1. Overview

   1. Plato begins with two simple premises:

      Knowledge is of what is.
      Knowledge is infallible.

   2. He then moves on to conclusions about what is, or being.

   3. Thus Plato bases metaphysical (ontological) conclusions on epistemological premises.

      Epistemological Side	Ontological Side
      Knowledge	Being (= what is)
      Infallibility	?

      Plato is looking for the feature of what is that accounts for the fact that knowledge can’t be mistaken. The infallibility of knowledge is a feature (on the epistemological side) that must be matched (accounted for?) by some feature on the metaphysical side.

   4. Plato tries to find this feature by considering a state of mind which is like knowledge but is not infallible: belief, or opinion (doxa).

   5. What accounts for the errors that belief (opinion) is prone to? What accounts for mistakes in judgment? Plato’s answer:

      The cognitive unreliability of the objects of belief.

      That is, our judgments are unreliable because and in so far as the things our judgments are about let us down. In what ways do they let us down?

      • They change.
      • They can cease (or fail) to exist.
      • They can be false.

      All of these possibilities may come into play (each involves a different sense of “is” - a different sense in which the objects of belief or opinion can fail to “be.”

   6. This distinction between knowledge and belief is crucial for Plato - without it, he would not have his main support for the theory of Forms. That he continues to have this concern (after the Republic) is made clear in this passage in the Timaeus (51d):

      If understanding and true opinion are distinct, then these “by themselves” things definitely exist - these Forms, the objects not of our sense perception but of our understanding only. But if - as some people think - true opinion does not differ in any way from understanding, then all the things we perceive through our bodily senses must be assumed to be the most stable things there are. But we do have to speak of understanding and true opinion as distinct, of course, because we can come to have one without the other, and the one is not like the other . . . Since these things are so we must agree that (i) that which keeps its own form unchangingly, which has not been brought into being and is not destroyed, which neither receives into itself anything else from anywhere else, nor itself enters into anything else anywhere, is one thing. It is invisible - it cannot be perceived by the senses at all, and it is the role of understanding to study it. (ii) The second thing is that which shares the other’s name and resembles it. This thing can be perceived by the senses, and it has been begotten. It is constantly borne along, now coming into being in a certain place and perishing out of it. It is apprehended by opinion, which involves sense perception. . . .

2. The general structure of the argument:

   1. There is knowledge. (implicit premise)
   2. Knowledge is of what is. (premise)
   3. Knowledge is infallible, belief is fallible. (premise)
   4. Therefore, what is known must be, what is believed may not be.
   5. That is, what is known is something that “purely and absolutely is,” what is believed is something that “partakes of both being and not-being.”
   6. Therefore, there are things that purely and absolutely are - things we call Forms (the F Itself, etc.). The participants in the Forms (the many Fs, etc.) both are and are not.
   7. That is, Forms are the objects of knowledge; their participants are objects of belief.

3. Interpreting the argument

   1. Plato’s three claims:

      (K) Knowledge is of what is. (477a1)

      (I) Ignorance is of what is not. (477a3)

      (B) Belief is of what is and is not. (477a-b)

   2. What is the sense of “is” (“be”) involved?
      • is_e: existential
      • is_p: predicative
      • is_v: veridical

   3. So Plato’s first premise is one or more of the following: Knowledge has as its objects:
      • what is_e ( = what exists).
      • what is_p (= what is real[ly F].
      • what is_v (= what is the case, i.e., is true).

      It is most plausible to construe these as conditionals:

      • (K_e) if Kx, then x exists
      • (K_p) if Kx, then x [really] is [F]
      • (K_v) if Kq, then q is true

      In (K_e) knowledge = acquaintance: If you know (i.e., are acquainted with) something, then that thing exists.

      In (K_v), we have propositional knowledge: If you know something, then that thing is true.

      (K_p) seems to dissolve into the other two, depending on whether we take knowledge to be acquaintance or propositional knowledge:

      • If you are acquainted with something, then that thing is real (i.e., exists).

      • If you know, about something, that it is F, then (it is true that) it is F.

      So we can restrict our attention to (K_e) and (K_v).

   4. Plato’s second premise (“knowledge is infallible”) seems to make the truth of his first premise a matter of necessity:

      Necessarily, (K_e): What you know must exist.

      Necessarily, (K_v): What you know must be true.

      All of these seem plausible enough; but as we shall see, Plato slides from these innocuous sounding premises to rather startling conclusions.

4. Evaluation of the argument

   1. Phase One:

      Are the premises innocuous? That is, can they be accepted by one not antecedently committed to the Theory of Forms? (Remember, Plato is arguing for the existence of Forms from features of the concept of knowledge.) To claim that knowledge is infallible seems innocent enough, for all it seems to say is that knowledge entails truth: Necessarily, if you know that q, then q is true.

      But Plato slides from this innocuous reading of the premise to a more controversial one: that the things that we know are necessary truths; that what we know is not merely an existent, but something which must exist (a necessary being).

      In the case of ‘is_e’, the transition is from “What is known must exist” to “What is known is a necessary existent.”

      In the case of ‘is_v’, the transition is from “What is known must be true” to “What is known is a necessary truth.”

      But this is a now-familiar modal fallacy, conflating the necessity of a conditional statement (necessitas consequentiae) with the necessity of the consequent of that statement (necessitas consequentis).

