying were the “insertion” of nothingness into being, causing a hole in being, then nothingness would be acting as an “effective presence” within being, which would be to transform nothingness into its contradictory: being! Rather, the chicken’s death appears more like a passing of being from one of its manifestation in a living chicken, to that of being in another manifestation, always within the Totality. The Totality is not destroyed by this “relative destruction”, that is more a transference of being than an annihilation of being. (It is a kind of movement, a “corruption”, which I plan to discuss in upcoming posts.)

So it’s safe to say that the Totality can exist without many actually present finite beings, such as the chicken. But is it possible that the Totality exist with absolutely no finite beings within it, therefore, with no internal oppositions? If such were the case, and it existed without internal oppositions, it would be structurally analogous to the One (i.e., the Totality would have no internal limitations), which would make it internally and externally infinite, which would make it a repetition of the One, which would contradict the uniqueness of the One.

Therefore, the Totality necessarily contains at least one finite being. This establishes T4:

T4: The Totality necessarily contains at least one finite being.

Were all finite beings annihilated within the Totality, the Totality would also be annihilated. God alone would exist then.

The importance of this result of T4 is that it makes clear that the Totality is not necessary for the One. The One is not compelled to create the Totality for the sake of the Ones own existence. No, the Totality is necessary as a sort of “umbilical” cord necessary for the sake of the finite beings’ existence, but not for the sake of the Ones existence. The Totality’s necessity is greater than that of the individual finite beings, and less than that of the One. The Totality itself is entirely contingent on the One, which is absolutely independent and transcendent with respect to all other beings, including the Totality.

This metaphysical system is therefore adequate to express the relations of metaphysical necessity between God and the creation. God’s absolutely sovereign freedom is not made subject to or in any way compromised to subordinate necessities. Not so in dualistic metaphysical systems (e.g., the ying-yang systems of Eastern Philosophy), or in the “bipolar” systems such as Plato and Aristotle propose (One-dyad, act-potency). In this system of being, God is free to create and free not to create, unconstrained by created necessities in any way. The pagan metaphysical systems of antiquity do not have this feature, and I assure the reader that this is no small feat. This is crucial for an orthodox Christian theology and for sidestepping some of the difficulties inherent in relativism and nihilisms afflicting our culture.

Farther along this same line, the “Theological Problem”, which is related to what I call, “the Problem of Infinity”, does not arise in this metaphysical system. An absolutely infinite God that creates a finite creation filled with finite creatures seems to be contradictory: Wouldn’t the being of finite creatures put a boundary on the absolute boundlessness of God? Indeed, it would seem that God has to somehow punch a hole in his own infinite being to make space for the creation and creatures. Otherwise, the being of creatures and the Being of God become a confused immanent and pantheist “mixture”.

But, in this developing metaphysical system, the Theological Problem does not arise if we take the One and the Totality of the system to correspond to the God and the creation of divine revelation (as given in the Bible). This metaphysics has the Problem of Infinity anticipated and resolved. As the being of the One is intrinsically infinite and the being of the Totality and of finite creatures intrinsically finite, there cannot be any “mixing” of divine and created being. Instead, the system shows that there is nothing contradictory in conceiving The Infinite God as the origin and principle of the realm of finite being.

Furthermore, thesis T4 implies that the Totality’s structure is more cohesive than that of a plurality. Structurally, it’s closer to that of an indivisible substance, insofar as some aspects and finite realities of the Totality can be removed without destroying the Totality. But the Totality must nonetheless have some internal boundaries.

T5: The absolute indivisible oneness of the Totality. The oneness of the Totality is such that its ontological dependents stand to it, as accidents inherent in a substance stand to the substance (i.e., the Totality is indivisible and one).

I want to show that the Totality is not only one (already known from above) but indivisible. It is not merely a sameness such as that of a cloud that can be dissipated or separated by winds into several smaller clouds. It is not the sameness of an animal species that is repeated in separate individuals that make up the oneness of the species. The oneness of the Totality is much more compact, absolutely incapable of separations or internal divisions. How to establish this?

Argument for T5. The oneness specific to the Totality derives from the fact that all things that exist in it depend directly on its continued existing. Every finite reality is constitutively in metaphysical opposition with the Totality and depends on the Totality for its existence. Hence its “removal” from this metaphysical opposition with the Totality is tantamount to extracting the finite reality out of existence. It therefore stands to the Totality (and to the One) as an accident stands to an indivisible substance: the Totality can neither be separated nor divided from the being of finite beings actually existing within it; though it can be separated from the actual determination finite beings assume (as the dying chicken, above).

Furthermore, the Totality cannot exist without finite beings (“accidents”) within it (as per T4).
Therefore, the Totality is structurally analogous to an indivisible finite substance, with the exception that it is externally infinite. This concludes the argument for T5.

Although the Totality presents us with a jumble of jostling finite realities in its myriad phenomena surrounding us on all sides, overwhelming sense experience, yet, the deep (ontological) reality of the Totality is that of a tightly packed, absolutely indivisible substance, open in its core to its total dependence on the One.

