Thread: Do You Think Mathematics Is Natural Or Man-Made?

I tend to agree with you.

But to be fair, as far as I know the leading physicists at the moment do
think that the rules of the universe are in fact universal and while these
might be applied in a different way (e.g. gravity) they are still based on the
same mathematical theorems. This would at least have to be the case if
string theory is right.

Another thing to consider is that along with humans, other animals also use math.
Like let's say a cat has to jump from one table to the other and there's five feet between the tables. In the cat's mind it thinks "okay I've done this before, I remember how tight I have to make my muscles to jump (insert five feet) and how to land correctly.)
That's cat math.
Of coarse the animal doesn't speak English, and doesn't use the same symbols that us humans have come up with, like plus signs and X's and etc.
So math does exist in nature there's just different ways to interpret it.
So no I don't believe it's man made, only how we describe it.

This reminds me of a lecture by Leonard Susskind and how he explains that
leopards are well aware of complex physics and mathmatics when it comes
to hunting their prey. (For example slowing it down by running up against it)

I think the key is that humans are the only ones to have conscious mathematics. This gives us the ability to discover and prove new theorems, and analyse mathematical thought as a whole.

In other animals, it's unconcious. Neural networks are mathematical structures so it's not surprising that mathematics is at the very foundation of our being (though they are extremely poorly understood at the moment).

A good example is that ant brains perform integral calculus when moving around. Needless to say the ant consciously has no understanding of how to do calculus.

I don't agree with this, or rather I think it would be impossible for us to make any sort of assumptions about what an extraterrestrial race might assume about reality. The axioms are built fundamentally on the particular way in which we perceive reality and how we group sensory data. We take our view of reality for granted since its the only one we know, but its entirely possible that an alien species could evolve to perceive reality in a way that we are unable to imagine. As long as the intelligence is able to successfully interact with its surroundings, the perceptions need not conform to what we consider real or normal.

I don't know if this strays too far off topic or not; make of it what you will.

It's a good point but I'm not so sure. We've only had mathematics for a few thousand years and already we're at the point where we actually make a point of totally detatching it from reality. Today, pure mathematics is simply symbols, and doesn't have an application.

I'm pretty sure any alien being would encounter the same axioms, and not be able to encounter any new, interesting ones. The most important ones are those of arithmetic, and I think any intelligent being needs to be able to know that a + b = b + a. From this and a very small number of other axioms, pretty much the whole of arithmetic can be generated. This includes extremely complex theorems to do with the distribution of primes, for instance. I also think aliens would have Euclidian axioms built in. You can't survive in a natural environment without understanding how to move around. I'm not sure if there are any other relevant axioms.

Originally Posted by Xei

General relativity is correct. K? I don't see any point in this line of discussion. There's empirical confirmation, end of. I don't care who teaches what in what manner.

I am cool beans with general relativity. It does not disprove the existences of planes and other figures. Geometric figures are zones and do not have to conform to the curvature rules of space or matter. However, there is a separate set of laws for the principles of projections of such figures curving with space.

Just imagine space becoming uncurved for a moment. Now imagine a plane in that space that does not curve with space as space is curved back. That zone would still be real. Euclidian geometry is concerned with such realities, and it is taught as Gospel at every school in the modernized world as a discipline of exactness for a reason.

Originally Posted by Xei

I don't see how that makes sense. Clearly these planes only exist in your imagination.

No, they are zones of reality, like the boundaries of a football field that is part of a bigger field and is not marked by anything drawn.

Originally Posted by Xei

How about spheres? Do they exist? Is there a continuum of spheres of every concievable radius permeating every point in the universe? What are the empirical consequences of these spheres? They don't do anything.

They don't have to do anything, and they don't have to be made of matter. They are still there. Does the equator exist? What is it made of?

Originally Posted by Xei

What about other mathematical objects? Is every single value on the real number line somehow squashed into every point in space? What about the complex plane? What about all of the n-tuples? I can invent any kind of invisible shape or object I want and say it 'exists in space'. Why are planes special?

Yes to your first question and no to your second. The complex plane does not exist anywhere. It is all hypothetical. Planes are not. N-tuples are just symbols for real things.

Originally Posted by Xei

Well, 'square root' is something only with meaning in arithmetic. So you'd need to have already assumed the axioms for your question to make any sense.

The rules pi is based on can be changed. Specifically the parallel postulate which when assumed gives you Euclidian geometry and when not assumed gives you other geometries.

