I dedicate this post to our Denyse O’Leary (UD News desk), who suggested me to deal a bit with this topic.

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A “whole” (or “all” or “total”) can be a “true whole” or a “false whole”. A “true whole” (or “unit”) is anterior and independent from the consideration of parts, is not obtained from their sum, it doesn’t presuppose them. A “false whole” (or “set”) is the mere sum of parts, is logically posterior to them, and is a fictitious “one” only because we consider it so. While a simple set is artificially composed bottom-up by its parts, a real unit overarches top-down any part.

The above distinction is strictly related to the difference between analysis and synthesis, and the related kinds of knowledge. While analysis is to look at things and data from bottom, by considering any item individually, synthesis is a top vision and global understanding of a true whole. In short, analysis is to see multiplicity in a thing, synthesis is to see its organic unity. Unity is related to the very principle of a thing, and in fact, as A.K.Coomaraswamy said, “the principle of a thing is neither in one of its parts nor in the sum of its parts, but where all its parts are a unity without composition.” Therefore any science entirely and uniquely based on analysis will never reach the ultimate meanings or principles of things:

“Differently from the common opinion, according to which analysis is somehow preparatory to synthesis and leads to it, so that one should always begin with analysis, also when one doesn’t want to stop at it, the truth is one never can effectively reach synthesis by starting from analysis; any synthesis, in the real sense of this term, is something immediate and direct, which is not preceded by any analysis and is fully independent from it, like the mathematical integration is an operation done in a single shot, and that doesn’t presuppose at all the consideration of elements amenable to those of an arithmetic sum; and, as this arithmetic sum cannot provide the means to reach and exhaust the indefinite, so there exist, in all domains, things that resist, for their very nature, to any analysis and whose knowledge is possible only by means of synthesis.” (R. Guénon, “Les Principes du Calcul Infinitesimal”, chap. 21, [my translation from French]).

Let’s consider then a mathematical analogy, taken indeed from infinitesimal calculus, which can help to clear the issue (see the picture).

Consider a circle and, inside it, a set of evenly-spaced orthogonal lines describing squares with equal side. If you sum the area of all squares you obtain an imprecise value of the circle’s area. If you thicken the orthogonal lines by decreasing the square’s side and sum their areas you get a better measure. You can iterate this analytic process *ad libitum* (obtaining always better approximations) but you will never get the **exact** circle’s area, because the circle is something qualitatively different from squares or any sum of squares or polygons. Circle and square are different archetypes, and the synthetic understanding of the former cannot in principle be reduced to any analysis of the latter. In particular, the exact circle’s area is obtainable only by means of a synthetic operation: the operation that in infinitesimal calculus is called “integration”. This mathematical integration is able to suddenly catch the limit of the succession of all square sums, a limit that is unreachable in the endless analytic process of “squaring”. Just in an example like this one can appreciate how synthesis is different and more powerful than analysis.

As Guénon says, the integration of calculus is only an example / symbol, in the quantitative field of math, of other synthetic operations applicable on higher qualitative fields.

As another application, we can say that analysis vs. synthesis has something to do with the ID / evo debate. Example, when scientists try to reverse-engineer a living being with the mindset and methods of scientism, they are necessarily applying analytic processes, which always will miss the more important aspects of the living beings. Differently, the Designer of the living beings, to design them, used a synthetic knowledge. For this reason any living being entails a organizational principle of organic unity, thanks to which any conception of the being as a simple bottom-up puzzle of plug-in parts or devices is unavoidably reductionistic and simplistic. In short, in principle, in any field, intelligent design is related to synthesis while any non-teleological perspective is related to analysis. What applies to the microcosmos also does to the macrocosmos. So any analytic materialist conception of the cosmos as a bottom-up “evolution of intelligence from matter” is unable to grasp the integrated unity of this grand design.

Last but not least, in ontology, only a synthetic operation of our intellectual intuition can help us to conceive the supreme Being. The Being is not whatever sum of beings or existent things, like a circle is not a sum of squares. The Being transcends any existence, likewise the circle transcends any succession of inscribed polygons. As a consequence, pantheism or other similar modern ideas, which considers God as the analytic sum or set of all existent things, is an entirely absurd conception, since God is the metaphysical supreme Synthesis, or, in a math-symbolic sense, — as mathematician Sara Voss wrote in her “What Number Is God?” — the infinite-dimensional supreme Integral.

