Deductively, a->b->c... means b, c... are TRUE. The issue is how do we know "a" is true? i) Revelation, though the bible... ii) authority, Oprah... iii) induction, specific to the general ie length vs temp graph, points plotted (premises)=> specific, and best fit straight line made (conclusion for ALL "a" s)=> general iv) from the mind eg. even though there were insufficient data points (taken from Brahe) for J. Kepler to deduce that the path of the planets, he neverless surmised correctly they were ellipses.
Lastly, pi theory, 25/8 Babylonian, 256/81 Egyptian, 339/108 Indian... each succession closer to the real value of pi, is analogous to pursuing "a" (JH Lambert proved pi is irrational), as we get closer ratio's to pi, we get clearer truths (better predictability, explanations and control of nature) of what pi is but we will never find an absolute ratio b/c it does not exist. PS pi is described as the ratio circumference/diameter BUT is irrational with integers, seems funny to me
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