# Mathematics doesn't provide universal truth with human perspective being irrelevant **URL:** \ **Category:** Great Debates\ **Created:** [March 3, 2011, 12:40am UTC](https://boards.straightdope.com/t/mathematics-doesnt-provide-universal-truth-with-human-perspective-being-irrelevant/573286 "2011-03-03T00:40:50Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![shiftless](https://avatars.discourse-cdn.com/v4/letter/s/e9c0ed/32.png) [@shiftless](https://boards.straightdope.com/u/shiftless)\ **Post date:** [March 3, 2011, 3:13pm UTC](https://boards.straightdope.com/t/mathematics-doesnt-provide-universal-truth-with-human-perspective-being-irrelevant/573286/21 "2011-03-03T15:13:40Z")
> [@Candyman74](#): > > This says nothing about mathematics, and merely points out vaguaries in the English language. It’s not that there are two different answers to the same question, it’s that two different questions have been asked, each with a correct mathematical answer. Right. Mathematics attempts to address the answerable parts of questions with its own well defined language and rules. It purposely avoids questions of coin ownership by cartoon characters, for example. That is left for the philosophers. ---
**Author:** ![Blaster\_Master](https://avatars.discourse-cdn.com/v4/letter/b/cab0a1/32.png) [@Blaster\_Master](https://boards.straightdope.com/u/Blaster_Master)\ **Post date:** [March 3, 2011, 3:39pm UTC](https://boards.straightdope.com/t/mathematics-doesnt-provide-universal-truth-with-human-perspective-being-irrelevant/573286/22 "2011-03-03T15:39:11Z")
I think I see where the OP is coming from, but I can’t really agree with his conclusion. Math is a universal truth, but it is only as good as the assumptions and models upon which it is built. Similarly, I’d say models and assumptions are only useful if one can perform operations on them with logic and math to obtain new and interesting conclusions. So, I’d say the that problem that the OP is seeing is that both Calvin and Hobbes are using valid mathematical processes and achieving different conclusions, therefore there is some issue with the math. But the real issue is that their initial assumptions are different, so expecting the results to be the same is rather naive. So, the OP is both right and wrong. Math, by itself, doesn’t provide any universal truth, because it is simply method of manipulating abstract concepts. But at the same time, it is necessary to achieve truth because it is logically consistent and allows for the manipulation of one set of concepts into another set of concepts. It is up to humans to meaningfully convert real concepts into mathematically usable abstract concepts, apply the appropriate mathematical processes, and then convert the results back into real concepts. ---
**Author:** ![Voyager](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/voyager/32/133_2.png) [@Voyager](https://boards.straightdope.com/u/Voyager)\ **Post date:** [March 3, 2011, 5:40pm UTC](https://boards.straightdope.com/t/mathematics-doesnt-provide-universal-truth-with-human-perspective-being-irrelevant/573286/23 "2011-03-03T17:40:02Z")
> [@Deeg](#): > > I thought non-Euclidean geometry and Godel put an end to the notion that mathmatics are a universal truth? First, Godel just showed that there are some things which cannot be proven. That is different from mathematics not being universal - in fact the theorem is universal. Euclidean and non-Euclidean geometries begin with different sets of postulates. Given those, they are both correct in all universes. What is interesting is which of them describes our universe the best, but that is a different problem. ---
**Author:** ![Revenant\_Threshold](https://avatars.discourse-cdn.com/v4/letter/r/f1d935/32.png) [@Revenant\_Threshold](https://boards.straightdope.com/u/Revenant_Threshold)\ **Post date:** [March 3, 2011, 6:00pm UTC](https://boards.straightdope.com/t/mathematics-doesnt-provide-universal-truth-with-human-perspective-being-irrelevant/573286/24 "2011-03-03T18:00:11Z")
> [@ITR\_champion](#): > > Well you’d be wrong since this thread has nothing to do with religion and I’ve never made a thread arguing aganist evolution periodically or non-periodically. I seem to recall your thread on evolutionary psychology. Perhaps that’s what **Der Trihs** is hyperboling from? ---
