Heller M, Woodin W.H. (eds.) Infinity. New research frontiers (CUP, 2011)(ISBN 1107003873)(O)(327s)_MAml_

CHAPTER 12Notes on the Concept of theInfinite in the Historyof Western MetaphysicsDavid Bentley Hart12.1 The Infinite as a Metaphysical Concept1. There is not – nor has there ever been – any single correct or univocal conceptof the infinite. Indeed, the very word by which the concept is named typically – andappropriately – possesses a negative form and is constructed with a privative prefix:a[-peiron, aj-perivlhpton, aj-ovriston, aj-pevranton, aj-mevtrhton, in-finitum, Unendliche,and so on. In order, therefore, to fix on a proper conceptual “definition”of the infinite, it is necessary to begin with an attempt to say what the infinite is not.2. Before that, however, one ought to distinguish clearly between the “physical” (ormathematical) and “metaphysical” (or ontological) acceptations of the word “infinite.”The former, classically conceived, concerns matters of quantitative inexhaustibility orserial interminability and entered Western philosophy at a very early date. Even inpre-Socratic thought, questions were raised – and paradoxes explored – regarding suchimponderables as the possibility of infinite temporal duration, or of infinite spatialextension, or of infinite divisibility, and mathematicians were aware from a very earlyperiod that the infinite was a function of geometric and arithmetical reasoning, even ifit could not be represented in real space or real time (that is to say, a straight line mustbe understood as logically lacking in beginning or end, and the complete series of real,whole, even, odd, etc., numbers must be understood as logically interminable). Theparadoxes of Zeno, for example, apply entirely and exclusively to this understandingof the infinite and concern the apparent conceptual incompatibility between the logicalreality of infinite divisibility and the physical reality of finite motion (inasmuch as theinfinite divisibility of space would seem to imply the necessity of an infinite, ever more“local” seriality within all actions in space or time).3. The metaphysical concept of the infinite is rather more elusive of definitionand, as a rule, must be approached by a number of elliptical and largely apophaticpaths. Perhaps its most essential “negative attribute” is that of absolute indeterminacy:the infinite is never in any sense “this” or “that”; it is neither “here” nor “there”; it isunconditioned; it is not only “in-finite” but also “in-de-finite.” Granted, in the developed255