You say: (1) axiom is implicit in all knowledge,
(2) needs no proof, and
(3) has no alternative.
(1) is not clear to me, as what is "all knowledge" (flat Earth, etc.).
As for (3) -- Vicki has made it quite clear in her previous posts with
non-Euclidian geometry that axioms may have alternatives (at least in math).
This is how I understand it.
We can't prove something, so we say "this is obvious", but honestly we say
"we can't prove it and we just assume it is true". If one wants to assume
otherwise, one is welcome to. This is how non-Euclidian geometry started,
and apparently with some good results.
Once we "assume" an axiom we can say "if this IS true, then..." and we can
prove many useful things. You brought Ayn Rand's axioms. If we treat them
as something we *assume* is true, Richard is welcome to come up with an
assumption that reality *does not* exist (like non-Euclidian geometry).
Fine. What are the consequences then? How practical is it (or, as Richard
likes to put it, "how useful")? None of it has come up from Richard yet.
If we agree to use Ayn Rand's axiom that "existence exists" we are back to
our discussion on TT (this "something" about reality which makes it so
consistent -- as I put it then). Last time we ended up accusing some
"geographically able" members of not going to Richard's workshop in Seattle
(incidentally the next one is coming up shortly :-)).
Now, let's go to the cheating, or as Richard calls it in the "Virus of the
Mind" -- "hypocrisy". There are different ways we can approach our
relationship with this axiom (N = No, Y = Yes):
1. Don't think of it at all (N).
2. Think of it (Y) and:
2.1 believe it (YY) and
2.1.1 encourage others to believe it (YYY)
2.1.2 discourage others as if they did not believe it (YYN).
2.2 do not believe it (YN).
The YYN people say "don't be obsessed with truth" when it is convenient for
them. The same people, when somebody has a different opinion can say: "This
is your simple prejudice, and an inaccurate one." As if they were saying:
"nobody knows what is accurate except me". These are the hypocrites.
Regards, Tadeusz (Tad) Niwinski from planet TeTa
tad@teta.ai http://www.teta.ai (604) 985-4159