Axioms

by Robert G. Brown Duke University Physics Department Durham, NC 27708-0305 Copyright Robert G. Brown, 2024

Warning Warning Warning! This is totally a draft release and is liable to change without warning, to contain twinned chapters, to contain material that will not be in the final version, and to be incomplete and inconsistent or worse!

Stumble It!

This is the official pre-publication distribution website for the Axioms project. This work is basically about what we know: the foundations of all human knowledge. It is revealed that we don't know much of anything -- that the basis for most of what we know are a set of assumptions that are rarely enumerated or examined (at least outside of mathematics and science) because even to examine them requires additional assumptions. These assumptions are the axioms upon which the whole shaky edifice of human knowledge is built.

Here is a very short outline of how they book may eventually be organized:

Reason and Its Limitations

A look at the so-called "laws of thought", at set theory, at Jaynes' notion of conditional belief or probable belief, and at the closely allied ideas of logic (including what might be called "zen logic"), mathematics, and computer science. Godel's theorem is examined in some detail. Finally, it is shown that when it comes right down to it, we cannot prove a whole lot about the world we see using these tools one at a time or all together.

Philosophy

Here it is shown (basically restating the conclusions of the first part in context) that Philosophy is Bullshit. This is a deliberately provocative way of phrasing it, a way that that no longer admits any possibility that there is an answer out there to be found by means of pure reason, let alone that some particular answer is the One True Answer. It asserts that as a necessary prior condition for any sort of philosophical discussion all participants need to agree on their axioms, the unprovable assumptions and methods of reasoning upon which their conclusions are ultimately based. It then examines at least some of the near-infinity of often mutually contradictory and self-referential axioms that underlie major subsystems of human society. Only the axioms of mathematics and science are seen to be reasonably consistent and clearly stated (if still largely unknown even to many scientists), and even there the axioms are "bullshit" in the sense that they are logically unprovable assumptions.

Axioms

In this section a first pass is made at proposing (or if you prefer and more honestly, cobbling together from the previous efforts of many philosophical giants) a set of axioms upon which human society might be based. It differs significantly from previous axiom sets (at least those from outside of science) in that it is openly acknowledged from the beginning that it is neither complete nor correct, merely provisional and practical. It is intended to be discussed, argued over, tried and rejected, modified and tried again, with the stated goal being (paradoxically enough) a rational society based on irrational assumptions that -- work. In this society there is room for God, for Self, for realization and enlightenment. Humans can talk about what they know in the full understanding of what it means to say that they "know" anything at all. The one thing that is no longer possible in such a society is to claim that one is in possession of absolute truth, as it is absolutely true that no such thing can be proven to exist.

Fairly ambitious, to be sure. This work strips off the undergarments of the philosophical basis for knowing anything and lays it out naked for us all to see that -- there is nobody and nothing there. Far from the Emperor being there and the clothing being imaginary, we find the Emperor entirely missing and that all the Reality that we've every seen or imagined is nothing but traditional and colorful undergarments! Fortunately, the clothes do make the man, metaphorically speaking...

If you accept its conclusions, this will be the last work of philosophy you'll ever need to read. When you're done, you may or may not know the deepest answers to the deepest pseudoquestions, but you'll at least be able to tell a real question (one with a real -- derivable -- answer) from a pseudoquestion (one with no derivable answer, only a meta answer -- an axiom -- for an answer). You'll understand that all real answers are connected by inevitable chains of logic and reason to axioms, and hence are always subject to doubt.

At the end of it all, you should end up well-equipped to choose your axioms as the most important human freedom, the one that underlies all the rest. A wise choice can lead to the greatest human society that one can imagine. Foolish, conflicted choices can lead to the extinction of the human race. Can't do any better than that. Really.

Hmmm, maybe philosophy is bullshit, but just maybe it is important bullshit as well...