Comment by layer8

Comment by layer8 5 days ago

> all things that exist are things that can be written down. And therefore there is a single countable list that includes all things that might possibly have any mathematical existence at all. Anything not on that list does not truly exist.

The universe (in the cosmological sense) can be written down as a single countable list, and anything different would be impossible? Or are you saying that it does not truly exist? I’m not sure how that makes sense.

btilly 5 days ago

We can create a countable list that contains every possible description that can ever be created. For example just write down numbers in base ASCII, using a programmable markup language (like TeX) that lets us represent anything that we want. (OK, TeX can only describe shapes down to the wavelength of visible light, but that's good enough for me.)

In what sense does an idea exist when it cannot be described by anything on that list?

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layer8 5 days ago

To quote an old adage, the map isn’t the territory. That we can’t fully write it down (which we can’t even for countable infinities, or even something like 10^10^10 symbols) doesn’t mean that it doesn’t exist. All of the territory still exists, even if any map that we can draw will only capture certain aspects of it.
Regarding “ideas”, to me math is primarily exploration and discovery, rather than invention. That’s one way how it corresponds to the territory analogy.

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