(October 17, 2014 at 12:40 pm)ChadWooters Wrote:(October 17, 2014 at 12:34 pm)Chas Wrote: It is done all the time by mathematicians. Create some axioms, some rules of inference, and boom! new formal system with new theorems and new truths.All those do is place limits on what mathematical truths can be drawn from those specific limitations. They have no effect on mathematical truths as a whole.
There is no "mathematical truths as a whole". That is an incoherent concept.
There are only truths within formal systems.
Skepticism is not a position; it is an approach to claims.
Science is not a subject, but a method.
Science is not a subject, but a method.