But the suggestion is not that we arrive at the idea of equality by seeing empirical objects of equal size, because empirical objects are not absolute, which the idea of equality is. — Wayfarer
... take all animals and all plants into account, and, in short, for all things which come to be, let us see whether they come to be in this way, that is, from their opposites ... Let us examine whether those that have an opposite must necessarily come to be from their opposite and from nowhere else, as for example when something comes to be larger it must necessarily becomelarger from having been smaller before. [emphasis added] (70e)
I'll tell you how I've always done it. — frank
I don't know what you're asking. — frank
Yes. And then there's my all time favorite Platonic argument: the Cyclic Argument, which shows that there can be no "bigger" without the preceding "smaller".
So tell me how you resolve this, and I'll tell you how I've always done it. — frank
I don't think we have any common ground from which to proceed, so vaya con dios! — frank
I don't find the argument persuasive. — Fooloso4
...in thinking*, [says Aristotle] the intelligible object or form is present in the intellect, and thinking itself is the identification of the intellect with this intelligible. Among other things, this means that you could not think if materialism is true… . Thinking is not something that is, in principle, like sensing or perceiving; this is because thinking is a universalising activity. This is what this means: when you think, you see - mentally see - a Form which could not, in principle, be identical with a particular - including a particular neurological element, a circuit, or a state of a circuit, or a synapse, and so on. This is so because the object of thinking is universal, or the mind is operating universally.
For Empiricism there is no essential difference between the intellect and the senses. The fact which obliges a correct theory of knowledge to recognize this essential difference is simply disregarded. What fact? The fact that the human intellect grasps, first in a most indeterminate manner, then more and more distinctly, certain sets of intelligible features -- that is, natures, say, the human nature -- which exist in the real as identical with individuals, with Peter or John for instance, but which are universal in the mind and presented to it as universal objects, positively one (within the mind) and common to an infinity of singular things (in the real). — Jacques Maritain, The Cultural Impact of Empiricism
'argument from imperfection' anticipates Kant's Transcendental Arguments.
— Wayfarer
Sure reads that way. — Mww
What are the advantages of doing that? It seems absurd at face value. — frank
Still working on it. — Wayfarer
I find it more than persuasive; I'm compelled by it. And why? Because, in the broadest sense, as soon as you appeal to reason then you're already relying on something very like the knowledge of the forms. — Wayfarer
Now the Theaetetus will later have much to say about memory. Why is there no mention of that peculiar impersonal memory of knowledge before birth? There is no ground for supposing that Plato ever abandoned the theory of Anamnesis. It cannot be mentioned in the Theaetetus because it presupposes that we know the answer to the question here to be raise afresh: What is the nature of knowledge and of its objects? For the same reason all mention of the forms is excluded. The dialogue is concerned only with the lower kinds of cognition, our awareness of the sense-world and judgments involving the perception of sensible objects. Common sense might maintain that, if this is not all the 'knowledge' we possess, whatever else can be called knowledge is somehow extracted from such experience. The purpose of the dialogue is to examine and reject this claim of the sense-world to furnish anything that Plato will call 'knowledge'. The Forms are excluded in order that we may see how we can get on without them; and the negative conclusion of the whole discussion means that, as Plato had taught ever since the discovery of the Forms, without them there is no knowledge at all. — F.M. Cornford, Plato's Theory of Knowledge, page 28
There is for Aristotle no "equal itself" existing by itself timeless and unchanging. — Fooloso4
The discussion in Theaetetus advanced well beyond where Cornford placed it. — Paine
The dialogue is concerned only with the lower kinds of cognition, our awareness of the sense-world and judgments involving the perception of sensible objects. — F.M. Cornford, Plato's Theory of Knowledge, page 28
But the members of the dialogue find no way that anything which is commonly called "knowledge" could have the possibility of falsity ruled out. — Metaphysician Undercover
Soc: Therefore, knowledge is not present in the experiences, but in the process of gathering together what’s involved in them, for in the latter, as it seems, there is a power to come in touch with being and truth, but in the former there is no power. — Plato. Theaetetus, 186d, translated by Joe Sachs
Theae: That true opinion is knowledge. Having a true opinion is surely something safe from error at least, and all the things that come from it are beautiful and good. — ibid, 200e
Soc: Then whenever the jurors are justly persuaded about things it’s possible to know only by seeing them and [C] in no other way, at a time when they’re deciding these things from hearing about them and getting hold of a true opinion, haven’t they decided without knowledge, even though, if they judged well, they were persuaded of correct things? — ibid, 201c
Looking at 74b, we can see the inkling of something new and different just beggin’ to be exposed. Socrates says stuff like…when we think……but leaves it at that. Kant steps in with a new notion of what is actually happening when we think, and the transcendental arguments are the necessary conditions that justify those speculative notions. It’s Aristotle’s logic in spades: if this is the case, which the LNC says it is, and that follows necessarily from this case, which the Law of Identity says it does, then the entire systemic procedure is only possible if this certain something is antecedent to all of it.
