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Hypothe(co-­‐Deduc(ve Method The general scien9ic method   Lars-­‐Göran Johansson   Department of Philosophy   Uppsala University   lars-­‐goran.johansson@filosofi.uu.se W.V.O. Quine (1908-­‐2000): ”We and other animals notice what goes on around us. This helps us by suggesting what we might expect and even how to prevent it, and thus fosters survival. However, the expedient works only imperfectly. There are surprises, and they are unsettling. How can we tell when we are right? We are faced with the problem of error.” . Richard Feynman: Richard Feynman:   There is always the possibility of proving any definite   If you approach every science article you read [well-­‐defined] theory wrong; but notice that we can never prove it right. Suppose that you invent a good guess, calculate the consequences, and discover every time that the consequences you have calculated agree with experiment. The theory is then right? No, it is simple not proved wrong. In the future you could compute a wider range of consequences, there could be a wider range of experiments, and you might then discover that the thing is wrong... We never are definitely right, we can only be sure we are wrong. thinking, "how do they really know this is true?", keeping in mind that there may (or may not!) be some assumed background knowledge you're missing, you'll learn to think like a scientist. 1
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Hypothe(co-­‐Deduc(ve Method Thesis: HDM is the least common denominator for all ac(vi(es that deserve the label ’science’ Francesco Redi (1668): ”I began to think that worms found in meat came from flies and not from rottening. I was convinced when observing that flies were flying around the meat before it was full of worms. Beliefs not corroborated by experiment are worthless. Therefore I put a dead snake, pieces of fish and a slice of veal in four big jars with wide openings, which I covered and sealed. Then I filled another four jars with the same stuff but left these open. Flies were repeatedly seen passing in and out in the open jars and the meat in those were full of worms. But the covered jars contained no worms, even though the meat was rotten. Hence, meat from dead animals cannot generate worms without egg from living creatures are put in it.” Structure of argument Con(nued   Hypothesis: Worms are spontaneously generated Auxiliary Assumption: Covering a jar with waxed paper does not affect the self generating process. in rottening meat.   Empirical Consequence: If rottening meat is kept in a covered jar, worms will be seen in the jar after some time. If H, then E E false _________ H false If (H and A), then E E false _________ H or A false 2
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Con(nued E. Durkheim:De la Suicide (1900) ”Since the air could not circulate in the covered jars, I performed a new experiment in order to exclude all doubts. I put meat and fish in a beaker which I covered with gauze. In order to further protect it from flies I put the beaker in a cage of gauze. I saw no worms in the meat, in spite of many worms outside the cage and flies all the time landed on the cage and put their worms there.”   H: The incidence of suicide is higher in societies with a lower degree of integration than in those with a higher degree.   A1:Catholic societies are more integrated than protestant ones,if other aspects are similar.   A2: Swiss cantons are socially similar, except form of religion   E:Catholic cantons have a lower suicide incidence than protestant ones. Claude Bernard (1813-­‐ 1878) Observa(ons  Type of society: suicide/miljon inh.  Catholic cantons  Mixed  Protestant cantons 86,7 212,0 326,3   Found that the following generalisations hold:   Carnivores have acid and clear urine   Herbivores have alkaline and muddy urine   But   A number of newly arrived rabbits had acid and clear urine!   Hypothesis needed! 3
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Tes(ng of hypothesis H: Hypothesis: They had been starving and thereby metabolised their own meat. E1: Giving the rabbits grass will result in normal alkalic urine E2: Dissection will show that the rabbits have metabolised their own meat E3: If horses starve they too will get acid and clear urine Hypothe(co-­‐Deduc(ve Method   Formulate a hypothesis   Deduce empirical consquences from the hypothesis and auxiliary assumptions.   Compare these consequences with empirical data   Form a conclusion: is the hypothesis falsified or supported by evidence? If H & T, then E1, E2 and E3. ‘E1’, ‘E2’ and ‘E3’ are true. ____________________________ H is supported! General theory of relativity
Laws:
1. E=mc2
2. E=hf
________________
m=hf/c2
the
sun
In words: A photon with frequency f has a mass,
albeit very small!
It will be attracted by the sun!
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General conclusions: 1.One can never give a conclusive proof for an empirical hypothesis 2: One can never by purely logical means decide which of the hypotheses, auxiliary assumptions or observation reports are false, if one have an inconsistency.(Duhem-­‐
Quine-­‐thesis) Defini(ons Hypothesis =def A statement such that i)  we are not convinced about its truth ii)  ii) we use it as premise in a deduction of empirical consequences. Empirical Consequence =def.A statement such that i) follows from the hypothesis and auxiliary assumptions ii) under appropriate conditions can be decided by observations. Auxiliary assumption =def. A statement such that i) it is necessary for deducing an empirical consequence from a hypothesis ii) it is in the given situation not tested but taken to be true. Ad hoc-­‐hypothesis Ad hoc-­‐hypothesis = def.   An assumption which is introduced solely for the purpose of saving an othervise refuted theory, and   It does not simplify the theory or enables any new predictions. 5
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Complete eclipse Ringformed eclipse Baye’s theorem H0 = ’zero’ hypothesis H = test hypothesis U= outcome of test P(H /U ) =
P(H )P(U / H)
P(H )P(U / H ) + P(H 0 )P(U / H 0 )
Sta(s(cal tes(ng: Neyman-­‐Pearson method   We would like to know the probability of a hypothesis, conditional on the evidence,, i.e. P(H|E)!   Without strong assumptions that cannot be calculated!   But we can calculate the probability for the outcome of an experiment, conditional on a hypothesis, P(U|
H), which is called likelihood.   P(U|H)+P(U|H0)=1 6
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Sta(s(cal tes(ng of a hypothesis  Formulate a hypothesis H. Medical treatment tes(ng (simplified example)   Select a sample On of size n.   Decide the significance level. (usually 0.05, 0,01 or 0,001)   Calculate the probability that, if H is true, a random sample of size n disagrees with H.   If this probability is not greater than the significance level, reject H. Calcula(on of likelihood   In how many ways can we sort 7 black (=alive) and 11 white (dead) balls in two sets each containing 9? ( 23540)   How many of these ways are such that 6 black and 3 white is in the first set (treated)? (385)   The fraction of these numbers (≈0,016) is the probability for the observed distribution, provided that the colours have nothing to do with the distribution, i.e., the distribution was purely random.   P(U|H0)=0,016 hence P(U|H)=0,984   From this one cannot calculate P(H|U)! Alive Dead Total Treated 6 3 9 Not Treated 1 8 9 W.V.O. Quine: “The totality of our so-­‐called knowledge or beliefs, from the most casual matters of geography and history to the profound laws of atomic physics or even of pure mathematics and logic is a man-­‐made fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experiences. A conflict with experience at the periphery occasions readjustments in the interior of the field. Truth values have to be redistributed over some of our statements. 7
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Cont. Cont. Reevaluation of some statements entails reevaluation of others because of the logical interconnections. …..But the total field is so underdetermined by its boundary conditions, experience, that there is much latitude of choice as to what statements to reevaluate in the light of any single contrary experience. No particular experience are linked with any particular statements in the interior of the field, except indirectly through considerations of equilibrium affecting the field as a whole.” ”The total field is so underdetermined by its boundary conditions, experience, that there is much latitude of choice as to what statements to reevaluate in the light of any single contrary experience. No particular experiences are linked with any particular statements in the interior of the field, except indirectly through considerations of equilibrium affecting the field as a whole." 8