An exercise in imagining possibilities and impossibilities
(DRAFT: Liable to change)
Aaron Sloman
School of Computer Science, University of Birmingham
Last updated:
This paper is
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/tricirc.html
A PDF version may be added later.
A partial index of discussion notes is in
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/AREADME.html
Background
My 1962 DPhil thesis defended Kant's view of many mathematical discoveries, including those presented in Euclid's Elements, as- synthetic (non-analytic, not derivable from definitions and logic alone)
- non-contingent (involving propositions that if true are necessarily true, and if false necessarily false, i.e. impossible)
- non-empirical (not requiring confirmation by observation and experiment, though they can be discovered accidentally in that way).
Possible numbers of points common to a triangle and a circle
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Aaron Sloman
School of Computer Science
The University of Birmingham