**Author:** ![Buck\_Godot](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/buck_godot/32/6573_2.png) [@Buck\_Godot](https://boards.straightdope.com/u/Buck_Godot)\ **Post date:** [March 3, 2011, 6:13pm UTC](https://boards.straightdope.com/t/mathematics-doesnt-provide-universal-truth-with-human-perspective-being-irrelevant/573286/25 "2011-03-03T18:13:00Z")
The axioms that humans decide are interesting and useful are subjective, but that a given set of axioms leads to a given set of conclusions is a universal truth. There is no conceivable universe in which the axiom system and definitions of real analysis would not lead to all closed and bounded sets being compact, and even an omnipotent god can’t construct a bi-jection between the reals and the integers within the confines of set theory axioms, unless the minds of all of the mathematicians on our current earth have somehow been fogged and there is actually a mistake in the proof that no one noticed. ---
**Author:** ![Deeg](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/deeg/32/2955_2.png) [@Deeg](https://boards.straightdope.com/u/Deeg)\ **Post date:** [March 4, 2011, 1:37am UTC](https://boards.straightdope.com/t/mathematics-doesnt-provide-universal-truth-with-human-perspective-being-irrelevant/573286/26 "2011-03-04T01:37:56Z")
> [@Voyager](#): > > First, Godel just showed that there are some things which cannot be proven. That is different from mathematics not being universal - in fact the theorem is universal. > > Euclidean and non-Euclidean geometries begin with different sets of postulates. Given those, they are both correct in all universes. What is interesting is which of them describes our universe the best, but that is a different problem. Both of these cases showed that mathematics is a human construct. Russell and Whitehead tried to make mathematics an unassailable truth in _Principia Mathematica_ and while it’s a brilliant book it still requires unprovable axioms. I have been perhaps been overly influenced by Morris Kline’s _Mathematics: The Loss of Certainty_ but math as “universal truth” is dead. ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [March 4, 2011, 1:47am UTC](https://boards.straightdope.com/t/mathematics-doesnt-provide-universal-truth-with-human-perspective-being-irrelevant/573286/27 "2011-03-04T01:47:34Z")
> [@even\_sven](#): > > I think this is a bit of an “if a tree falls in a forest…” debate. > > Humans (well, maybe some of the more intelligent animals as well) are the only creatures that can give numbers any meaning. In a world without intelligence, “12” is as absolutely meaningless as any other number. We are the ones, by interpreting and attaching significance to it, who make “12” mean “12.” How can “truth” have any meaning without someone to perceive it? Without people, what is just is, and doesn’t have or have the possibility of any description. > > Math is a language. It is a way to describe things. It is language that is well suited to describing the world in a way that is useful because it is predictive. But the math itself is still just a metaphor. It doesn’t have any inherent meaning of it’s own. It might take an intelligent being to be aware of mathematics but that doesn’t mean intelligent beings invented mathematics. Mathematics is a discovery not an invention. In a world without intelligence, 12 would still be greater than 11 and less than 13. Nobody has to count it to make it so. ---
**Author:** ![The\_Hamster\_King](https://avatars.discourse-cdn.com/v4/letter/t/8edcca/32.png) [@The\_Hamster\_King](https://boards.straightdope.com/u/The_Hamster_King)\ **Post date:** [March 4, 2011, 1:54am UTC](https://boards.straightdope.com/t/mathematics-doesnt-provide-universal-truth-with-human-perspective-being-irrelevant/573286/28 "2011-03-04T01:54:27Z")
> [@Little\_Nemo](#): > > Mathematics is a discovery not an invention. In a world without intelligence, 12 would still be greater than 11 and less than 13. Nobody has to count it to make it so. Where in the universe is 12? Can you detect it experimentally? 12 is a human construct that often proves quite useful in predicting the evolution of the universe. But the universe does not contain 12. ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [March 4, 2011, 1:57am UTC](https://boards.straightdope.com/t/mathematics-doesnt-provide-universal-truth-with-human-perspective-being-irrelevant/573286/29 "2011-03-04T01:57:46Z")
