Mizsó wrote:Tell me if I'm wrong, but in my opinion she isn't right, not even technically. Three is two plus one by definition, unless defined otherwise previously. One can't say a word not meaning what it usually means consensually, without declare it beforehand. (Sorry if I made some grammar mistake, english is not my native language.)

That's only sorfta right, though. Like, in an academic context it's usually okay to

not define commonly-used terms in a field, but "commonly-used" changes as soon as you get outside of that field. Not only do lots of communities studying related phenomena have a completely separate set of vocabulary for it depending on the traditions they came from, communities studying mostly unrelated stuff probably don't have any idea what the commonly-used terms in the other fields even are.

That's how you get stuff like the

medical researchers who invented calculus a few years back. They didn't even know that "trapezoid rule" referred to something in the mathematical field, let alone that it was well-understood and wouldn't require specific definition in a paper.

And that's among humans, who all live on the same planet and have means of communicating with one another. Why would we assume that the aliens in the thought experiment would even agree with us on using a base-10 system for counting? Which is the point -- numbers refer to something specific in order for math to work correctly (i.e., in a math system where sorf = 3,

and 2 < sorf < 3, then 0=1, 1=2, etc. and the math system we just defined prevents any useful logical inference) but

numerals can be defined arbitrarily.

Like, if sorf is to represent a specific number we could say there are sorf dots in an ellipsis ("...") and not break math, but we can't say that a colon (":")

also has sorf dots in it. (And if "sorf" means "less than what we'd call 4 in any other context" then we can't use it for counting.)

[quote="Mizsó"]Tell me if I'm wrong, but in my opinion she isn't right, not even technically. Three is two plus one by definition, [i]unless[/i] defined otherwise [i]previously[/i]. One can't say a word not meaning what it usually means consensually, without declare it beforehand. (Sorry if I made some grammar mistake, english is not my native language.)[/quote]

That's only sorfta right, though. Like, in an academic context it's usually okay to [i]not[/i] define commonly-used terms in a field, but "commonly-used" changes as soon as you get outside of that field. Not only do lots of communities studying related phenomena have a completely separate set of vocabulary for it depending on the traditions they came from, communities studying mostly unrelated stuff probably don't have any idea what the commonly-used terms in the other fields even are.

That's how you get stuff like the [url=https://fliptomato.wordpress.com/2007/03/19/medical-researcher-discovers-integration-gets-75-citations/]medical researchers who invented calculus a few years back[/url]. They didn't even know that "trapezoid rule" referred to something in the mathematical field, let alone that it was well-understood and wouldn't require specific definition in a paper.

And that's among humans, who all live on the same planet and have means of communicating with one another. Why would we assume that the aliens in the thought experiment would even agree with us on using a base-10 system for counting? Which is the point -- numbers refer to something specific in order for math to work correctly (i.e., in a math system where sorf = 3, [i]and[/i] 2 < sorf < 3, then 0=1, 1=2, etc. and the math system we just defined prevents any useful logical inference) but [i]numerals[/i] can be defined arbitrarily.

Like, if sorf is to represent a specific number we could say there are sorf dots in an ellipsis ("...") and not break math, but we can't say that a colon (":") [i]also[/i] has sorf dots in it. (And if "sorf" means "less than what we'd call 4 in any other context" then we can't use it for counting.)