James Appleby
School of Computing and Mathematics
Resolving the paradoxes of lawless choice sequences
Intuitionism is a theory of the foundations of mathematics put forward by Brouwer in
the early 1900s. Its main points are that mathematics does not rely on logic, that all
mathematics is based on the two acts of Intuitionism, that excluded middle (A or
Not(A)) does not hold generally and that we replace the idea of 'A is true' with 'A is
proven'. Three common notions in intuitionistic analysis are choice sequences
(sequences generated indefinitely), lawless sequences (choice sequences whose
generation is not restricted in any way and whose elements are not predictable in
advance, a sequence of coin tosses for example) and open data (any predicate on a
choice sequence holds by virtue of finite information about that choice sequence, in
the conventional theory this finite information is some finite initial segment of the
sequence). This poster outlines a paradox attributed to Peter Fletcher that arise from
this notion of ]