RE: My new YouTube video about atheism
September 26, 2020 at 1:15 pm
(This post was last modified: September 26, 2020 at 1:42 pm by Sal.)
Top->down vs up->Top is all you're saying, John.
Only thing I'm getting at is that there are gaps in our knowledge on a fundamental level.
Axioms are a priori assumptions about the nature of this knowledge. The problem with any axiom of any caliber is of this incompleteness in our knowledge, such that we can even reach conclusions that expand the pool of axioms or revise them. That's it. Doesn't happen often, but we have done so with Euclid in the modern day in philosophy of mathematics.
This is easy to see why for any non-self identity axiom (which are mere tautologies, like the self-identity A=A), because this rests on the use of them as identities.
(September 25, 2020 at 1:05 pm)FlatAssembler Wrote:Sal Wrote:But can't you see this fundamental limitation?I am not sure what you mean.
Sal Wrote:Even in maths?Well, at least, in mathematics, you don't have to deal with unknown intial variables. You can prove he four-color theorem by brute-forcing, something like that is probably impossible in any other science.
Sal Wrote:Even in logic?Again, I am not sure what you mean.
Sal Wrote:Axioms?Again, I am not sure what you mean.
Only thing I'm getting at is that there are gaps in our knowledge on a fundamental level.
Axioms are a priori assumptions about the nature of this knowledge. The problem with any axiom of any caliber is of this incompleteness in our knowledge, such that we can even reach conclusions that expand the pool of axioms or revise them. That's it. Doesn't happen often, but we have done so with Euclid in the modern day in philosophy of mathematics.
This is easy to see why for any non-self identity axiom (which are mere tautologies, like the self-identity A=A), because this rests on the use of them as identities.
"The first principle is that you must not fool yourself — and you are the easiest person to fool." - Richard P. Feynman
