(I posted this on philosophy stackexchange as well. Let me know if it belongs there more than here.)
Is the success of classic mathematics in predicting the outcome of experiments in our physical world a valid argument for the consistency of classical mathematics? (that is math using LEM/DNE, completed infinity, etc.) We can use classical calculus/analysis or probability theory/measure theory to model the physical world. Then we can make a prediction of an experiment within that model and compare it to the physical outcome. And to my understanding, any inconsistency between the expected and actual outcomes have always been an insufficient model and never a result of the math itself being bad--for, with most experiments we can change the model to be more accurate.
Is it possible to recreate every mathematical model and prediction in constructive/intuitionistic math? If not, and there are some models that only hold in classical math, is the success of that model a good argument for classical mathematics? How strong is it? What are some counterpoints?