Really tiny, part 2

Great minds think alike! Bertrand Russell:

But at last Weierstrass discovered that the infinitesimal was not needed at all, and that everything could be accomplished without it. Thus there was no longer any need to suppose that there was such a thing.

And myself, just yesterday:

This is what makes Cauchy's idea so revolutionary -- he did not need to define "infinitesimal" in order to deal with the infinitesimal...

Anyway, now that the philosopher and I agree, let's get back to the original post that led to all this confusion. If I may be so bold as to paraphrase, Barsenas wished that Bishop Berkeley had succeeded in his attack against Newton's calculus. Barsenas has also made it clear that he is staunchly anti-science.

Unfortunately for Barsenas, Newton's calculus is one of the great triumphs of science. Newton made repeatable observations about the motion of the planets and moons, and developed mathematics to quantify his observations. As holes were found in his mathematics, other mathematicians and scientists used pure mathematical logic to fully develop Newton's theories. Indeed, mathematics is built on such rigor that a certain math professor of mine once offered an A to anyone who could find a logical contradiction in the course material, or in mathematics in general. (To my knowledge, no one ever found such a contradiction.)

I would like to thank Bishop Berkeley for inspiring many generations of mathematicians to build their developments on pure mathematical logic, for it actually strengthens mathematics, and thus science in general. And when science succeeds, history shows that human understanding and the overall quality of life improve.