Revision: 30 May 2026
This is a seed post. It will be fleshed out over the next few months.
As someone who loves mathematics and the sciences, and who studied mathematics and physics intensively in college, I offer the following with a mixture of shock, curiosity, and optimism for the future of human investigation into the nature of reality.
The second and tenth axioms of Zermelo-Fraenkel set theory with the axiom of choice (see below) calibrate in the YES range for falsehood, though neither is all the way false. The other eight calibrate in the YES range for truth, though none of them are all the way true. If total, unambiguous truth is the goal of mathematics, then a new mathematics is required.
Three questions arise immediately:
- What is mathematics without the axiom of choice? The framework of modern mathematicians relies on the axiom of choice. However, a mathematics that does not require it would be more true.
- Perhaps more foundationally, what could mathematics look like without the null set? Without the second axiom, Zermelo-Fraenkel set theory would seem to be, well, nullified.
- What if none of the other axioms of Zermelo-Fraenkel set theory are actually fundamental?
Regarding the second question, and the second axiom, a potential replacement comes to mind: There is a set that contains all that is (rather than nothing). In this way, we start with what is—and what is is one and all simultaneously—rather than what is not. What is not is pure abstraction. There is no truth, and consequently no power, in building on a foundation that is not.
As for the third question, the following statement calibrates as all the way YES: “Axioms that are totally fundamental calibrate as all the way YES.” In the coming months, I will calibrate other axioms of mathematics, logic, and the sciences to see whether any such axioms satisfy this requirement.
Updates:
- So far, none of the established axioms of logic, mathematics, and science calibrate as totally fundamental. It looks like the sciences are going to need a new foundation.
- A second axiom is emerging that calibrates as totally fundamental. A set is a collection of perspectives on all that is. Each perspective on all that is is still all that is, yet there is also distinctness in terms of what is emphasized, visible, and/or in the foreground.
- Finitude calibrates as totally false. It is the basis of unreality. As such, a mathematics of reality cannot involve finite numbers or finite arithmetic. That is going to be a tough sell!
To be continued…
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