Tuesday, March 11, 2008

Stumped

"We use faith in maths, too, Lito". These were the words that came from the lips of my thesis Professor, a few days ago as we discussed philosophy of maths.

"We have no proof that our axioms in maths are true, we assume them to be TRUE, but we have not proven them to be TRUE", he added.

"Assume? You mean this is by faith too"? I retorted. "Yes", he smilingly replied, "but it is all good, it works, doesn't it"?

All the while the discipline I so love and believe to be objective is not so objective after all. It is a known fact, axioms in logic and maths are not proven to be so, we believe them to be so, not that we have evidence that they are thus and so.

If maths is the foundation of science, and the other disciplines like physics etc are building on top of it and utilizing it etc., then the whole world is founded on faith.

I am stumped. That threw me. I think I will go home and be depressed.

Heb 11:3
By faith we understand that the worlds were framed by the word of God, so that the things which are seen were not made of things which are visible.

Don't read that so loud, these so called objective scientists might hear you.

9 comments:

Carrie said...

That is interesting.

Does that mean all science evetually reduces down to faith? That would take a bit of sting out of the lofty claims of evolutionists versus creationists.

The Scylding said...

Ah, at long last, we're all waking up to Godel.... (LOL)

L P Cruz said...

Carrie,

Absolutely, they are fooling themselves if they think they are not running on gas called 'faith'.

Almost all applied maths is done today, they do not expect major discoveries.

Hence, physicists are into theology and mathematicians are into philosophy...to while away their time.

LPC

L P Cruz said...

Sylding,

I knew you would pick up the Godel-ness of this post, bro. I thought about you after I posted this hahahah (LOL).

I have been reading on Godel and Einstein's friendship, and plan to post of some Godelian insights.

Many people do not know that Godel did not believe in science, but no scientist is talking about it, why?

Godel - ah, there is a gifted (but disturbed) Lutheran! Another Lutheran contribution to the world (LOL).


LPC

Past Elder said...

God bless me, Lito, they didn't tell you that?

That's precisely what an axiom is, a general statement that is not proven and from which proven statements are deduced! In any given system, the axioms should not be able to be deduced from each other, and the theorems deduced from them should not be contradictory, though what is an axiom in one system may be deduced in another.

I don't find this so much an indication that everything is faith based, just differing on faith in what, but this: That really, nothing can be proven true, only false, that our proofs demontrate nothing more than that under certain circumstances language behaves in certain ways. A false statement is one for which a contradictoty state of affairs has been found, but a "true" statement is one for which no such contradiction has been found, yet.

For example, which is true, Newtonian mechanics or quantum physics? We can now observe states of affairs which Newtonian mechanics does not fit, yet, within states of affairs where that is not a factor, it works quite well. IOW, you can build a bridge quite well using classic physics, but subatomic particle behaviour doesn't fit it so well, but it would needlessly complicate bridge building to get into quantum mechanics.

Oddly enough, the word axiom derives from the Greek word axios, meaning "worthy" -- which is, I think, a salutation in Orthodox ordinations! -- something we find worthy, not proven, on which we rest our proofs.

God bless me ten times, Lito, you're in the club now! I gotta hop a Qantas flight for some Aussie Runzas. Judas, maybe I'll blog on Boethius' De arithmetica after all! Which reminds me, most worthy Scylding, either I missed your answer or you missed my question some posts ago -- what did you think of the movie Beowulf?

L P Cruz said...

P.E.,

My faith in science is shaken, I am quite disillusioned now. (hehehehawhaw).

No wonder, Einstein said - he did not believe in maths!

Yep, they did not tell me that in grad school, it just looked obviously true when I was studying geometry.

For example, given a straight line and a point only one straight line is parallel to that! Well I can see that! That is obviously true. Who can doubt that! My eyes can see that.

Then they comeback and tell me --well we have no proof it is true, Lito! Caramba, I need some proof otherwise my scientific mind can not belive that.


Here is another one, my prof said "we have always assumed consistency"! Huh, I said, but I have been proving consistency of my logics! What do you mean? He said, what you were doing was deliverating Lito, you assume if such and such is true then the system must be consistent, you have not proven that it is actually consistent! You can't have possibly have done that since we have not proven our axioms to be true, we are not sure if our system will not actually produce contradictory statements!

I said, hang on, is this some kind of joke? Prof, you are kidding me, no? He said nope!

I said, I want my money back!

(LOL) (LOL)

LPC

Jeff Tan said...

Well I'm buying it. Consider how much theory these days revolve around instrumentation that are really only understood by a few people (who designed them). Or theories that rely on other theories being true, recursively and so on. When someone says "empirical", we must be sure to understand that this cannot assume that we have the entirety of data in all the universe. We do rely a fair bit on generalizations, approximations, probabilities and.. yes.. faith.. Not the supernatural kind, but a faith on something outside ourselves nonetheless.

L P Cruz said...

Jeff,

The point is that is founded still on faith and my point that science is objective i.e. requires no faith or does not make use of faith is quite false.

LPC

Jeff Tan said...

Oh yes, and I was agreeing. Pardon my fuddled comment. :-)