| tl;dr: Your argument doesn't make any sense. Don't copy math arguments from hipster blogs or wikipedia. They rarely make any sense. I am fully aware of the constructionist approach to mathematics. But your argument goes somewhat like this: The reals are real In computer programs however, we can only do so much Every computer program represents a real number For every bounded amount of bits, there is only a countable set of computer programs Therefore, the reals are countable. This is not how math works. You extrapolate from a bounded set that is countable to the collection of all those bounded sets - and then claim because every one set is bounded, the collection must be bounded as well - and therefore countable. Let me make a similar argument just to show how silly your argument is. Here we go:
1. Every set of integers with only one element is finite. Call it a trivial set, for example: {1} 2. Every finite union of such trivial sets is finite 3. Every finite union of such a finite union of trivial sets is finite 4. and so on - after many iterations, your finite set will look pretty big to the human eye - almost as if it was the set of integers. 5. Therefore, the set of integers must be finite. Sounds pretty silly, right? Thats what you've done for a different property of a different set. That is nonsense. This is why arguing with illiterates about math is so annoying. They think they can write non-stringent arguments and then claim they have "somewhat proof". In math, there is no such thing as "somewhat proof". You are either right or you are wrong. The reals are the reals by definition. You can not make them countable. What you can make countable is sets of numbers that you work with. Sure. You wont ever create a computer that has access to all the reals, PRECISELY because it operates from a position of countable-ness (even quantum computers). But thats not what I care about when I talk math. The real numbers are not accessible to in a "reality" way. They lie fully in the realm of arcane mathematics. Like many other things do. You would never claim that the hyper-exponentiation operator had anything to do with reality, and it doesn't. Neither do the reals. You're just confused about them because they appear so prominently in middle school mathematics. Accept it and move on. Mathematics is the realm of absolute truth. Everything we have proven is de facto true. You can make an argument that we are doing the "wrong kind of mathematics". And that may actually be true. But it doesn't change anything about our discipline. If you want to get philosophical and create a new Mathematics discipline based on different arbitrary rules (axioms), you are free to do so. But you will have to prove a lot of very mundane things and go through centuries of early day fuckups and its very likely that you will soon seek to merge with the already established mathematics. Call it math2.0. I'll play with it. If its interesting, why not. But don't expect your new math to be more interesting than the one we've got. |
But let's move on to the critical point. You said this:
The real numbers are not accessible to in a "reality" way. They lie fully in the realm of arcane mathematics. Like many other things do.
You are lecturing me on the nature of the nature of existence of things which cannot be described or verified by any process that can be carried out or imagined by any process that can exist in our universe. In a discussion about whether we should accept any existence for such things. And are failing to address the point that assuming axioms that lead to the conclusion of existence is an entirely unprovable assumption!
Do you see the obvious problem here?