It doesn’t really work this way. And to demonstrate, I bring up the prime numbers.
What many people don’t quite understand is that mathematics, like the sciences does not invent things, it discovers them. The structures are already there. We did not invent cells, electricity, or gravity. They were already there. All Mathematics does is name them, categorize them, and show properties that they have. There is nothing human about the prime numbers, for instance. There really is nothing human about mathematics.
Counting is essentially the building block of all of mathematics. 1 2 3 etc… There is no other way to count than the way we count. Is this because of our definition of counting? Well of course, but it is nonetheless true. If Aliens were to count, they would have to count this way. Can I construct systems where 1+1=1? Of course. Consider clouds. If you add two clouds together, you just get a cloud. However, counting is still not changed. In order to even ask the question, I need to be able to discretely differentiate clouds, which means that counting is still there. You simply have a bizarre algebra on top of it.
To even consider a universe where counting goes by different rules is mind-boggling, because it would require the impossibility of discrete objects. Even waves would have peaks and valleys they would be able to be counted. Time generates rhythm and beats that would be counted. And there is only one way to count.
And once you realize there is only one way to count. You realize that addition gives us multiplication and that gives us the prime numbers. We didn’t invent prime numbers. We discovered them.
What many people don’t quite understand is that mathematics, like the sciences does not invent things, it discovers them. The structures are already there.
That is not such an unquestionable truth, there are many different schools of thoughts. None overly useful.
I’m not quite sure what you mean by that, but Platonism has been useful for inspiring Tegmark’s Ultimate Ensemble, which has been useful for inspiring UDT.
Can’t say that I find either very useful (in the instrumentalist sense, anyway), but I suppose if you count inspiration for a couple of rather speculative ideas as useful, I agree.
This is only true to a point. In some sense, yes, the real numbers are the only complete & [canonically] totally-ordered field, up to isomorphism; but this last part is a bit of a snag for the language being used here, since the tools used to develop the real numbers in those different ways are certainly created as much as language & software are created.
You could cling to the idea that even these things are merely “discovered,” but eventually you’d find yourself talking about the Platonic ideal of the wobbly, scratched up table in the neighbors’ house, and how the carpenter originally discovered the Form of this particular table.
This is more a criticism of the English words for invention, creation, discovery, & the like; but then, philosophy of math that gets too far afield from actually doing logic is basically just philosophy of language.
It doesn’t really work this way. And to demonstrate, I bring up the prime numbers.
What many people don’t quite understand is that mathematics, like the sciences does not invent things, it discovers them. The structures are already there. We did not invent cells, electricity, or gravity. They were already there. All Mathematics does is name them, categorize them, and show properties that they have. There is nothing human about the prime numbers, for instance. There really is nothing human about mathematics.
Counting is essentially the building block of all of mathematics. 1 2 3 etc… There is no other way to count than the way we count. Is this because of our definition of counting? Well of course, but it is nonetheless true. If Aliens were to count, they would have to count this way. Can I construct systems where 1+1=1? Of course. Consider clouds. If you add two clouds together, you just get a cloud. However, counting is still not changed. In order to even ask the question, I need to be able to discretely differentiate clouds, which means that counting is still there. You simply have a bizarre algebra on top of it.
To even consider a universe where counting goes by different rules is mind-boggling, because it would require the impossibility of discrete objects. Even waves would have peaks and valleys they would be able to be counted. Time generates rhythm and beats that would be counted. And there is only one way to count.
And once you realize there is only one way to count. You realize that addition gives us multiplication and that gives us the prime numbers. We didn’t invent prime numbers. We discovered them.
That is not such an unquestionable truth, there are many different schools of thoughts. None overly useful.
I’m not quite sure what you mean by that, but Platonism has been useful for inspiring Tegmark’s Ultimate Ensemble, which has been useful for inspiring UDT.
Can’t say that I find either very useful (in the instrumentalist sense, anyway), but I suppose if you count inspiration for a couple of rather speculative ideas as useful, I agree.
This is only true to a point. In some sense, yes, the real numbers are the only complete & [canonically] totally-ordered field, up to isomorphism; but this last part is a bit of a snag for the language being used here, since the tools used to develop the real numbers in those different ways are certainly created as much as language & software are created.
You could cling to the idea that even these things are merely “discovered,” but eventually you’d find yourself talking about the Platonic ideal of the wobbly, scratched up table in the neighbors’ house, and how the carpenter originally discovered the Form of this particular table.
This is more a criticism of the English words for invention, creation, discovery, & the like; but then, philosophy of math that gets too far afield from actually doing logic is basically just philosophy of language.