Formalism in the Philosophy of Mathematics (2015)
plato.stanford.edu
Formalism in the Philosophy of Mathematics (2015)
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Re: Formalism in the Philosophy of Mathematics (2015)
#2The working mathematician is a Platonist on weekdays, a formalist on weekends. On weekdays, when doing mathematics, he’s a Platonist, convinced he’s dealing with an objective reality whose properties he’s trying to determine. On weekends, if challenged to give a philosophical account of this reality, it’s easiest to pretend he doesn’t believe in it. He plays formalist, and pretends mathematics is a meaningless game
Reuben Hersh
Re: Formalism in the Philosophy of Mathematics (2015)
#3"An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure" by J. Franklin.
Re: Formalism in the Philosophy of Mathematics (2015)
#4Let's not forget constructivism. https://plato.stanford.edu/entries/mathematics-constructive/
Re: Formalism in the Philosophy of Mathematics (2015)
#5Argh..too much jargon, had to stop reading..
Re: Formalism in the Philosophy of Mathematics (2015)
#6The working mathematician is a Platonist on weekdays, a formalist on weekends. On weekdays, when doing mathematics, he’s a Platonist, convinced he’s dealing with an objective reality whose properties he’s trying to determine. On weekends, if challenged to give a philosophical account of this reality, it’s easiest to pretend he doesn’t believe in it. He plays formalist, and pretends mathematics is a meaningless game R…
Frankly I think you could call a mathematician a fictionalist or meta-fictionalist since a proof can be construed as a narrative in the ZFC canon. I'd be willing to call a mathematician "someone who investigates the laws of fiction" for a while. In a sense, a contradiction means that a fiction can't be sustained, and mathematicians must be constantly on the lookout for contradictions.
Re: Formalism in the Philosophy of Mathematics (2015)
#7The working mathematician is a Platonist on weekdays, a formalist on weekends. On weekdays, when doing mathematics, he’s a Platonist, convinced he’s dealing with an objective reality whose properties he’s trying to determine. On weekends, if challenged to give a philosophical account of this reality, it’s easiest to pretend he doesn’t believe in it. He plays formalist, and pretends mathematics is a meaningless game R…
This seems paradox. Did he perhaps say that on a weekend?
Most paradoxes are actually solvable, so I take issue with this metamathematical dissonance. I'll take it as a humble admission of ignorance and a resolution to (syn-)tactfully avoid getting into philosophical (sem-)antics to, instead, teach the first ground truth of the fight club by example (don't talk about it, do it).
Re: Formalism in the Philosophy of Mathematics (2015)
#8Nice article, but too specialized and it can be a bit complicated to read it. So, if you need problems with understanding it, write me at https://handmadewritings.com and I will explain to you any tough moments!