> Well of course axioms historically have always been the mathematical > way. In their pursuit of a priori knowledge mathematicians routinely > resorted to axiomatic assumptions of truth. In my experience it is > only since the invention of arithmetic that mathematikers routinely > resorted to assumptions of truth with respect to definitions.
That makes you the mathematiker in my eyes.
Definitions to mathematicians are neutral as far as truth or falsehood are concerned, they are merely abbreviations. > > >> so we can > >> properly examine the basis of axiomatic assumptions regarding > >> definitions of things such as curves, straight lines, transcendental > >> numbers, angular momentum, and quantum effects on a sound unassuming > >> analytical foundation. > > > >Analysis cannot be done on an "unassuming foundation" as without some > >foundation of assumptions, there is nothing to work with . > > Well you know, Virgil, we've been over this before as I recall.
> Assumptions as a starting point are one thing and assumptions as > finishing points something else. We all start with assumptions. Some > of us demonstrate the truth of our assumptions; some of us don't.
Some of us realize that in mathematics we can never "demonstrate the truth of our assumptions" as without assumptions, a set of of axioms, as a basis, there is nothing to work with.
> >As "real scientists" are, by definition not mathematicians, at least to > >the extent that they are only "real scientists", Zick is implying the > >"real scientist" fallacy that no mathematics has any existence or > >validity outside of its scientific usage. > > Not sure I follow. The "real scientists" you refer to are empirics.
If you mean by that that they are concerned with the empirical world rather than the mental world of mathematics, that is what separates science from mathematicsc.
> Empirics are not real scientists. They're educated guessers. The real > scientists I refer to demonstrate the truth of their assumptions.
No one in science bothers with "demonstrating the truth of one's assumptions". Scientists only amass more and more evidence supporting their conclusions, once they have made them.