By Alex C. Michalos
1 In 1954 Karl Popper released a piece of writing trying to express that the id of the quantitative notion measure of affirmation with the quantitative proposal measure of chance is a significant errors. the mistake was once most likely devoted by way of J. M. Keynes, H. Reichen bach and R. Carnap. 2 It was once Popper's purpose then, to reveal the mistake and to introduce an explicatum for the prescientific suggestion of measure of affirmation. a number of months later Y. Bar-Hillel released a piece of writing trying to convey that no critical blunders have been devoted (particularly by means of Carnap) and that the matter brought via Popper used to be easily a "verbal one. "3 Popper answered instantly that "Dr. Bar-Hillel forces me [Popper] now to criticize Carnap's thought further," and he [Popper] brought additional objections which, if permitted, smash Carnap's idea. four approximately 8 years after this alternate happened i used to be in graduate university on the college of Chicago looking for an issue for a doctoral dissertation. An research of the problems focused on this alternate looked to be excellent for me simply because I had (and nonetheless have) a superb advert miration for the paintings of either Carnap and Popper. A completely revised and that i desire more advantageous account of that research seems within the first 5 chapters of this booklet. positioned very in brief, what i discovered have been 4 details of contention.
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Additional info for The Popper-Carnap Controversy
Sample text
If w is the width of M, w/k is its relative width. a:; The width of each Q-predicate in Figure 1 is (by convention) w = 1 and the relative width of each of these predicates is wjk = 1. w is the second of the two most important variables in the theorems to be introduced. 6. THE DEGREE OF CONFIRMATION OF UNRESTRICTED UNIVERSALS According to Carnap's definition of 'degree of confirmation,' the degree of confirmation of unrestricted universals approaches zero as the number of individuals in the universe approaches infinity.
Bar-Hillel, "Comments on 'Degree of Confirmation' by Professor K. R. , VI (1955), 155-157 and Y. , VII (1956), 245-248. , pp. 68-72. 3B Popper, The Logic of Scientific Discovuy, p. 399. ''' 28 28 28 TWO EXPLICANDA AND THREE ARGUMENTS 2. Comparative concept: z confirms x more than z' confirms x'. 3. Quantitative concept: The degree of confirmation of x given z is u. , p(x, z) > p(x) and p(x, z) -p(x) = u. On the other hand, the classificatory, comparative and quantitative concepts corresponding to Carnap's explicandum (if he had used only one) may be expressed thus.
Then in symbols we have c~i(M, M', e) = c*(h', ej) df We cannot make Carnap's summary of the two theorems more concise. ' Let 'MI' be defined by 'M. - Mil (Non-white swan) and 'M2' by 'M. Mil (White swan). Let the widths of 'Ml' and 'M2' be WI and W2, respectively. Let e be a report about s observed individuals saying that SI of them are Ml (negative cases) and S2 are M 2, while the remaining ones are -M (Non-swan) and hence neither Ml nor M 2. Then the following holds: (1 ) • cdU, e) (2) • Cqi(M, M', e) = 1 - = 1 - SI s + WI +k SI SI + WI 4 + WI + S2 + W2' Since N, the number of individuals in the universe, does not appear in these theorems, the fact that we might have N = 00 presents no problem.