Does the disagreement, whatever it is, have any more impact on anything outside itself than semiotics does?
I can’t say how it compares to semiotics because I don’t know that field or its history.
If you’re just asking whether foundations-of-math questions have had any impact outside of themselves, then the answer is definitely Yes.
For example, arguments about the foundations of mathematics led to developments in logic and automated theorem proving. Gödel worked out his incompleteness theorems within the context of Russell and Whitehead’s Principia Mathematica. One of the main purposes of PM was to defend the logicist thesis that mathematical claims are just logical tautologies concerning purely logical concepts. Also, PM is the first major contribution that I know of to the study of Type Theory, which in turn is central in automated theorem proving.
Also, if you’re trying to assess whether you believe in the Tegmark IV multiverse, which says that everything is math, then what you think math is is probably going to play some part in that assessment. Maybe that is just a case of one pragmatically-pointless question’s bearing on another, but there it is.
It’s about numbers. Problem solved. :)
Does the disagreement, whatever it is, have any more impact on anything outside itself than semiotics does?
I can’t say how it compares to semiotics because I don’t know that field or its history.
If you’re just asking whether foundations-of-math questions have had any impact outside of themselves, then the answer is definitely Yes.
For example, arguments about the foundations of mathematics led to developments in logic and automated theorem proving. Gödel worked out his incompleteness theorems within the context of Russell and Whitehead’s Principia Mathematica. One of the main purposes of PM was to defend the logicist thesis that mathematical claims are just logical tautologies concerning purely logical concepts. Also, PM is the first major contribution that I know of to the study of Type Theory, which in turn is central in automated theorem proving.
Also, if you’re trying to assess whether you believe in the Tegmark IV multiverse, which says that everything is math, then what you think math is is probably going to play some part in that assessment. Maybe that is just a case of one pragmatically-pointless question’s bearing on another, but there it is.