The 'one & the many' problem in philosophy involves synthesizing unity and diversity, universals and particulars, laws and contingencies, permanence or change, the exact and perfect with the inexact and imperfect. Are things in time and space, or are they timeless and spaceless? We doubtfully have any practical problems with the 'one and the many' in our daily routines, so how is it a problem? It is a problem in philosophic debate in trying to determine if unity is ultimate or plurality is ultimate. Is unity in the world just a function of our mind or is diversity an illusion of our mind? Is reality mind or matter, or both? The one & many seem to be related yet having completely different characteristics.
Heraclitus was famously reported to have said, "No man ever steps in the same river twice" Do we step into the same river twice? In the 'many' sense, no because it is only the identical same river for one instance in time at one location in space. And we are moving through space occupying different spaces at different times. But in the 'one' sense yes, because the same river is the same river because there is a unifying essence which makes it identifiable and therefore 'step-in-able'. As well as a unifying of our sense data of the river and our thoughts related to it. You will realize there is an essence or nature of a river or 'river-ness' by which you identify it as a river and not a muskrat. A river and river-ness are very different, for example I step into a river but not into 'river-ness'. River-ness is a thing separate from but related to the material river but very different; the problem of the one & the many. And even being able to say, 'I stepped into the river', I'm assuming both this particular river and river-ness to make any meaningful statement. How could I say, 'the grass is green' if I had to have a different word for every blade of grass and every shade of green? Our minds distinguish particulars individually. We have a word for 'river', but not a word for 'river, this temperature, with fish in these positions, with one bank higher in this bend, with partly cloudy conditions in mid-afternoon, prevailing winds out of the East'. Communication and thought would be so fractured or so all encompassing that it would be impossible. And likewise, if there was no distinction between green and grass and my sense datum, then communication is also impossible. What would I be communicating and to whom? So how is communication possible?
If I can't step into river-ness but into a time/space river, where exactly is river-ness? I'm acquainted with it in order to observe and communicate observations. What is it? It does not appear to be material in a location but timeless and spaceless. It is everywhere whenever anyone thinks about it. Is it the same in everyone's thoughts about it? Or in the same person thinking about it twice? It is commonly considered to be among the universals since it refers to more than one particular river. Bertrand Russell interestingly observes:
"It will be seen that no sentence can be made up without at least one word which denotes a universal. The nearest approach would be some such statement as “I like this.” But even here the word like” denotes a universal, for I may like other things, and other people may like things. Thus, all truths involve universals, and all knowledge of truths involves acquaintance with universals.
Seeing that nearly all the words to be found in the dictionary stand for universals, it is strange that hardly anybody except students of philosophy ever realises that there are such entities as universals." (The Problems of Philosophy, pg.146)
I'm acquainted with universals in my mind, so they appear to be conceptual in nature. But they were around before my mind so are all minds the same mind? Are the universals themselves unified? Do they participate in the same mind or some collective consciousness with all other minds? If there is a plurality of minds, are we in fact communicating the same information to each other? There is some unity of minds along with the universals which makes communication possible. We do communicate. It's outside our scope here to explore the multiplicity of accounts for this through the history of thought. Philosophers do have a tendency to know less and less about more and more until they finally know nothing about everything. But the goal here is to identify the problem of the one & many and note that to make these observations and come to conclusions, we are already assuming and exercising ourselves in laws of logic and math. These laws themselves are universals that encompass everything (material & immaterial), including our thoughts, and we use these laws conceptually. The interdisciplinary fields within math (algebra, geometry, arithmetic, calculus, etc.) are all interconnected harmoniously (without contradiction) as well. These entities and equations have stable properties (e.g., geometric ones such as Pi, Pythagorean Theorem, Triangle Sum Theorem) that we discovered. And they reveal the mathematical framework concealed in the material world and are discovered by our minds not invented. The ancients used these discovered formulas to invent and build.
What we are calling the 'essence' of a thing as a universal is its identity assuming the 'law of identity' in logic. 'Whatever is, is.' If this river is a river, it is because it has the essence of river-ness and not some other essence and retains this identity over time. River-ness does not include size, direction, speed of flow or location or rocks or jungle, but it does include gravity and moving water through a channel with a bed and banks. If it changes too much, it loses its river-ness and dries up and becomes possibly a rocky path. Does river-ness cease existing if that particular river dries up along with all rivers? It would not seem so for if we have memory of a river or propositions recorded of rivers then river-ness still exists, somewhere. Does it exist in the particular instances of rivers and we abstract river-ness in our minds from the instances? We have an abstract idea of river-ness in our minds. Our minds seem to automatically do this sort of thing. As Christians we see this as 'thinking God's thoughts'. We see or sense something and after that apply a name and proposition to it in our minds. Our minds seem to create a representation of the thing as a concept. The thing, in this case the river was there, and we abstracted its identifying features (God's design for it) in our minds through our senses of it, which distinguish it from this or that other river. But also, we acquire an acquaintance with river-ness which necessarily existed independent of our minds. And there is a resemblance or relation between our idea of river-ness and the river. Its uniform persistence in identity as a river is necessary in our afterward abstracting river-ness.
