A famous (or infamous) and false dichotomy, like the one about character (whether inborn or made, whether nature or nurture counts for more in our lives.) The answer, clearly is both: knowledge is discovered AND invented.
Let's think about the history of mathematics, which begins with counting, the natural numbers (1,2,3 . . .),the invention of proper notation, the invention of the zero together with the rules for its use by Hindu mathematicians in the ninth century, the algorithms of basic arithmetic, and plane geometry which was perfected by the ancient Greeks and axiomatized by Euclid in the late fourth century BC. It may be that the phrase "natural numbers" begs the question i.e. assumes that which is to be proved. Still, the natural numbers would seem to deserve to be called 'natural': nature really does allow one to select groups or clusters of things each of which has the same cardinality. So we encounter various sets of stones, trees, ducks, deer, fishes etc. While the algorithms of arithmetic had to be invented they proved their usefulness (and therefore truth?) by making accurate calculations possible. And that is how it has gone with all the inventions of physicists and mathematicians.
The calculus was invented by Newton (and Leibniz) along with the laws of accelerated motion (f=ma) in order to generalize Kepler's laws of planetary motion. Using this mathematical tool, Newton's formula for the acceleration of an object in a gravitational field then followed logically from Kepler's laws.
Kepler was building on the work of the Danish astronomer Tycho Brahe, as well as Galileo and Copernicus. Almost two hundred years of astronomy and physics are summarized in Newton's equations.
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ReplyDeletei believe that knowledge is discovered based on the steps of scientific generalization which begins with observation, problem identification, hypothesis, data collection, data analysis etc. since there is no new thing under the sun, meaning that all knowledge is based on experience, study and discovery, it can be said that all scientific knowledge is an addition to already existing knowledge.for example, Daltons atomic theory and its modification.
ReplyDeleteThe pythagorean theorem could not have been discovered by experience alone nor could the value of pi. No one would ever have known that the class of prime numbers is infinite unless someone (Euclid) had proven that that in fact is the case. These proofs had to be invented by people who had the wit and imagination to ask the right questions. They were not sitting out there waiting for someone to stumble upon them, though they were true before there was anyone capable of thinking about such matters and they will remain true when no one capable of thinking about such matters exists.
ReplyDeleteThe numbers, 0, -1, and i (the square root of -1) provide further examples of what I am talking about. No one "discovered" them, exactly; mathematicians discovered that they already existed in the sense that these "numbers" were implicit in the mathematics they already knew; and that without making them explicit, mathematics would soon reach the end of the line.
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