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Would numbers exist if no one had ever invented them?

Pindar, you should probably provide the source for what seems to surely be a cut and paste job.
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I don't think that this was so clear.
...
To elaborate on my prior post, I meant to reject the entire dichotomy of the question previously posed. Our investigations of the universe are part of the universe as an event. Thus, numbers can be derived neither by inferring directly from empirical practices nor via some transcendental structure prior to the possibility of the universe investigating itself via us. Rather, numbers are an emergent epistemological and ontological level of analysis that co-emerges with our investigations, consequential of axioms embraced in that investigation.

ebola
 
I'd say that numbers exist and we just made labels for them, as alasdair said.
Like, pi exists because circles. And circles are in nature. Well, more spheres, but you get the point I hope.

I think mathematics as we have discovered it is funny, almost like a game, because it has rules. We start with a number and the laws of multiplication and addition, etc. Then we figured out that you can graph stuff, and integrate, and it's all built off the laws that we discovered before it.

Kind of like music, where the laws of the octave give rise to an increasingly complex system of pleasant sound.
I think it would be funny if we went from addition and multiplication straight into advanced calculus because we all just understood "if this, then thiiiiiiiiisssss" like how some people work with music.

I guess some people can do that with math which astounds me.
 
yeah, only approximations of shapes, never the "pure shape" itself, are featured in our physical existence.
 
stars?
they don't have any solid mass to interfere with the perfect sphere of gravitational influence, like how our planet is slightly elongated. But that might be due to our spin. Does the sun spin? Is the sun's outline a perfect circle?

sound waves are perfect circles. So are ripples.

I think. Don't quote me on it.
 
And light travels at a certain speed in a vacuum that is a constant... So that is a number, but it is defined by our definitions of length and time. Or is it?

Sorry for the DP lol.
 
ebola? said:
Rather, numbers are an emergent epistemological and ontological level of analysis that co-emerges with our investigations, consequential of axioms embraced in that investigation.
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I fapped to this post.

But seriously, mathematics is a language. The numbers we use are merely a vocabulary -- a voice used to interpret. Much like coordinates on a map are used to denote locations. And just as the map is not the actual territory itself, mathematics is not inherent to Reality.
 
I was trying to make a thread that provokes intelligent discussion, and it looks like I succeeded... :)

To those who think that mathematics is man-made, like a language: consider a proposition like "there exist infinitely many twin primes". Isn't it natural to think that this proposition has some truth value(either true or false) that is independent of whether we know which one it is(we don't) or whether we are thinking about this question at all. The fact that the truth value of this kind of statements isn't at all obvious, looks strongly like mathematics is investigating something that exists external to ourselves.

Also about comparing mathematics to a language: what is linguistically correct is a matter of convention, what is mathematically correct is a matter of logical proof.
 
A Blind Guy said:
stars?
they don't have any solid mass to interfere with the perfect sphere of gravitational influence, like how our planet is slightly elongated. But that might be due to our spin. Does the sun spin? Is the sun's outline a perfect circle?
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Yes, stars do spin... Even a black hole can be a rotating 'Kerr black hole' that deviates from exact spherically symmetric shape.

The quantum ground state of a hydrogen atom or a noble gas atom has an exactly sperically symmetric electron density distribution, AFAIK.
 
a star cannot be a "natural-sphere" even if there is no rotation and other factors like interstellar wind, because it's not one shape, it's 10^10^whatever shapes. it'd be the same problem as trying to get a natural circle on the computer screen--there are pixels.
 
polymath said:
I was trying to make a thread that provokes intelligent discussion, and it looks like I succeeded... :)

To those who think that mathematics is man-made, like a language: consider a proposition like "there exist infinitely many twin primes". Isn't it natural to think that this proposition has some truth value(either true or false) that is independent of whether we know which one it is(we don't) or whether we are thinking about this question at all. The fact that the truth value of this kind of statements isn't at all obvious, looks strongly like mathematics is investigating something that exists external to ourselves.
Click to expand...
"Truth values" connotes subjectivity. It is worthless without a subject.

Also about comparing mathematics to a language: what is linguistically correct is a matter of convention, what is mathematically correct is a matter of logical proof.
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And so where is this logic located?
 
L2R said:
"Truth values" connotes subjectivity. It is worthless without a subject.



And so where is this logic located?
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If science's epistemological breaks of the 17th and 20th Century are any indication, the subject is nothing, for if he wasn't not nothing, then he wouldn't possess a lack or ambiguity of knowledge shown by, other things, by our fruitful discussions on the ontology of number. Therefore "Truth Values" and "Logic" find their existence in axiomatic systems, in structure, from which we can make analogies between number and language, and etc...
 
I think it makes the most sense to say that Math is both. Math is a system(s) of signifiers that take place within space-time within 1st person subjects. The objects that mathematical symbols signify don't exist within the stream of space-time. The symbols are the "shadows cast" by the ungraspable transcendent forms as are any other phenomena said math grasps.
 
i find using numbers to explore this concept just confuses things... was the evolution on mankind an amazing and beautiful thing before mankind had the ability to appreciate it as such? i believe so, therefore these things can have existed before humanity could define them. i feel numbers fall in the same category. the universe is not infinitely divisible, and therefore it's smallest elements can be defined and counted. unless your rather religious, humanity had nothing to do with this.
 
L2R said:
"Truth values" connotes subjectivity. It is worthless without a subject.
Click to expand...

i think you're possibly being misled by the word 'value' here.... in a way you are correct, sets of axioms have various (possibly infinite) models and in logic you usually define truth as being the case in a particular model, i.e. set of objects instantiating the axioms you're considering. but then something being true in that model is not a subject fact. truth in a model is an unsatisfying general definition of truth, but since we're talking about maths here, it is the definition of truth....

i don't think mathematical objects need a consciousness to interact with them in order to exist. i certainly don't see how the empty set, which numbers are built from (and it doesn't matter which way you build them,{{o}} or {o,{o}}), can require anything to exist. its just emptiness. how can you say nothingness only exists if you think about it?
 
to mutate orwell, everything is objective, but some things are more objective than others! ;)

I have no question that mathematical functions work and interact in the absence of observation, but i think that is more "natural order" than mathematics. We define that observable order as mathematics.

Pindar said:
If science's epistemological breaks of the 17th and 20th Century are any indication, the subject is nothing, for if he wasn't not nothing, then he wouldn't possess a lack or ambiguity of knowledge shown by, other things, by our fruitful discussions on the ontology of number. Therefore "Truth Values" and "Logic" find their existence in axiomatic systems, in structure, from which we can make analogies between number and language, and etc...
Click to expand...

several too many negatives, i think
 
I have no question that mathematical functions work and interact in the absence of observation, but i think that is more "natural order" than mathematics. We define that observable order as mathematics.
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That's just the thing. Mathematical objects don't work or interact. That would require the property of time which isn't part of the ontology.
 
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