logical foundations of probability by Unknown

Author:Unknown
Language: eng
Format: epub

B. The Null Confirmation

For the next step in the reduction we make use of T53-ib. This theorem shows that c (h,e) is the quotient of the c-values of certain sentences with respect to the tautological evidence */’. Since ‘ t ’ does not give any factual information—we say sometimes that it has the null content (T73-ib)— c (j,t) is the extreme case of c before any factual knowledge is available; we call it the null confirmation of j. Since this concept is often used in inductive logic, we introduce a simple notation for it:

(2) Co O') = D f c(j,t) .

Now we use T53-ib, but restricted to the systems 2 n. There is first the condition that c 0 (e) 5^ o. We shall see later that for all c-functions which come into consideration as explicata for probability!, NC 0 (e) = o only if e is L-false. (This holds only for 2 n, not for £<» ; that is the reason why we make the present step of reduction after the first.) Thus we obtain from T53-ib:

(3) In any system 2n, if e is not L-false,

c 0 (e.h)

c(h,e) =

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