They are all based on reality, and that is why they cannot be changed. You cannot make the principal square root of 64 be 3. You can use the symbol 3 to express what is really 8, but what the symbol 8 represents is the principal square root of what the symbol 64 represents. That cannot be changed. The same principle applies to pi. Axioms are based on reality, not just wild ideas people pulled out of their asses.

Originally Posted by Xei

No you didn't. That's the definition of pi.

Yes, it is what pi is. What exactly are you asking? Your original question is a needle in a hay stack now.

Originally Posted by khh

You totally ignored my argument. That's not very nice -.-

You said this...

Originally Posted by khh

Because in a mathematical system where pi = one it'd be very hard to tell someone how many apples they're holding.

I thought you were agreeing with me. Sorry I didn't thank you for it. You were saying that to call the value of pi 1, all other number symbols would have to be arranged accordingly. That illustrates exactly what I am saying. We create the symbols, not the rules. We can't just make pi = 1 and leave all of the other symbols as they are. Mathematical reality is what it is, and we have to work with it accordingly.

They don't have to do anything, and they don't have to be made of matter. They are still there. Does the equator exist? What is it made of? (etc.)

Well here we differ in our opinions. I don't think the equator exists anywhere else but in the mind of humans and human language. It is just a concept, like the complex plane is just a concept. The equator isn't objectively real, it's a line on a map; and a map is a conceptualisation of pictures of the world made of ink on paper. I think the whole idea that every single possible mathematical object (except complex numbers for some reason; complex numbers can be made to model physical phenomena just as well as real numbers) is squished into every point of the universe is simply meaningless.

Axioms are based on reality, not just wild ideas people pulled out of their asses.

We're going in circles here, I keep explaning to you: yes, axioms are based on our observed reality and I've never claimed that they are 'wild ideas'. We believe that if two infinite straight lines are at 180 degrees to each other they can never cross, based on our observations on Earth. But in fact these axioms aren't physically correct. Throughout our entire 4 billion year evolution and our entire lives, we have only been able to observe Euclidian geometry so it's no surprise your brain finds it contradictory, but there is no logical argument you can give that shows it is inherently contradictory. Now we have access to technology which can prove that these axioms are incorrect in our universe.

Yes, it is what pi is. What exactly are you asking? Your original question is a needle in a hay stack now.

lolwut, the question I was asking was directly below what you quoted but you deleted it. :l

No you didn't. That's the definition of pi.

The question is how we go from there to obtaining an approximation for pi. If you didn't know what the value for pi is, how do you think you would obtain the digits 3.14159265358979323... ? That's my question.

Originally Posted by Universal Mind

I thought you were agreeing with me. Sorry I didn't thank you for it. You were saying that to call the value of pi 1, all other number symbols would have to be arranged accordingly. That illustrates exactly what I am saying. We create the symbols, not the rules. We can't just make pi = 1 and leave all of the other symbols as they are. Mathematical reality is what it is, and we have to work with it accordingly.

Is that what you're saying. Well, then we are in agreement, it seems

Originally Posted by stonedape

I think it is both natural and man made. It occurs naturally and man makes observations and finds patterns.

Yes, man may notice the patterns, however the patterns still exist whether we notice them or not.

I'm not gonna get into any of the other arguements, I'm no math genius and have no clue what you guys are talking about

Originally Posted by Xei

Well here we differ in our opinions. I don't think the equator exists anywhere else but in the mind of humans and human language. It is just a concept, like the complex plane is just a concept. The equator isn't objectively real, it's a line on a map; and a map is a conceptualisation of pictures of the world made of ink on paper. I think the whole idea that every single possible mathematical object (except complex numbers for some reason; complex numbers can be made to model physical phenomena just as well as real numbers) is squished into every point of the universe is simply meaningless.

Real numbers can represent real things, such as distances. A number line can coincide completely with distances and degrees of difference, etc. Complex numbers, on the other hand, include imaginary numbers, which are called "imaginary" as opposed to "real" for a very literal reason. They can represent unrealistic hypotheticals, but not actual realities.

I can walk along the equator and point at it even though it is not made of matter.

Originally Posted by Xei

We're going in circles here, I keep explaning to you: yes, axioms are based on our observed reality and I've never claimed that they are 'wild ideas'. We believe that if two infinite straight lines are at 180 degrees to each other they can never cross, based on our observations on Earth. But in fact these axioms aren't physically correct. Throughout our entire 4 billion year evolution and our entire lives, we have only been able to observe Euclidian geometry so it's no surprise your brain finds it contradictory, but there is no logical argument you can give that shows it is inherently contradictory. Now we have access to technology which can prove that these axioms are incorrect in our universe.

