In a recent post “Are human rights something imaginary -- made up stuff” http://exmormon.org/phorum/read.php?2,819754 comments by “Human” and “rationalguy” deserve additional consideration.

[HUMAN] “I've said before that I believe Universals exist apart from our minds knowing them. Therefore I believe it possible that Natural Rights exist even if there wasn't a human left on earth to enjoy them.”

[COMMENT] This, of course, is a metaphysical conclusion unsupported by any evidence. If you are going to give universals ontological status over and above the use of language, and social convention, as generated by the minds who conceive of them, you owe us an account as to just what these items are; i.e. the nature of their existence. It is very difficult to even conceive of such an account, except as purely mystical.

[HUMAN] “For those who don't believe human rights exist apart from humans believing/agreeing in them, those of you who are nominalists, I ask, what about Math? Does math exist apart from our minds knowing it?”

[COMMENT] This is controversial, especially among mathematicians themselves. Roger Penrose, certainly one of the foremost mathematicians of our time, answers affirmatively. But then, he too owes us an account of their Platonic, ontological status.

Note that the reason mathematics is thought by some to have independent ontological status, over and above abstractions of the mind, is the remarkably close association of mathematics with natural law and the natural world. When one has an appreciation of how mathematics reveals itself in the natural world, it is indeed tempting, if not compelling, to think that somehow mathematics exists in its own right, and that physicists “discovery” mathematical laws and principles, rather than merely abtract them as a merely a logical exercise of the mind. After all, even irrational numbers reveal themselves in the natural world quite apart from theoretical mathematics. Notwithstanding, personally, for the ontological difficulties noted above, I remain convinced that they are mental abstractions. However, I acknowledge that the fact that the real world is mathematical is a remarkable anthropic fact that requires explanation by materialist scientists.

[HUMAN]

“1. Most would agree that Math exists.”
“2. Most would agree that Math is abstract.”
“3. But who believes that Mathematical objects exist independently of human cognition?”
“If 3 isn't also true then I don't know how Science, especially physics, can say anything at all.”
“If 3 is true then I don't see why other existing abstract objects cannot also exist independent of human cognition.”

[COMMENT] Your point here (if I understand it) is more philosophically important than most would appreciate, and it relates to the materialist science point I raised above. The question is as follows: Given mathematics is understood by most scientists to be a mere mental abstraction, without ontological status, how is it possible for physics, which is so dependent upon mathematics, to proceed at all? In other words, if our understanding of the physical world is dependent upon mathematics, and mathematics is not part of the physical world, doesn’t science have to explain mind before it can draw conclusions about the physical world.

My answer to this is to note that mathematics is a tool of science that requires the human mind. Using that tool, science has been shown to work; i.e. to generate reliable predictions about the world. As such, we can take the achievements of science at face value, without understanding mind, or the nature of mathematics. Notwithstanding, the role of mathematics in science, and particularly physics (broadly speaking) reveals that mind is an important part of reality and when left unexplained leaves a gaping hole in our understanding of reality—including the physical world which it reveals. This fact, in my view, undermines the dogmatic materialist view of science.

[rationalguy]

“Does math really exist outside the mind? The physical realities exist which are repeatable and describable via the language of mathematics, but it is a human language, a logical construct that helps us describe the world. I think it is somewhat similar to "reasons" in nature. All sorts of elaborate things happen, but no mind contains or comprehends them at all until people observe and study them. A bee comprehends no reason to make honey, even though it is the beneficiary. The reason is not represented anywhere until a person sees that reason.”

[COMMENT] I agree that mathematics is a human language and logical convention that helps us describe the world. However, this statement alone does not fully appreciate the fact that the underlying mathematical structure of the world seems to transcend this view, as Human suggests. The “reasons in nature” need to be explained, and that cannot be explained simply by invoking human mathematical constructs. There must be transcendent reasons why the natural world is mathematical, beyond the language of mathematics that humans invented.

[rationalguy] “I'm a specialist in industrial measurement and control. It's true that a variable can be represented any way desired. 50 degrees centigrade can be converted to ten milliamperes of current, sent over a wire, changed to a radio wave of a particular modulation pattern, changed to digital data and then finally presented as digits on a video screen. Until someone sees those digits, the value isn't represented in the mind of a conscious being anywhere. It is meaningless.”

[COMMENT] The key word here is “meaningless,” pointing out that it is mind that subscribes meaning to physical relationships, which otherwise are merely cause and effect events. Language and mathematics are human tools to ascribe such meaning. However, the physical relationships you describe, and particularly their mathematical relationships, exist independent of whether humans ascribe meaning to them. It is that which needs to be explained!

I think that the burden of proof lies on the instrumentalists (those who think mathematics is just a man-made tool).

The fact that we make discoveries (not inventions) in mathematics indicates to me a ontological existence on some level. I'm not necessarily advocating full-on mathematical Platonism, but I think this view is closer to what is going on than the instrumentalist view.

Mathematics is a concept that did not exist until humans created it as a way of describing the universe.



Edited 1 time(s). Last edit at 03/10/2013 11:52AM by MJ.

I totally agree, MJ.

