Confirmation, Falsification, and Fallibility

Transcription

1 Confirmation, Falsification, and Fallibility Phil 12: Logic and Decision Making Winter 2010 UC San Diego 1/15/

2 Review Key feature of scientific reasoning: confirming or falsifying hypotheses based on the truth or falsity of predictions Goal: sound arguments for confirmation and falsification - valid + true premises Simple model of falsifying a hypothesis: If the hypothesis is true, then the prediction is true. The prediction is not true. The hypothesis is not true. 2 2

3 The case of parallax Copernicus heliocentric theory of the solar system predicts parallax But no one observed parallax for centuries. Does this falsify the heliocentric theory? Not necessary. A mistaken auxiliary assumption could be to blame - mistaken auxiliary assumption about distance from earth to planets/stars 3 3

4 The case of parallax Modified auxiliary assumption (large distance to planets/ stars) helps yield new prediction of very small parallax Still couldn t detect parallax. Does this mean heliocentric theory is false? Not necessarily. The observational/experimental procedure might be to blame 4 4

5 Difficulty in observing parallax Failure to observe parallax due to inadequacies of observational/experimental procedure Parallax finally detected in

6 Lesson of the parallax case Heliocentric theory predicts parallax But failure to observe parallax didn t necessarily falsity heliocentric theory Other factors at play in generating a prediction: - auxiliary assumptions - observational/experimental procedure If the earth is revolving around the sun and if all other auxiliary assumptions are true and the experimental procedure is adequate, then parallax should be observed. Parallax is not observed. Either the earth is not revolving around the sun or one of the other assumptions is false or the experimental procedure is inadequate. 6 6

7 How to handle false predictions If the hypothesis is true AND all auxiliary hypotheses needed to make the prediction are true AND the experimental setup is adequate, then the prediction will be true The prediction is not true Either the hypothesis is false, an auxiliary hypothesis is false, or the experimental setup is not adequate. Challenge: When to reject one of the auxiliary hypotheses or the experiment, and when to reject the main hypothesis? 7 7

8 Clicker question 1 What form of inference is being used in this argument? If Galen s theory is right, people need to replenish the stuff of blood from food and drink People do not eat or drink enough to replenish the stuff of blood Galen s theory is wrong A. Modus ponens B. Affirming the consequent C. Modus tollens D. Denying the antecedent 8 8

9 Clicker question 2 If you disagree with the conclusion of this argument, what strategy should you take? If Copernicus heliocentric theory is right, then parallax should be observed. Parallax is not observed Copernicus heliocentric theory is wrong. A. Simply assert that Copernicus could not be wrong B. Question the correctness of the first premise C. Suspect that scientists are lying about not seeing parallax D. Suspect that scientists need better telescopes in order to observe parallax 9 9

10 Clicker question 3 What is an auxiliary assumption? A. An alternative hypothesis to the one being tested B. An additional hypothesis required to derive a prediction from the main hypothesis being tested C. A hypothesis that should be rejected if possible D. A hypothesis which has not yet been adequately confirmed and so requires more testing 10 10

11 The challenge of confirmation A seemingly obvious model for confirming hypotheses: If the hypothesis is true, then the prediction is true. The prediction is true. The hypothesis is true. But there is a serious problem with this argument

12 Clicker question 4 What is the problem with the following simple argument for confirmation? If the hypothesis is true, then the prediction is true The prediction is true The hypothesis is true. A. The second premise is false B. It is valid because it an instance of modus tollens C. It is invalid because it is an instance of modus ponens D. It is invalid because it is an instance of affirming the consequent 12 12

13 The challenge of confirmation What seems to be the obvious way to confirm hypotheses faces a serious problem: If the hypothesis is true, then the prediction is true The prediction is true The hypothesis is true. This is the form affirming the consequent, and is invalid We can also see what is intuitively wrong with it - Make up a theory (a really bad one) from which you predict that sunlight feels warm. - Check the prediction. Sure enough, it is true - That doesn t make your bad theory true 13 13

14 Using a prediction not otherwise expected to be true Focus not on any prediction of a theory, but a prediction that, if one did not accept the hypothesis, one would not expect to be true That is, one connected to the hypothesis in the following conditional: If the hypothesis were not true, then the prediction would not be true Now you can invoke the valid argument form modus tollens in the confirmation: If the hypothesis were not true, then the prediction would not be true The prediction is true The hypothesis is true 14 14

15 Problem of Alternative Hypotheses If the hypothesis were not true, then the prediction would not be true The prediction is true The hypothesis is true This argument is valid, but is it sound? - we have to be sure that the first premise is true Problem: typically there will be alternative hypotheses (some slight variants of the one under consideration) that make the same prediction 15 15

16 Refining the Argument for Confirmation If the hypothesis were not approximately true and there is not a plausible alternative hypothesis that is true, then this prediction would be very unlikely to be true The prediction is true The hypothesis is approximately true or a plausible alternative hypothesis is true If there are no plausible alternatives, then we can conclude our hypothesis is approximately true - But what if an alternative is discovered next month? 16 16