I have major doubts about the parallel lines thing, and it goes counter to what I was taught and seems to go counter to logic and common sense. However, I don't claim to be a Harvard Calculus professor and don't claim to be able to pick apart the proof it is based on. I used to teach algebra and geometry, and from where I am sitting, the idea seems absolutely insane.

So I guess you agree that mathematical reality is what it is and humans just come up with symbols to represent it?

Originally Posted by Xei

lolwut, the question I was asking was directly below what you quoted but you deleted it. :l

Woops. Yeah, I thought my answer got to the heart of that the first time I addressed it. I assume pi was calculated by taking a circle's exact circumference and dividing by its exact diameter and the figure was used to apply to all circles because all circles are similar. If there was some other method, I have no idea what it was.

Real numbers can represent real things, such as distances. A number line can coincide completely with distances and degrees of difference, etc. Complex numbers, on the other hand, include imaginary numbers, which are called "imaginary" as opposed to "real" for a very literal reason. They can represent unrealistic hypotheticals, but not actual realities.

I can walk along the equator and point at it even though it is not made of matter.

Actually historically the nomenclature just came from a derision for the maths of the French. Nowadays they're just an artifact. 'i' itself can represent a positive rotation of 90 degrees, which is just as real as the 5 dogs or 5 trees or 5 beans that '5' represents.

I have major doubts about the parallel lines thing, and it goes counter to what I was taught and seems to go counter to logic and common sense. However, I don't claim to be a Harvard Calculus professor and don't claim to be able to pick apart the proof it is based on. I used to teach algebra and geometry, and from where I am sitting, the idea seems absolutely insane.

There is no proof. This is what I'm trying to say about the whole of mathematics. There is no proof of Euclid's axiom, and there is no disproof. When we assume it we get one branch of mathematics, when we don't we get others. The results we get from the assumptions are incontrovertible if we take the assumption as incontrovertible, but in reality assumptions are nothing more than assumptions and in the real world can turn out to be off.

So I guess you agree that mathematical reality is what it is and humans just come up with symbols to represent it?

Well going back to my original point, you can have contradictory results in mathematics depending on which axioms you choose, so I don't think it makes sense to view there as being some kind of objective reality of mathematical truths.

To put it in terms of your question, I suppose I believe that mathematics is the symbols and their manipulation, and is hence not objectively real, in the sense that we have language to describe objectively real objects but language itself is not objectively real.

Yeah, I thought my answer got to the heart of that the first time I addressed it. I assume pi was calculated by taking a circle's exact circumference and dividing by its exact diameter and the figure was used to apply to all circles because all circles are similar. If there was some other method, I have no idea what it was.

Nah that's just a rephrasing of the question. If the circle had diameter 1 then the circumference would be pi and then in attempting to find out what this circumference is you'd be back to the original problem again. How would you calculate the circumference? Clearly we don't actually build massive circles and measure them.

My reflex-reponse upon hearing claims of "absolute truth" : man is NOT the center of the universe. Forced to accept that in the physical sense we cling all the more dearly to the hope that at least the thought-world still revolves around us.

That as of a preliminary response. I often find that what is a lot more important in any (semi)philosophical discussion is the intuition being aimed at, in other words prejudice. So better expose it early, which I tried to do above.

Here's a question: how will you tell the difference between the two positions, that mathematics is manmade, or that it is universal? Is there anything that all observers can agree upon that is different in these cases?

I suspect no. I suspect that the only difference is a lessening of that human, all-too-human attempt to look away from the absurdity of our existence.

Responding to the original topic here:

I would say mathematics is both natural and man-made in varying quantities. Whilst numbers themselves are an abstract concept to represent the quantity of an item or a value, in some cases these values are natural, such as Pi.

Some of the numbers being manipulated are derived from human constructs, some are from natural phenomenon*.

*okay technically you could argue that even man-made items are natural, but for the purposes of this discussion we are treating the two as separate.

Maths are like colour. They've been there, we just gave them names.

Originally Posted by ReachingForTheDream

When I think about it... it still exists in nature. If I have a group of objects, and I take away from them, it becomes lesser. If I add to them, it becomes greater. If I add the same amount, it is doubled, multiplied by 2. If I divide them, they are divided by 2. These are all basics of math.

