(October 16, 2018 at 1:46 am)vulcanlogician Wrote: So (concerning right triangles) it is only true that the square of the hypotenuse is equal to the square of the sum of the other two sides because we say it's true. This is not a fact that we discovered about right triangles? Is this what you're saying?
Or to use the example of PI, you could ask if that was discovered. But there are no perfect circles in nature. Presumably true of right angle triangles. Our mathematical descriptions are just approximations of them.
Take numbers. We think in terms of single objects. Like one or two oranges. But actually you don't have to think in this way. It's useful for every day situations but maybe an alien race would think entirely differently depending on how they evolved. Like part of a hive mind for example. Because we are making an arbitrary distinction between what is and is not an orange. That sounds like a daft statement but take humans and the debate about when life begins, is it at conception? When an egg is fertilised? When it is born etc? What about a bee? Is it a single object or part of a super organism? Why can't we say the same thing about a human? After all, there is never only one thing in existence, everything is part of a larger environment. The orange is part of a tree and part of its life cycle. But for convenience we talk about multiples of a single orange. Sometimes though it is not convenient to think in these terms.
