If you specify that decimal numbers, 0, and negative numbers don't count, no more definition would be needed.
My chair is not a decimal number, zero, or a negative number, but I suspect it's not what you meant by "standard number".
Hence my referring to "1, 2, 3 etc". Yes this appeals to a little bit of human intuition, but so do all definitions- even a theoretical world in which absolutely everything was defined in terms of other definitions would be useless if a human did not have conceptions of what some of the words meant using intuitive associations.
This gets rid of all ambiguity as to standard numbers.
I'm not sure about this, but presenting it anyway for scrutiny.
I was thinking that it doesn't matter if a concept is undefined, or even cannot be defined, if hypothetically speaking said concept can exist without any ambiguity within it then it is still a tenable concept. The implications, if this is true, would be that it would knock down Quine's argument against the analytic-synthetic distinction.
Your thoughts, Lesswrong?