T6: The opposition between any finite reality, U, and the Totality, i.e., U–T, resolves only in the One.

This result points to the One, or God, as the ultimate resolver of each and every metaphysical opposition. The One intervenes directly in the constitution of each and every unity that exists, including that of the Totality.

Argument for T6. U–T cannot resolve in T. Why not? Because then, U = T, which is not in accord with the hypothesis. U and T are different, in opposition, therefore, by the principle of metaphysical induction, U–T must resolve in a preexistent sameness above T, and that only leaves the One. This concludes the argument.

T7: The One is the Arché: it is both the supreme and an immediate origin of all existent unities.

Argument for T7. In T6, U is any finite being that exists, and the One is a principle (together with the Totality) that intervenes to permit the oneness of being of U in its opposition with T. The One truly causes and gives origin to the oneness of U. So T6 implies that thesis T7 holds for all finite, existent unities. This last assertion, however, implies that the Totality, in its myriad determinations (via its opposition with each finite unity) is also made one through its concurrence with the One (Thesis T6), so that the One is also cause and origin of the absolute oneness of the Totality. Therefore, the One is the universal origin of unities that exist. And it does this both through the mediation of subordinate unities AND directly, in each unity U, through its resolving of the opposition U–T. This concludes the argument for T7.

“Being” is sometimes characterized as the principle through which each thing is at once constituted in communion with everything else, and constituted in its specific individuality. By T7, this applies also to oneness, particularly, to the oneness of the One, and of the Totality, but also to the other unities found in the Totality.

I believe that the One, or God, is the Arché, which the ancient Greeks sought and failed to find in their researches for reasons too involved to discuss here. But I am happy and privileged to be able to present these results that, I firmly believe, will prove to be ground breaking. They open a new direction in Philosophy and Metaphysics that has been abandoned for 2400 years due to aporias unresolved, but which are starting to yield.

From The Summit of “Mount Everest”: What a View!

Ladies and gentlemen: I, or we, if you have followed me all the way, are at the summit of a “Mount Everest” far greater than the familiar geographic entity on the Nepalese-Chinese border!

Oh, what a pitiful, puny perspective provided by this jpg, compared to the gigantic, grandiose vista this metaphysical system is unveiling before my (our?) light-starved eyes! The One, the Totality, Reality challenge us, as if crying out, “Ascend higher, much higher, than that wretched piece of rock!”

But the challenge goes unheard except by the few with the guts to look at the evidence of metaphysical oppositions that reality does not ever cease thrusting in our faces, and all that these oppositions imply. Only the “climber” who dares look up towards the “Sun”, can discern the call!

[Cf. the “Sun” of Plato’s “Cave”, https://en.wikipedia.org/wiki/Allegory_of_the_Cave]

Think about it. Mount Everest, this outstanding fact of world geography, is always present in its fixed locality, “out there”. Yes, it fills out the picture printed out or projected onto the screen of the monitor, massive and mute; it might even take up a significant portion of ones personal “outer space” (especially if you’re the photographer); but it does almost nothing to my inner space. For me, for most of us, it could just as well be an axiom of Mathematics: totally inert, forever circumscribed within its narrow factuality; something for others to study, and about which they can write ponderous papers if they like. For me and my life, the Mount Everest between Nepal and China could just as well not exist.

Not so, the One, the Totality, and the fascinating complex of finite realities embedded in them. These and the henology I have elaborated aren’t inert axioms or theorems for someone else to study. These are monumental realities that reach into me. They CONSTITUTE me and my thinking! They are in me, and I am in them! If I have climbed this ontological “Mount Everest”, it’s only because the colossus had first, somehow, invaded me, empowering me to be, and to think.

What have I done? I started out from the metaphysical oppositions of daily experience, and swept upwards on the eagle’s wings of the Principle of Metaphysical Induction, and reached the summit of the eternal One. Then I stooped downwards to delineate the shoulders of this great, ontological mountain, the Totality. I have filled out – not this panorama of natural beauty of an earthly Mount Everest – but the far vaster landscape sculpted by God. And I am now here reporting on this glorious “Sun” that I have seen, and certify the general contours of a cartography still to be explored and further refined.

Won’t you join me?

What’s next?

I know there are other difficulties, especially regarding the actual infinite I propose in “the One”. Formal logic in particular believes it’s “unthinkable”. But I want to keep these posts manageably short. These and other issues I plan to address in upcoming posts.

I have, as promised in my last posting, articulated more fully the oneness aspects of the Totality (the henology). I plan to fill out the “effective presence” aspects (the ontology) to complete the henological treatment regarding the multi-layered “oneness” in Reality discussed in this post.

I also promised to feed some humble pie to the atheists, agnostics and sundry nihilists in my last posting. I plan to do that with a few postings “deconstructing” the Italian philosopher, Dario Antiseri and some of his relativist “heros”, Rene Descartes and David Hume. At the same time, I’ll anticipate the development of the ontology. The readers of this and my other previous posts should have no trouble breezing through the next two or three posts more or less putting Professor Antiseri in his place. Politely, of course.

It’ll be fun.