> [@ITR\_champion](#): > > In our society we use mathematics defined in a certain way to handle economic transactions. However, that’s not the only possible way. In this particular example Calvin is refusing to accept the mainstream, emotionally loaded approach to economic transactions that prevails in his society. He’s thinking outside the box. However, from a mathematical perspective he has as much claim to correctness as his father does. To say that he’s “dishonest or clueless” because he refuses to be boxed in by the narrow-minded approach to mathematics that’s popular in his society is merely conformist thinking. Find one practicing mathematician who agrees with you that Calvin has as much claim to correctness as his Dad. If you can’t, you should wonder whehter there may be a good reason for that… ---
**Author:** ![Sitnam](https://avatars.discourse-cdn.com/v4/letter/s/6a8cbe/32.png) [@Sitnam](https://boards.straightdope.com/u/Sitnam)\ **Post date:** [March 4, 2011, 2:44am UTC](https://boards.straightdope.com/t/mathematics-doesnt-provide-universal-truth-with-human-perspective-being-irrelevant/573286/30 "2011-03-04T02:44:42Z")
An OP title that makes as much sense as the OP. ---
**Author:** ![Sitnam](https://avatars.discourse-cdn.com/v4/letter/s/6a8cbe/32.png) [@Sitnam](https://boards.straightdope.com/u/Sitnam)\ **Post date:** [March 4, 2011, 2:52am UTC](https://boards.straightdope.com/t/mathematics-doesnt-provide-universal-truth-with-human-perspective-being-irrelevant/573286/31 "2011-03-04T02:52:07Z")
> [@Naxos](#): > > Math is the result of the capability of the human brain to express its own abstract ideas with more simplified abstract symbols, and of our need to try to devise _deterministic_ rules that govern those symbols. This way we are trying to comprehend nature independently of human bias, something I called a _universal truth_ in the previous threads. > > The every day language we’re using trying to communicate social situations, as the economy example you mentioned, is severely inadequate to describe math and its rules. So, be careful when you use common language to refer to math and all its amazing glory. You’ve made this mathematician smile. 🙂 ---
**Author:** ![Candyman74](https://avatars.discourse-cdn.com/v4/letter/c/ad7895/32.png) [@Candyman74](https://boards.straightdope.com/u/Candyman74)\ **Post date:** [March 4, 2011, 3:14am UTC](https://boards.straightdope.com/t/mathematics-doesnt-provide-universal-truth-with-human-perspective-being-irrelevant/573286/32 "2011-03-04T03:14:31Z")
> [@The\_Hamster\_King](#): > > Where in the universe is 12? Can you detect it experimentally? > > 12 is a human construct that often proves quite useful in predicting the evolution of the universe. But the universe does not contain 12. Sure it does. Just because we haven’t named it doesn’t mean it doesn’t exist. Objects have quantity, whether we are able to count them or not. We use “12” as a linguistic tool to communicate that quantity, but the quantity is there nevertheless. I can’t describe 12 without using these linguistics because our language does not enable me to do that. Any example I present will contain numbers; but that’s my limit, not the universe’s. The fact is that if there are 11 trees and one falls down, there are now 10. The fact that I can’t describe that without using the words “10” and “11” doesn’t change that fact. ---
