OK, but the variable name and mapping something to something is not the point here, as that is not a choice of a natural number.
It assumes that you can even computationally determine that there is ANY possible choice of concrete natural number for X.
That is not true. It is logically true that it could be there is not a possible choice of X, and you can choose for example to say it is equal to any of the variables A,B,C,D,AA,AB,AC,AAAAB,ABBBAABA,… or any other number of variables. It could also be meta variables, like meta variable [A] that can be assigned a variable for example AAAAB, or AAAAB. If I assign it the variable AA, [A]=AA, I now know I am talking about AA, which is a natural number of the set of natural numbers.
That did not get me close to actually choosing a natural number and defining X to be that natural number. Physically we could just be creating more variables, without actually defining X to be anything. That is logically perfectly valid, but does not really address the question posed in any way.
There is no computational choice of X, so what you are saying here is a variable. The question is what the variable 1 you are talking about here is. It could mean the pixels on the screen (the symbol 1 as it appears on my or your screen), it could in principle mean a variable symbolized by 1 that can take the value of a natural number.
It could also mean the natural number one, but based on what you said, that would just be my interpretation.
Based on what you said, it is not clear what definition you operate based on.
I am not talking about interpretations here. Well I am, evidently, but here we leave bivalent logic for sure.
There are always many many interpretations for anything. That is another rabbit hole to go down to. Very interesting for sure, but it doesn’t get us any closer to the semantic and epistemological question the post poses. Which is, what is X?
I can just define it to be a natural number 1, but that is not a computation, but a definition, as I define it as such.
OK, but the variable name and mapping something to something is not the point here, as that is not a choice of a natural number.
It assumes that you can even computationally determine that there is ANY possible choice of concrete natural number for X.
That is not true. It is logically true that it could be there is not a possible choice of X, and you can choose for example to say it is equal to any of the variables A,B,C,D,AA,AB,AC,AAAAB,ABBBAABA,… or any other number of variables. It could also be meta variables, like meta variable [A] that can be assigned a variable for example AAAAB, or AAAAB. If I assign it the variable AA, [A]=AA, I now know I am talking about AA, which is a natural number of the set of natural numbers.
That did not get me close to actually choosing a natural number and defining X to be that natural number. Physically we could just be creating more variables, without actually defining X to be anything. That is logically perfectly valid, but does not really address the question posed in any way.
There is no computational choice of X, so what you are saying here is a variable. The question is what the variable 1 you are talking about here is. It could mean the pixels on the screen (the symbol 1 as it appears on my or your screen), it could in principle mean a variable symbolized by 1 that can take the value of a natural number.
It could also mean the natural number one, but based on what you said, that would just be my interpretation.
Based on what you said, it is not clear what definition you operate based on.
I am not talking about interpretations here. Well I am, evidently, but here we leave bivalent logic for sure.
There are always many many interpretations for anything. That is another rabbit hole to go down to. Very interesting for sure, but it doesn’t get us any closer to the semantic and epistemological question the post poses. Which is, what is X?
I can just define it to be a natural number 1, but that is not a computation, but a definition, as I define it as such.