Great points. The only "proofs" are in mathematics. Everything else is dependent on a body of evidence and interpretation of data which is always going to be limited by human perception, bias and incompetence.
For some people Science has become a religion of sorts. Much as I love Science I think that is a mistake.
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Real proofs only exist within a closed mathematical system. Outside mathematics itself, mathematics is used for modelling, but doesn't prove anything. Also note that not everything is necessarily provable within a closed mathematical system, as a spoil-sport called Gödel proved.
Actually, Gödel proved that a system can not be both complete (closed) and consistent, i.e. logical fallacies necessarily arise in a complete system.
The best one could hope for is to be incomplete and consistent solely because inconsistency would be madness!
Aren't mathematics themselves though based on axioms which in turn come to prove themselves? Mathematics are a tool. They can make pretty good scientific predictions only when applied properly. e.g engineering
Not necessarily but I'm not the best person to explain it - I think a mathematician would be better placed.
Even applying scientific theory is restricted by the potential for our own perceptions to be altered and distorted so if you are looking at it from a philosophical standpoint nothing in the physical world can be proven as there is no means of ascertaining an objective reality. One can only look at probabilities and even those can be open to distortion and misinterpretation.
Indeed there is no way of knowing if an objective reality even exists.
All we can do is make models and alter or reject them if they don't predict well. All the rest is metaphysics, which I think is an interesting but useless pastime.
exactly :) . what are mathematical axioms but expressions of three dimensional beings bounded by the space-time continuum
Yes but don't let a mathematician hear you say that they won't accept it! This comes down to the religious belief thing again:)
I actually debated with mathematicians before on this very subject. They also seem to disagree with each other.
and this is good actually. debate and disagreement are very good. when we start being sure about things around us, this is when the trouble begins.
Spot on! We really must stop agreeing like this lol:)
Axioms are not proven by other axioms, by definition.
Indeed. This is where the philosophy of mathematics gets tricky and I am sure in no position to delve deeper into it.
There is nothing philosophical about it, actually. It is a matter of definitions and running with them.
Even crazier things start happening in logic when you start assuming certain set theoretic axioms and seeing which other theorems are proved or not proved under these axioms. Look into the Axiom of Choice.
Thanks, I will check it out