by Mordecai Plaut
(Page 2)
From the book "At the Center of the Universe".
Actually, Hintikka would substitute "there exists an alternative model set with respect to a" for "it must be possible." Also, the discussion following should refer only to model sets. The conclusion is that there can be no such alternative model set.
Informally we can present the argument more directly. It is acknowledged to be a necessary condition for someone's knowing p that p be true. It is not correct to say that someone knows something false. Someone might think he knows something which he later discovers to be false, but he would not say that before he knew p and now he knows not-p. Rather he would say that he was mistaken before.
Objectively, too, we would not be inclined to call something knowledge if we knew it to be false. We might concede that it is strongly held belief, but we would not call it knowledge. (Belief can be false.)
Thus, if b knows p then p must be true. If a knows that b really knows p, then a should reason that p is true and hence should know p himself. It might be said that knowing that p is true is included in the knowledge (of a) that b knows p.
The standard definition of knowledge in modern epistemology is "justified, true belief." There are many problems with the requirement for justification, but the discussion here is based only on the specification that it be true belief. This much about knowledge is uncontroversial, and whatever the outcome of the work on justification, this theorem will still stand.
Carefully speaking, however, there is the problem raised by the medieval Pseudo-Scotus. He argued that a person might not always deduce what he may from what he does know. Even though our theorem shows that a person could know p from the knowledge that another knows p, we might be rash to conclude that he does know p himself. Hintikka has avoided this sort of problem by speaking of the theorem as being self-sustaining rather than true. A statement is said to be self-sustaining when its negation is indefensible. This approach is what leads him to use the reductio form of proof.
For our purposes it is sufficient to construe the theorem as a license for inference. If one knows that another knows something, then he may infer that he also knows it. If he does infer then, of course, he really does know it. We will find use for the theorem in support of some who do infer knowledge of p from their knowledge that another knows p.
If there is ever a need to provide it, this theorem could serve as a formal basis for accepting G-d's word. One suspects that direct reception of communication from G-d might provide some sort of experiential foundation in support of His word. However, lacking the experience, we can objectively evaluate the formal support provided by theorem (I), and understand clearly what basis there is for such acceptance.
It is clear that the only relationship that G-d could have to any information is knowledge. An all good G-d would hardly lie, and it is hard to see why an omniscient being would want to. Thus, G-d knows what he talks about. So, if He were to tell us something, we would know that He knew what He told us. By theorem (I), we would also know that which He told us.
Just as the theorem provides a basis for accepting the word of G-d, it also provides a basis for accepting the word of a person who is godlike in the relevant aspects. The person would have to be a veritably formal being, one whose general areas of interest and whose motivations in general were as clear and pristine as the realm of format logic. Such a one would make only unassailable claims. If we knew some such one, in virtue of that knowledge we would also know that he knew anything of which he claimed knowledge. This would prove another instance in which our theorem would prove handy.
With this in mind, it is interesting to note the requirement that the Talmud imposes for the choice of a teacher. The requirement is:
(II) If a Rav is like an angel of the G-d of hosts, one should seek teaching from him, and if he is not (like an angel of the G-d of hosts), one should not seek teaching from him. (5)
In Talmudic law, a condition is legally incorporated in a contract only if the results of both the fulfillment and the nonfulfillment of the condition are spelled out. If only one of these is specified, then the contract is enforceable regardless of whether the condition is fulfilled, that is, unconditionally. It would seem that the only reason that there is for such an elaborate specification of the idea in this passage is to give it the force of a contractually binding clause. This indicates that the requirement imposed in the Talmud is intended seriously and not as poetic hyperbole of some sort.
Though he may have other desirable properties as well, an angel certainly knows whereof he talks. An angel is a completely abstract, formal being who could have no relation to facts other than knowledge, nor would he have motivation, inclination, or ability to say anything but what he knows. Thus an angelic instructor would know what he talked about (and taught) and, by (I), so would his pupil or so could his pupil.
This essay is from the book "At the Center of the Universe". Order the book