Niw:

As ever, a refreshingly fresh look at matters.

I think two linked concepts, courtesy Oxford Dictionaries online, may help the onlooker:

There are some wholes that are mere collections, indeed. For these the whole is the sum of the parts, save for the mental dotted line that connects. For instance, a cluster of pennies on a table whose value sums to five. (Notice, how “value” effects the mental dotted line.)

Other wholes are composed of assembled interacting parts such as those of the table. These, often reflect contrivance.

Others yet have an indivisible character, forming a “substance” or “form” in the phil sense. We are like that. In Mathematics, integration — being crucially dependent on an infinitesimal limit process — is like that. In this case we cannot sever the part without loss to the whole, and fresh “parts” must be assimilated, not just coupled. The whole-part relationship takes on an organic character and the two must be considered at once, and the complex unity involved cannot be decomposed without loss — at least as far as the irreducible core is concerned.

BTW, a good further example is the hologram.

In connecting to ID, I think the tendency to imagine successful additive incrementalism from a simplistic initiation is one of the core errors of our time.

The so called simple cell isn’t, it has a shockingly high threshold of complexity before we see the emergent behaviour we term biological life. That behaviour is critically dependent on organisation driven by complex functionally specific — and in material part CODED — information. And that information guides the assimilation of materials to form functional aspects of the whole.

Similarly, major body plans up to our own exhibit this same character of a whole-part integration with a high threshold of complexity.

In terms of the physics and composition of the observed cosmos, I find there the same pattern of functionally specific complex organisation and associated information [FSCO/I] that leads to organic unity. We may study aspects, but that is a mental isolation, not a disassembly.

And of course FSCO/I has but one source that is observed. Design. Which tends to come from designers who exhibit intelligent creativity.

KF

As to the circle-square, synthesis-analysis, paradox and the apparent fact that the ‘Designer of the living beings, to design them, used a synthetic knowledge’, the following may be of interest.

Apparently God can create creatures in His image, who can reason about squares and circles, and who can understand the circle-square, synthesis-analysis paradox.

Here is a very informative comment, from a UD blogger, on Da Vinci’s circle-square drawing of man:

Verse, Video and Music

Supplemental notes:

Also of interest are two other places in the universe where ‘unexpected roundness’ is found:

and also this ‘unexpected roundness’:

The delicate balance at which carbon is synthesized in stars is truly a work of art. Fred Hoyle (1915-2001), a famed astrophysicist, is the scientist who established the nucleo-synthesis of heavier elements within stars as mathematically valid in 1946. He is said to have converted from his staunch atheism into being a Theist after discovering the precise balance at which carbon is synthesized in stars.

The Vitruvian Man – static image

https://upload.wikimedia.org/wikipedia/commons/thumb/2/22/Da_Vinci_Vitruve_Luc_Viatour.jpg/441px-Da_Vinci_Vitruve_Luc_Viatour.jpg

Of Related Note:

Gödel’s Incompleteness Theorem says:

“Anything you can draw a circle around cannot explain itself without referring to something outside the circle – something you have to assume but cannot prove.”

http://www.perrymarshall.com/a.....s-theorem/

Kurt Gödel – Incompleteness Theorem – video

https://vimeo.com/96082228

Taking God Out of the Equation – Biblical Worldview – by Ron Tagliapietra – January 1, 2012

Excerpt: Kurt Gödel (1906–1978) proved that no logical systems (if they include the counting numbers) can have all three of the following properties.

1. Validity … all conclusions are reached by valid reasoning.

2. Consistency … no conclusions contradict any other conclusions.

3. Completeness … all statements made in the system are either true or false.

The details filled a book, but the basic concept was simple and elegant. He summed it up this way: “Anything you can draw a circle around cannot explain itself without referring to something outside the circle—something you have to assume but cannot prove.” For this reason, his proof is also called the Incompleteness Theorem.

