Corpus ID: 9897844

The Classical Continuum without Points Geo ¤ rey Hellman and

  title={The Classical Continuum without Points Geo ¤ rey Hellman and},
  author={S. Shapiro},
We develop a point-free construction of the classical onedimensional continuum, with an interval structure based on mereology and either a weak set theory or logic of plural quanti…cation. In some respects this realizes ideas going back to Aristotle, although, unlike Aristotle, we make free use of classical "actual in…nity". Also, in contrast to intuitionistic, Bishop, and smooth in…nitesimal analysis, we follow classical analysis in allowing partitioning of our "gunky line" into mutually… Expand


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