I studied the philosophy of science at the post-graduate level, for two years, at The Catholic University of America. I chose CUA because they have an entire school of philosophy. Pretty impressive, eh? Except, most of the faculty there study St. Thomas, John Duns Scotus, and the existentialism of this Polish guy named Karl Wojtyla who repudiated pretty much everything he wrote once he became Pope John Paul II. I did get a chance to read Wittgenstein, Heidegger, Nietzsche (and Heidegger on Nietzsche, a kind of neo-Nazi love-fest), and had my studies of Karl Popper and Thomas Kuhn approved by the committee.
One of the classes I took was a seminar on Isaac Newton's Principia Mathematica, which was the basis for much of physics until Einstein, then Heisenberg, came along and upset the apple cart. We looked closely at several aspects of Newton's work, including several "lemmas", or computational conundrums that Newton claimed to have solved. One of those involved determining curvilinear motion, and is labeled Lemma III and reads as follows:
The same ultimate ratios are also ratios of equality, when the breadths, AB, BC, DC, etc., of the parallelograms are unequal, and are all diminished in finitum.
I suppose it is unfair to quote this directly without the accompanying diagram, in which Newton proposed using a series of parallelograms, corresponding to a two dimensional graph of the shape of any rectilinear curve. The proposal Newton was offering was that it was possible to approximate a computation of the angular motion using the sum of the areas of the various parallelograms. More important was his little insertion of in finitum. This was the opening that would lead, in a few years time, to his computational breakthrough with integral and differential calculus, which rely upon infinitesimals for more precise calculation.
One student taking that class took this particular ball and ran with it. In the class session, which should be familiar to any graduate and post-graduate student, in which our research papers were summarized and critiqued by fellow-students, one of my classmates wrote an entire paper on how this entire proposal was flawed because Aristotle, in both Physics and Metaphysics "proved" that an actual infinite set was impossible; to rely upon even a potentially infinite set of calculations, therefore, was to introduce an absurdity in to one's calculations. Thus, Newton was disproved (he actually said that). Rather than toss this entire proposal on the trash heap, the professor actually spent about fifteen minutes reviewing Aristotle and pointing out the wonderful ways my classmate had interpreted him.
During comments, I said that since Newton was right, the entire paper was bunk. I had Aristotle tossed in my face. I repeated that quoting Aristotle didn't matter; Newton was right, the calculations, and their later fruit in the calculus, were far more fruitful than Aristotelean musings on the impossibility of an infinite regress. I had Aristotle tossed in my face. I realized, somewhat surprisingly, that I was in the presence of someone who had no idea what they were talking about, and was far more concerned with showing off how he could quote Aristotle from memory than he was with actually discussing the fact that he was full of crap.
After pointing out that modern science kind of showed that Newton was right (actually, that isn't true, but it is true enough to be getting on with) and Aristotle was wrong, relying on Aristotle to prove Newton wrong was intellectually dishonest, I shut up.
To be fair to my professor, my paper on Newton's theory of gravity as an ad hoc addition, following Imre Lakatos' discussion of ad hoc additions in his essay, "On the Structure of Scientific Research Programmes", received an "A". When I read my proposal and my brief synopsis, however, there was little comment from my fellow classmates. No one seemed interested in the fact that Newton basically invented gravity in the same way modern scientists invented "dark matter" and "dark energy" to account for the fact that the census of elementary particles is falling about 90% short. This doesn't mean dark matter and energy do not exist; it merely means these are ad hoc additions to cosmology, to be filled in by further research. Newton was uncomfortable with his theory of gravity, even though he spent a good deal of time showing how its effects could be calculated. Gravity is action at a distance, and there was at the time no way on understanding the mechanisms behind gravity. There still isn't, which is why General Relativity and Quantum physics are, at a fundamental level, in contradiction. We don't know what gravity is, except as a property of elementary particles themselves. There aren't gravity particles, and no one (yet) has observed gravity waves. Yet it is very much real, and behaves in the ways Newton, Einstein, Heisenberg, Schrodinger, and others proposed it worked, even if the theories behind these actions cancel each other out.
I find this last fascinating, but is irrelevant to the central point here. A young man, obviously impressed with Aristotle's breadth of study and wealth of proposals, missed something important. He. Was. Wrong. I, too, am impressed not only by Aristotle, but Plato, Heidegger, St. Thomas, John Calvin, Thorstein Veblen, Karl Barth, Hegel, Marx, and many other thinkers I have read whom I find both brilliant and utterly wrong. i do not let myself miss the fact that being smart is no protection against being incorrect.