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Geometry Without Points

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If you have a question about this talk, please contact Ceinwen Cushway.

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 the basic concepts of geometry are too abstract and too idealised.

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 emphasised in 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 possible solution is 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.

Professor Scott is an internationally recognised mathematical logician whose work has spanned computer science, mathematics, and philosophy. He made seminal contributions to automata theory, modal logic, model theory, set theory, and the theory of programming languages. He has made fundamental contributions to contemporary logic and is known for his creation of domain theory, a branch of mathematics that is essential for analysing computer programming languages.

Professor Dana Scott began his academic career with a BA from the University of California, Berkeley followed by a PhD at Princeton University. Highlights of Professor Scott’s career included receiving the Turing Award of the Association of Computing Machinery (1976) with Michael O. Rabin for their joint paper ‘Finite Automata and Their Decision Problem’ which introduced the idea of nondeterministic machines.

This talk is part of the Computer Science Distinguished Seminars series.

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