1 (edited by Justinian I 03-Jun-2011 15:39:00)

Topic: Maths and Dogmatism

Mathematics is given an absolutist status not unlike that given to scripture by religious followers. Yet mathematics, like scripture, does not deserve this status. The major reason is that one of Godel's incompleteness theorems prove the impossibility of having a mathematical system that is both consistent and complete. This means that a consistent system in maths, meaning its axioms do not prove a contradiction, will also have "true" statements that are unprovable - thus another system must be added to prove them.

The implications of this are profound. First, a foundation for mathematics is impossible because it is impossible to use a single mathematical system to prove every "true" mathematical statement. Thus, several systems must be used to prove every mathematical statement, yet two systems can not be merged together for completeness without also proving a contradiction. Consequently, it is futile to claim that our present understanding of mathematics can prove everything about the world. I say this because maths has an undeserved status not just among common people, but also among people who should know better such as mathematicians and physicists. Physicists also come off as being the most dogmatic members of the scientific community with an almost religious devotion to their theories based almost entirely on mathematics, while other scientific fields that depend on more empirical research are much more humble about the limits of their theories.

Re: Maths and Dogmatism

This might be more persuading if you were to provide more explanation/examples regarding the one argument meant to prove your thesis, i.e. Godel's incompleteness theorem.

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3 (edited by Justinian I 03-Jun-2011 16:23:18)

Re: Maths and Dogmatism

The only example of the theorem I could provide is the theorem's proof, which you can find yourself. But what is important is the conclusion of the theorem I mentioned. A mathematical system can not be both consistent and complete, and thus you can not have a single system capable of proving everything. In other words, it's impossible to find a foundation for mathematics. It would be nice if you could, because then you would have the necessary inputs to answer any question you had. But with that possibility proven impossible, you can not just go ahead and use maths to justify a dogmatic certainty in a scientific theory that is hundreds or thousands of steps ahead of empirical research.

Re: Maths and Dogmatism

I'm going to be very blunt:

You posted a thread with a conclusion, yet without substantiation within this thread (which we can find ourselves).

What kind of discussion did you think would happen here?

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5 (edited by Justinian I 03-Jun-2011 17:16:57)

Re: Maths and Dogmatism

My substantiation is the logic of my reasoning, provided that the incompleteness theorem (there are 2) I cited is true. I acknowledge I am human and that my reasoning may be flawed, and that is the most practical way to disprove my position should you find fault with it.

But since you seem to be suggesting that I have not justified the incompleteness theorem I cited, then you are right but that isn't relevant. Yes, I am assuming it's true, but my assumption is reasonable because it is accepted by general consensus between mathematicians, scientists and other relevant intellectuals. Since I considered this obvious, I never bothered to prove that such a consensus exists. And anyone skeptical of my claim of consensus can verify it with little effort on their part. However, provided that this consensus exists, that does not mean individuals in these fields have truly considered the implications of it, nor that people in general are aware of it.

Since it appears to me that those who should know better haven't given it the thought it deserves and consequently subscribe to wishful fantasies of mathematics, I wanted to raise it to their attention (and I know such people exist on IC, even if less active) or receive critical feedback from them. Secondly, I wanted to raise it to the attention of those who are not familiar with it by providing it with the best explanation I could, and possibly receive critical feedback from them as well. For all I know I could have misrepresented the theorem or my understanding of its implications could be wrong. And maybe those physicists who I made no secret that I disapprove of are in fact perfectly justified in their seemingly overly-confident attitude.

6 (edited by Godwin's Law 03-Jun-2011 17:20:40)

Re: Maths and Dogmatism

Eh... fair enough, I guess...

*sits on the sidelines to watch*

EDIT: Actually, though, this sort of thread may set up a bad precedent for threads.

Picture, if you will, me doing the exact same thing in another thread:



Title: Global warming will kill us all.

Post:
[Me explaining that there's a theory that CO2 is causing global warming, and stating its implications.]

Response:
Proof?

My reply:
You can find the proof yourself.


Note the problem?  Though I'll admit, by citing the theorem itself (albeit without a link or anything), it may be less problematic.  Just highlighting the issue.

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Re: Maths and Dogmatism

1+1=2

Everything bad in the economy is now Obama's fault. Every job lost, all the debt, all the lost retirement funds. All Obama. Are you happy now? We all get to blame Obama!
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Re: Maths and Dogmatism

I resent any "science" which tells me I can't have my cake and eat it. X( I am however a very big fan of quantum physics.

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Re: Maths and Dogmatism

"Godel's incompleteness theorems prove" Godel's theorem is a theory! it isn't proven, so it can't prove other things.

10 (edited by Key 19-Jul-2011 07:50:24)

Re: Maths and Dogmatism

tongue   You know, even I watched that particular episode of Through the Wormhole with Morgan Freeman.

Ok, here's an example for you brainiac, which is my own theorom, positively to rock your world view.

Came up with the idea that humanity will never understand the multiverse.  Not just the universe mind you, but the multiverse.  Why is that?  Because there are answers to every single question, unfortunately the answers as we know it are constantly changing, because the relationship of the question continuously changes as well.  How theory's are proven to be fact, and then those facts change when a better theory comes along.  Take a Triangle.  That Triangle = Q.  Now place another triangle inside that Triangle.  That triangle is an answer, but oddly enough, that triangle is surrounded by three other triangles.  The answer has given us more questions to answer, because inside the First Triangle is four triangles.  Now you perceive 4 triangles inside a larger triangle.  Now you have to ansswer the other questions, by placing an answer inside each by placeing another triangle...which creates another set of 3 questions surrounding the answer.

Add infinitum...you will always have more questions, than answers.  Therefor, the multiverse can never be fully explained.  It would be an infinite number of questions surrounding an infinite amount of answers.  So in the end we will never know, or answer all of the universal questions.

So my answer to you is, "What, me worry?"

So know your asking, what does this have to do with incompleteness theorem....well if you look at it really closely it doesn't really answer everything, thefor it's a perfect analogy for incompleteness.  Because you will never ever ever ever ever ever ever ever...get the WHOLE answer to life, and the meaning of the universe.

Sucks to be you don't it?

I call this Key's Theory to Infinite Harmonic Question Regression.  And YES, it is my personal theory on how I perceive the multiverse.

=^o.o^= When I'm cute I can be cute.  And when I'm mean, I can be very very mean.  I'm a cat.  Expect me to be fickle.

Re: Maths and Dogmatism

Of course you cannot have your cake and eat it. Logically best to eat your cake and take someone else's

Re: Maths and Dogmatism

Funny, I thought that was what politicians, board of directors corporate america, and my boss was doing right now.

=^o.o^= When I'm cute I can be cute.  And when I'm mean, I can be very very mean.  I'm a cat.  Expect me to be fickle.

Re: Maths and Dogmatism

I stand by 2*2 = 4.

Dogmatism? Yes

Truthful? Yes

Correct? Yes

Relevant? Yes

Everything bad in the economy is now Obama's fault. Every job lost, all the debt, all the lost retirement funds. All Obama. Are you happy now? We all get to blame Obama!
Kemp currently not being responded to until he makes CONCISE posts.
Avogardo and Noir ignored by me for life so people know why I do not respond to them. (Informational)