Lecture 7 Hypothetical Deductive Method

1. Lecture 7Hypothetical Deductive Method WANG Huaping Philosophy Department, Shandong University

2. Contents 1. Hypothetico-Deductive Model 2. Cases 3. Questions 4. Problems

3. Hypothetico-Deductive Model The hypothetico-deductive model or method is first so-named by William Whewell. According to it, scientific inquiry proceeds by formulating a hypothesis in a form that could conceivably be falsified by a test on observable data. A test that could and does run contrary to predictions of the hypothesis is taken as a falsification of the hypothesis. A test that could but does not run contrary to the hypothesis corroborates the theory. It is then proposed to compare the explanatory value of competing hypotheses by testing how stringently they are corroborated by their predictions.

4. Hypothetico-Deductive Model The hypothetico-deductive model is commonly described as having five stages: observation, hypothesis, prediction, verification, and conclusion. 1. Observation: A possible pattern or relationship is noticed in a set of prior observations. 2. Hypothesis: Based on insight, prior knowledge, and inductive generalization, it is hypothesized that the pattern is not an artifact of the particular set of observations but one that should be found in any similar set of observations. The hypothesis may merely assert that the pattern is real (scientific law) or it may go further and offer an explanation about why the pattern exists (scientific theory).

5. Hypothetico-Deductive Model 3. Prediction: A prediction is deduced from the hypothesis and embodied in a conditional proposition. The proposition’s antecedent clause is the hypothesis and its consequent clause is the prediction. The pre­diction tells us what should be observed in a new set of observations if the hypothesis is indeed true. For example: If the hypothesis is true, then X should be observed if operation O is performed. The set of outcomes defined by X makes clear which future observations would confirm the prediction and, more importantly, which future observa­tions would be in conflict with it.

6. Hypothetico-Deductive Model 4. Corroboration: New observations are made in accordance with the op­erations specified and compared to the predictions. In some sciences the operation is a controlled experiment. In other sciences it is an ob­servational study. 5. Conclusion: An inference about the truth or falsity of the hypothesis is made based on the degree to which the observations conform to the prediction. This stage involves statistical inference methods such as confidence intervals and hypothesis tests.

7. Two Concepts

8. Two Concepts • A hypothesis h is well-corroborated if and only if: • h entails all/most of the relevant available observable evidence; • h does not entail anything contradicting the available observable evidence, i.e., is not falsified; and • h is highly falsifiable, i.e., h’s observable consequences were highly unexpected when first h was first conjectured.

9. Prediction D Prediction A Prediction C Prediction B hypothesis hypothesis hypothesis hypothesis Do new observations match predictions? “Accepted truth” Multiple failed falsifications Hypothetico-Deductive Model Initial observation suggests YES, repeat attempts to falsify New observations NO, falsify hypothesis

10. Hypothetico-Deductive Model • HD reasoning could be useful in everyday life. Here is an example: 1.Suppose your portable music player fails to switch on. You might consider the hypothesis that perhaps the batteries are dead. You decide to test whether this is true. 2.Given this hypothesis, you predict that the music player should work properly if you replace the batteries with new ones.

11. Hypothetico-Deductive Model 3. You proceed to replace the batteries, which is the “experiment” for testing the prediction. 4. If the player works again, then your hypothesis is confirmed, and you throw away the old batteries. If the player still does not work, the prediction was false, and the hypothesis is disconfirmed. You might reject your original hypothesis and come up with an alternative one to test, such as the batteries are fine but your music player is broken.

12. Case 1: Newtonian illustration • Hypothesis: Centripetal acceleration = velocity2 / radius (a = ω2r) • Deducing consequences from hypothesis: • If this hypothesis is correct, then the larger the radius of the circle traveled, the larger the centripetal acceleration. • Since the earth is a sphere, there are different sized radii an object travels. • Thus, gravitational acceleration will be lowest at the equator, the largest circle an object can travel on the surface of Earth.