Kurt Gödel had dropped a bomb on the foundations of mathematics. Math could not play the role of God as infinite and autonomous. It was shocking, though, that logic could prove that mathematics could not be its own ultimate foundation.

Christians should not have been surprised. The first two conditions are true about math: it is valid and consistent. But only God fulfills the third condition. Only He is complete and therefore self-dependent (autonomous). God alone is “all in all” (1 Corinthians 15:28), “the beginning and the end” (Revelation 22:13). God is the ultimate authority (Hebrews 6:13), and in Christ are hidden all the treasures of wisdom and knowledge (Colossians 2:3).

http://www.answersingenesis.or...../equation#

I’m wondering, as a non-native English speaker, which term most aptly describes a “true whole”; one indivisible thing which does not contain distinct parts? The problem with the term “whole” is expressed in Niwrad’s post. Is “unit” indeed a better option? Is “a oneness” an alternative?

Thanks kairosfocus, bornagain77, Box,

Yes, maybe the term “unit” can be improved, by using “oneness”, “one”, “unity” … or whatever you prefer.

Anyway, all terms of a language, at the very end, have symbolic functions, they point to over-linguistic realities. So, what more matters is to understand somehow such higher realities themselves, and you all seem to grasp well the general concept of “true whole”.

Timely post, thank you (and Denyse).

Which can be truly maddening for those who prefer “exact” answers. When I studied calculus it was very difficult for me to get my head around the concept of “when X approaches zero.” What is this approaching zero nonsense? I asked myself. Why not just get there and be done with it? 🙂

Niwrad, on a serious note, I understand the point of your post I think. But it seems to me you are creeping along a precipice here, and one false move will cause you to fall into materialist “emergentism,” which, as you know, I have no use for. How do you avoid this?

Barry,

There is a big equivoque. Materialist “emergentism” is exactly the opposite of synthesis, the reaching of the limit (the knowledge of a true whole) bypassing any analysis on it. The former is the impossible arise of more from less (gradual evolutionism), the latter is the direct understanding by intelligence (the more) of an integrated reality, without any gradualism. What precipice? If you understand, my post is what is more distant from any materialism / evolutionism, because states in principle that synthesis (intelligent design if you want), the more, is always higher and truer than analysis (evolution if you want), the less.

KF, maybe ‘complex and ‘construct’ could be synonyms for ‘set’, here, couldn’t they?

A lot of this thread-header of yours reminds me of Aldous Huxley’s essay on comparative religion, The Perennial Philosophy; notably, the inaptness of the analytical intelligence to get beyond mechanistic reductionist physics, to reach the higher realm of the spirit, still less the Creator of all things: the Hindu Brahman, the One without a Second. If you haven’t read it, KF, I think you’ll like it a lot.

To arrive at some kind of apprehension of the numinous, what Huxley calls, ‘the unitive intelligence’ must be engaged; a faculty honed by modifying one’s being through the discipline of some measure of religious discipline/asceticism. Interesting, the word, ‘integrity’, in relation to character, isn’t it?

It also reminded me of an Aussie soldier in our battalion, who told me in the used car business in Aussie at that time, they’d say of a car, ‘Yes. She’s a nice, clean unit.'(!!) To which, I replied, ‘When they really meant, “She’s a dirty, disintegrating complex”…?’

BA: The limit of course is when it all BUT vanishes. I think the non-standard approach of Robinson from the 1960’s may help those mystified by the post 1870 limits approach. The slope of a line is the slope of its tangent, the limit of the slope of chords as they approach the point, and area in that circle is the limit of area of squares as they approach minimal but non-zero side. Hitting a zero of course runs a product to zero, and shoots a division up without limit. Ya gotta stop just short, about the thickness of an electron — in the modern approach, roughly: any smaller and there’s nowt there. KF

Axel, this is one time I dunno. (Sorta like what is beginning to happen a fair bit with some of my son’s questions these days.) KF

I’m reading Feser’s Scholastic Metaphysics

He provides, imo, a wonderful analogy of atomism.

Toss a lump of gold. Toss a handful of marbles. Why does the former cohere while the latter does not?

It’s pretty amazing to see how many modern questions were raised millennia ago and answered.

Parmenides and Zeno