**Author:** ![The\_Hamster\_King](https://avatars.discourse-cdn.com/v4/letter/t/8edcca/32.png) [@The\_Hamster\_King](https://boards.straightdope.com/u/The_Hamster_King)\ **Post date:** [March 4, 2011, 3:30am UTC](https://boards.straightdope.com/t/mathematics-doesnt-provide-universal-truth-with-human-perspective-being-irrelevant/573286/33 "2011-03-04T03:30:58Z")
> [@Candyman74](#): > > Objects have quantity … And what is an “object”? > [@](#): > > The fact is that if there are 11 trees and one falls down, there are now 10. How many is “a tree”? Designating a particular chunk of the universe as “a tree” is a human convention. “Counting” is an abstract model we use for manipulating chunks of the universe that we’ve designated as “things.” It’s a very useful way of organizing our experiences into a comprehensible system, but it’s not a fundamental part of the universe. ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [March 4, 2011, 4:18am UTC](https://boards.straightdope.com/t/mathematics-doesnt-provide-universal-truth-with-human-perspective-being-irrelevant/573286/34 "2011-03-04T04:18:59Z")
> [@The\_Hamster\_King](#): > > “Counting” is an abstract model we use for manipulating chunks of the universe that we’ve designated as “things.” It’s a very useful way of organizing our experiences into a comprehensible system, but it’s not a fundamental part of the universe. You’re claiming quantity is an abstract term which has no inherent meaning? Okay, fine. Tell me how many stars the Earth is in orbit around. Now construct some definition of quantity that would make it possible to say that quantity is something other than one. ---
**Author:** ![The\_Hamster\_King](https://avatars.discourse-cdn.com/v4/letter/t/8edcca/32.png) [@The\_Hamster\_King](https://boards.straightdope.com/u/The_Hamster_King)\ **Post date:** [March 4, 2011, 4:38am UTC](https://boards.straightdope.com/t/mathematics-doesnt-provide-universal-truth-with-human-perspective-being-irrelevant/573286/35 "2011-03-04T04:38:11Z")
> [@Little\_Nemo](#): > > You’re claiming quantity is an abstract term which has no inherent meaning? Okay, fine. Tell me how many stars the Earth is in orbit around. Now construct some definition of quantity that would make it possible to say that quantity is something other than one. Designating a part of the universe as “a star” is a human abstraction. It’s just as correct to say that the Earth orbits around 10^57 “atoms”. So how many things does the Earth orbit? As I said, counting is a human-invented tool for manipulating the abstractions we call “things”. Grouping chunks of the universe into “things” is something that we do for our own convenience. It’s a very useful conceptual framework. But that doesn’t mean that things really exist as things, or that they are countable apart from our conception of them as such. ---
**Author:** ![CJJ](https://avatars.discourse-cdn.com/v4/letter/c/ecc23a/32.png) [@CJJ](https://boards.straightdope.com/u/CJJ)\ **Post date:** [March 4, 2011, 5:30am UTC](https://boards.straightdope.com/t/mathematics-doesnt-provide-universal-truth-with-human-perspective-being-irrelevant/573286/36 "2011-03-04T05:30:29Z")
The idea of “mathematical truth” vs. truth that “depends on human opinion” is, IMO, a distinction between the methods used to justify/verify truth. Pure mathematics gains validity by means of its coherence–to put it glibly, everything “fits together perfectly”. This validation is somewhat different from observational or scientific truths, which gain validity based on their correspondence with reality. If I develop a scientific theory that explains a class of observed phenomena, but then come across a counter-example, I’m obliged to reveiw what’s wrong/untrue about my theory. However, if someone tells me they have a counter example which demonstrates “1+1=3”, my first reaction is to look at what’s wrong/untrue about the counterexample. It’s tempting to label these “deductive” and “inductive” truths. In a specific sense, coherent truth can be verified with 100% certainty, whereas correspondence truth is only as good as the last example. ---
