Don't they get tired from pretending?
>undergrads and high schoolers pretend that ZFC refers to something, and so since it's provable within ZFC that some set exists and is unique, the reals are supposedly well-defined
>no matter that more than 50 years ago set theorists showed that provided ZFC refers to something (i.e. there's a model of ZFC) then there are infinitely many different models which all satisfy the axioms and in which the supposed reals have radically different properties (e.g. cardinality could be aleph_1 or aleph_23123133 or aleph_w_w_w_3)
>no one has demonstrated that ZFC refers to anything, or that ZFC is even consistent
>no one has specified which of the infinitely many different models they mean when they talk about the reals
>even though such choices have consequences in day-to-day mathematics with the reals (see Shelah's proof of independence of the Whitehead problem).
>we're supposed to be alright with this situation and still accept the reals as a precise mathematical concept
>given the shitty situation with the reals the only tenable position is the false notion that it's all just axioms and all mathematics is meaningless (a dogma which can only be repeated by people who have never actually tried to implement the mathematics on a computer or work out arithmetic examples by hand to see its empirical content)
When can mathematicians expect to recover from this mass delusion? Or is it just dishonesty rather than delusion? Either way the situation is very embarrassing for the mathematical community. Mathematicians have no right to brag about how rigorous they are when they've rejected the firm foundation of natural number arithmetic for the flimsy sand castle of infinitist la-la-land of Cantorian pretend-symbol-combinations-refer-to-something.
>undergrads and high schoolers pretend that ZFC refers to something, and so since it's provable within ZFC that some set exists and is unique, the reals are supposedly well-defined
>no matter that more than 50 years ago set theorists showed that provided ZFC refers to something (i.e. there's a model of ZFC) then there are infinitely many different models which all satisfy the axioms and in which the supposed reals have radically different properties (e.g. cardinality could be aleph_1 or aleph_23123133 or aleph_w_w_w_3)
>no one has demonstrated that ZFC refers to anything, or that ZFC is even consistent
>no one has specified which of the infinitely many different models they mean when they talk about the reals
>even though such choices have consequences in day-to-day mathematics with the reals (see Shelah's proof of independence of the Whitehead problem).
>we're supposed to be alright with this situation and still accept the reals as a precise mathematical concept
>given the shitty situation with the reals the only tenable position is the false notion that it's all just axioms and all mathematics is meaningless (a dogma which can only be repeated by people who have never actually tried to implement the mathematics on a computer or work out arithmetic examples by hand to see its empirical content)
When can mathematicians expect to recover from this mass delusion? Or is it just dishonesty rather than delusion? Either way the situation is very embarrassing for the mathematical community. Mathematicians have no right to brag about how rigorous they are when they've rejected the firm foundation of natural number arithmetic for the flimsy sand castle of infinitist la-la-land of Cantorian pretend-symbol-combinations-refer-to-something.
