In philosophy of math, we often present platonicism and formalism as the two only and opposite views about the meaning of truth. I think that there is (at least) a third one, that we could call "modelism".
Platonicism: There is an absolute mathematical truth, independant of us, which is not a human construction. CH is true or false.
Formalism: There are plenty of logical systems, none of which is better than the others, and between which you can choose arbitrarily. Truth only exists relatively to a logical system. A sentence which is independant of the system you choosed has no fixed truth value.
Modelism: Mathematics are a model for reality. As a model, they are a human construct, therefore there is no absolute trruth. But our logical system is not arbitrary and is guided by what we want to model. Good axioms are those which are well-fitted to what we want to --
-- represent, and this can guide our choices on what we want to consider as true.
Of course, "modelism" is closer to formalism since it does not consider truth as absolute but as dependant of choices we make. But for me it is not exactly the same: there is, in it, the idea that not all systems are equally valuable, and that our choices depend on something --
-- that is independant of us (that is, the real world); an idea that resonates with something in platonicism.
I often present myself as a formalist, and I thought for long that I was a pure one, but I'm actually more somewhere inbetween formalism and "modelism". In the sense that mathematics were, at first, thought for modelling reality, but that their subsequent formalisation allowed --
-- them to become autonomous from it; hence we now can choose our working logical systems arbitrarily and have fun with all of them, without needing to think about reality.
You can follow @NdeRancourt.
Tip: mention @twtextapp on a Twitter thread with the keyword “unroll” to get a link to it.

Latest Threads Unrolled:

By continuing to use the site, you are consenting to the use of cookies as explained in our Cookie Policy to improve your experience.