> these undecidable/uncomputable statements are computed by humans all the time
This is a far stronger statement than I think even Platonists would accept. What examples of non-computable statements that are computed by humans do you have in mind?
Even putting on my Platonist hat (which I'll wear for the rest of this reply), I would still argue, in line with xyzzyz's comment, that at most humans deal with computable descriptions of non-computable things. For example, the description of the real numbers is computable even if the real numbers themselves are not. Likewise even if the real numbers are not computable, we can only ever work with computably-definable (indeed only finitely definable) real numbers rather than arbitrary real numbers.
To use the map-territory analogy, while the territory is the thing we care about, the only things we can work with, manipulate, and compute are computable maps.
For example Chaitin's Constant is a non-computable real number. However, we never work with Chaitin's Constant directly, but rather with our finite description of it, from which we deduce all sorts of other facts.
There are therefore many things about Chaitin's Constant we will never know. But that is the Platonist's lot in life.
As an aside, there's in fact a formalization of this that states that a mathematical universe consisting solely of finitely definable entities and nothing else is perfectly reconcilable with ZFC. See https://mathoverflow.net/questions/44102/is-the-analysis-as-...). Now as I continue to wear my Platonist hat I don't believe for a second that this is in fact how the mathematical universe actually operates, but it is a good explanation for why it is beyond the mathematical abilities of humans to distinguish between this definable universe and the real universe we live in.
This is a far stronger statement than I think even Platonists would accept. What examples of non-computable statements that are computed by humans do you have in mind?
Even putting on my Platonist hat (which I'll wear for the rest of this reply), I would still argue, in line with xyzzyz's comment, that at most humans deal with computable descriptions of non-computable things. For example, the description of the real numbers is computable even if the real numbers themselves are not. Likewise even if the real numbers are not computable, we can only ever work with computably-definable (indeed only finitely definable) real numbers rather than arbitrary real numbers.
To use the map-territory analogy, while the territory is the thing we care about, the only things we can work with, manipulate, and compute are computable maps.
For example Chaitin's Constant is a non-computable real number. However, we never work with Chaitin's Constant directly, but rather with our finite description of it, from which we deduce all sorts of other facts.
There are therefore many things about Chaitin's Constant we will never know. But that is the Platonist's lot in life.
As an aside, there's in fact a formalization of this that states that a mathematical universe consisting solely of finitely definable entities and nothing else is perfectly reconcilable with ZFC. See https://mathoverflow.net/questions/44102/is-the-analysis-as-...). Now as I continue to wear my Platonist hat I don't believe for a second that this is in fact how the mathematical universe actually operates, but it is a good explanation for why it is beyond the mathematical abilities of humans to distinguish between this definable universe and the real universe we live in.