13. Case 1: Newtonian illustration • Testing the consequences • Cayenne experiment: Jean Richer (1630–1696), a French astronomer, measured the length of a seconds pendulum at Cayenne, that is a pendulum with a half-swing of one second, and found it to be 1.25 lignes (2.8 millimeters) shorter than at Paris. • Repeat ad nauseum for all available evidence • Conclude that the hypothesis a = ω2r is well-supported/confirmed/justified

14. Case2 Young’s Double-slit Experiment • If light is indeed a wave, we expect that it will show the phenomenon of interference. A beam of light is shot at an opaque plate that has two • Yong designed the following experiment: A beam of light is shot at an opaque plate that has two open slits in it. Behind the plate, there is a white screen where the light that passes through the slits is recorded. Figure 1: The setup of Young's famous double slit experiment

15. Case2 Young’s Double-slit Experiment • If light is indeed a wave, we expect that wave fronts emerge from each slit, propagate in concentric circles, interfere with each other and yield an interference pattern that is characteristic of a wave. Indeed, when both slits are open, we see such an interference pattern { a pattern of alternating light and dark bands on the screen (see figure 1). • Background assumptions and the hypothesis under test work together to yield predictions that, if vindicated, confirm the wave nature of light.

16. Case3 de Broglie Waves

17. Case3 de Broglie Waves • Einstein’s postulate was confirmed experimentally by Robert Millikan and Arthur Compton over the next two decades. Thus it became apparent that light has both wave-like and particle-like properties. De Broglie, in his 1924 PhD thesis sought to expand this wave-particle duality to all particles: When I conceived the first basic ideas of wave mechanics in 1923-24, I was guided by the aim to perform a real physical synthesis, valid for all particles, of the coexistence of the wave and of the corpuscular aspects that Einstein had introduced for photons in his theory of light quanta in 1905.

18. Case3 de Broglie Waves • Einstein’s postulate was confirmed experimentally by Robert Millikan and Arthur Compton over the next two decades. Thus it became apparent that light has both wave-like and particle-like properties. De Broglie, in his 1924 PhD thesis sought to expand this wave-particle duality to all particles: When I conceived the first basic ideas of wave mechanics in 1923-24, I was guided by the aim to perform a real physical synthesis, valid for all particles, of the coexistence of the wave and of the corpuscular aspects that Einstein had introduced for photons in his theory of light quanta in 1905.

19. Case3 de Broglie Waves

20. Case3 de Broglie Waves

21. Case3 de Broglie Waves • Elementary particles • In 1927 at Bell Labs, Clinton Davisson and Lester Germer fired slow-moving electrons at a crystalline nickel target. The angular dependence of the reflected electron intensity was measured, and was determined to have the same diffraction pattern as those predicted by Bragg for x-rays. • Just as the photoelectric effect demonstrated the particle nature of light, the Davisson-Germer experiment showed the wave-nature of matter, and completed the theory of wave-particle duality.

22. Case3 de Broglie Waves • Neutral atoms • Experiments with Fresnel diffraction and specular reflection of neutral atoms confirm the application of the de Broglie hypothesis to atoms. Advances in laser cooling have allowed cooling of neutral atoms down to nanokelvin temperatures. At these temperatures, the thermal de Broglie wavelengths come into the micrometre range. Using Bragg diffraction of atoms and a Ramsey interferometry technique, the de Broglie wavelength of cold sodium atoms was explicitly measured and found to be consistent with the temperature measured by a different method.

23. Case3 de Broglie Waves • Waves of molecules • Recent experiments even confirm the relations for molecules and even macromolecules, which are normally considered too large to undergo quantum mechanical effects. In 1999, a research team in Vienna demonstrated diffraction for molecules as large as fullerenes. The researchers calculated a De Broglie wavelength of the most probable C60 velocity as 2.5 pm. More recent experiments prove the quantum nature of molecules with a mass up to 6910 amu. In general, the De Broglie hypothesis is expected to apply to any well isolated object.

