In the 'interesting number paradox' the smallest non-interesting number is chosen. By convention every ordered set has a smallest element which is arbitrarily chosen.
The logic is flawed for the main reason that partitioning sets in any non-objective manner and then drawing conclusions from that is folly, which is the point of such so-called paradoxes.
I tend to think of "interestingness" as a fuzzy property that is at or near 1 on the obviously interesting integers {0, 1, ...} and approaches 0 as N -> infinity. But that obviously doesn't alter the fact that "interestingness" is extremely subjective.
Another cool paradox is the one surrounding "the smallest positive integer that cannot be expressed using twenty or fewer English words".
Indeed. I never noticed how ambiguous it is until I took a class where I tried to teach a computer to understand it.
Yet somehow, we still communicate. I guess that says something interesting about our evolution.
On a related note, how many linguists does it take to change a broken light bulb? Two. One to decide what it should change into, and one to find out what kind of bulb emits broken light.
You mean it's interesting how irregular natural languages are, but those are the ones we use instead of well-defined ones? Yeah, I guess it is interesting. But then again, nature comes before science, right? (Well, not if you asked a string theorist.) We're trying to impose logical systems where they do not exist, like reliable computers built on top of unreliable transistors (or relays, or vacuum tubes, for that matter). Heck, we even mix countable and uncountable, continuity and discreteness. We count two rocks and therefore we think we can have exactly two meters of something.
Why can't we just be well-defined formal systems? :/
