My First Axioms

In my last post ('Axiomatic Thought') I pointed out that all systems need one or more (usually many more than one) axiom from which to build. However, none of my reasoning during any of the previous posts was formal or complete; the reason is simply that I had not posted my own axioms, so I was working in an axiomatic vacuum. Indeed, while people are creating their own axioms, they work in a vacuum devoid of any logical justification whatsoever; the only alternative is emotional and psychological justification. From this perspective, it is easy to see the appeal of religion - and this appeal is exactly what I hope to counter.

As a cure to this axiomatic null, I introduce my first two, self-justifying axioms:

Axiom 1:

For every set of beliefs, there is an axiomatic set defined to be the minimal set of beliefs needed to be taken on faith before the remainder of the system can be logically (as defined by the system) deducted. Each axiom is a weakness - it is vulnerable to simply not being accepted by virtue of not having justification to back it up - so the smaller and more emotionally acceptable the axiomatic set, the stronger the system.

Axiom 2:

For my second axiom, I assume the rules of mathematical logic and set theory. I feel safe in this assumption since anyone who is reading this is probably operating (consciously or implicitly) by these rules anyhow (anyone who doesn't accept these rules probably isn't in a position to read this anyhow, being either a toddler or in a psych ward). This axiom (a) defines a few terms I used in axiom 1 and (b) gives me the tools to begin deduction. Note that this axiom is actually a small set of axioms (far smaller than any comparable religious axiom set, since (a) all of God's opinions are separate axioms, and (b) religious people probably use these axioms too).

With these minimal and necessary axioms in place, I am free now to begin building my system, as they lay the foundation for my system to be axiomatic and deductive in the first place.