
Matheology § 254
Posted:
Apr 18, 2013 3:42 PM


Matheology § 254
1. Finite cannot comprehend, contain, the Infinite.  Yet an inch or minute, say, are finites, and are divisible ad infinitum, that is, their terminated division incogitable. 2. Infinite cannot be terminated or begun.  Yet eternity ab ante ends now; and eternity a post begins now. So apply to Space. 3. There cannot be two infinite maxima.  Yet eternity ab ante and a post are two infinite maxima of time. 4. Infinite maximum if cut in two, the halves cannot be each infinite, for nothing can be greater than infinite, and thus they could not be parts; nor finite, for thus two finite halves would make an infinite whole. 5. What contains infinite quantities (extensions, protensions, intensions) cannot be passed through,  come to an end. An inch, a minute, a degree contains these; ergo, &c. Take a minute. This contains an infinitude of protended quantities, which must follow one after another; but an infinite series of successive protensions can, ex termino, never be ended; ergo, &c. 6. An infinite maximum cannot but be allinclusive. Time ab ante and a post infinite and exclusive of each other; ergo, &c. 7. An infinite number of quantities must make up either an infinite or a finite whole. I. The former.  But an inch, a minute, a degree, contain each an infinite number of quantities; therefore an inch, a minute, a degree, are each infinite wholes; which is absurd. II. The latter.  An infinite number of quantities would thus make up a finite quantity, which is equally absurd. [John Stuart Mill: "An Examination of William Hamilton?s Philosophy", The Collected Works of John Stuart Mill, Volume IX, CHAPTER XXIV: "Of Some Natural Prejudices Countenanced by Sir William Hamilton, and Some Fallacies Which He Considers Insoluble" (1865), John M. Robson (ed.), Routledge and Kegan Paul, London (1979)] http://oll.libertyfund.org/?option=com_staticxt&staticfile=show.php%3Ftitle=240&chapter=40898&layout=html#a_761210
Regards, WM

