> Why? Can't you have distinction without geometry?
Maybe but I don't see how.
> It's not only position which can be distinct, you can have other properties.
Properties like what? Color, sound, temperature, etc., all of these are geometric, no? Can you think of a concrete physical property that doesn't reduce to some kind of geometry?
> You can encode them not by shape, but, say, by kind of particle?
Sure, but then that particle must have some distinction from every other particle, either intrinsic or extrinsic (in relation to other particles), no?
Any sort of real-world distinction-making device has to have form, so that eliminates real non-geometric distinctions.
It may be possible to imagine a formless symbol but I've tried and I can't do it.
The experience of Dr. Taylor indicates to me that the brain constructs the subjective experience of symbolic distinction. (Watching her talk from an epistemological POV is really fascinating!)
So that only leaves some kind of mystic realm of formless, uh, "things". My experience has convinced me that "the formless" is both real and non-symbolic, however by the very nature of the thing I can't symbolize this knowledge.
In the Beginning was the Void
And the Void was without Form
If you can come up with a counter-example I would stand amazed. Cheers!
> Can you think of a concrete physical property that doesn't reduce to some kind of geometry?
How would you reduce charge to geometry? Or spin?
Can we differentiate by space the electrons in an atom of helium?
But we sort of digress. The question was if a concept of space is required to a concept of math, and specifically, if we can have distinction without space. Surely we can at least think of distinction without space, even if we'd fail to present that in our physical world?
Maybe but I don't see how.
> It's not only position which can be distinct, you can have other properties.
Properties like what? Color, sound, temperature, etc., all of these are geometric, no? Can you think of a concrete physical property that doesn't reduce to some kind of geometry?
> You can encode them not by shape, but, say, by kind of particle?
Sure, but then that particle must have some distinction from every other particle, either intrinsic or extrinsic (in relation to other particles), no?
Any sort of real-world distinction-making device has to have form, so that eliminates real non-geometric distinctions.
It may be possible to imagine a formless symbol but I've tried and I can't do it.
The experience of Dr. Taylor indicates to me that the brain constructs the subjective experience of symbolic distinction. (Watching her talk from an epistemological POV is really fascinating!)
So that only leaves some kind of mystic realm of formless, uh, "things". My experience has convinced me that "the formless" is both real and non-symbolic, however by the very nature of the thing I can't symbolize this knowledge.
If you can come up with a counter-example I would stand amazed. Cheers!