Abstract

In lieu of an abstract, here is a brief excerpt of the content:THE ACTUAL INFINITE IN ARISTOTLE Prolegomena: Philosophy and Theology Related HENEVER PHILOSOPHY is taken to be the handmaiden of theology, then the autonomy of reason is destroyed." Such a daim should be distinguished from a still 1stronger thesis. Compare: " A philosopher may not legitimately try to fortify an argument by bringing in new premises from another discipline which has a special aura of authority." Quite how Aristotle would have reacted to the first generalization, if it had been suitably translated for his scrutiny, is a question on which commentators might agree to differ. But Aristotle would have been as!'eluctant as Aquinas, or Maimonides, or later Monotheists who treasured the Physics, to leave the second general claim unquestioned. Natural and revealed theology, like physics or mathematics, are domains where extremely subtle reasoner1s have studied and published widely for a very long time. So an elementary respect for induction suggests that philosophers should e:x;pect to benefit from,applying some premises and some ways of arguing, which are found in theology, to their own issues. I speak of premises and ways of arguing that philosophers qua philosophers have not provided before. Thinkers in all four disciplines could thus profit from each body of work. Even the law of averages is set pitilessly against the second general claim.1 1 The late Father F. C. Copleston, S.J., covers many important topics regarding theology and philosophy in Aquinets (Baltimore: Peng11in, 1955), pp. 12-14, 19, 54-63, 65-68, 74, 116, etc. But the point put forward here about human power to strengthen intuition in one field seems to be partly missed. Copleston also fails to dwell enough on infinity in various passages. See John King-Farlow, "The First ·way in Physical and Moral Space", The Thomist 427 428 JOHN KING-FARLOW By focussing on some arguments of Aristotle's against the admissibility of an,actual infinite, we shall find deeper, less obvims reasons for rejecting that second claim. Other philosophical points of intrinsic value should emerge as well foom the short investigation. But this one is especially interesting because of its curious pertinence to perennial disagreements among those who address the relations of theology, theism and philosophy. At any rate, the search for such deeper reasons will involve the application to Aristotle's texts of a somewhat modern way of using the term " intuition ". Introduotion: A Relevant Kind of Intuitive Thinking Diss,atisfaction with modern Platonism in higher mathematics may be added to disenchantment with Platonism's modern opponents. Such opposition may seem too technical for issues of intuition or, indeed, of common reason. And so one is led back to consider certain rightly famous arguments of Aristotle. But before turning to Aristotle and his grapplings with ideais and claims about an actual infinity, let us 1ook at a few very ordinary uses of the sometimes charismatic word "intuition." Webster's Dictionary (1978) offers: "immediate and instinctive perception of a truth; direct understanding without reasoning." In his classic study Evolution of JJ;Jathematieal Concepts, Wilder writes at least once in the spirit of Webster: "Counting with fingers (and toes) clearly involves intuitive recognition of (1-1)-correspontreme, excessive gene:msity, and, next, irion unwillingness to give ·anything to others, lies usually much closer to the first extreme. Between utter recklessness and self-paralyzing caution the Mean may oscillate in relative distance, according to the demands of the context. Near recklessness may offer the only means to win one kind of battle and a stubborn refusal to move may be needed for the nex>t victory. By pursuing such a nonmechanical and variably positioned ideal of a Mean, a really wise father usually oould show special favor to one specially deserving child in some ways and some contexts, yet generally show very satisfying love to a;ll his children. 11 Richard Bosley, " What Is a Mean? The Question Considered Compara· tively and Systematically." PhiloB.