Russell again: "Also, in memory I perceive that what I am remembering came before the present time. From either of these sources, I can abstract the universal relation of before and after, just as I abstracted the universal relation “being to the left of.” Thus, time - relations, like space - relations, are among those with which we are acquainted.
Another relation with which we become acquainted in much the same way is resemblance. If I see simultaneously two shades of green, I can see that they resemble each other; if I also see a shade of red at the same time, I can see that the two greens have more resemblance to each other than either has to the red. In this way I become acquainted with the universal resemblance similarity.
Between universals, as between particulars, there are relations of which we may be immediately aware. We have just seen that we can perceive that the resemblance between two shades of green is greater than the resemblance between a shade of red and a shade of green. Here we are dealing with a relation, namely “greater than,” between two relations. Our knowledge of such relations, though it requires more power of abstraction than is required for perceiving the qualities of sense-data, appears to be equally immediate, and (at least in some cases) equally indubitable." (pg. 160-1)
Are universals just names that people apply to things and qualities and relations externally? If we assume the material world or particulars exists as brute unintelligible facts out there (i.e. no unity of a universal mind), then our minds are providing the uniformity necessary to communicate and think. Why assume this set up will continue or be accurate after the next thought or that it has in prior thoughts? But if uniformity of identity exists independently, then it is partially causing our thoughts of it by continuing to exist. And our minds are naming and defining what we observe. How do we justify believing that the thing and our thoughts of it will continue to be uniform or related and are not delusion? Or how do we account for conceptual entities beginning to exist in our minds? Or that the abstractions in our minds will continue to represent the item in the world of particulars as our memory fades? Is there a singular unifying force of the universals and also of the particulars? These are also problems of philosophy albeit not in Christianity.
Everyday experience shows that particulars exist and maintain their identities over time, including us. Revelation in scripture shows us that this will continue (justification for induction). It would also seem that we abstract propositions (intentionally and unintentionally) about the particulars (as do other people's minds) to perceive universals, regarding things true and untrue, real and fiction. We participate in the timeless spaceless world of abstract universals (logic, math, geometry, etc.) as well as the time/space world of particulars. These worlds harmoniously coexist. And we hold the idea that these things will continue to exist as we will, along with our ability to function in the world. The universals exist in as much as they are the cause of our thoughts about them, causation itself being among the universals. All these thoughts are framed and expressed within laws of logic and math which likewise exist independently of our minds. For our minds assume these laws necessarily in order to have thoughts. We can't even think to decide to use them or not use them without using them. They preexisted our minds and the only way to escape using them is to not exist.
These laws of math & logic are objective and independent while our minds are subjective. They are universal where our minds are particular. They are always precise and exact and correct while our minds are imprecise, inexact and wrong many times. Our minds change but these laws do not. These laws are necessary, and our minds are not. They seem to have eternal, infinite, universal qualities where our minds do not. How can this be explained?
That these laws of math and logic always work exactly and unerringly in the world of constant flux is not something that they communicated to us. Math didn't explain its scope of function to us. They are not personal or volitional. Just because we cannot imagine it otherwise without contradiction does not necessitate that conclusion. If there is no sufficient guarantor maybe the world is full of contradictions. They need a grounding that is of proportionate causality. An eternal, immutable, infinite, universal transcendent entity would require a related justifying source for their existence. We wouldn't conclude that infinite, eternal, universal, immutable abstract entities came from our neighbor Joe and his dog, for example. Evidence and cause require an equivalent relation (e.g. crackers in the pantry fallacy); ergo the Christian God.
These problems vex us only when we assume our limited, finite, changing, temporal minds are required to justify these universal, infinite, immutable, eternal categories and how we can use them constantly in the material changing world of flux. The other philosophical problem underlying 'the one & many problem' is the uniformity of existence. How can our minds account for this either? The problems of philosophy in general and the one & many in particular are epistemological in nature. How can we know these necessary things which end in subjectivity, skepticism and arbitrary assertions when our mind is the presupposed starting point. This subjective dilemma is not a dilemma if the universal objective mind of the Creator as described in scripture exists. For he has the proportionate causality to justify how knowledge is possible and why it will continue to be. He has the power to impose this reality and the infinite mind to communicate it. He is omnipotent and omniscient. The Christian God is the revealer and guarantor of these realities we experience, and the problems of philosophy find their resolution in him the necessary being.
Col.2:2 That their hearts might be comforted, being knit together in love, and unto all riches of the full assurance of understanding, to the acknowledgement of the mystery of God, and of the Father, and of Christ; 3 In whom are hid all the treasures of wisdom and knowledge. 4 And this I say, lest any man should beguile you with enticing words.
8 Beware lest any man spoil you through philosophy and vain deceit, after the tradition of men, after the rudiments of the world, and not after Christ.
