# Mathematics is the only Subject that can Provide Universal Truths

1. Feb 27, 2010

### FeDeX_LaTeX

"Mathematics is the only Subject that can Provide Universal Truths"

"Mathematics is the only subject that can provide complete and utter universal truths, whereas no other subject can."

Is this statement true? Trying to win a science vs religion argument with a friend.

I have constantly been told that the Qur'an is completely and utterly true and is direct proof of God and how some guy made predictions that turned out to be true about science. But I argue that the book could've been altered to encompass all of these "supposed scientific truths", and that physics can provide us with stronger evidence to support their theories than religion can.

As an atheist, how can I win this argument? And what are your thoughts and opinions?

Thanks,
F.L.

2. Feb 27, 2010

### Gib Z

Re: "Mathematics is the only Subject that can Provide Universal Truths"

What are you trying to achieve?

Mathematics is the only thing that can produce "complete and utter universal truths" *directly*, but there is no reason something else can deliver a true statement through mathematics.

Also, you made understand that the ability of mathematics to provide statements that are nessicarily true is not as godly and impressive as you may think. It is because it derives statements from a set of defined axioms, which are essentially starting rules that we think are something good to start from. The statements we produce, called theorems, are true, but always on the prerequisite that the axioms behind them are "true". For the purpose of mathematics, axioms are always "true", but they may not correspond to the physical world.

For example, in Euclidean geometry, it is true that parallel lines will never meet. The theorem I have stated is true, and would be true in any universe, or even if the universe didn't exist. But we know that our universe's space-time is generally not Euclidean, so the statement "Parallel lines never meet" by itself, is not true.

You can never win an argument of this type. He will most likely never really consider your ideas seriously enough to change his view, and neither will you.

3. Feb 27, 2010

Re: "Mathematics is the only Subject that can Provide Universal Truths"

I don't agree. Why should something abstract be more true than something direct like an experience? Mathematics provides a self consistent framework, which has nothing to measure its own truth against but itself. It's a limited kind of truth in my opinion. Here's an interesting quote on the matter by Neizshce:

"How did logic come into existence in man's head? Certainly out of illogic, whose realm originally must have been immense. Innumerable beings who made inferences in a way different from ours perished; for all that, their ways might have been truer"

4. Feb 27, 2010

### Werg22

Re: "Mathematics is the only Subject that can Provide Universal Truths"

It's funny how those "predictions" about science are only discovered after the science.

5. Feb 27, 2010

### Hurkyl

Staff Emeritus
Re: "Mathematics is the only Subject that can Provide Universal Truths"

If you don't have an argument for your beliefs, then maybe you should be less certain of them, eh?

Anyways, mathematics is, roughly speaking, applied deductive logic. Among the things it can tell you about is what statements deductively follow from other statements, given a system of deduction.

One thing mathematics does not really say anything about is Truth. If you believe certain statements are True, and Truth propagates by a system of deduction, then you can use mathematics to deduce other True statements -- but mathematics cannot get you "started".

(Formal logic does include technical terms like "truth valuation". We may wish to assume Truth is a kind of truth valuation. But there are lots of truth valuations, and mathematics cannot shed any light upon which one corresponds to Truth)

Another thing mathematics cannot tell you about is the philosophical question of the relative merits of rationalism, empiricism, or any other epistemological position.

Anyways, your question is more philosophical in nature and you should go over to the philosophy forum. But really, you won't make any reasonable progress if you are coming into the subject with the mindset of "I believe X. How can I verbally spar with others who don't?"

6. Feb 27, 2010

### Tinyboss

Re: "Mathematics is the only Subject that can Provide Universal Truths"

Don't have it. Seriously, it goes like this:

Him: You haven't experienced <whatever> for yourself, you can't understand.
You: You don't really know what real math is all about, you can't understand.
<Whatever happens next does not involve one of you winning the argument>

I'm not implying equivalence of your positions here--I agree with you. But it's probably because I'm an atheist mathematician. ;-)

One thing you can point to about math (though maybe not in a math-vs-religion "debate", which is guaranteed to be fruitless) is that, uniquely among academic pursuits, each new generation doesn't tear down what the previous generation made (that's a bad paraphrase of someone else's quote, sorry I don't recall whose). The results of Euclid, Archimedes, Pythagoras, etc. are as solid today as they were then. We may use different words now, in a more general context, but mathematical truth, once established, is not subject to fads or revision. Even very rigorous sciences like physics can't claim this--who knows when a new advance in measurement will relegate our current models to "useful approximation" status? That's not a knock on physics! Just illustrating what I love best about math.

