Information and content: A semantic analysis

When asked to compare the statements (1) The temperature in Amersfoort on August 15, 1953, at 3 P.M. is 23.6 and (±0.1) °C (2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (+__ 0.2) °C with respect to the amount of information they convey, few secondary-school educated English speakers will hesitate to answer that the amount of information conveyed by (1) is greater than that conveyed by (2). If challenged to justify their reply, they might point out that (1) L-implies ('L' for 'logically') (2) but not vice versa. In other words, one-sided L-implication between two statements i and j is generally taken to be a sufficient, though perhaps not a necessary, condition for i's conveying more information than j. If further asked, how much more information is conveyed by (1) over (2), our hypothetical informants would probably at first look somewhat puzzled and then say either that they would not know or that they don't believe that this second question makes much sense. Some would insist that though they are quite able, for certain pairs of statements, to determine whether they convey the same information or whether the one conveys more information than the other, there is no way of transforming these comparative judgments into quantitative ones. These people would then also denounce as unfair the prima facie even simpler question: How much information is conveyed by (1)? There is nothing especially new and surprising in this situation. The state of affairs is completely analogous to that prevailing with respect to the probability of statements. Here, too, we have scientists who deny the meaningfulness of assigning numerical values to the probability of statements, in general, but believe that comparative probability judgments for certain pairs of statements are quite in order. The analogy is of course more than a pure accident. In order to deal with the problem of the information conveyed