Here is a trio of propositions that are jointly inconsistent but individually plausible:
1. Knowledge entails belief.
2. Belief is essentially tied to action.
3. There are items of knowledge that are not essentially tied to action.
Clearly, any two of these propositions is logically inconsistent with the remaining one. Thus the conjunction of (1) and (2) entails the negation of (3).
And yet each limb of the triad is very plausible, though perhaps not equally plausible.
(1) is part of the classical definition of knowledge as justified true belief, an analysis traceable to Plato's Theaetetus. (1) says that, necessarily, if a person S knows that p, then S believes that p. Knowledge logically includes belief. What one knows one believes, though not conversely. For example, if I know that my wife is sitting across from me, then I believe that she is sitting across from me. (At issue here is propositional knowledge, not know-how, or carnal knowledge, or knowledge by acquaintance.)
(2) is perhaps the least plausible of the three, but it is still plausible and accepted by (a minority of) distinguished thinkers. According to Dallas Willard,
Belief I understand to be some degree of readiness to act as if such and such (the content believed) were the case. Everyone concedes that one can believe where one does not know. But it is now widely assumed that you cannot know what you do not believe. Hence the well known analysis of knowledge as "justified, true belief." But this seems to me, as it has to numerous others, to be a mistake. Belief is, as Hume correctly held, a passion. It is something that happens to us. Thought, observation and testing, even knowledge itself, can be sources of belief, and indeed should be. But one may actually know (dispositionally, occurrently) without believing what one knows.
[. . .] belief has an essential tie to action . . . .
Although I am not exactly sure what Willard's thesis is, he seems to be maintaining that the propositions one believes are precisely those one is prepared to act upon. S believes that p iff S is prepared to act upon p. Beliefs are manifested in actions, and actions are evidence of beliefs. To determine what a person really believes, we look to his actions, not to his words, although the words provide context for understanding the actions. If I want to get to the roof, and tell you that the ladder is stable, but refuse to ascend it, then that is very good evidence that I don't really believe that the ladder is stable. I don't believe it because I am not prepared to act upon it. So far, so good.
But if belief is essentially tied to action, as Willard maintains, then it is not possible that one believe a proposition one cannot act upon. Is this right? Consider the proposition *Everything is self-identical.* This is an item of knowledge. But is it also an item of belief? We can show that this item of knowledge is not an item of belief if we can show that one cannot act upon it. But what is it to act upon a proposition? I don't know precisely, but here's an idea:
A proposition p is such that it can be acted upon iff there is some subject S and some circumstances C such that S's acceptance of p in C makes a difference to S's overt, nonlinguistic behavior.
For example, *It is raining* can be acted upon because there are circumstances in which my acceptance of it versus my nonacceptance of it (either by rejecting it or just entertaining it) makes a difference to what I do such as going for a run. Accepting the proposition, and not wanting to get wet, I postpone the run. Rjecting the proposition, I go for the run as planned.
In the case of *Everything is self-identical,* is there any behavior that could count as a manifestation of an agent's acceptance/nonacceptance of the proposition in question? Suppose I come to know (occurrently) for the first time that everything is self-identical. Suppose I had never thought of this before, never 'realized it.' Would the realization or 'epiphany' make a difference to my overt, nonlingusitic behavior? It seems not. Would I do anything differently?
Consider characteristic truths of transfinite set theory. They are items of knowledge that have no bearing on any actual or possible action. For example, I know that, while the natural numbers and the reals are both infinite sets, the cardinality of the latter is strictly greater than that of the former. Can I take that to the streets?
(3) therefore seems true: there are items of knowledge that are not items of belief because not essentially tied to action.
I have shown that each limb of our inconsistent triad has some plausibility. So it is an interesting problem. How solve it? Reject one of the limbs! But which one? And how do you show that the rejection of one is more reasonable than the rejection of one of the other two? And why is it more reasonable to hold that the problem has a solution than to hold that it is insoluble and thus a genuine aporia?
I'm just asking.
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