A problem for the Socratic search for definitions: how do you know when a definition is correct? You have to (at least) understand the definition, i.e., you have to understand the terms in the definiens. But how do you do that? By understanding their definitions? This leads to either circularity or an infinite regress.
The problem arises if we try to give a linguistic account of understanding. The knowledge of a definition according to such an account would have to be propositional knowledge. That is: we explain what X is by offering the definition
X =df ABC.
This just invites the question: how do we know that X is ABC? If we answer this by saying that we know what A, B, and C are, and if we have to explain our understanding of A, B, and C in a similar way, there is no way out.
Platos idea: at some point, one must invoke a kind of knowing that is not propositional - i.e., not a matter of knowing that something-or-other - but is more like knowledge by acquaintance. More graphically: one must invoke a kind of knowing that is not a matter of grasping a definition of one term by means of other terms, but of grasping the thing itself.
This is the way recollection seems to be understood in the Phaedo. Recollection is the epistemological mechanism, and the Forms are the objects to which the mechanism is applied.
[Plato may be right in rejecting the idea that understanding can be adequately explained in terms of knowing that, but wrong in proposing a kind of knowledge by acquaintance in its place. The proper contrast is not between knowledge by description (knowing that p) and knowledge by acquaintance (knowing x), but between knowing that and knowing how. That is, having a concept is not a matter of being acquainted with an item available only to the gaze of an intellect, but of having certain abilities and capacities. Cf. Aristotle and Ryle.]
Forms are sometimes called Ideas - Platos words are eidos and idea, and the latter suggests the English idea. But this gives the wrong idea.
For Platos Forms are not mental entities, nor even mind-dependent. They are independently existing entities whose existence and nature are graspable only by the mind, even though they do not depend on being so grasped in order to exist.
Platos objection to the physical universe: its Heraclitean (as he conceived Heraclituss theory). Objects in flux cant be known.
The two-worlds theory: Cf. the Allegory of the Cave in Republic VII. The intelligible world is Parmenidean, the visible world is Heraclitean. Forms in the intelligible realm are postulated to be the objects of knowledge. The metaphysical theory is thus designed to fit epistemological requirements.
For Plato, goodness and being are intimately connected. Platos universe is value-ridden at its very foundations: value is there from the start, not imposed upon an antiseptic, value-neutral reality by the likes of us - external imposers of value on what in itself has no intrinsic value.
This connection explains why it is a single theory that aims to answer both metaphysical and ethical questions. Understanding how this can be so is one of the hardest - but most important - things to do in understanding Plato.
The Form of the Good is at the top of the hierarchy of Forms, illuminating all of the others (as the sun illuminates objects in the visible realm, to use Platos famous metaphor from the Republic).
An interpretation of this: knowing what something is cant be divorced from knowing whether it's good. One cant know what it is to be an F unless one knows what it is to be a good F: a non-defective example of its kind. Here is one way to see the connection: imagine a good head of lettuce. Now imagine another head of lettuce, but not as good as the first. And so on. There comes a point at which our example becomes so bad that it ceases to be a head of lettuce at all. If there were no connection between goodness and being, there would be no reason to expect this.
Plato sometimes writes as if he takes the existence of Forms for granted, as a matter of faith. But sometimes he offers arguments for them. Each argument is connected to a function Plato has in mind for Forms to play. Some of these reasons for believing in Forms dont really add up to arguments, but some do. Plato, in any event, was not very systematic about his arguments.
Plato believes that there is a non-conventionalist answer to questions of meaning: there is some one thing that is referred to by just whenever it is used. Hence, when you talk about justice and I talk about justice, we are talking about the same thing. We belong to the same world, not each of us in his own private world. If we disagree in what we apply the term just to, we cannot both be right.
The last three of these arguments are especially important. They correspond to three of the problems the Forms are supposed to solve. Well look at the first of these in the Phaedo, and at the others later.
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