- Hello world! – Welcome to User’s blog Sites. This is your first post. Edit or delete it, then start writing!
- BottomUp and TopDown – A well-known dualism in cognitive science is the distinction between top-down and bottom-up processing. These features of cognition are often linked to concepts and emotions, or the systems of dual process theory (System 1 and System 2). In relation to the thesis of this book, bottom-up processing is encapsulated by the mathematics of set theory, […]
- Mathematical Paradoxes of Infinity – There are a large number of mathematical puzzles associated with infinity, and because I don’t accept the notion of a completed infinity, I feel that most of them are not actually paradoxical. Many people (even mathematicians who do not study mathematical philosophy) are not clear about the difference between potential and actual (completed) infinity: here […]
- Cognitive Set Theory: A Summary – This is a brief synopsis of Cognitive Set Theory. It covers primarily the epistemological aspect of Cognitive Set Theory, the distinction between percepts and concepts, and relates that distinction to several major trends in Psychology, Philosophy, and Mathematics. The slides for the summary are probably the best starting point: CST Presentation.pdf The summary covers a […]
- Cup: Reflected – Cognitive Set Theory was not intended to be complicated, but enough details were included in the book that I sometimes feel that the main points were thereby obscured. So, I have written a short book about a cup, called “Cup: Reflected”. It’s about 30 sentences, and has 10 pictures. It serves as an introduction to […]
- A Buddhist Critique of Boolean Logic – Summary: although Boolean algebra works perfectly well for singular subjects, things in the world are not singular: they have multiple parts. We argue that the application of a Boolean predicate to a compound subject (i.e. a physical object) should result in a compound truth value. The four compound truth values are {true}. {false}, {true,false}, and […]
- Mathematics of Enlightenment – This page is dedicated to a poster session that was given at the 2014 Mind and Life conference in Boston, Massachusetts entitled “Mathematics of Enlightenment”. The slides corresponding to the presentation are available as a PDF: emath.pdf . There are two pages on this blog with related content: Svalaksana Mathematical primitives There is also a post […]
- Svalaksana – Svalaksana literally means “the real”. The ancient Indian debate concerning svalaksana essentially asks, what is real? When we identify an object, is it that we identify that object by first identifying all of its constituent atoms, and then assembling them together? Or do we (also) identify an object in virtue of its larger context? Are […]
- Mathematical Primitives in Point-Free Topology – The mathematical equivalent of the Madhyamaka (and especially Gelukpa) view of svalaksana (“the real”) requires an alternative to point-sets as the mathematical basis for space: these are known as “point-free” topologies. Mathematically, these theories avoid several paradoxes associated with point sets (which involve the distinction between open/closed intervals). We nominate the following tenets for a […]
- Cognitive Set Theory and Buddhism – Cognitive Set Theory makes a number of claims (particularly about mathematics and syntax) which are in no way Buddhist, so it seems inappropriate to label CST as a Buddhist work. That said, much of Cognitive Set Theory can be understood using Buddhist terminology, which might be of interest to the Buddhist readers of this work. […]