there's an argument in the Phaedo (which I don't recall being discussed in the thread on that dialogue) called The Argument from Imperfection (reference). Basically this revolves around the 'idea of Equals'. It points out that there is no physical instantiation or example of 'Equals'. It argues that things that we see as equal - two sticks, or two stones - are not really equal but merely alike. Plato argues that the ability to grasp 'Equal' amounts to grasping the Form of Equal, which is something that is done solely by the Intellect, not by sensory apprehension.
That argument has intuitive appeal to me, because I believe that it is indeed true that 'Equal' has no physical instantiation, and yet it is a fundamental element of mathematical and indeed general reasoning. — Wayfarer
I don't see that at all
— Wayfarer
Don't see what? — frank
Any basis for your response to fooloso4's posts. If you say they're neo-platonic, or Protestant. then produce an argument for that. As for 'having one religion based on Platonism', aside from being a pretty big claim, it doesn't amount to any kind of argument, either. — Wayfarer
It seems germane to the topic. — Wayfarer
I agree. At first glance, it appears to me like "equal" is a completely arbitrary designation. But such a designation must be justifiable, so it requires a reason. — Metaphysician Undercover
If the word may be used in any way one wants, then how is it that the idea of equality is not arbitrary? Put it this way, there's a word I can use, "equal", to assign a relation between two things, the relationship of "equality". I can assign that relationship to any two things I want. How is it that the meaning of this idea "equality" is not completely arbitrary? What it means to be equal could be anything I want. — Metaphysician Undercover
Actually the "idea" got reduced to the way that the word may be used. — Metaphysician Undercover
Neoplatonist interpretations of Plato continued to dominate until the early modern period. From then on, Neoplatonic readings tended to be displaced by the idea, now almost universally accepted, that Plato was properly to be understood from his own dialogues, not from or through anyone else. It is extraordinary, given how obvious that idea may seem to us, how recent in origin it is. But underlying its emergence is a much more significant switch: from using Plato as a source of ideas to think with to treating him as an object of study. — Christopher Rowe
now almost universally accepted, that Plato was properly to be understood from his own dialogues, not from or through anyone else. — Christopher Rowe
But underlying its emergence is a much more significant switch: from using Plato as a source of ideas to think with to treating him as an object of study. — Christopher Rowe
We should take seriously the fact that Plato is only mentioned in a few places in the dialogues and never speaks. — Fooloso4
Any comments on the Argument from Imperfection? — Wayfarer
I don't find the argument persuasive. Socrates says he is not talking about one thing being equal to another (74a), but I think that is where we get the idea from. We can see that one thing is larger than or more than another. The less the difference the closer they come to being equal. — Fooloso4
An abstract ideal, in this case equality which is indeed different than being equal. is not properly a knowledge but more an intellectual presupposition, later to be transformed into Aristotle’s categories, thus not technically derivable from instances of perception. — Mww
The first thing that comes to mind for me is that while no two sticks are equal to one another, they are equal to themselves. So Socrates is equal to Socrates -- the actualization of the relationship of equality is that relationship which any individual has with itself. — Moliere
I suggest you're not finding it persuasive for the reason that the empirical philosophers always give in such instances - that it is derived from experience. The counter to that is that we already have to have the conception of Equals to arrive at such judgements. — Wayfarer
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? (74b)
The problem is that if each Form is one, singular and distinct, then we must confront the problem of dyads. Bigger is unintelligible without smaller, same is not intelligible without different. So too, equal cannot be separated from unequal. — Fooloso4
Now it seems to me that not only Bigness itself is never willing to be big and small at the same time, but also that the bigness in us will never admit the small or be overcome, but one of two things happens: either it flees and retreats whenever its opposite, the Small, approaches, or it is destroyed by its approach. (102 d-e)
Rather than looking at it in terms of empiricism, I look at it in terms of practice. A carpenter determines that two boards are of equal length. If they are not then one will either not fit or be too loose. A merchant puts things on a scale. They are of equal weight or not. They either balance or not. Rather than thinking of it in terms of equality they might be thought of in terms of bigger and smaller or the same. — Fooloso4
“Whence did we derive the knowledge of it [i.e. equality]? 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 not 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 those 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.”
“Now then,” said he, “do the equal pieces of wood and the equal things of which we were speaking just now affect us in this way: Do they seem to us to be equal as abstract equality is equal, or do they somehow fall short of being like abstract equality?”
“They fall very far short of it,” said he.
“Do we agree, then, that when anyone on seeing a thing thinks, 'This thing that I see aims at being like some other thing that exists, but falls short and is unable to be like that thing, but is inferior to it, he who thinks thus must of necessity have previous knowledge of the thing which he says the other resembles but falls short of?”
“We must.”
“Well then, is this just what happened to us with regard to the equal things and equality in the abstract?”
“It certainly is.”
“Then we must have had knowledge of equality before the time when we first saw equal things and thought, ‘All these things are aiming to be like equality but fall short.’”
“That is true.”
“And we agree, also, that we have not gained knowledge of it, and that it is impossible to gain this knowledge, except by sight or touch or some other of the senses? I consider that all the senses are alike.”
“Yes, Socrates, they are all alike, for the purposes of our argument.”
“Then it is through the senses that we must learn that all sensible objects strive after absolute equality and fall short of it. Is that our view?”
“Yes.”
“Then before we began to see or hear or use the other senses we must somewhere have gained a knowledge of abstract or absolute equality, if we were to compare with it the equals which we perceive by the senses, and see that all such things yearn to be like abstract equality but fall short of it.”
“That follows necessarily from what we have said before, Socrates.”
“And we saw and heard and had the other senses as soon as we were born?”
[75c] “Certainly.”
“But, we say, we must have acquired a knowledge of equality before we had these senses?”
“Yes.
“Then it appears that we must have acquired it before we were born.”
“It does.”
“Now if we had acquired that knowledge before we were born, and were born with it, we knew before we were born and at the moment of birth not only the equal and the greater and the less, but all such abstractions? For our present argument is no more concerned with the equal than with absolute beauty and the absolute good and the just and the holy, and, in short, with all those things which we stamp with the seal of absolute in our dialectic process of questions and answers; so that we must necessarily have acquired knowledge of all these before our birth.”
“That is true.”
“And if after acquiring it we have not, in each case, forgotten it, we must always be born knowing these things, and must know them throughout our life; for to know is to have acquired knowledge and to have retained it without losing it, and the loss of knowledge is just what we mean when we speak of forgetting, is it not, Simmias?”
“Certainly, Socrates,” said he.
“But, I suppose, if we acquired knowledge before we were born and lost it at birth, but afterwards by the use of our senses regained the knowledge which we had previously possessed, would not the process which we call learning really be recovering knowledge which is our own? And should we be right in calling this recollection?”
“Assuredly.” — Phaedo
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