I think Physicist is taking what is known as the "intuitionist" position. Loosely, intuitionists regard mathematical concepts as truths rather than as the consequences of logical or formal derivations.
Most mathematicians (and scientists, whether they know it or not) are "formalists." There is no such thing as mathematical truth. There are only theorems derived from a fundamental set of axioms -- we are free to use whatever axioms we want so long as they are consistent. One set of axioms may lead to a theorem that is demonstrably false using another set. Engineers and physicists simply pick axiom sets allowing them to describe their observations, but, fundamentally, all sets are equally valid.
Turns out that, if you take a rigorously intuitionist approach, it's pretty tough to impossible to come up with most of calculus . You can find some interesting links by searching on "axiom of choice," "Godel's Theorem," and "Lowenstein-Skolem Theorem."
Most mathematicians (and scientists, whether they know it or not) are "formalists." There is no such thing as mathematical truth. There are only theorems derived from a fundamental set of axioms -- we are free to use whatever axioms we want so long as they are consistent. One set of axioms may lead to a theorem that is demonstrably false using another set. Engineers and physicists simply pick axiom sets allowing them to describe their observations, but, fundamentally, all sets are equally valid.
Thanks. Your explanation makes sense to me.