Last edited: Feb 27, 2010
7. Feb 27, 2010

### dx

Re: "Mathematics is the only Subject that can Provide Universal Truths"

The statements of mathematics are 'universally true' only in so far as they refer to imaginary concepts. Once we axiomatically define the elements of a mathematical scheme, then propositions about this scheme can be deduced logically, but at this stage this mathematical structure has nothing to do with Nature.

Often people confuse the difference between mathematical propositions and physical statements, and want to 'mathematically prove' things about Nature. This is a misunderstanding of the role of mathematics in science. It can be discovered through experiment that a conceptual/mathematical scheme reflects approximately the structure of a certain domain of physical experience, but this can never be considered exact, just as we never consider a map of a city to be an exact representation of the city.

8. Feb 27, 2010

Re: "Mathematics is the only Subject that can Provide Universal Truths"

"how some guy made predictions that turned out to be true about science."

There are no cases where "predictions based on religion" (any religion) have turned out to be true. ask for evidence of the original "prediction" and what actually transpired. you will find the crap from religion falls short, or has been couched in language so broad that any statement can be viewed as true, every time.

9. Feb 27, 2010

### CheckMate

Re: "Mathematics is the only Subject that can Provide Universal Truths"

I thought their was supposed to be no discussions on religion on this forum ?

Not that I have something against it but other discussions were halted by moderators for that reason.

10. Feb 28, 2010

### Hurkyl

Staff Emeritus
Re: "Mathematics is the only Subject that can Provide Universal Truths"

Generally speaking, if the discussion remains about epistemology, then it's fine. But when someone declares by fiat that X is true because the Bible says so, or that the scientific method is the One True Path to knowledge, it has definitely crossed the line.

That said, it's certainly not math, so I've kicked it over to philosophy to let MiH decide if it's acceptable here.

P.S. statdad: the existence of crackpottery does not reflect on the source material the crackpot tries to use.

11. Feb 28, 2010

### disregardthat

Re: "Mathematics is the only Subject that can Provide Universal Truths"

The way truth is defined in mathematics makes necessary truths easily found. The premises are set by our choice of laws. Truth about nature in general however (which depends on definition/notion) cannot be absolute in principle. It all depends on the current context in which you are situated. In my opinion, one cannot differentiate between absolute and relative truth. I think truth is a matter of semantics, and a true statement is a statement which is consistent with other statements which are considered true. The only differentiation we can make is between what is considered true, and what is not. Truth is a property within a perspective, and statements does not have the same meaning outside the perspective. Thus a Christian can claim absolute truth, but this truth does only make sense within the Christian perspective. Biblical truths are not scientific truths and vice versa. To believe that one can "disprove" biblical statements when interpreting them in a religious sense is an illusion, in the same way "disproving" mathematics by science (or vice versa!) is an illusionary notion.

Last edited: Feb 28, 2010
12. Feb 28, 2010

### Jimmy Snyder

Re: "Mathematics is the only Subject that can Provide Universal Truths"

Does this help?
http://www.brainyquote.com/quotes/authors/b/bertrand_russell_4.html" [Broken]

Last edited by a moderator: May 4, 2017
13. Feb 28, 2010

### disregardthat

Re: "Mathematics is the only Subject that can Provide Universal Truths"

It all depends of the way you are interpreting the semantics of mathematics. I do not subscribe to the set-theoretic foundationalist approach to mathematics (as presumably Russell does). This aspect is purely definitional, for example the wikipedia article on mathematics opens with this:

"Mathematicians ... establish truth by rigorous deduction from appropriately chosen axioms and definitions."

Last edited by a moderator: May 4, 2017
14. Feb 28, 2010

### Jimmy Snyder

Re: "Mathematics is the only Subject that can Provide Universal Truths"

I'm not sure if that is what I am about to do:
The "we never know what we are talking about" part comes from the undefineds at the basis of any mathematical theory, and the nor whether what we are saying is true" part comes from the unproven axioms. Was I just interpreting the semantics of mathematics?

15. Mar 2, 2010

### sidestreet

Re: "Mathematics is the only Subject that can Provide Universal Truths"

On the maths side, couldn't say it better than dx.

Science isn’t about certainty, it’s about doubt. It works by removing falsehoods. What is left may be labeled truth, but only in the sense that a theory does a good job until a better one comes along.

If the Qur'an really does make statements in line with current theories, and those theories are replaced in the future, your friend is on thin ice. People who believed the Earth is the center of the universe got badly hurt when it turned out that it isn’t. Mixing religion with science is never a good idea.