The problem is that there is no intrinsic object in nature. We decide what is a discreet thing and what is not. Therefore, in order to count a group of things you must first define what is one thing and what is another thing. Someone else may very well decide that what you count as two... diamonds for instance, are really not two diamonds but xbillion carbon atoms, or what have you. The designation of things to count is in itself a construct created by humans.

several people have brought up the example of pi. While no one "decided" what pi is, what we did decide was what a circle is, and what a circumference is and what a radius is. Pi is merely the result of these decisions. If someone were to claim that a circle is not something that is decided because it is merely all points on a plane that are equidistant from another point, then I can easily say that we decided what points are, and how to define distance. It all comes back to the mental constructs that we use to define our world.

Originally Posted by Universal Mind

No, they are zones of reality, like the boundaries of a football field that is part of a bigger field and is not marked by anything drawn.

Do you mean to say that you believe "football field" to be an intrinsic part of reality or is it merely defined by the rules of the game set forth by it's creators? If it is intrinsic, does this mean that Australians live in an alternate universe because their idea of what a football field is has different dimensions (and is shaped like an oval)?

I basically agree with that.

Unless one is directly perceiving the true nature of reality, one is perceiving a man-made concept. Concepts, ideas, notions and the like are useful because they help us to classify and to discuss our perceptions.

In this sense, the notion of a chair, or of a cloud, or of a symphony is no less different than the notion of, say, an integer, or a differential, or of a connected bipartite graph.

In fact, we are especially fond of creating concepts to describe concepts. Math is full of this, but this does not make math any more special than, say, the idea that a string of words can be called "a poem."

From this perspective, math is entirely man-made. But so is everything else.

Cheers,
-BR

Quote: "2+2=4"

Well.. it depends how you conceptualise it. If I had 4 blobs of bluetack, I could prove that 2+2=1 by moulding them all together. If I had 81 blobs of bluetack 75+6=1 would be a possibility etc etc. I demonstrated this to my Maths Professor friend and won a bet with her. It's all in how you think about it. Another one: take an atom (2 protons) and add 1 proton. You still only get one atom. So, in this case, you could also conceptualise that 2 protons+proton = atom, which could be written as 2+1=1 etc etc. There are loads of these examples. Of course, this doesn't disprove that 2+2=4, it just gives another conceptualisation to it.

Back to the OP. Having learnt yesterday about a theory of looping time, theoretically someone in the past/future may have already devised Pure Mathematics and used it to create our universe. Well.. it's a theory! )

You professor friend probably conceded the bet because somebody who is a professor in mathematics should have known better than to enter the bet without agreeing to a definition of 2, 4 and +.

Originally Posted by DuB

Math cannot be a "pure" science, because math is not science at all. That's why I named this forum Science & Mathematics. They are distinct entities.

Thank you! I can't begin to tell you how many times I need to try to explain this. One operates by proof. The other operates by empiricism (either falsification or confirmation depending on who you ask). End of story.

Originally Posted by Xaqaria

The problem is that there is no intrinsic object in nature. We decide what is a discreet thing and what is not. Therefore, in order to count a group of things you must first define what is one thing and what is another thing. Someone else may very well decide that what you count as two... diamonds for instance, are really not two diamonds but xbillion carbon atoms, or what have you. The designation of things to count is in itself a construct created by humans.

I'm not sure that this has any content. I see where you are going and generally agree but the same rules of counting apply regardless of if we designate the subject as two diamonds or xbillion carbon atoms.

Originally Posted by Xaquaria

several people have brought up the example of pi. While no one "decided" what pi is, what we did decide was what a circle is, and what a circumference is and what a radius is. Pi is merely the result of these decisions. If someone were to claim that a circle is not something that is decided because it is merely all points on a plane that are equidistant from another point, then I can easily say that we decided what points are, and how to define distance. It all comes back to the mental constructs that we use to define our world.

This is more on point. The point of math though is that after we agree upon our definitions and axioms, the rest is inescapable. This is why I agree that an extraterrestrial race would end up with the exact same knowledge(see edit) about mathematics as we have. They may have started with a different set of definitions and axioms but the content of their math would be the same. We frequently consider different ways of measuring distance. For example, a circle is only recognizable as such using the euclidean metric, d(x, y) = sqrt((x1 - y1)^2 + (x2 - y2)^2). But what if we use the metric d(x, y) = max(|x1 - y1|, |x2 - y2|)? Then a circle looks like a square. A surprising amount of topology still goes through.

