I've partially answered this before, but not to my own satisfaction. I find the scholastic imagery of pure Philosophy to be superfluous, unneeded, unnecessary... worthless even. The terminology reeks of elitist self-adoration by man, IMHO, and the Bible has nothing positive to say about the subject.
I think you presented and answered your own question... presumably to your own satisfaction.
All people naturally pursue and embrace some form of what you would label "philosophy," - a love for that particular knowledge approximating wisdom of their chosen career, hobby or obsession, which I would define as being the natural result of being created (even though fallen) in God's image.
Most of us have the innate ability to reason, and to think logically, without submerging ourselves in multi semesters of "Philosophical Inquiry." If we did not, God would have informed us of that fact, in His writing to us.
This room has wall wide bookcases at each end. On the southern wall are five tiers of books on every manner of Physics, Mathematics and Sciences.
They belong to my son - many from his college years studying Biology, Environmental Science, then Soil and Plant Research, Atmospheric Science, Atmospheric Physics, etc., etc., I avoid them at all cost, preferring the opposite wall of books, reflecting my own interests.
I just took down a book titled "Elementary Differential Equations and Boundary Value Problems" - couldn't locate anything within it identifiable as Mathematical Philosophy?
Pythagorean theorem is the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle) - or, in familiar algebraic notation, a2 + b2 = c2.
Although the theorem has long been associated with Greek mathematician-philosopher Pythagoras (c.570â500/490 B.C.), it is actually far older. Four Babylonian tablets from circa 1900â1600 B.C., indicate some knowledge of the theorem, with a very accurate calculation of the square root of 2 (the length of the hypotenuse of a right triangle with the length of both legs equal to 1) and lists of special integers known as Pythagorean triples that satisfy it (e.g., 3, 4, and 5; 32 + 42 = 52, 9 + 16 = 25). The theorem is mentioned in the Baudhayana Sulba-sutra of India, which was written between 800 and 400 B.C.. Nevertheless, the theorem came to be credited to Pythagoras. It is also proposition number 47 from Book I of Euclidâs Elements.
According to the Syrian historian Iamblichus (c. 250â330 A.D.), Pythagoras was introduced to mathematics by Thales of Miletus and his pupil Anaximander. In any case, it is known that Pythagoras traveled to Egypt about 535 B.C., to further his study, was captured during an invasion in 525 B.C. by Cambyses II of Persia and taken to Babylon, and may possibly have visited India before returning to the Mediterranean.
Pythagoras soon settled in Croton (now Crotone, Italy) and set up a school, or in modern terms a monastery (see Pythagoreanism), where all members took strict vows of secrecy, and all new mathematical results for several centuries were attributed to his name. Thus, not only is the first proof of the theorem not known, there is also some doubt that Pythagoras himself actually proved the theorem that bears his name. Some scholars suggest that the first proof was the one shown in the figure. It was probably independently discovered in several different cultures.
Book I of the Elements ends with Euclidâs famous âwindmillâ proof of the Pythagorean theorem. Later in Book VI of the Elements, Euclid delivers an even easier demonstration using the proposition that the areas of similar triangles are proportionate to the squares of their corresponding sides. Apparently, Euclid invented the windmill proof so that he could place the Pythagorean theorem as the capstone to Book I. He had not yet demonstrated (as he would in Book V) that line lengths can be manipulated in proportions as if they were commensurable numbers (integers or ratios of integers).
A great many different proofs and extensions of the Pythagorean theorem have been invented. Taking extensions first, Euclid himself showed in a theorem praised in antiquity that any symmetrical regular figures drawn on the sides of a right triangle satisfy the Pythagorean relationship: the figure drawn on the hypotenuse has an area equal to the sum of the areas of the figures drawn on the legs. The semicircles that define Hippocrates of Chiosâs lunes are examples of such an extension.
In the Nine Chapters on the Mathematical Procedures (or Nine Chapters), compiled in the 1st century A.D. in China, several problems are given, along with their solutions, that involve finding the length of one of the sides of a right triangle when given the other two sides. In the Commentary of Liu Hui, from the 3rd century, Liu Hui offered a proof of the Pythagorean theorem that called for cutting up the squares on the legs of the right triangle and rearranging them (âtangram styleâ) to correspond to the square on the hypotenuse.
Pythagorean theorem has fascinated people for nearly 4,000 years; there are now more than 300 different proofs, including ones by the Greek mathematician Pappus of Alexandria (flourished c. 320 A.D.), the Arab mathematician-physician ThÄbit ibn Qurrah (c. 836â901), the Italian artist-inventor Leonardo da Vinci (1452â1519), and even U.S. Pres. James Garfield (1831â81).
Similarly traceable are many of the flashes of wisdom attributed to the Greek Socratic threesome.
manning5 wrote:
Zemirah, do you not see that the two things, scripture and philosophy are complementary? That study of the one leads to answers in the other? And vice versa? In my view they merge, of course, with the scripture dominant as it should be. Properly construed, philosophy is a framework for relating the wisdom of the Bible to our daily lives, versus what we observe all around us.
Then too, it is quite obvious that not all people with a philosophical bent are atheists. By far the majority are not. I suppose it is all in the way you look at it and apply it in the context of a Christian worldview.
Put another way, the essence of faith is from the Bible, and while it is quite encompassing, the Bible does not cover 100% of the knowledge and wisdom we need to learn and use in this life.
This is quite easily demonstrated, don't you think? Some demonstrations are very clear to me: the Standard Model of Particle Physics; The General Theory of Relativity, Quantum Mechanics, even Neuton's Laws. and the Philosophy of Science that establishes them, all have early hints from the Bible that they exist and are true. Chuck Misler showed us that very nicely.
Zemirah, do you not see that the two things, scrip... (
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