**John Lane Bell**, University of Western Ontario (emeritus), London, Ontario

ArXiv: _{Cover Schemes, Frame-Valued Sets and Their Potential Uses in Spacetime Physics, 2003}

• Reference by D Perlis: Taking physical infinity seriously, 2016

• Reference by Michael O’Connor, An Introduction to Smooth Infinitesimal Analysis, 2008

Homepage

Wikipedia

Youtube: Lecture at Ecole Normale Superieure, May 2007

**A sample of articles**:

*The Continuous, the Discrete, and the Infinitesimal in Philosophy and Mathematics*, Springer, 2019*Oppositions and Paradoxes: Philosophical Perplexities in Science and Mathematics.*Broadview Press, 2016*Intuitionistic Set Theory*. College Publications, 2013.*Set Theory: Boolean-Valued Models and Independence Proofs*. Oxford University Press 2011*The Axiom of Choice*. College Publications, 2009.*The Continuous and the Infinitesimal in Mathematics and Philosophy*, Polimetrica, 2005- (With D. DeVidi and G. Solomon)
*Logical Options: An Introduction to Classical and Alternative Logics*. Broadview Press, 2001. *The Art of the Intelligible: An Elementary Survey of Mathematics in its Conceptual Development*. Kluwer, 1999.*A Primer of Infinitesimal Analysis*. Cambridge University Press, 1998. Second Edition, 2008.*Toposes & Local Set Theories: An Introduction*. Clarendon Press, Oxford, 1988.^{[2]}Reprinted by Dover, 2008.

**A sampling of books**:

**Higher-Order Logic and Type Theory**, Cambridge Elements, Cambridge University Press, 2022**The Continuous, the Discrete, and the Infinitesimal in Philosophy and Mathematics**(New and Revised Edition of 8), Springer, 2019.**Oppositions and Paradoxes: Philosophical Perplexities in Science and Mathematics,**Broadview Press, 2016.**Intuitionistic Set Theory. College Publications, 2014.**__Perpetual Motion: The Making of a Mathematical Logician.__Llumina Press, 2010.**The Axiom of Choice. Front Matter. College Publications, 2009.**- The Continuous and the Infinitesimal in Mathematics and Philosophy. Polimetrica, 2005.
**The Art of the Intelligible: An Elementary Survey of Mathematics in its Conceptual Development.**Kluwer, 1999.**A Primer of Infinitesimal Analysis.**Cambridge University Press, 1998. Second Edition, 2008. Review by W.A. J. Luxemburg.**Toposes & Local Set Theories: An Introduction.**Clarendon Press, Oxford, 1988. Reprinted by Dover, 2008. Reviews (?) thereof.**Boolean-Valued Models and Independence Proofs in Set Theory.**Clarendon Press, Oxford, 1977. 2^{nd}edition, 1985. 3^{rd}edition, 2005. Paperback edition, 2011.

Appearing within this website: Intuition https://81018.com/intuition/

Second email: 21 June 2022 at 1:16 PM

Dear Prof. Dr. John Lane Bell:

In 2011 we followed Zeno down into a tetrahedron (and its octahedron) by dividing the edges by 2 and connecting the new vertices. It creates a rather unique path down into particle physics in about 45 steps and down to the Planck base units in another 67 steps.

That’s simple geometry. When we multiplied by 2, we found just 90 additional steps to the approximate age and size of the universe. No mystery. Boeke did a base-10 version in 1957 with his high school class.

We thought it was a great little STEM tool: 202 notations to see the universe as an integrated whole. Naiveté can be invigorating at first, then it becomes confusing within its own idiosyncrasies:

1. It was more simple than big bang phenomenology.

2. It had 67 notations that had never been explored per se. Here the infinitesimal is truly outlined.

Is our logic so naive, it would be too much trouble to just slap it down? You’ve only got a couple of years on me. At this stage in our life, you can be brutal!

Thanks so much.

Warmly,

Bruce

PS. Embedded links above:

1. STEM: https://81018.com/stem/

2. 202 Notations: https://81018.com/chart/

Other references:

1. Our page about your work: https://81018.com/2022/06/20/bell/

2. Tetrahedron: https://81018.com/tot-2/

3. Boeke: https://81018.com/Boeke/

Thanks. -BEC

First email: Monday, September 4, 2017, 2:27 PM

https://plato.stanford.edu/entries/continuity/

http://publish.uwo.ca/~jbell/

Dear Prof. Dr. John Lane Bell:

I thank you again and again for your body of work and the work of your doctoral students (now professors) who studied with you.

Our work is focused on base-2 notation from the Planck units, out to Observable Universe and the Age of the Universe in 202 notations: http://81018.com. Chart of numbers: https://81018.com/chart

We are entirely idiosyncratic, often naive, yet hopefully open to learning as much as we can about why we are wrong, and, if by chance, why we are right.

Thanks again for all your work so germane to our discussions.

Warmly,

Bruce

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