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3 revisions | lynda8322343 at May 22, 2019 05:48 AM | |
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1Section 1. The Essence of Mathematics. It was Benjamin Peirce, whose son I boast myself, that in1870 first defined mathematics as "the science which grows necessary conclusions." This was a hard sayingat the time; but today, students of the philosophy of mathematics generally acknowledge its substantial correctness. The common definition among such people as ordinary schoolmasters still is that mathematics is the science of quantity. As this is inevitably understood in English, it seems to be a misunderstanding of a definition which may be very old*, the original meaning being that mathematics is the science of quantities, that is, of forms possessing quantity. We perceive that Euclid was aware that a large branch of geometry had nothing to do with measurements (unless as an aid in demonstration); and, therefore, a Greek geometer of his *From what is said by Proclus Diadochus A.D. 485 would mean that the Pythagoreans understood mathematics to be the answer to the two questions 'how many' and 'how much'? | 1Section 1. The Essence of Mathematics. It was Benjamin Peirce, whose son I boast myself, that in1870 first defined mathematics as "the science which grows necessary conclusions." This was a hard sayingat the time; but today, students of the philosophy of mathematics generally acknowledge its substantial correctness. The common definition among such people as ordinary schoolmasters still is that mathematics is the science of quantity. As this is inevitably understood in English, it seems to be a misunderstanding of a definition which may be very old*, the original meaning being that mathematics is the science of quantities, that is, of forms possessing quantity. We perceive that Euclid was aware that a large branch of geometry had nothing to do with measurements (unless as an aid in demonstration); and, therefore, a Greek geometer of his *From what is said by Proclus Diadochus D.A.D. 485 would mean that the Pythagoreans understood mathematics to be the answer to the two questions 'how many' and 'how much'? |