It may seem like that metric is contrived but it's a natural metric for measuring function spaces. where if f1 and f2 are bounded functions on some set S then we can define their distance from each other as d(f1, f2) = sup(|f1(x) - f2(x)|, x in S). The former is straight forward specialization of that for the case of functions on {1, 2} which is all points in 2-space really are. (sup is sort of like max but works when there are an infinite amount of elements that might not ever achieve a strict maximum. Think of the image of cos on (0, 1]. Here, there is no maximum but the surpremum is 1. The supremum is the maximum for the case of finite sets. )

The deeper you get into mathematics, the more you see how universal it really is. Any failure of our particular knowledge of mathematics is merely an artifact of that particular set of definitions and axioms not yet having proved themselves useful to us (in a mathematical, not practical sense).

EDIT:

By "exact same knowledge", I mean that we would not have accepted contradicting claims and our mathematics could be extended to include everything which they've discussed and vice versa.

Originally Posted by PhilosopherStoned

You professor friend probably conceded the bet because somebody who is a professor in mathematics should have known better than to enter the bet without agreeing to a definition of 2, 4 and +.

What I actually bet her was that I could prove that "one plus one equals one" (spoken, not written). She probably fell for it because I used such basic units, and there was no money involved. She tells me she has used it to great effect with her colleagues. I've told her to call it "The Oneiro Conundrum". Heh.

BTW.. "..a definition of 2, 4 and +."

Now, I understand how 2 and 4 can be defined in different ways, but +? Apart from the obvious, what other definition could there be? Does the symbol have more than one possible meaning? (I'm not a mathematician, as you probably can tell).

Originally Posted by Oneiro

What I actually bet her was that I could prove that "one plus one equals one" (spoken, not written). She probably fell for it because I used such basic units, and there was no money involved. She tells me she has used it to great effect with her colleagues. I've told her to call it "The Oneiro Conundrum". Heh.

This makes more sense. For example any mathematician would know that 2 + 2 = 1 mod 3 but there's no n so that 1 + 1 = 1 mod n. 1 + 1 = 0 mod 2 and 2 for all greater n. The integers mod n is pretty much the canonical example redefining +.

BTW.. "..a definition of 2, 4 and +."

Now, I understand how 2 and 4 can be defined in different ways, but +? Apart from the obvious, what other definition could there be? Does the symbol have more than one possible meaning? (I'm not a mathematician, as you probably can tell).

Yes, the symbol has a lot of potential meanings and they're all tied to the set of elements that it operates on. The relevant definition here is "Group". A group is a set of elements, G and a definition for + on those elements. We would right the group (G, +). + has to satisfy four axioms and its conventional to reserve the actual symbol + for those operations which satisfy a fifth.

1. (closure) a + b is in G
2. (associative) (a + b) + c = a + (b + c) = a + b + c
3. (identity) There exists e in G such that e + a = a for all a in G
4. (inverse) for all a in G, there is an element B such that a + b = e.

If the operation further satisfies

1. a + b = b + a

Then we call it an abelian group and write the operation as +, the inverse of a as -a and e as 0. Otherwise, we write the operation using infix notation (that as ab instead of a + b), the inverse of a as a^-1 and e as 1.

Your example of adding clay fails to be a group because there are no inverse elements. That is there is no amount of balls of clay that I can add to any given amount of balls of clay to get zero balls of clay. Unless of course you have balls of anti-clay.

It is a monoid though which just means that it satisfies all the other axioms except having an inverse. The natural numbers are the canonical example of a monoid.

Some examples of groups:

• The integers, rationals, reals, and complex numbers, all with addition. These would be (Z, +), (Q, +), (R, +) and (C, +)
• The cartesian product of the integers with themselves (so elements of the form (a, b) where a and b are integers) with addition defined "point wise". So (a, b) + (c, d) = (a + b, c + d) where the inner addition is the regular addition.
• The set of continuous functions on [0, 1] with addition again defined pointwise. That is (f1 + f2)(x) = f1(x) + f2(x)
• The set of rotational symmetries of a square. We can rotate it pi/2, pi, 3pi/2 and 2pi=0 radians. a + b is defined as rotating a radians and then rotating it b radians. If I rotate it pi/2 radians and then 3pi/2 radians, I've rotated it by 2pi=0 radians.
• The set of rotational symmetries of a circle. I can rotate it by any amount of radians betwee 0 and 2pi and the inverse of a rotation a is the rotation 2pi-a

Well that's as clear as mud, but thanks for giving it a bash anyway.

