Saying it's pretentious was just my opinion. Here's why I say it's logically unsound:

1. Existence exists. Define existence to be all things that exist. Thus the axiom states "All things that exist exist." That is silly. Of course it's true. Also all ducks are ducks, all red things are red, and everything that farts farts. It's a meaningless axiom and it DOES NOT suggest that anything exists even if you take it to be true. The statement "all blorgs are blorgs" is very true, but there is no such thing as a blorg.

2. Identity. The stated proof of this one goes, "Since it exists in a particular way, it has no contradictions." What?! That's not a logical foundation. I could claim that about anything!

3. Consciousness. The site doesn't even bother to suggest a proof for this one. It does mention Descartes' "proof," but then says he was wrong and does not go back to try to justify the "axiom." As to Descartes' argument, "You cannot logically deny your minds existence at the same time as using your mind to do the denying." This is very reasonable, but it is not logically rigorous. It assumes that your mind exists and that you must actively engage in denying something in order for that thing to be false. If something is false, then it is false whether I deny it or not. I happen to agree with Descartes', but the argument is not "irrefutable."


I quit reading after I got through the axioms. If the very foundation of the logical system is unsound, then the rest necessarily is also.