      	Necessitas consequentiae				Necessitas consequentis
      	necessarily (if p, then q)		vs.		if p then necessarily q
      	(p → q)		vs.		p → q

      (p → q) may be true even though both p and q are contingent truths. Hence, it does not entail p → q. Example: Necessarily, if Tom’s shirt is crimson, then Tom’s shirt is red. (Being crimson entails being red.) But although Tom’s shirt is crimson, it is not a necessary truth that Tom’s shirt is red (since it is not a necessary truth that Tom’s shirt is crimson). The color of Tom’s shirt is a contingent matter.

      Cf. Parmenides’ treatment of the claim “what exists must exist.”

      This fallacy vitiates phase one of Plato’s argument: the argument that takes us from the truism that knowledge entails truth to the controversial thesis that what is known is a necessary truth.

   2. Phase Two:

      The transition from “Knowledge is of necessary truths” to “The objects one has knowledge about are invariable, fixed, permanent, unchanging - i.e., the Forms.”

      This appears to be a different sort of fallacy: that of transferring a property of a proposition to the thing(s) the proposition is “about.” It’s not in general true that if p is about x and p has property F, then x has F. (E.g., one may have a complex proposition about a simple object, a short proposition about a tall object, etc.)

      Two comments on Plato’s move in Phase Two:

      1. Plato’s inclination to suppose that invariable objects are required as the things invariable (i.e., necessary) truths are about may have been fostered by his assimilation of propositional knowledge (“knowing that”) to knowledge by acquaintance (“knowing someone”). For the unalterability of the propositional object of knowledge seems to require a proposition that cannot ever fail to be true. And if one stresses the unalterability of the object of propositional knowledge and slides (unwittingly) into thinking of it as knowledge by acquaintance, then it appears that an unalterable object that one can be directly acquainted with is required: a non-propositional object of contemplation which always remains the same, etc.

         The slide from knowledge_p to knowledge_a is partially concealed by the fact that, in both cases, what is known can be described as a being, something that is. Cf. the plausibility of both of principles (K_v) and (K_e):

         What you know_p must be (= be true).
         What you know_a must be (= exist).

         Plato’s move from invariable truths to invariable objects of knowledge may be made to seem more plausible if one thinks of the bearers of truth-value - the sorts of things that can be true or false - in a non-standard way.

         The standard way (nowadays): the bearer of truth-value (and hence the object of propositional knowledge) is what is expressed by a fully explicit declarative sentence, viz., a proposition. Such things are either true (eternally) or false (eternally), and don’t go around changing truth-value. So the proposition that it rained in Seattle on March 14, 1876 is, if true, true forever. It won’t change in truth-value. It does not differ at all in that respect from the proposition that 2 + 2 = 4. Thus, on this model it is hard to see why necessity should have anything to do with fixity of truth-value.

         But suppose we think of the bearers of truth-value (i.e., the things our cognitive states are about) as corresponding not to fully explicit declarative sentences, with all the local and temporal parameters filled in (like “It rained in Seattle on March 14, 1876”) but as corresponding to what Quine calls “occasion sentences,” i.e., sentences like “It’s raining.” Such sentences have implicit indexical elements (here, now, I, you, this, etc.) Such sentences are true on some occasions of utterance, and false on others.

         So if, on Monday, you have a belief that you express by saying “It’s raining,” and, on Wednesday, I have a belief that I express by saying “It’s raining,” you and I are in the same belief-state. The content of your belief looks (from the inside) exactly like mine. But we believe different propositions: what you believe is true, and what I believe is false. So if all one has to rely on is the contents of one’s mind, one’s belief-state, one cannot be guaranteed to arrive at the truth. Here, then, is a cognitive state (belief) that can sometimes go wrong.

         But now contrast these (seemingly present tense) sentences:

         • “Two plus three equals five” (i.e., 2 + 3 = 5)
         • “The sum of the interior angles of a triangle is equal to two right angles.”

         These cannot change in truth-value. And why is that? Contrast them with “It’s raining.” That can change in truth-value because the weather can change. But these mathematical statements have fixed truth-values because they are about objects that don’t change. The eternal truth of “3 + 2 = 5” is guaranteed by the fact that the entities involved, and the relations asserted to obtain among them, are not capable of changing in the respects needed to make the statement turn out to be false.

      Plato’s argument in Phase Two now seems much more plausible than it did before. But there is still room to lodge a complaint:

   3. Plato has not allowed for the possibility of fixed and unchanging relationships among noneternal (contingent) objects. If there were such relationships, his demands for the objects of propositional knowledge would be met without the need for immutable objects of acquaintance (= the Forms).

      Are there such relationships? Consider these propositions:

      • Zebras have stripes.
      • Salt dissolves in water.
      • Gold has atomic number 79.

      These propositions seem to be invariably true, even though they are not about invariable objects. What makes “Zebras have stripes” invariably true is not the existence of an invariable zebra, but the fact that an invariable relationship exists among ordinary, variable, corruptible, flesh-and-blood zebras.

      The discovery, examination, and explanation of such regularities in nature is the business of natural science, for which Plato makes no provision. His idea that things that can move and change are cognitively unreliable, and cannot be known, has the consequence that natural science is impossible!

      For natural science - as Aristotle was quick to notice - “must take for granted that the things that exist by nature are, either all or some of them, in motion (i.e., subject to change)” (Phys. 185a12-13). And physical science maintains that there can be invariable, necessary truths about changeable, corruptible objects.

      Instead, Plato supposes that necessary truths are about Forms. If it really is invariably true that zebras have stripes, this is because of some invariable feature of the Zebra Itself, an incorruptible and eternal object of contemplation.

      Note that a consequence of the line Plato takes is that propositions that appear to be about sensible, spatio-temporal particulars turn out, if they are to be objects of knowledge, not to be about those things at all. Which is to say, our knowledge gets cut off from the world of experience.

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