20 July 2023
Notes and Comments on Phaedo – 19
“’Now see,’ said he (Socrates), ‘if this is true. We say there is such a thing as equality. I do not mean one piece of wood equal to another, or one stone to another, or anything of that sort, but something beyond that – equality in the abstract. Shall we say there is such a thing, or not?’
“’We shall say that there is,’ said Simmias, ‘most decidedly.’
“’And do we know what it is?’
“’Certainly,’ said he.
“’Whence did we derive the knowledge of it? Is it not from the things we were just speaking of? Did we not, by seeing equal pieces of wood or stones or other things, derive from them a knowledge of abstract equality, which is another thing? Or do you think it is another thing? Look at the matter in this way. Do not equal stones and pieces of wood, though they remain the same, sometimes appear to us equal in one respect and unequal in another?’
“’Certainly.’
“’Well, then, did absolute equals ever appear to you unequal or equality inequality?’
“’No, Socrates, never.’
“’Then,’ said he, ‘those equals are not the same as equality in the abstract.’
“’Not at all, I should say, Socrates.’
“’But from these equals,’ said he, ‘which are not the same as abstract equality, you have nevertheless conceived and acquired knowledge of it?’
“’Very true,’ he replied.
“’And it is either like them or unlike them?’
“’Certainly.’
“’It makes no difference,’ said he. ‘Whenever the sight of one thing brings you a perception of another, whether they be like or unlike, that must necessarily be recollection.’
“’Surely.’
1. In this passage Socrates turns the discussion to purely abstract realities; in this case ‘equality’. The inquiry is where does our understanding of equality come from? Socrates points out that when we say two sticks are equal, we mean that they are equal in some respect, such as their length, or that they are both made of oak. But we have the idea of equality in our minds, and we have the idea of equality as such. Two equal sticks are instantiations of equality, imperfect instantiations, but they are not equality itself.
2. When we see a cloak that is like a cloak worn by someone we know, we think of that person. When we see two equal sticks, we think of equality as such. Both are examples of recollection. But the recollection of the person is a recollection of a material presence, while the recollection of equality is the recollection of a noetic, immaterial, reality.
3. Under materialism abstractions are thought of as arising from material encounters and the mind abstracts concepts out of these encounters. From this perspective there is no need to assert the prior existence of abstract entities, prior to material reality (metaphysically prior).
The Platonist position differs. Platonism understands abstract realities as residing in the second hypostasis, or nous. And from these noetic realities, or abstractions, are emanated understanding like equality into the third hypostasis, the world of soul and material existence. Material things participate in these noetic realities and by that participation we perceive there, for example, equality.
4. One of the supports for the Platonic understanding is the power that abstract realities have in the material world. This is a topic of discussion in the philosophy of mathematics: where does the power of numbers come from? By ‘power’ is meant range of relevance, influence, explanatory extent, and causal effectiveness. Looked at in this way numbers are enormously powerful.
But if numbers are simply distilled material observations it is difficult to understand why numbers have so much power; shouldn’t their power be no greater than the rocks, apples, and chairs that we count if they are ultimately material realities? The discussion is more complex than this, for sure, but framing the question in this way is, I think, helpful.
5. The noetic reality ‘equality’ is, like numbers, a powerful presence in material reality and in human consciousness. The power of noetic realities like ‘equality’ comes from their greater unity; greater than the unity found in the material realm. This unity is from equality’s participation in the One. And those of us who reside in the third hypostasis participate both in the unity of the One, and the equality of the Noetic. Socrates has skillfully moved from referring to material realities in the context of recollection to noetic realities in the context of recollection, showing how recollection is a pervasive means whereby human beings arrive at knowledge.
While the main point of this passage seems to be knowledge from recollection I think it also skillfully shows how difficult it would be to reduce concepts such as equality to mere fabrications abstracted from observable phenomena. Lloyd P. Gerson talks about this in his book Platonism and Naturalism. The judgements we make about things being equal imply that "equality as such" must exist in some way beyond mere abstraction as naturalists/nominalists posit. The platonist position that concepts such as equality eyist "as such" in the way of forms seems silly to most people and the nominalist position more immediately plausible, but upon closer examination it seems very difficult to explain our mental operations without forms. And for this reason I also think Gerson was right when he posited that, broadly speaking, there are only two philosophies: Platonism and variations thereof and everything else, which falls under naturalism/nominalism.
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