For an image to be a number, I demand a one-to-one correspondence between images and numbers. Lacking that, I merely say that an image can be represented by a number, but this is trivial. Hence, I repeat: we're not even discussing the same thing.

>> "So, I ask again, how can an image be a number?

>> "Lacking that, I merely say that an image can be represented by a number, but this is trivial"

I think you're arguing with yourself at this point.

Note that: "is" and "is represented by" are not the same on my book (which is obvious from the previous comments). If you want to counter-argument, try harder.

I wonder what you mean by "is". Nothing really "is" anything but itself. The only other "is", the one that real people actually use, is "is represented by" or "is a representation of", or "is an instance of", etc.

For example, this --> A <-- looks like the letter A. But it isn't the letter A. It "is" only a representation, a bit-pattern with decimal notation 65, a glyph drawn from a font, a set of pixel elements on a graphics surface, a pattern of light on a display, a bunch of photons traveling through space, a group of excited photoreceptor cells, a set of signals traveling through neurons, etc. And it is none of these things, because none of them capture the essence of the pattern, repeated over human experiences.

So it seems to me that if you're trying to win an argument by drawing a distinction between "is" and "is represented by", you are not going to convince anyone who's put much thought into it. "Ceci n'est pas une pipe"; but a representation of a pipe is a (more or less faithful) representation of a pipe, whether you are blind or not, and so a number is a digital image, and vice versa.

I think one must draw a distinction between the physical world and the metaphysical one. For a platonist, numbers do exist outside of any physical reality and, therefore, a number and its representation are not the same thing.

I am not a mathematician, but to me this discussion reminds me of a vector having different coordinates, depending on what coordinate system we choose. Those are all different representations of the same thing. Likewise, a number can be represented in many different ways (binary, oct, hex, etc), but they all represent the same number. Is the vector its representation? If so, then the vector is many things, which is a funny definition of "to be". If the vector is itself, then it cannot be equal to any of its representations, it's something beyond its representation.

I don't think it's at all a given that Hylaean Theoric Worlds exist independently the Arbran Causal Domain.

I think that the main reason you are being downvoted is not so much that you are technically wrong, but rather because you are being pedantic ad nauseum.

This is a programmers' forum, not a philosophers' forum. We should not be discussing the meaning of "is". That's too low-level and fundamental for our purposes. This does not imply it's not an interesting question, it's just not appropriate.

There is a one-to-one correspondence between numbers and their doubles, {0..n} and {0..2n}. Does that mean that numbers are their doubles?