Abstract

In lieu of an abstract, here is a brief excerpt of the content:242 HISTORY OF PHILOSOPHY his political and religious predispositions prodded him to demonstrate that the roots of modern science were in the Christian Middle Ages. Sarton's particular foibles are best understood by referring them to his pacifist commitments and the moralistic assumption that the values of science are transferable to other human endeavors. Categories such as inductivism, conventionalism and Popperianism are of little help in gaining historical understanding. For this, they are in fact Platonic ideals which have little heuristic value. I would venture that a truly historical historiography of science would aid us in spotting errors in the past and help us in the future. My guess is that a good analysis would reveal a major source of trouble to have stemmed from preconceived notions which the history of science was meant to illustrate. Surely some of them have been philosophical in character, and even Baconian or conventionalist. But until recent times, most of these preconceptions have stemmed from religious, nationalistic, or personal motivations, or from scientists who wanted support for a particular concept. I agree with Agassi only in the suggestion that a parti pris was at the root of our troubles. Why, then, substitute a Popperian preconception for a conventionalist one? Why not, on the contrary, combat their distorting influence and reduce their impact? This is in fact what has happened in recent times. As the history of science has fallen into the hands of a gradually organized profession, the blatant motivations --of any type--which colored past historical writings have slowly receded. By a constant and critical confrontation of opposing views among specialists, the purpose for examining the history of science has slowly been transformed. The older external motivations have given way to an interest in the subject for its own sake and a gradual transformation has been in the making for the last few decades. As happens in other human endeavors, professionalization has already raised the standards in the discipline and there is every reason to think it will continue to do so in the future. We need not really be as pessimistic as Agassi, nor embrace his particular salvation. ROGEa HAm~ University o] Cali]ornia, Berkeley A MEDIEVAL ANALYSIS OF INFINITY IN THE COURSEof arguing that time must have had a beginning, St. Bonaventure (1221-74) put forward a demonstration which in some ways seems to anticipate Cantor's definition of infinity.1 Bonaventure pointed out that, if the world were infinitely old, then there would have been an infinite number of annual revolutions of the sun around the ecliptic. But during each such period there occur (roughly) twelve revolutions of the moon, i.e. lunar months or lunations. Thus there would be one infinity which was twelve times another--which, says Bonaventure, is impossible. This attempted proof might be formulated as the following For other adumbrationsof this definition,see I. Thomas,"A TwelfthCentury Paradoxof the Infinite,"Journal o] Symbolic Logic, XXIII (1958), 133-134, and W. & M. Kneale, The Development of Logic (Oxford,1962),p. 440. NOTES AND DISCUSSIONS 243 reductio ad absurdum, in which a revolution of the sun is specified as the period between successive vernal equinoxes. If there could be an infinite set of past lunations, then clearly it could be put in a one-to-one correspondence with a proper sub-set of itself--viz., with the set of past lunar months during which vernal equinoxes occurred. But this consequence is preposterous; no set could be so correlated with its own sub-set. Therefore the set of past lunar months cannot be infinite, and the world must have had a beginning. The passage, which is found in Bonaventure's commentary on the Sentences of Peter Lombard, reads as follows :2 Si mundus est aeternus, revolutiones solis in orbe suo sunt infmitae ; rursus, pro una revolutions solis necesse est fuisse duodecim ipsius lunae: ergo plus revoluta est luna quam sol; et sol infinities: ergo infinitorum ex ea parle, qua infinita sunt, est reperire excessum. Hoe autem est impossibile : ergo etc. PA~-r~asoN BROWN Harpur College, State University o] New York Sententiarum L/b. H, Dist. I, P.I, Art. I, Quaest. II, as found in S. Bonaventurme, Opera Omnla...