ELLIPSES
My contention is that A understands q only if
(1) ($p)(A knows of p that it is a correct answer to Q, and p is a complete content-giving proposition with respect to Q).
In accordance with this, one cannot understand how high the Matterhorn is simply in virtue of knowing of “The height of the Matterhorn is 14,700 feet” that it is a correct answer to “How high is the Matterhorn?” Still, there are situations in which we might speak of understanding how high the Matterhorn is.
If John knows that it is sufficiently high to require equipment and a guide for climbing we might well say that he understands how high the Matterhorn is. In such a case we are treating “John understands how high the Matterhorn is” as elliptical for something like(2) John understands what significance the height of the Matterhorn has for the prospective climber.
The constituent question in (2) is
(3) What significance does the height of the Matterhorn have for the prospective climber?
John knows of the proposition
(4) The significance of the height of the Matterhorn for the prospective climber is that this height is sufficient to require equipment and a guide for climbing
that it is a correct answer to (3). But (4) is a complete content-giving proposition with respect to (3). Therefore, by (1), J ohn satisfies a necessary condition for understanding with respect to (3).
Bobby who knows nothing about physics sees a certain instrument for the first time and is informed that it is a bubble chamber. Does he now understand what instrument this is simply in virtue of knowing of the proposition
This instrument is a bubble chamber
that it is a correct answer to the question
What instrument is this?
No, but if he is now informed that this instrument is used in physics to record the tracks of subatomic particles, then we might conclude that now he understands what instrument this is.
If so, our claim is elliptical forBobby understands what the function of this instrument is.
The constituent question here is one for which there is an answer that is a complete content-giving proposition, namely,
The function of this instrument is to record the tracks of subatomic particles.
More generally, “A understands q” may be elliptical for “A understands q'” where condition (1) is satisfied with respect to Q' but not Q.
Another case of this sort involves questions of the form “What is (an) X?” (where X is a type of thing or substance). Do I understand what copper is in virtue of knowing of the proposition
(5) Copper is a metal
that it is a correct answer to the question
(6) What is copper?
If so, then we have a violation of condition (1) since proposition (5) is not a complete content-giving proposition with respect to (6). (All the conditions for content-giving sentences are violated.) It might be concluded that this result is welcome, since one cannot be said to understand what copper is simply in virtue of knowing (5). But suppose I know of the proposition
(7) Copper is the metal of atomic number 29 which has the melting point 1083° C, is reddish in color, is malleable and ductile, etc.
that it is a correct answer to (6). It might now be concluded that, in virtue of this wealth of knowledge, I understand what copper is. Yet (7), like (5), is not a complete content-giving proposition with respect to (6).
This case can be accommodated by construing “understanding what (an) X is” as elliptical for (something like) “understanding what fact about X is important (in the context in question),” or perhaps for “understanding what significance or importance X has (in the present context).” On such a construction, one who knows of the proposition
(8) A fact about copper that is important (in the context) is that copper is the metal of atomic number 29 which has the melting point 1083° C, etc.
that it is a correct answer to
(9) What fact about copper is important?
might be said to understand what copper is, in virtue of (8)'s being a complete content-giving proposition with respect to (9).
Moreover, there will be contexts in which a fact about copper that is important (or in which what significance copper has) is that it is a metal. In such contexts it will be possible to say that one who knows the relevant information understands what copper is. (The relativity of understanding is an idea that will be explored in section 5.)Finally, there are cases in which, although we may be reluctant to speak of understanding q, there is something about the situation—some related q'—that we do understand, even though “understanding q” is not elliptical for “understanding q'.” Mary intends to leave her money to a certain university. Do I understand what university Mary intends to aid in virtue of knowing of the proposition “The university Mary intends to aid is Johns Hopkins” that it is a correct answer to “What university does Mary intend to aid?”? Not on the account of understanding presented here. Nevertheless, on this account, there is something about the situation that I do understand, namely, what Mary’s intention is.
5.