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No! But I am not going to re-explain it; I have already said precisely why the information content is different, in the comment to which you replied. I shall me

No! But I am not going to re-explain it; I have already said precisely why the information content is different, in the comment to which you replied. I shall merely quote it again. > It's pedagogically important to distinguish between genuinely new things that the reader is going to have to put some effort into rearchitecting their worldview around, versus things the reader already knows but might not have seen in this form before. Since it is common knowledge that nobody already knows what a "foo" is, but it is common knowledge that everyone already has a pretty uniform idea of what a "number" means in everyday life (really, how many ways are there you can count from 1 to 10), my assertion applies.

lisper 5y ago
> everyone already has a pretty uniform idea of what a "number" means in everyday life Well, that's true, but that common notion is wrong. So if that is what you are appealing to then you have different problems. For example, on the common notion of number, there is no number whose square is negative one. (And indeed mathematicians got hung up on that for centuries before they figure out that they were wrong!)
- Smaug123 5y ago
  Oh come now, it's not wrong. I shall quote the article. > # The natural numbers > Numbers are objects you build to act like the concept of a number. Here we begin to construct the natural number object. This is obviously referring to the natural numbers. It says so both before and after the statement you're talking about. There is no natural number whose square is negative one.
  - lisper 5y ago
    Let's not lose the plot here. I was critiquing a piece called "Math Foundations from Scratch". It's a little hard to tell whether it was intended to be pedagogical, targeted toward people who didn't already understand the foundations of math, or a sort of review or reference, targeted at those who did. But either way I think it fails, notwithstanding the fact that the specific flaw that I cited, a circular definition of the word "number", appeared in the context of a discussion of natural numbers. That's my opinion. I've explained at some length why I hold this opinion, but it's still just my opinion.

lisper 5y ago

> everyone already has a pretty uniform idea of what a "number" means in everyday life Well, that's true, but that common notion is wrong. So if that is what you are appealing to then you have different problems. For example, on the common notion of number, there is no number whose square is negative one. (And indeed mathematicians got hung up on that for centuries before they figure out that they were wrong!)

Smaug123 5y ago
Oh come now, it's not wrong. I shall quote the article. > # The natural numbers > Numbers are objects you build to act like the concept of a number. Here we begin to construct the natural number object. This is obviously referring to the natural numbers. It says so both before and after the statement you're talking about. There is no natural number whose square is negative one.
- lisper 5y ago
  Let's not lose the plot here. I was critiquing a piece called "Math Foundations from Scratch". It's a little hard to tell whether it was intended to be pedagogical, targeted toward people who didn't already understand the foundations of math, or a sort of review or reference, targeted at those who did. But either way I think it fails, notwithstanding the fact that the specific flaw that I cited, a circular definition of the word "number", appeared in the context of a discussion of natural numbers. That's my opinion. I've explained at some length why I hold this opinion, but it's still just my opinion.