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Article: Grit or Gunk: implications of the Banach-Tarski Paradox.
- Article from:
- The Monist
- Article date:
- July 1, 2004
- Author:
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This paper concerns the structure of any spatially extended things, including regions of space or spacetime. I shall use intuitions about the quantity (measure) of extended things to argue for a dichotomy: either a given finite extended thing is point-free gunk, that is, it has no points as parts, or it is made of grit, that is there are only finitely many points.
This Grit or Gunk dichotomy excludes what I call the orthodoxy, namely that: (1) there are points; and (2) not merely are points represented by coordinate triples; but (3) every set of triples of reals represents a region of space. (1) It does not, however, exclude the trivial grit thesis, "Nihilism," ...