¹ International Encyclopedia of Unified Science, Vol. I, No. 2.

² See Blumberg and Feigel: “A New Movement in European Philosophy.” Journal of Philosophy, Vol. 28, 1931. Reichenbach, Hans: Experience and Prediction, p. 69ff.

³ The essential difference between the conception of the a priori held by the rationalists such as Descartes and Kant, and that of the exponents of logical empiricism and pragmatism is that the latter believe we have some control over the a priori, whereas the rationalists assumed that we did not. Some consider a priori truths as matters of decision and choice, and even conventionalities, whereas the rationalists thought of them as somehow inevitably forced upon all of us alike and as completely beyond our control. Kant held that the a priori is legislative in that it determines prior to experience what some of its essential characters must be like. However the innovation of non-Euclidian geometries puts his view in question and leads to the view that experience itself is to a certain extent legislative over the a priori.

⁴ See Mind and the World Order, esp. Chaps. VIII, IX, X. Lewis' work anticipates many of the ideas later developed by men of the Vienna Circle and might well be considered a prolegomenon to many of the more recently developed ideas of such men as Carnap, Reichenbach, Nagel, Morris.

⁵ Concerning Carnap's view Rcichenbach writes:

If we believe that propositions such as, say, ‘in twelve years the polar star will have changed its position relative to the axis of the earth by four minutes,’ have any other signification than a reassertion of my momentary impressions, we are entirely mistaken. ‘I see a sparkling spot on a black line and some numbers on a brass instrument’ is all that astronomy aims to say; and it can not wish to say more because that would be impossible. Journal of Philosophy, Vol. 33, p. 157.

Although 1 do not think Carnap holds such a position today, it represents an attempt to have absolute certainty even in predictions. If Carnap's older view were accepted, then prediction would be a re-statement of the immediately present. This would assure certainty if the Machean view that immediate impressions are known with certainty were correct.

⁶ Experience and Prediction, p. 349. See also “Logistic empiricism in Germany and the Present State of its Problems.” Journal of Philosophy, Vol. 33, p. 157.

⁷ The following quotations are from Experience and Prediction: “If we do not know the truth about the future, there may be nonetheless a best assumption about it; i.e., a best assumption relative to what we know.” p. 349. I think Hume would answer correctly that our “best assumption” is simply the more firmly established habit and cannot be classified as “knowledge.” “I do not know whether an operation will save the man, but if there is any remedy, it is an operation.” p. 349. There is a tone of certainty about this which is quite close to, if not identical with, that of the rationalists. Reichenbach should say more consistently, “I believe the only remedy is an operation.” “We know that hⁿ is our best wager, therefore, we posit it.” p. 352. This should be interpreted, “We feel or believe that hⁿ is our best wager.“

⁸ See Reichenbach: Wahrscheinlichkeitlehre, Experience and Prediction; von Mises, Wahrscheinlichkeillehre, Statistik und Wahrheit; Nagel, “Principles of the Theory of Probability,” International Encyclopedia of Unified Science, Vol. I, no. 6.

⁹ Reichenbach holds that a statement whose probability measure approaches 1 falls under a “causal law,” whereas others are statistical. In fact however, one can be just as certain (practically) that ½ is the measure of a given statement as is I of another statement. If we define the caused as the strictly predictable, there is no basis for distinguishing (from the point of view of causation) between sentences of varying degrees of probability. There have been and may be exceptions even to statements whose probability was said to be 1. E.g., Boyle's law, PV = C, was thought to be universally applicable until Amagat discovered deviations.

¹⁰ The question: “How much evidence?” cannot be answered in terms of the number of instances. Rather it depends on the development of conviction in persons. Sometimes fewer instances are needed than at other times. Also, we are quite aware that some scientists, past and present were prevented from making progress simply because of certain convictions. We say of them that they did not have sufficient evidence for their convictions or beliefs. This is an inadequate explanation, for there is no fixed number of instances agreed upon by scientists and necessary for valid conviction. If there were, we would not have mere hypotheses in science, but absolute knowledge a priori.