I do not want to poison this forum with politics. But I want to understand, precisely, what is meant by the bolded statement. It is made by a physicist who used to work at Harvard regarding the relationship between pure math and physics.
A physics-oriented question appears at the end of Chapter 3: Are we
really talking about continuous objects themselves or about finite
sequences of symbols that talk about continuum?That's a good question and I am inclined to say the latter. If we talk
about specific things, these specific things are always countable
because they must be describable by a finite sequence of symbols. Even
when we talk about intervals of real numbers that arguably contain an
uncountably infinite number of real numbers, we must still specify the
endpoints of the interval by a finite sequence of words or symbols –
and such sequences are "discrete" i.e. "countable".This is why I tend to consider the very fact that real numbers are
uncountable to be nothing else than a linguistic curiosity: the
actual, well-defined real numbers you may ever encounter form a
countable set! This is why the uncountability of the real numbers –
and the whole discipline of maths based on this formally provable
claim and similar claims – doesn't have implications for "talking
about physics".
Here is the link to the full blog. If you want more context, I would suggest to start reading from the "Chapter 2 talks about sets, their elements…" part.
It appears he is talking about the symbols and notation we write down to describe the real numbers. But the bolded part is explicitly referring to the set of real numbers.
Best Answer
He's saying that the definable numbers are countable. In some sense we cannot talk directly about a real number that isn't definable. (However, we can still talk about the set of real numbers even without being able to talk about each of its elements individually.)
The quote seems to be advocating some form of finitism.