(June 5, 2020 at 8:16 am)Belacqua Wrote:(June 5, 2020 at 7:46 am)polymath257 Wrote: If you allow intelligence great enough to discover all available patterns, then all patterns can be studied.
It depends on what we mean by "nature."
The definition I've borrowed here from the Neoplatonic mystics says that nature is a portion of the world. It is the portion which can be known by the senses -- or the scientific method. But there is more to the world than this, and the part which is not known by the senses is the supernatural.
So to them, the supernatural has patterns and its own ways of doing things which are not a part of nature. These patterns can be known -- and indeed are known by beings that are higher than people. But not through empirical repeatable quantifiable methods, which is the scientific method.
And it includes much that is knowable only to higher beings, not people.
You've been talking about numbers as if they were part of nature. Are they really? Do we know about numbers through the scientific method? Or do we know of them in other ways -- through pure logic, for example? Do we conduct scientific tests that are empirical, repeatable, quantifiable, and published in scientific journals, to know about numbers? I don't think so. And if something as important as mathematics is not known through the scientific method, then it is false to say that everything is known that way.
As all polymaths know, Plato's God is much like a number.
Blake made a traditional Neoplatonic statement by saying that the body is a portion of the soul. It is the portion of the soul which is perceived by the body's own senses. But this part (which is knowable by science) is not all. The rest of the soul, and the rest of the world, is knowable in part but not through the senses. It is not a part of the sensible world, which is by definition that part which science studies. If a scientist made assertions about the non-sensible part of the world -- that part which is not known through empirical repeatable quantifiable testing -- then he wouldn't be doing science.
So yes, the supernatural has its patterns and is knowable in principle by beings more intelligent than us. That's a part of what the supernatural is, according to this very traditional definition.
No, numbers are NOT part of nature, at least not in the sense most people think about them. They are part of the *language* of mathematics. So, numbers are like words in any other language: they are ways that we organize our ideas to be better able to talk about the world around us.
And no, we do NOT know about math from pure logic alone. We have *axioms* that are simply assumed. Sort of like rules of a game. And then we have rules of deduction from those axioms which are sort of like the valid plays in the game.
But, it is quite possible to have very different axioms for math and/or logic.
I know that Plato made a very fundamental philosophical mistake when he suggested the 'forms' and pointed to math as an example of such. I also know that, unlike Socrates' belief, our learning is not the same as remembering.
So, in math I am most certainly NOT a Platonist. I am a formalist.
And once again, the problem is that the term 'nature' or 'world' is ill-defined. And when attempts are made to define it (like those you have made), it is quickly found that the whole notion of a supernatural is simply incoherent.
Plato believed that logic alone could give us information about the real world. And that is simply false. In order to find out anything about the real world, we have to actually look at the real world.