17 Harvey s Alternative Hypothesis Rejecting Galen s hypothesis, Harvey proposed that: - - there is only one kind of blood that it circulates out from the heart in the arteries and returns to the heart in the veins 17 17

18 Harvey s proposal Since all things, both argument and ocular demonstration, show that the blood passes through the lungs and heart by the force of the ventricles, and is sent for distribution to all parts of the body, where it makes its way into the veins and porosities of the flesh, and then flows by the veins from the circumference on every side to the centre, from the lesser to the greater veins, and is by them finally discharged into the vena cava and right auricle of the heart, and this in such a quantity or in such a flux and reflux thither by the arteries, hither by the veins, as cannot possibly be supplied by the ingesta, and is much greater than can be required for mere purposes of nutrition; it is absolutely necessary to conclude that the blood in the animal body is impelled in a circle, and is in a state of ceaseless motion. - Harvey (1628) On the movement of the heart and blood in animals 18 18

19 How to secure positive evidence? Harvey could not see the connecting capillaries - would be positive evidence for his theory What kind of prediction could he make on the basis of his hypothesis that would be specific to it (i.e., not expected on other grounds)? - What would happen if Harvey is right and you permit blood to flow through arteries in your arm but not through the veins? Harvey predicted and demonstrated swelling of the limbs 19 19

20 Harvey s circulation experiments By bandaging the upper arm (Fig.1), the veins swell up. The vein s valves then show up as lumps (G,O,H). By pressing a finger along the vein (Fig. 2 and 3) from one valve to the next in the direction away from the heart (from O to H), the section of the vein between the valves is emptied of blood. It will stay empty. This is because valve O will not allow blood flow away from the heart

21 Resistance and slow acceptance in the olden days patients were healed without the knowledge of the circulation, and that therefore, this doctrine, even if true, would be useless. (James Primrose, 1630) "If Harvey's idea of the circulation was correct, there would be many concoctions of the blood, an unlikely phenomenon, especially if one upheld the philosophical principal that in nature, simplicity and perfection remain inviolate." (Caspar Hofmann, 1636) Descartes (1637) accepted circulation, but proposed that heart was a furnace that heated the blood 21 21

22 Confirming a mental rotation hypothesis Hypothesis: People use mental images and operate on them in problem solving Prediction: If asked whether two rotated figures match, response times will vary with degree of rotation. If an image is not being rotated, reaction times should not correspond to degree of rotation Reaction times do correspond to degree of rotation An image is being rotated mentally 22 22

23 Kosslyn on mental scanning Subjects memorize this map with landmarks such as a hut, a swamp, and a well. With the map gone, subjects were asked to: Imagine the map Focus on one object (e.g., the well), imagine a speck there Then move the speck in a straight line to a second object (e.g., the tree), and press button once there 23 23

24 Kosslyn on mental scanning 2.1 The time it took Kosslyn s subjects to perform the scan corresponded to the distance on the map 1.9 8,.7 tu z LU o: DISTANCE (cm.) If subjects were not mentally scanning and moving the speck in their mental map, reaction times would not correspond to distances between objects. Reaction times do correspond to distances between objects. Subjects are mentally scanning and moving the speck in their mental map

25 Bruner & Goodman (1947) Traditional view: perceiving is independent of one s beliefs and relies on what is there to be seen Bruner & Goodman s hypothesis: Perception is affected by one s beliefs Prediction: judgments of the size of a cardboard circle are quite accurate, but judgments of the size of a coin is affected by its value 25 25

26 Bruner & Goodman s results - 1 Size of coins significantly overestimated Up through quarter, overestimate larger for larger valued coins Further prediction: poor children will overestimate more than rich 26 26

27 Bruner & Goodman s results - 2 Poor children did overestimate the sizes of coins more than rich children Rfch 10-yr. dds Poor lo-yr olds If value did not influence perception, then there should be no overestimates of coin sizes. There are overestimates of coin sizes. Value does influence perception Fio. 2. SIZE ESTIMATIONS OF COINS MADE BY WELL-TO-DO AND POOR TEN-YEAR-OLDJ (Method of average error) 27 27

28 Evaluating Hypotheses: The Simple and the Subtle In principle the logical evaluation of a hypothesis given evidence is simple: - If a hypothesis predicts something not otherwise expected, we tend to think it is true - If a hypothesis makes a false prediction, that counts against its truth But most interesting hypotheses in science both make new, unexpected predictions that turn out to be true and make predictions that turn out to be false No simple recipe for deciding whether to reject a hypothesis once it has made a false prediction or to hold onto it because of its record of true predictions 28 28

29 Fallibility Issues in science are seldom resolved by decisive experiments that once and for all falsify or confirm a hypothesis Hypotheses often take a long period to become established - And once established, a long period is often required to overthrow them All judgments in science are fallible subject to revision with more evidence Yet, making the best judgment about our hypotheses is important 29 29