**Author:** ![MrDibble](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mrdibble/32/114_2.png) [@MrDibble](https://boards.straightdope.com/u/MrDibble)\ **Post date:** [March 4, 2011, 8:03am UTC](https://boards.straightdope.com/t/mathematics-doesnt-provide-universal-truth-with-human-perspective-being-irrelevant/573286/37 "2011-03-04T08:03:01Z")
> [@CJJ](#): > > It’s tempting to label these “deductive” and “inductive” truths. The way you’ve defined them, I think[analytic-synthetic](http://en.wikipedia.org/wiki/Two_Dogmas_of_Empiricism) is a better label-set > [@](#): > > In a specific sense, coherent truth can be verified with 100% certainty. But only in that specific (vaguely incestuous) sense. They can’t be verified at all, in another sense, because they spring from axioms themselves _a priori_. Which is fine as it goes, but hardly qualifies for Universal Truth status, IMO. “Because I say so” isn’t a basis for Truth, especially once we drag modality into it, because there could exist a possible world where you said different. Take counting - I can \*easily \*imagine a possible world where adding 1+1=3, even when counting objects (say, extra units of anything \*always \*pops out of nowhere like a vacuum quantum particle, _as soon as you start counting_). So how is mathematics a Universal Truth now? But I’m not sure what the debate is here - in Maths everyone \*does \*get the same answer, but so what? _It’s set up that way_! That’s why it’s an uninteresting field from a philosophical point of view. ---
**Author:** ![Voyager](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/voyager/32/133_2.png) [@Voyager](https://boards.straightdope.com/u/Voyager)\ **Post date:** [March 4, 2011, 5:30pm UTC](https://boards.straightdope.com/t/mathematics-doesnt-provide-universal-truth-with-human-perspective-being-irrelevant/573286/38 "2011-03-04T17:30:08Z")
> [@Deeg](#): > > Both of these cases showed that mathematics is a human construct. Russell and Whitehead tried to make mathematics an unassailable truth in _Principia Mathematica_ and while it’s a brilliant book it still requires unprovable axioms. I have been perhaps been overly influenced by Morris Kline’s _Mathematics: The Loss of Certainty_ but math as “universal truth” is dead. Are you confusing math is a universal truth with math describes our universe accurately? If axioms could be proven, the mathematical system they are based on is weak, since you should start with simpler axioms. What Russell and Whitehead tried to do and could not do is to prove mathematics complete. None of this has anything to do with math as a human construct. Of course the set of theorems we will prove is based on our humanity, and how we prove them is based on our humanity, but once we do prove them, correctly, they are true in all possible worlds. ---
**Author:** ![Voyager](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/voyager/32/133_2.png) [@Voyager](https://boards.straightdope.com/u/Voyager)\ **Post date:** [March 4, 2011, 5:35pm UTC](https://boards.straightdope.com/t/mathematics-doesnt-provide-universal-truth-with-human-perspective-being-irrelevant/573286/39 "2011-03-04T17:35:43Z")
> [@The\_Hamster\_King](#): > > Where in the universe is 12? Can you detect it experimentally? > > 12 is a human construct that often proves quite useful in predicting the evolution of the universe. But the universe does not contain 12. The set of symbols 1 and 2 making 12 is a human construct. The name “twelve” is a human construct. But “12” can be rigorously defined from the axiomatic definition of 1 and the successor function. As for your other posts, what we humans tag things with has nothing to do with the underlying mathematical truth. As Lincoln asked, if you call a tail a leg, how many legs does a horse have? ---
**Author:** ![The\_Hamster\_King](https://avatars.discourse-cdn.com/v4/letter/t/8edcca/32.png) [@The\_Hamster\_King](https://boards.straightdope.com/u/The_Hamster_King)\ **Post date:** [March 4, 2011, 5:41pm UTC](https://boards.straightdope.com/t/mathematics-doesnt-provide-universal-truth-with-human-perspective-being-irrelevant/573286/40 "2011-03-04T17:41:12Z")
> [@Voyager](#): > > But “12” can be rigorously defined from the axiomatic definition of 1 and the successor function. And where does the successor function exist in the universe? [Previous page](https://boards.straightdope.com/t/mathematics-doesnt-provide-universal-truth-with-human-perspective-being-irrelevant/573286.md?page=1) [Next page](https://boards.straightdope.com/t/mathematics-doesnt-provide-universal-truth-with-human-perspective-being-irrelevant/573286.md?page=3)