Geometry without Points

Start: 12/03/2014 - 4:15pm
End  : 12/03/2014 - 5:15pm


Dana Scott, Carnegie Mellon University


Ever since the compilers of Euclid’s Elements gave the “definitions” that “a point is that which has no part” and “a line is breadthless length”, philosophers and mathematicians have worried that the basic concepts of geometry are too abstract and too idealized. In the 20th century writers such as Husserl, Lesniewski, Whitehead, Tarski, Blumenthal, and von Neumann have proposed “pointless” approaches. A problem more recent authors have emphasized is that there are difficulties in having a rich theory of a part-whole relationship without atoms and providing both size and geometric dimension as part of the theory. A solution will be proposed using the Boolean algebra of measurable sets modulo null sets along with relations derived from the group of rigid motions in Euclidean n- space. (Joint work with Tamar Lando, Columbia University.).

Freeburg Forum, Kravis Center (LC 62), Claremont McKenna College

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