Like some have said here Philosopher, the only reason why you take these things to be truths is because of the very specific way in which you are capable of perceiving reality. Xei brought up the example of non intersecting parallel lines. We believe this to be a self evident truth because we are beings that are limited to non-relativistic temporal-spatial conditions. A being that spends its life traveling near the speed of light would have a very different idea of what is self evident about nature than you do.

Perhaps you don't like my example of diamonds and carbon atoms. We can just as easily use UM's example using random symbols. you may look at **** and say clearly that is 4 astrixes (astrices?) but someone else may say that it is clearly just one dotted line. If you define the question by saying that we are counting astrixes then first you have to agree what an astrix is, which would be a rule that you are arbitrarily assigning to the question and therefore would not be natural or intrinsic.

In your responses to me you kept saying things like, "if we designate" or "if we agree". These are subjective rules that you are applying meaning that it would not be intrinsic to nature. There are many things that we all feel are intrinsic to nature but that is only because we all share very similar ways of apprehending reality, and therefore are operating under the same assumptions or rules. You say that the point lies after we have made these assumptions, but that would mean that you agree that the math is definitely man made, since it is us who have to first make the assumptions for it to be true.

Originally Posted by Xaqaria

Like some have said here Philosopher, the only reason why you take these things to be truths is because of the very specific way in which you are capable of perceiving reality. Xei brought up the example of non intersecting parallel lines. We believe this to be a self evident truth because we are beings that are limited to non-relativistic temporal-spatial conditions. A being that spends its life traveling near the speed of light would have a very different idea of what is self evident about nature than you do.

This just isn't a good example. It depends on what the lines are embedded in. If they're embedded in flat euclidean space, then it is a fact that they'll never intersect. This is old news. If we model the space with the reals, then we can prove it. It's also old news that two straight lines in a sphere that are perpendicular to a great circle and parallel at their intersection with it will intersect at both of the poles determined by that great circle. Think of two of the lines (lat or long? I always forget) that are perpendicular to the equator on earth. They intersect at the north and south poles. So it all depends on our definitions.

Perhaps you don't like my example of diamonds and carbon atoms. We can just as easily use UM's example using random symbols. you may look at **** and say clearly that is 4 astrixes (astrices?) but someone else may say that it is clearly just one dotted line. If you define the question by saying that we are counting astrixes then first you have to agree what an astrix is, which would be a rule that you are arbitrarily assigning to the question and therefore would not be natural or intrinsic.

No of course it's not intrinsic. It could be either, neither or both. It's just a matter of definitions, I agree. But the point is that after I suitably define asterisks and dotted lines, it is already objectively determined within the context established by those definitions whether it is either, both or neither. The only freedom we have in talking about the universe is in definitions. That's why I think that, generally, they're the only things that are really worth arguing about. After the definitions are established, we either have an answer to our question or we don't.

There are many things that we all feel are intrinsic to nature but that is only because we all share very similar ways of apprehending reality, and therefore are operating under the same assumptions or rules.

I want to try to go deeper than this. The direct reason that we feel that many things are intrinsic to nature is not because we have similar modes of perception but that those similar modes of perception cause a nearly identical set of definitions to be useful to us. Viewed through the lens of that common set of definitions, those properties are inherent in the universe because that's how the universe is. That is, it is inherent in the universe that when viewed through a particular set of definitions, it will be seen to have such and such a property. It's very true that we are seeing the universe through definitions and not as it actually exists (not possible in my opinion but irrelevant here) but that does not make the truth value of some statement P about the universe subjective when it is accompanied by the appropriate definitions. This is my principle point here.

You say that the point lies after we have made these assumptions, but that would mean that you agree that the math is definitely man made, since it is us who have to first make the assumptions for it to be true.

Honestly, I'm not really interested in this question. I would refrain from stating whether it is a product of humans and simply state that we choose what we want to look at by choosing our definitions and axioms. That choice uniquely and absolutely constrains what is true, what is not true, and what is undecidable in some body of mathematics. This is an interesting phenomenon and the question of whether it is "out there" or "in here" doesn't really strike me as meaningful or interesting.

I guess we agree on the essentials. As long as we recognize that we are starting with inherently human definitions then we will continue to agree on the outcomes of those definitions. The only logical leap that I am unable to agree on is your belief that these outcomes would necessarily hold for any extraterrestrial that may or may not be operating on completely different assumptions that we are unable to imagine.

Edit: I just realized how old this thread is and that I had already posted pretty much the same opinion. Oh well.