24. Case3 de Broglie Waves

25. Case3 de Broglie Waves • Spatial Zeno effect • In the system of coordinates related to the ridges, this phenomenon appears as a specular reflection of a particle from a ridged mirror, assuming the grazing incidence (small values of the grazing angle). Such a ridged mirror is universal; while we consider the idealized "absorption" of the de Broglie wave at the ridges, the reflectivity is determined by wavenumber k and does not depend on other properties of a particle.

26. Questions • A student put a drop of blood on a microscope slide and then looked at the blood under a microscope. As you can see in the diagram below, the magnified red blood cells look like little round balls. After adding a few drops of salt water to the drop of blood, the student noticed that the cells appeared to become smaller.

27. Questions • This observation raises an interesting question: Why do the red blood cells appear smaller? Here are two possible explanations: 1. Salt ions (Na+ and Cl-) push on the cell membranes and make the cells appear smaller. 2. Water molecules are attracted to the salt ions so the water molecules move out of the cells and leave the cells smaller.

28. Questions • To test these explanations, the student used some salt water, a very accurate weighing device, and some water-filled plastic bags, and assumed the plastic behaves just like red-blood-cell membranes. The experiment involved carefully weighing a water-filled bag in a salt solution for ten minutes and then reweighing the bag. What result of the experiment would best show that explanation I is probably wrong? A. the bag loses weight B. the bag weighs the same C. the bag appears smaller

29. Questions • What result of the experiment would best show that explanation II is probably wrong? A. the bag loses weight B. the bag weighs the same C. the bag appears smaller

30. Questions • The figure below shows a drinking glass and a burning birthday candle stuck in a small piece of clay standing in a pan of water. When the glass is turned upside down, put over the candle, and placed in the water, the candle quickly goes out and water rushes up into the glass (as shown on the right).

31. Questions • This observation raises an interesting question: Why does the water rush up into the glass? • Here is a possible explanation. The flame converts oxygen into carbon dioxide. Because oxygen does not dissolve rapidly into water but carbon dioxide does, the newly-formed carbon dioxide dissolves rapidly into the water, lowering the air pressure inside the glass. • Suppose you have the materials mentioned above plus some matches and some dry ice (dry ice is frozen carbon dioxide). Using some or all of the materials, how could you test this possible explanation?

32. Questions 1. Saturate the water with carbon dioxide and redo the experiment noting the amount of water rise. 2. The water rises because oxygen is consumed, so redo the experiment in exactly the same way to show water rise due to oxygen loss. 3. Conduct a controlled experiment varying only the number of candles to see if that makes a difference. 4. Fill the glass with carbon dioxide, then turn it upside down and place it in the water.

33. Questions What result of your test (mentioned in the previous question) would show that your explanation is probably right? 1. The water rises the same as it did before. 2. The water rises less than it did before. 3. The water rises more than it did before.

34. Problems 1# Underdetermination • One criterion for choosing two empirically equivalent hypotheses: choose the more falsifiable hypothesis. • HDM favors hypotheses that: • are simpler in one sense (e.g., exceptionless laws) • tend to have more predictive and explanatory power • tend to be make more precise predictions

35. Problems 2# Corroboration is not truth • In general, confirming the predictions of a theory increases the probability that a theory is correct. But in itself this does not prove conclusively that the theory is correct. • To see why this is the case, we might represent our reasoning as follows : If H then P P Therefore H

36. Problems 3# Disagreement need not be falsity • Very often a hypothesis generates a prediction only when given additional assumptions (auxiliary hypotheses). In such cases, when a prediction fails the theory might still be correct. • To see why this is the case, we might represent our reasoning as follows : If ( H and A ) then P. It is not the case that P. Therefore, it is not the case that H.

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