The Architecture of Matter: Galileo to Kant

By Thomas Holden | Go to book overview

APPENDIX PARADOXES OF INFINITE M-DIVISIBILITY THAT DO NOT TURN ON ACTUAL PARTS

Much of Chapter 1 was given over to arguing that the most popular, most important, and most worrisome paradoxes of infinite m-divisibility—what I have been calling the 'classic paradoxes'—arise only within the framework of the actual parts metaphysic. They are not general problems for the notion of infinite divisibility in abstracto. But this does leave some paradoxes—'non-classic paradoxes'—also found in the Enlightenment literature that do not depend on the actual parts metaphysic. These paradoxes are motivated purely by the notion of endless divisibility, and do not turn on any particular metaphysical account of the status of the parts of matter. In this appendix I want, simply for the sake of completeness, to briskly enumerate these non-classic paradoxes. As we shall see, not only are the non-classic paradoxes much less popular in the Enlightenment literature than the classic paradoxes I have already set out in section VIII, they are also much more easily disarmed and of much less intrinsic philosophical interest.

Some period philosophers rejected infinite divisibility simply because an endless division into smaller and smaller parts with no stopping place was too staggering—too mind-boggling—to accept. No formal contradiction is adduced, but it is simply asserted (typically with a rhetorical flourish invoking bewilderingly large numbers) that infinite divisibility beggars belief. Walter Charleton stands as a good example here, writing in his 1654 Physiologia as follows:

What Credulitie is there so easie, as to entertain a conceit, that one granule of sand (a thing of very small circumscription) doth contain so great a number of parts, as that it may be divided into a thousand millions of Myriads; and each of those parts be subdivided into a thousand millions of Myriads; and each of those be redivided into as many; and each of those into as many: so as that it is impossible, by multiplications of Divisions, ever to arrive at parts so extremely small, as that none can be smaller; though the subdivisions be repeated every moment, not only in an hour, a day, a month, or a year, but a thousand millions of Myriads of years? 137

-75-

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The Architecture of Matter: Galileo to Kant
Table of contents

Table of contents

  • Galileo to Kant iii
  • Preface vii
  • Contents xi
  • Contents xii
  • Problems of Material Structure 1
  • Appendix Paradoxes of Infinite M-Divisibility That Do Not Turn on Actual Parts 75
  • 2 Actual Parts and Potential Parts 79
  • 3 The Actual Parts Doctrine and Shortcircuit Arguments 132
  • 4 The Actual Parts Doctrine and the Argument from Composition 169
  • 5 The Case for Infinite Divisibility 206
  • Appendix: Minor Arguments 232
  • 6 The Kant-Boscovich Force-Shell Atom Theory 236
  • Conclusion 273
  • Bibliography 280
  • Index 295
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