Milo Schield Conceptual Literacy Project
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1 July 2010 Induction Seminar 1 July 2010 Induction Seminar 2 Induction in Science Milo Schield Conceptual Literacy Project Summer Seminar Chicago Illinois RIF July 24, 2010 wwwstatlitorg/pdf/2010schield1seminar6uppdf Induction versus Deduction Philosophy: Induction and deduction are two distinct methods of reasoning: Deduction: From general to particular All swans are white, thus my swan is white Induction: From particular to general, from observed to unobserved, from present to future All swans I ve seen are white So, all swans are white July 2010 Induction Seminar 3 Inductions in Deductive Reasoning All valid deductions involve a generalization a universal as a premise AI-A Valid: All men are mortal; Socrates is a man Thus, Socrates is mortal OI-I Valid: No men are immortal; Socrates is a man Thus Socrates is not immortal II-I Invalid: Some men are tall; some tall things have four legs So, some men have four legs July 2010 Induction Seminar 4 Deduction may be Valid but Unsound 1 All men are immortal 2 Socrates is a man 3 Thus, Socrates is immortal The universal is false so the argument is unsound 1 All men are mortal 2 Socrates is a man 3 Socrates is [will be, must be] mortal Q How can we tell if a universal is true? July 2010 Induction Seminar 5 Induction versus Deduction If a deduction is valid then the truth of the premises guarantees (is sufficient for) the truth of the conclusion In cases of inductive reasoning, it is possible for the conclusion to be false even though the premises are true [because the premises are not universals] July 2010 Induction Seminar 6 Problem of Induction Wikipedia the philosophical question of whether inductive reasoning leads to knowledge That is, what is the justification for either: generalizing about the properties of a class of objects based on some number of observations of particular instances of that class? [All swans are white] presupposing that a sequence of events in the future will occur as it always has in the past? For example, for presupposing that the laws of physics will hold as they have always been observed to hold Hume called this the Principle of Uniformity of Nature 2010Schield1SummerSeminar6uppdf 1
2 July 2010 Induction Seminar 7 Critiques of Induction: Pyrrhonian skeptic Sextus Empiricus first questioned the validity of inductive reasoning David Hume: In general, it is not necessary that causal relation in the future resemble causal relations in the past, as it is always conceivable otherwise Hume was actually advocating a practical skepticism based on common sense, wherein the inevitability of induction is accepted Someone who insists on reason for certainty might, for instance, starve to death, as they would not infer the benefits of food based on previous observations of nutrition Wikipedia July 2010 Induction Seminar 8 Induction: Modern Philosophy Is-ought dilemma (the fact-value dilemma): Arguing that something is good based on related observable facts The naturalistic fallacy: Arguing that something is good based on related natural properties Problem of Induction in Ethics: No amount of factual particulars are sufficient to guarantee the truth of an evaluative universal July 2010 Induction Seminar 9 3 Induction: Success in Physics Success in Astronomy: The Big Four 1, 2 Johannes Kepler 3 4 Let s review their achievements July 2010 Induction Seminar 10 Induction in Science: 1 (Denmark) Aristotle: 1 Heavens are immutable 2 Earth is center of the heavens (Nova Man): Star appears; heavens change 2 All planets revolve around sun 3 Moon and sun revolve around earth July 2010 Induction Seminar 11 (Denmark) July 2010 Induction Seminar 12 Sven Island, Sweden 2010Schield1SummerSeminar6uppdf 2
3 July 2010 Induction Seminar 13 Sven Island, Sweden July 2010 Induction Seminar 14 Uraniborg: Dedicated to Urania Museum Ship dock July 2010 Induction Seminar 15 Stjerneborg: Castle of the Stars Underground observatory: Measurement accuracy: sec 1 part in 700 2,100 July 2010 Induction Seminar 16 Induction in Science 2 Johannes Kepler Aristotle: 1 Heavenly bodies move in circles 2 Earth is the center of the heavens Ptolemy: 1 Some circular orbits have epicycles Kepler: 1 All orbiting bodies have elliptical orbits 2 Earth revolves around the sun July 2010 Induction Seminar 17 July 2010 Induction Seminar 18 Kepler Statue at Linz Kepler at Prague 2010Schield1SummerSeminar6uppdf 3
4 July 2010 Induction Seminar 19 Prague, Czech Republic July 2010 Induction Seminar 20 Prague: Kepler Museum in Kepler s Home: Karlova 4 July 2010 Induction Seminar 21 Induction in Science 3 Galilei Aristotle: 1 Heavier bodies fall faster 2 Natural state of things is rest : 1 Every body s fall is independent of weight 2 All bodies in motion stay in motion 3 Every pendulum s period is independent of angle and varies with the square of the length July 2010 Induction Seminar 22 Florence July 2010 Induction Seminar 23 Florence Museum Newly opened July 2010 Induction Seminar 24 Describing Falling Motion Downtown Florence 2010Schield1SummerSeminar6uppdf 4
5 July 2010 Induction Seminar 25 Comparing Falling Motions July 2010 Induction Seminar 26 s Telescope A small piece of glass July 2010 Induction Seminar 27 Correcting Jupiter moon data with analog Parallax Computer July 2010 Induction Seminar 28 Induction in Science: 4 was born in 1642 in Lincolnshire, England His genius soon became obvious and an uncle declared it would be wrong 'to bury so extraordinary a talent in rustic business' In 1661 left Lincolnshire to continue his studies at Cambridge However, in 1665 and 1666 he was forced to return to Woolsthorpe to escape the plague It was at Woolsthorpe Manor that formulated three great discoveries - the principle of differential calculus, the composition of white light and the law of gravitation He later observed, 'In the two plague years I was in the prime of my age for invention and minded mathematics and philosophy more than at any time since' July 2010 Induction Seminar 29 Grantham England July 2010 Induction Seminar 30 : Lived near Nottingham in Lincolnshire Nottingham Grantham Woolsthorpe Cambridge London 2010Schield1SummerSeminar6uppdf 5
6 July 2010 Induction Seminar 31 Woolsthorpe in Lincolnshire July 2010 Induction Seminar 32 Woolsthorpe in Lincolnshire Woolsthorpe Manor B6403 Nottingham Grantham A1 Woolsthorpe July 2010 Induction Seminar 33 Law of Gravity Thesis: Force of gravity ~ m / R 2 Proof (for circular orbits): 1 Kepler s Third Law: R 3 ~ T 2 2 Circular acceleration: F = m*a = m (v 2 /R) A v = Circumference / period = 2 П R / T B Fgravity = m [2 П R / T] 2 / R = m R [2 П/T] 2 C Fgravity ~ m R [2 П] 2 / R 3 D Fgravity ~ m / R 2 QED July 2010 Induction Seminar 34 Induction in Science: Birth of the Social Sciences Economics, psychology, sociology, etc Differences in subject matter Empirically-based (scientific) Similar in their use of statistics (statistical inference) to validate generalizations Advantage: Scientific Problems: Limited scope: Unable to make relevant statements about the human condition July 2010 Induction Seminar 35 Philosophy of Science: 20 th Century Conclusion Very weak evidence in support of induction Definitions are man-made (socially constructed) Definitions are arbitrary Posited laws that fit the data (curve fitting) Scientists no longer speak of laws Einstein s theory of relativity is not a law Darwin s theory of evolution is not a law July 2010 Induction Seminar 36 Web references Museum on Swen/Ven [ museet, Hven, Landsvägen, Landskrona, Sweden]: Brahe_Museum_on_Venpdf Kepler Museum in Prague: Museum in Florence: Project: Schield1SummerSeminar6uppdf 6
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