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Wand/set theories: A realization of Conway's mathematicians' liberation movement, with an application to Church's set theory with a universal set
Tim Button
Consider a variant of the usual story about the iterative conception of sets. As usual, at every stage, you find all the (bland) sets of objects which you found earlier. But you al…
Against Cumulative Type Theory
Tim Button, Robert Trueman
Standard Type Theory, STT, tells us that is well-formed iff . However, Linnebo and Rayo (2012) have advocated for the use of Cumulative Type Theory, CTT, which ha…
Level Theory, parts 1-3
Tim Button
This document comprises Level Theory, parts 1-3. PART 1. The following bare-bones story introduces the idea of a cumulative hierarchy of pure sets: 'Sets are arranged in stages. Ev…
Grades of Discrimination: Indiscernibility, symmetry, and relativity
Tim Button
There are several relations which may fall short of genuine identity, but which behave like identity in important respects. Such grades of discrimination have recently been the sub…