By delving deeper into the human cognitive system, examining it from a transcendental point of view, claimed to be the only way to determine that antecedent something, Kant both sustains and refutes arguments from imperfection. Refutes insofar as purely logical systems can be perfectly formed and thereby perfectly concluded, hence can be absolutely certain in themselves; sustained insofar as being metaphysical, there are no possible empirical proofs for those transcendental points of view, which a proper science must have, hence is imperfect. — Mww
Like Macbeth, Western man made an evil decision, which has become the efficient and final cause of other evil decisions. Have we forgotten our encounter with the witches on the heath? It occurred in the late fourteenth century, and what the witches said to the protagonist of this drama was that man could realize himself more fully if he would only abandon his belief in the existence of transcendentals. The powers of darkness were working subtly, as always, and they couched this proposition in the seemingly innocent form of an attack upon universals. The defeat of logical realism in the great medieval debate was the crucial event in the history of Western culture; from this flowed those acts which issue now in modern decadence. — Richard Weaver, Ideas have Consequences
I simply meant that the natural numbers and such things as laws and principles, are real….. — Wayfarer
What makes that form of realism Platonic? — Mww
Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices. Just as electrons and planets exist independently of us, so do numbers and sets. And just as statements about electrons and planets are made true or false by the objects with which they are concerned and these objects’ perfectly objective properties, so are statements about numbers and sets. Mathematical truths are therefore discovered, not invented. ....
Mathematical platonism has considerable philosophical significance. If the view is true, it will put great pressure on the physicalist idea that reality is exhausted by the physical. For platonism entails that reality extends far beyond the physical world and includes objects which aren’t part of the causal and spatiotemporal order studied by the physical sciences. Mathematical platonism, if true, will also put great pressure on many naturalistic theories of knowledge. For there is little doubt that we possess mathematical knowledge. The truth of mathematical platonism would therefore establish that we have knowledge of abstract (and thus causally inefficacious) objects. This would be an important discovery, which many naturalistic theories of knowledge would struggle to accommodate. — SEP
In his seminal 1973 paper, “Mathematical Truth,” Paul Benacerraf presented a problem facing all accounts of mathematical truth and knowledge. Standard readings of mathematical claims entail the existence of mathematical objects. But, our best epistemic theories seem to deny that knowledge of mathematical objects is possible. Thus, the philosopher of mathematics faces a dilemma: either abandon standard readings of mathematical claims or give up our best epistemic theories. Neither option is attractive. ....
Mathematical objects are in many ways unlike ordinary physical objects such as trees and cars. We learn about ordinary objects, at least in part, by using our senses. It is not obvious that we learn about mathematical objects this way. Indeed, it is difficult to see how we could use our senses to learn about mathematical objects. We do not see integers, or hold sets. Even geometric figures are not the kinds of things that we can sense. ...
[Rationalists] claim that we have a special, non-sensory capacity for understanding mathematical truths, a rational insight arising from pure thought. But the rationalist’s claims appear incompatible with an understanding of human beings as physical creatures whose capacities for learning are exhausted by our physical bodies. — IEP, Indispensability Argument in Phil. of Math
Some scholars feel very strongly that mathematical truths are “out there,” waiting to be discovered—a position known as Platonism. It takes its name from the ancient Greek thinker Plato, who imagined that mathematical truths inhabit a world of their own—not a physical world, but rather a non-physical realm of unchanging perfection; a realm that exists outside of space and time. Roger Penrose, the renowned British mathematical physicist, is a staunch Platonist. In The Emperor’s New Mind, he wrote that there appears “to be some profound reality about these mathematical concepts, going quite beyond the mental deliberations of any particular mathematician. It is as though human thought is, instead, being guided towards some external truth—a truth which has a reality of its own...” ....
Other scholars—especially those working in other branches of science—view Platonism with skepticism. Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something existing “outside of space and time” makes empiricists nervous: It sounds embarrassingly like the way religious believers talk about God, and God was banished from respectable scientific discourse a long time ago.
Platonism, as mathematician Brian Davies has put it, “has more in common with mystical religions than it does with modern science.” The fear is that if mathematicians give Plato an inch, he’ll take a mile. If the truth of mathematical statements can be confirmed just by thinking about them, then why not ethical problems, or even religious questions? Why bother with empiricism at all? — What is Math
That description does not match the language in the dialogue. Socrates directly refutes Cornford's statement, "The dialogue is concerned only with the lower kinds of cognition", when he corrects Theaetetus' idea that knowledge is perception: — Paine
At 187a, Theaetetus takes a second shot and says opinion is knowledge. After Socrates shows that as inadequate, Theaetetus says: — Paine
The addition of an account does not repair the problem that true opinion is different than knowledge. Socrates statement here does stow, however, that true opinion can come from knowledge and good judgement. That is a far cry from not being able to rule out the "possibility of falsity." — Paine
Can you see the issue lurking behind these controversies? — Wayfarer
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