"Purity"
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I don't know, I always thought of math as another branch of philosophy, not a scientific application of it. Philosophy entails logic, which after all is all that math is.
ReplyDeleteMr. Cool, you may wish to revise your graphic. The Angelic Doctor of the Church may object to your gradations of science. I recommend reading the first page of the Summa Theologica:
ReplyDeleteSumma Theologica, Primma Pars, Questions 1:
Article 1. Whether, besides philosophy, any further doctrine is required?
Article 2. Whether sacred doctrine is a science?
Article 3. Whether sacred doctrine is one science?
Article 4. Whether sacred doctrine is a practical science?
Article 5. Whether sacred doctrine is nobler than other sciences?
Article 6. Whether this doctrine is the same as wisdom?
Article 7. Whether God is the object of this science?
Article 8. Whether sacred doctrine is a matter of argument?
Second, it is generally accepted that the only "perfect" science is one that predicates everything from first principles, and includes all the "middle terms" in the syllogistic reasoning to prove a something about the end terms.
ReplyDeleteTo this definition, the first perfect science composed would be Euclid's "Elements". Which starts with first principles and concludes with proving the 5 perfect solids and that there can be no more than the 5.
The second work that attempts to be a near-perfect science is the Summa, however, there are two or three questions within the Summa (if I remember properly) which can not be proved through human reasoning, but are taken on faith.
Other sciences use a "scientific method" but are far from proving anything based on reasoning of first principals (deductive reasoning), in fact, most are "sciences" that work from inductive reasoning, which is from what you experience and attempting to "reason" to what the causes may be.
Deductive is more pure than inductive reasoning.
The lowest of the sciences would probably sit squarely on those that were PURELY inductive, "the empiricists": Locke, Berkley and Hume. They go so far to say that things exist only so far as they are being perceived... which is silly. But then again, Descartes, while a brilliant mathematician, believed his own existence was caused by his own reasoning, "I think, therefore I am".... also silly.
However, he did supposedly solve the "four locus line" problem, and never wrote it down since he thought it would be better if his readers figured it out for themselves. (which I can't recall if anyone ever did)