If humans were less intelligent, we wouldn't use it.

If humans were more intelligent, we could probably find a better way of describing besides our conventional mathmatics.

Purely discriptive just like language.

Well, we didn't make up the digits of pi--we discovered them. In fact, we are still discovering them.

If we lost all knowledge of pi's digits, we could conceivably "re-discover" them.

The same could be said for some other irrational constants.

----

Another example of this is the set of prime numbers. We didn't make up the set of prime numbers--we discovered it.



Edited 3 time(s). Last edit at 03/10/2013 12:46PM by archytas.

We made up "one" as apposed to "mugly". Nobody "discovered" the digits 3.14... just laying on the ground. The digits are indeed made up and would be different if we used binary, base 5, base 1000, etc.. It is still an imaginary and in many ways ARBITRARY construct to describe the universe.



Edited 2 time(s). Last edit at 03/10/2013 12:58PM by MJ.

The underlying arithmetic is the same no matter what base you use (binary, octal, hexadecimal, whatever). If this weren't true, then calculators wouldn't be reliable, but they are.

If you think pi is arbitrary, then by all means submit a paper to a major math publication and demonstrate this. Pi is derived using an algorithm, so you would have to show that this algorithm gives arbitrary results. Good luck.

Also, since when do discoveries only happen by seeing things "laying on the ground"? Is astronomy made up too?

You are confusing the physical with the LANGUAGE CREATED to describe the physical.

Show me where the universe requires the LANGUAGE of MATHEMATICS.

The CONCEPT we call MATHEMATICS is made up. You do know what "concept" means right?

Pure mathematics (like number theory) is not necessarily used to describe the physical world (though application are sometimes found). You can study pure math, and make discoveries, without relying on the empirical world. Think back to my example of the prime number set.

So, you're wrong in saying math is just a language for describing the world.

Thus are IMAGINARY constructs, just like IMAGINARY NUMBERS.



Edited 2 time(s). Last edit at 03/10/2013 01:49PM by MJ.

The "just a theory" argument doesn't work against evolution, and it especially doesn't work here.

Number theory--despite the name, deals with theorems and proofs, not theories.

I think you're getting stuck on the label.



Edited 1 time(s). Last edit at 03/10/2013 01:59PM by archytas.

I never claimed "it's just a theory" as you unjustifiable quoted text seems to imply.

Theorems and proofs are again man made constructs. The universe got along just fine without any theorems being proven. When there was no intellect, what was the point of "proof"? Did the Universe have to prove its existence to itself?

Before intellect, was anything "proven"?



Edited 2 time(s). Last edit at 03/10/2013 02:07PM by MJ.

The universe got along fine without astronomers too.

It does not follow from this that astronomy is made up.

Yes or no.

Without intellect there is no science, there is no astronomy. There isn't even words to describe "science" and "astronomy".

Science and astronomy are creations of the intellect



Edited 1 time(s). Last edit at 03/10/2013 02:13PM by MJ.

Earlier you said:
"Nobody 'discovered' the digits 3.14... just laying on the ground. The digits are indeed made up and would be different if we used binary, base 5, base 1000, etc.. It is still an imaginary and in many ways ARBITRARY construct to describe the universe."

I'm arguing that pi could be discovered by anyone--even a hypothetical race of ET's on another planet. They would give it another name, and probably use a different base, but the properties would be the same.

I don't see how this would be possible if we "made up" an "arbitrary construct".

I can "discover" all sorts of ideas including fiction. Doesn't prove your point.

Pi is a REPRESENTATION of an IDEA and does not actually EXIST outside of mathematics.

It is ONLY a mathematical construct, as such does not prove that math is anything other than a man made set of tools.



Edited 3 time(s). Last edit at 03/10/2013 07:34PM by MJ.

Correct me if I'm wrong, but were not the Voyager space
probes fitted with depictions of numerical data, which
we earthlings believed could communicate mathematical
facts to some possible intelligent life form, who happened
across the probes in the distant future.

It seems likely to me that a rational being from elsewhere
than our planet could figure out what binary messages
meant -- what the third planet orbiting a star was meant
to represent (as being the origin point of the probes).

Or, perhaps I'm wrong and we put all that attempted
mathematical communication in the probes out of sheer
ego and ignorance. There is no such thing as universal
mathematics and and alien inspector of a Voyager probe
would have no idea what "third" planet meant, much less
be able to decipher binary coded messages.

???

UD

The most ->LIKELY<- way to communicate to a species that could have totally different ways of communicating is to use something that describes what both have in common, the physical universe. This way there is at least a -> CHANCE <- that they will be able to figure out what we are trying to say.

There was limited math sent as part of the messages on voyager.



Edited 1 time(s). Last edit at 03/10/2013 01:40PM by MJ.

As I recall voyager contained an actual picture. You might be
thinking of the message that has been beamed into space. It was
a string of 1's and 0's repeated with, I believe, a pause before
and after. The number of "bits" in the message was the product
of two prime numbers. It was assumed that an intelligent alien
culture could notice this fact and then write the 1's and 0's in
a rectangular grid whose length and width were the two prime
factors. If all the 1's were blackened in and the 0's left
blank (or vice versa) then it would show a picture which
schematically indicated our solar system with something special
about the third thing from the big central thing. The only
mathematical content was the fact the the number of bits in the
repeated message was the product of two prime numbers. It was
assumed that the concept of a prime number would be part of an
intelligent alien culture.

