The Gödel's contribution has only technical meaning (it is needed for the professional mathematicians) with no extend to philosophy and Religion, unless the Gödel's result would be formulated following simple way:
Quote:
"no theory can be proven completely. The blind faith remains."
Do you agree? If yes, then ask me to debunk this absurd.
As example, can the General Relativity be proven completely? If No, then why the Gödel has completely proven the Gödel's theorems?
Dmitri,
Are you confusing 'theorems' and 'theories'?
The former are subject to proof, given the acceptance of the most basic rules such as self-consistency; but if you throw even that constraint out (as some religious extremists are happy to do)** then there's no point trying to be rational at all.
But 'theories', as I'm sure you're well aware, are generally supposed to be falsifiable (Popper; even though more recent philosophers often argue that falsifiability is not a sufficient criterion for distinguishing scientific from unscientific ideas).
I think it's reasonable to argue that all theories, as summary-descriptions of observations, are tentative; and ultimately will be replaced by summary-descriptions of larger datasets that include all previous verified datasets.*
So, to try to answer your question directly:
1) I assert that it is true that no theory (encoding datasets open to further observations) can be proven completely.
2) As to 'blind faith', I think the answer has to be Pragmatism.
Of course there are, for utter sceptics and speculative philosophers, no certainties. (We might – though I doubt it – indeed be only a vast computer simulation inside another universe; incidentally, it has even been proposed that we could try to crash the sim... Duh!)
Nevertheless, I was hugely impressed when Neil Armstrong stepped out of the Lunar Lander (LEM) in 1969, and when he put his foot down, the moon really was there! (...as long as you accept that his transmissions were as real as the rest of the Apollo Program.)
Surely that was one of the great vindications of science and the technologies based upon it: until that time we had only the reception of electromagnetic radiation (light) as observational evidence for the moon’s reality, plus – through the prism of Newton’s theories – motion of the tides as supporting evidence.
So, yes there is blind faith, but practically speaking, science has been able to correlate and exploit so wide a range of communicated human observations that only a fool would completely discount its role and reliability underlying the exponential growth of the human population since the Scientific Revolution: Between modern medicine, food production and distribution technologies etc., etc., that ‘blind faith’ seems as justified as one can reasonably expect.
Show us an alternative?
Regards - Paul
* I have long been toying with the idea of a "paper bag theory of knowledge" in which humanity punches its way out of a succession of nested observational boundaries, but here is not the place to open that bag of worms
** Even though it's the benefits of modern science and technology that provide the means enabling some people to hold extreme irrational views...
Dr. Ellis, thank you. You could talk to me only via the [email protected], because the RG is blocking my personal messages. I would be glad to look into your "bag of worms". A theory (General Relativity) can be proved to be consistent, isn't it? Not consistent with nature, but mathematically? The axioms of GR can be proved or not? In this sense is meant "to prove theory."
Dear Dmitri,
Thank you for pointing out that I hadn't covered the self-consistency of theories (as opposed to that relating to theorems in maths and other formal language systems).
A well-formed theory about material things (physics, chemistry, biology etc.) ought to be self-consistent, and often may be; but I don't know enough to say whether GR is fully self-consistent as a mathematical structure.
However, when comparing consistency of a theory with observations of concern to the theory, then of course, as you indicate, it's an entirely different matter - such as the apparent breakdown of GR at the centre of a black hole singularity, or it's incompatibility with quantum mechanics.
As for axioms, I was taught that they are precisely the components of a theory that can not be proven and have to be taken as assumptions, though obviously one is generally going to take ones that make some sense:
Wikipedia defines "An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments." So it appears truth is not an essential characteristic of axioms.
Conversely, great discoveries have been made by eliminating apparently sensible axioms, such as the discovery/construction of non-Euclidean geometries.
As for the sense of "to prove a theory "
- A non self-consistent theory should be refined.
- I think that all you can do with a self consistent theory is find evidence that is consistent with it, until contrary evidence emerges.
Clearly, GR is not fully compatible with observation, so whatever its axioms, they cannot all be true. But you can take GR as a mathematical theory, and then it doesn't really matter whether the axioms are true, only the degree to which the models resulting from the application of the theory accounts for observations.
I'm sorry to say I don't have time to open the "bag of Worms" just yet.
Regards - Paul
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