Although I’m not at all religious, I'd tell your friend to put her faith in God rather than scripture. Muslims say "There is no god but God, and Muhammad is the Messenger of God", but I think they also say “God is unknowable”. She can put her faith in God without proofs, and her faith will be stronger for it.

Assuming you're not one of those evangelical atheists.

16. Mar 2, 2010

### JerryClower

Re: "Mathematics is the only Subject that can Provide Universal Truths"

Well what are you trying to prove exactly? Mathematics is not the only subject that provides universal truths. Everything that was alive on this earth, had a beginning. The sun rises in the east and sets in the west. What comes up must go down. Water takes the shape of its container in the liquid form. Animals need food and water to stay alive. One has never seen a single atom with his own naked eye. One has never seen his own brain. One has never seen the air, only the things in the air, like smoke. Eggs never break and then go back to their 'pre cracked' form. People never age backwards. Everthing that is alive today will someday die. Even if they don't agree, they are all true aren't they?

17. Mar 3, 2010

### disregardthat

Re: "Mathematics is the only Subject that can Provide Universal Truths"

Well, it depends on whether you consider mathematics itself separated from interpretation. I find that as absurd as consider a language whole if separated from any form of interpretation. Grammar does not in my opinion constitute a language itself.

Also, I consider axioms "defining properties" - not "unproved statements". We are talking about that which satisfies a given axiom, not "assuming" that what we are talking about satisfies the given axiom.

18. Mar 3, 2010

### Jimmy Snyder

Re: "Mathematics is the only Subject that can Provide Universal Truths"

If I consider myself to have wheels, does that make me a railroad engine?

19. Mar 3, 2010

### disregardthat

Re: "Mathematics is the only Subject that can Provide Universal Truths"

You are missing my point by repeating the supposed "undefinedness" aspect. Do you consider "to have wheels" to give meaning independent of context? In the same way, do you consider mathematics to be independent of the context we bring upon the statements? The point is that even if you do, I don't. There is a definitional aspect of "truth" in mathematics.

20. Mar 4, 2010

### Jimmy Snyder

Re: "Mathematics is the only Subject that can Provide Universal Truths"

No, I was addressing the 'unprovenness' aspect. You missed my point. Axiom 1 says that given two points, there is a line that passes between them. That is an unproven statement, even if you consider it to be a defining property. Just as I am not a railroad engine even if I consider myself to be one.

21. Mar 4, 2010

### Tinyboss

Re: "Mathematics is the only Subject that can Provide Universal Truths"

Would it be easier for you to grasp if the axiom said, "Given two bazzes, there is a unique foobar passing between them"? The whole point of the Euclidean axiom system is that words like "line", "point", and so forth are defined by the axioms.

The question on these guys' minds was, "Are we really thinking about the same thing when we say 'line'?" Euclid's solution was to require that everything we prove about lines has to come from the axioms. Then, even if we do have different ideas in our heads about what a "line" is, it won't matter, as long as our separate ideas satisfy the same axioms.

What you're thinking is, "but what if there is some pair of points with no line passing between?" Just because the axiom says so doesn't mean it's so, right? And the answer is, if you find a pair of points with no line passing between, then your idea of "line" and "point" is not the same as everyone else's. Hence the word "definitional".

22. Mar 4, 2010

### Jimmy Snyder

Re: "Mathematics is the only Subject that can Provide Universal Truths"

Thanks for letting me know what it is that I am thinking. This seems like a valid program for determining that a particular idea of line and point is wrong. However, I don't see how it can be used to prove that any particular one is correct. In other words, the axioms do not provide a definition for point and line because although they rule some concepts out, they fail to rule any in.

23. Mar 4, 2010

Re: "Mathematics is the only Subject that can Provide Universal Truths"

"P.S. statdad: the existence of crackpottery does not reflect on the source material the crackpot tries to use. "

I would argue that in this case it does. There may be some historical proof, in certain cases, that various religious figures actually existed, there is no proof of any supernatural powers, or that they were gods in human form. There are legends, passed down orally for many years, and then written and rewritten to fit the whims of those in power, but that's it. there may be some literary merit to those writings, but as a basis for predictions about reality - no, no more than astrology. the burden of proof for those claims is on the religious themselves, and so far none of the "proof" proffered has stood up.

24. Mar 4, 2010

### Hurkyl

Staff Emeritus
Re: "Mathematics is the only Subject that can Provide Universal Truths"

I cannot figure out how to construe any of your following text as a justification that the formal argument
A crackpot says X implies Y. Therefore X is false.​
is not fallacious in this case.

25. Mar 4, 2010