Can chimps be taught to understand ratios and fractions?
Are the numerical relationships generated in their minds
something entirely different than what we call math?

If every third banana being offered is always bitter, do
the chimps comprehend the abstraction "three?"

UD

It is funny that you are talking about a LEARNED behavior to justify the claim that Math is not a Learned concept.

Not only do I agree with your point, but thought your efforts were valiant.

Yeah, me too, Elder Berry.

I use math on a daily basis, and have even taught it in college. I've used it to come up with my own formulas because I know what the numbers *represent* and how they are related to each other. All sciences and math are tools. Man-made. Man conceived.

The analogy that some are using is like saying:

"Look, English describes this picture perfectly, therefore English is a universal truth".

The only theory we should be talking about in this thread is the Dunning-Kuger Effect.

Dunning–Kruger effect eh? I'm taking that as an ad hominem attack.

Couldn't I just turn it around and accuse you of the same cognitive bias?

And you seem to have struck a nerve.

Yay, more ad hominem.

I'm going to go drink. Cheers.

You have repeatedly made logical fallacy after logical fallacy without recognizing your mistakes. You fit the definition.



Edited 1 time(s). Last edit at 03/10/2013 07:33PM by MJ.

Nice to see you here again, Henry! So glad you took the time to pick up on this.

Had I seen rationalguy's responses I would have answered much as you have but as always sans your thoroughness and adequacy.


Henry Bemis Wrote:
-------------------------------------------------------


> I agree that mathematics is a human language and
> logical convention that helps us describe the
> world. However, this statement alone does not
> fully appreciate the fact that the underlying
> mathematical structure of the world seems to
> transcend this view, as Human suggests. The
> “reasons in nature” need to be explained, and
> that cannot be explained simply by invoking human
> mathematical constructs. There must be
> transcendent reasons why the natural world is
> mathematical, beyond the language of mathematics
> that humans invented.
>


> The key word here is “meaningless,” pointing
> out that it is mind that subscribes meaning to
> physical relationships, which otherwise are merely
> cause and effect events. Language and mathematics
> are human tools to ascribe such meaning. However,
> the physical relationships you describe, and
> particularly their mathematical relationships,
> exist independent of whether humans ascribe
> meaning to them. It is that which needs to be
> explained!



2+2=4 is true, whether it is described in a Hindu-Arabic script or a Roman script (ii+ii=iv) or something else. Language is a vehicle that carries something, a vessel for "content". Erase the language (vehicle) from mankind and I think we would be hard-pressed to claim that suddenly 2+2 didn't still = 4: specifically, what "2" stands for, what "+" stands for, what "=" stands for, and what "4" stands for. If this is true, then where exactly does this truth exist?

archytas's example above to MJ is exactly right. Pi is not arbitrary, it exists apart from the numerals that "carry" it. Math is a series of discoveries, not inventions.



But I have to ask, and Henry if you could shed a little more light on this I'd profit immensely, if we are willing to give ontological status to mathematical objects why not also to other conceptual objects? If our minds *discovered* Pi rather than invented it, why cannot we also say that our hearts *discovered* Love rather than invented it? Same with Justice, same with Mercy same with etc.............(the implication for recovery from Mormonism is clear here, this leads to, yes, God.)


I acknowledge that I am placing something into that "gaping hole in our understanding of reality" that is "a metaphysical conclusion unsupported by any evidence." But as you've said many times before, a materialist assumption which precludes the possibility of a metaphysical reality is no less an assumption.


Anyway, I fully admit to getting too drunk on Plato too young. I thought I loved philosophy because of it, but later, as I read more philosophy, I realized it was Plato's literary power that I fell in love with. And there my life changed. Now I read poetry.

But I still can't help *feeling* that poetry is a vehicle which carries a content that exists apart from the words that convey it. *Convey* here is an interesting, pregnant word.

I seek the numinous in the poetry I read, and I *feel* the ontological truth of numinosity. Mystical? Yep. Without evidence? Well, apart from my own feeling and the reported feelings of many a poet and reader of poetry, yep. Am I therefore wrong? Nope, I cannot conclude that. But I will not, based on my feeling, argue that I am right and another is wrong.

(Reed, if the Henry Bemis in you ever gets curious about this stuff, read Wallace Stevens's very short but resonating "The Necessary Angel". I have wondered more than a few years what you would make of that book. And I know I'd gain enormously from any comment you'd be willing to make about it.)


Well, gotta run, literally. 15K doesn't run itself.

Cheers and so glad you're still around lurking. One of the main reasons I still scan the first page of this site is in hope that you have something to say.

Human

I've often wondered if mathematical platonism opens the door for other abstract entities.

I don't have a good answer on this at the moment, but a nominalist angel (devil?) appears on my shoulder when I start thinking like this.

Fascinating thread. Thanks, Henry..