godelian wrote: ↑Wed Dec 04, 2024 3:08 am
Veritas Aequitas wrote: ↑Wed Dec 04, 2024 2:46 am
While the Peano Axioms might seem abstract, they are indeed rooted in our intuitive understanding of numbers and arithmetic operations.
Our intuitive understanding is empirical. Peano Arithmetic is blind symbol manipulation. So, it cannot possibly be rooted in our intuition.
Ask a child to use the Peano Arithmetic recursion rules for the addition. It won't be able to do it. Ask even most adults.
You still don't get it, so end up in throwing silly counters like the above.
Yours is fallacious, you cannot conflate 'intuition' solely with 'child'.
You seem to imply that when one is doing Peano, one is applying one's intuition and guesses.
Nope that is not the intuition we are referring to.
'Intuition' in this case refer to the deeper coded algorithm in the brain, deeper than the typical instincts.
Yes our 'intuitive' is empirical [but not intuitive understanding], it is not based on the empirical experiences at present, rather it is based on the empirical experiences [a priori] of our past humans ancestors [finger counting] and even to an extent to our non-human animals' experiences.
Since it is positive and adaptive, the sense of numerical quantity is coded embedded somewhere in our DNA [will be uncovered in the future].
I stated, as long as there is a use of numbers up to the most complex equations and formulas, it is reducible to our biological origin via adaption.
Peano Arithmetic uses numbers, so it is reducible human intuition, i.e. to the human biological origin via adaption.
It is not representing something that pre-existed as absolutely mind independent as claim by mathematical realism or platonic realism.
Veritas Aequitas wrote: ↑Wed Dec 04, 2024 2:46 am
Strawman. I did not state, science is the only FS is the only FS that can justify anything.
Well, that is even clearly unsustainable. The statement would fail to justify itself.
Veritas Aequitas wrote: ↑Wed Dec 04, 2024 2:46 am
My principle is:
'Anything' that is claimed real [or truth of it] is contingent [justified] upon a human based Framework and System [FS] of which the scientific FS is the most credible and objective, i.e. the gold standard.
If a claim is testable, then by all means, go ahead and test it. However, most claims are not testable. That is why bombarding the scientific method of experimental testing into some kind of "gold standard" is silly.
Regardless of your denial, that is what is going on in practice which is evident in most human activity at present.
AI provided a listing of scenario to support the above, in terms of medicine, technology, etc.
If you need to have a brain surgery, would you or most humans at present trust a shaman or a certified and qualified brain surgeon and the same for other similar scenarios where evidenced-based-science is king despite having its limitations.
Veritas Aequitas wrote: ↑Wed Dec 04, 2024 2:46 am
If the scientific FS is the gold standard, we can
indexed it as a standard 100/100, this mean that there are other FS_s which could be rated at 0.001/100 and others in between.
Generally, [detailed justifications need to be provided].
Philosophical Mathematical Realism as an ideology would be rated at 10/100 based on a rationally accepted methodology with rational criteria and weightages.
Philosophical mathematical antirealism would be rated at 90/100.
Philosophical theistic realism grounded on faith would be rated at 0.1/100.
You cannot test anything to support that view. You cannot measure anything either. Hence, your numerical approach to the problem is nonsensical.
Furthermore, the various epistemic methods exclude each other.
For example, if the axiomatic method is applicable then the scientific one is not, and the other way around. They are not in competition with each other.
Therefore, the ratings and/or weight tags that you attach to the various epistemic methods, are absurd in more than one way.
If you need to have a brain surgery, would you or most humans at present trust
1. a shaman or
2. a certified and qualified science-based brain surgeon to do it?
and the same for other similar scenarios where evidenced-based-science is king despite having its limitations.
If you are present normal human, you would definitely opt for 2 above.
Why??? do you choose option 2?
based on blind faith?
Why you choose option 2 has an implicit basis and an intuitive methodology.
My methodology with the ratings and/or weightages will make it explicit and make it objective on why I would choose option 2 above.
Thus my option is objective and transparent.
It is open to be verified by others.
If there are weaknesses or issues, the methodology can be improved via continuous improvements to make it more objective to justify why I opt for the scientific based option or other alternatives.
Thus the FS and its ranking via a continually improved rational methodology is the most pragmatic approach to ensure credibility and objectivity.