Closer to Truth: Is Mathematics Eternal?

Is Mathematics Eternal?

Mathematics is like nothing else. The truths of math seem to be unrelated to anything else—independent of human beings, independent of the universe. The sum of 2 + 3 = 5 cannot be untrue; this means that 2 + 3 = 5 would be true even if there were never any human beings, even if there were never a universe! When then, deeply, is mathematics?

Right off the bat, there are so many presumptions made about mathematics... it's like it's a god or deity or something. And considering modern physics is drowning is mathematics ~ a lot of it probably broken in various ways, but patched up to make it look like its working ~ no wonder mathematics seems godly to these kinds of thinkers.

Mathematics is like nothing else.

Mathematics is a human invention, using symbols created by humans, and understood by humans. No need to put a useful tool on a pedestal.

The truths of math seem to be unrelated to anything else—independent of human beings, independent of the universe.

Mathematics has never been independent from humans ~ we created it, as well forming it to match the patterns we see. And, different cultures have had different number systems. Base 10 wasn't the first system. I think there was one that used base 60...?

The sum of 2 + 3 = 5 cannot be untrue; this means that 2 + 3 = 5 would be true even if there were never any human beings, even if there were never a universe!

It might be, if you're using a different number system, and different symbols. And counting things differently.

2 + 3 = 5 can be false, if you redefine how the logic works, I suppose.

2 + 3 = 5 would have absolutely no meaning when there are no human beings to have created this meaning..

If there were no universe, mathematics would never have existed, no have had any purpose to.

What do they mean by "universe" anyways...?

I tend towards believing that Maths was discovered. Sorry Valmar 

https://www.closertotruth.com/episodes/m...discovered

Mathematics has never been independent from humans ~ we created it, as well forming it to match the patterns we see. And, different cultures have had different number systems. Base 10 wasn't the first system. I think there was one that used base 60...?

The base used for arithmetic is only a very superficial thing, though. It doesn't make a fundamental difference to mathematics, any more than the language it's written in, or the colour of the ink (or pixels).

If we think about the underlying mathematics, I reckon the strongest argument you could make for species-dependence is that another species might have concentrated on developing different areas of mathematics, rather than that the mathematics itself would have turned out differently.

I'd argue that the purest mathematics is even independent of the nature of the physical world. It's maybe clearest for number theory - theorems about prime numbers and so on. All you need to get started is a concept of counting. It's difficult to imagine any kind of conscious being without a concept of 1, 2, 3, ...

It's difficult to imagine any kind of conscious being without a concept of 1, 2, 3, ...

I'm sure I read of some tribe or culture somewhere where their worldview went: 1, 2, 3, many. That was it.

Good points, everyone... however, our current systems are peculiar to us. We created them in order to make sense of the measurable world around us.

The concepts of mathematics themselves arose from consciousness in the first place ~ mathematics makes no sense when it comes to the unmeasurable, however, like emotions, ethics, painting, music, meditating, thoughts, etc, etc. Majority of the time, we don't even think mathematically.

Does simply counting things count as mathematics? It may be a basis of mathematics, but I've always conceptualized it as a higher art based on abstract thinking beyond mere counting of objects or measuring things relative to other another, without numbers.

Feel free to correct any possible misconceptions.

Please note that I'm seeking to belittle mathematics or its usefulness, just that I want to highlight that I don't its some mystical or divine concept.

Maybe there is a divine mathematics, even, but I don't think it would be anything we'd recognize with our egos that are constricted to a narrow understanding of reality based on physical senses.

I'm not sure that the aim was to classify mathematics as divine, only as not physical. Being non-physical surely doesn't guarantee instant divinity, does it?

Well, the language used suggested a seeming glorification of mathematics, and it being put on something of a pedestal.

"Mathematics is like nothing else."

"The truths of math seem to be unrelated to anything else—independent of human beings, independent of the universe."

This is absurd thinking.

Mathematics does not have truths ~ it has models. Sometimes, these models inexplicably happen to match up with the likes of the Fibonacci Spiral, fractals and such.

But, that doesn't necessaily mean that mathematics is independent of humanity ~ the phenomena its models can match are, but not mathematics itself.

Mathematics is not reality... nor does physical reality adhere to any sort of mathematical principles. There is something... deeper going on, but I don't know even know what that is supposed to be.

It has been suggested that we're in, or even part of, a virtual reality simulation. If that is correct then aspects of our being, or our entire being, exist as mathematical constructs in a higher reality. That could explain the strange fact that abstract mathematical principles seem to underlie the universe (rather than chaos), and that these principles, against all odds, have so far been penetrable by human minds. 

The "higher reality" of the creator(s) of the virtual reality simulation could be interpreted as pure Mind, the ground of all being. To this Mind, all potential mathematical equations conforming to the rules of logic and number theory (a close to infinite number) would reflect all potential realities. Our particular reality and underlying set of "true" physics equations would just represent one choice of this Mind out of an infinitude of possible choices (for instance a choice of a world where an inverse cube law rules instead of inverse square, or where E = MC**3 not MC**2). 

What about a world in which 2 + 3 = 4, not 5? I don't think so: the basic principles of logic, number theory and counting would seem to be immutable aspects of all possible realities and the origin of these themselves would seem to be totally beyond any possible human comprehension. So no point in even asking.

"The truths of math seem to be unrelated to anything else—independent of human beings, independent of the universe."

This is absurd thinking.

Mathematics does not have truths ~ it has models. Sometimes, these models inexplicably happen to match up with the likes of the Fibonacci Spiral, fractals and such.

But, that doesn't necessaily mean that mathematics is independent of humanity ~ the phenomena its models can match are, but not mathematics itself.

I think you need to distinguish pure and applied maths. Applied maths is essentially mathematical modelling, and as you imply that isn't independent of what's being modelled. But the idea of pure maths is indeed that it's an abstract system that depends only on its axioms and on the logical processes by which the implications are derived from them. Any sufficiently intelligent species that studied number theory, for example, would discover the same properties of numbers that human mathematicians have discovered.

In my previous comment, I wasn't implying that counting qualified as mathematics, but that any conscious being with a concept of counting and with sufficient intelligence would be in a position to study number theory. I think that does make it independent of the particular properties of the physical universe, because we can imagine very different universes in which the concept of counting would still exist.

And if intelligent immaterial beings exist, surely they too will be capable of counting, and if they are curious enough to investigate, they will discover the same mathematical truths that human number theorists have discovered.