Wednesday, June 29, 2011

Foundations of Science and Mathematics



“If we consider, for instance, the concept of the electron and seek it’s meaning, we are led back to Faraday’s investigation of electrolysis, and to J.J. Thompson’s study of deflection of cathode rays acted upon by electric and magnetic fields. Faraday found that the weight of a metal deposited in electrolysis is proportional to the amount of electricity employed, and, in fact, that the amount of electricity required to deposit a given number of atoms of any metal is always the same or else a small whole-number multiple of the unit quantity. Since all chemical substances were regarded as consisting of atoms, he hypothesized that electricity was also atomic in character, that is, made up of discrete unit charges. This result depends, then, on the prior development of an atomic theory of matter, and on the prior development of means measuring quantity and intensity of electricity.” –- Curtis Wilson, Dean, St John’s College, Foundations of Science and Mathematics, 1960

The unearthing of presuppositions and buried meanings carries us back beyond Newton to the first deductive science of all, the science of geometry, which has its faraway origins in the everyday techniques of the surveyor and the carpenter….” –- Curtis Wilson, Dean, St John’s College, Foundations of Science and Mathematics, 1960

“… for the most part the best way to become acquainted with the methods of science is to read what great scientists themselves have to say about their discoveries – how they came to make them, how they interpreted them, and by what reasoning they arrived at their conclusions concerning them.” -- Mortimer J. Adler and Peter Wolff, Foundations of Science and Mathematics, 1960

“Falsity is not a problem in the mathematical works. The truths demonstrated by the ancients are still acknowledged to be true.” -- Mortimer J. Adler and Peter Wolff, polymaths, Foundations of Science and Mathematics, 1960

“The word itself [geometry], meaning ‘earth measurement,’ indicates the quite earthy and practical origin of the science in ancient Egypt and Babylonia.” – Mortimer J. Adler and Peter Wolff, polymaths, Foundations of Science and Mathematics, 1960

“The names of many ancient mathematicians and scientists are quite unfamiliar to most of us.” -- Mortimer J. Adler and Peter Wolff, polymaths, Foundations of Science and Mathematics, 1960

“We are inclined to think that, although the Greeks may have had keen mathematical insight, they entirely lacked knowledge of the structure of the physical world. We regard the science of physics as a modern development, dating back only to the 16th century. A cursory glance at Archimedes’ work on the equilibrium of centers of gravity of bodies should dispel this erroneous idea. Here is a work on theoretical physics, written in the 3rd century B.C. It deals with typical physical problems of weights, balances, and distances, and it demonstrates the solutions in much the same way as we do nowadays.” -- Mortimer J. Adler and Peter Wolff, polymaths, Foundations of Science and Mathematics, 1960

“Archimedes was not only a first rate scientist, but also a brilliant mathematician.” -- Mortimer J. Adler and Peter Wolff, Foundations of Science and Mathematics, 1960

“The motions of the heavenly bodies have played a prominent role in the thoughts and lives of men since the earliest known times.” –- Mortimer J. Adler and Peter Wolff, polymaths, Foundations of Science and Mathematics, 1960

1 comment:

Fungus FitzJuggler III said...

A valuable addition to the philosophy of hypothesis formation!

WE can only formulate what we already know. Combined with your other post on Sir Francis, it is clear that we prejudice formulation of more accurate hypothesis very frequently.

But experimental evidence quickly corrects errors. In sciences like astronomy, where experiment is absent, we can end up in a mire!