Are axioms beliefs?

[Darwin'sGoat]

Hey look! Robert G. Brown just had this same argument with himself.

http://www.phy.duke.edu/~rgb/Philosophy/axioms/axioms/

 

[T'ai Chi]

I've been watching this No True Scotsman maneuver with glee for a while now. That is not what you claimed at the outset. You claimed an equivalence. Here you are shifting into a claim that they are subsumed under "beliefs."

Ok, whatever.

 

[T'ai Chi]

I don't care what that dictionary says, this is epistemology. This isn't the correct use of "axiom" in math. An axiom in logic, in math, in philosophy are just not the same.

That said, I haven't read anything that contradicts what I posted to you above about the use of "axiom" or why you can't make it synonymous with belief.

Guess we'll just have to "agree to disagree!"

Sounds good.

And thanks for a polite argument Clancie. I think I see what you are saying here.

 

[T'ai Chi]

Hey look! Robert G. Brown just had this same argument with himself.

http://www.phy.duke.edu/~rgb/Philosophy/axioms/axioms/

And it looks like he is saying something close to what I am. Will wonders never cease?
(bold mine)

"It then goes after the memetic role of axioms in society, and attempts to illuminate some of the fundamental conflicts that arise because of the utterly mistaken but common belief that axioms are self-evident truths instead of what they really are: unprovable assumptions whose truth and falsehood cannot be assessed. Period."



After reading some peoples' comments in this thread and some stuff on the web, however, I will state now that I am about 50% - 50% on the issue. I'm willing to be swayed to either side by good arguments.

 

[T'ai Chi]

and
(bold mine)

"All of this digression is really only intended to show that axioms, far from being ``self-evident truths'' or even the gentler ``established principles'' are, in both mathematics and derived usage in physics, science, philosophy and other disciplines nothing greater than assumptions."

 

[Darwin'sGoat]

Tai Chi, what do you classify yourself as philosophically?

 

[Clancie]

Okay, one last thing...

Posted by T'ai Chi

axioms, far from being ``self-evident truths'' or even the gentler ``established principles'' are, in both mathematics and derived usage in physics, science, philosophy and other disciplines nothing greater than assumptions."

True. They are assumptions that are accepted as self evident truths in order to build on them. (That still doesn't make all axioms the equivalent of beliefs. Philosophically and mathematically, an "assumption" isn't the same as a "belief").

Posted by T'ai Chi

And thanks for a polite argument Clancie

Same here. (And, just to add...Even though we don't agree here, I always enjoy reading your posts. )

 

[T'ai Chi]

Same here. (And, just to add...Even though we don't agree here, I always enjoy reading your posts. )

One example out of many of her posts showing her posting style. Sorely missed.