Lecture 7Lecture 7Hypothetical Deductive Hypothetical Deductive

MethodMethodWANG HuapingWANG Huaping

Philosophy Department, Shandong UniversityPhilosophy Department, Shandong University

ContentsContents

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

The The hypothetico-deductive model hypothetico-deductive model is commonly is commonly described as having five stages: observation, described as having five stages: observation, hypothesis, prediction, verification, and conclusion. hypothesis, prediction, verification, and conclusion.

1. Observation: A possible pattern or relationship is 1. Observation: A possible pattern or relationship is noticed in a set of prior observations. noticed in a set of prior observations.

2. Hypothesis: Based on insight, prior knowledge, and 2. Hypothesis: Based on insight, prior knowledge, and inductive generalization, it is hypothesized that the inductive generalization, it is hypothesized that the pattern is not an artifact of the particular set of pattern is not an artifact of the particular set of observations but one that should be found in any observations but one that should be found in any similar set of observations. The hypothesis may merely similar set of observations. The hypothesis may merely assert that the pattern is real (scientific law) or it may assert that the pattern is real (scientific law) or it may go further and offer an explanation about why the go further and offer an explanation about why the pattern exists (scientific theory).pattern exists (scientific theory).

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

4. Corroboration: New observations are made in 4. Corroboration: New observations are made in accordance with the op erations specified and accordance with the op erations specified and compared to the predictions. In some sciences the compared to the predictions. In some sciences the operation is a controlled experiment. In other sciences operation is a controlled experiment. In other sciences it is an ob servational study.it is an ob servational study.

5. Conclusion: An inference about the truth or falsity of 5. Conclusion: An inference about the truth or falsity of the hypothesis is made based on the degree to which the hypothesis is made based on the degree to which the observations conform to the prediction. This stage the observations conform to the prediction. This stage involves statistical inference methods such as involves statistical inference methods such as confidence intervals and hypothesis tests.confidence intervals and hypothesis tests.

A hypothesis A hypothesis hh is well-corroborated if and is well-corroborated if and only if:only if: hh entails all/most of the relevant available entails all/most of the relevant available

observable evidence;observable evidence; hh does not entail anything contradicting the does not entail anything contradicting the

available observable evidence, i.e., is not available observable evidence, i.e., is not falsified; andfalsified; and

hh is highly falsifiable, i.e., is highly falsifiable, i.e., hh’s observable ’s observable consequences were highly unexpected when consequences were highly unexpected when first first h h was first conjectured.was first conjectured.

Initial observationInitial observation

New observationsNew observations

Prediction A

hypothesis

Do new observations match

predictions?“Accepted

truth”

suggests

NO, falsify hypothesis

YES, repeat attempts to falsify

hypothesis hypothesis hypothesis

Prediction B Prediction CPrediction D

Multiple failed falsifications

HD reasoning could be useful in everyday life. HD reasoning could be useful in everyday life. Here is an example:Here is an example:

1.Suppose your portable music player fails to switch 1.Suppose your portable music player fails to switch on. You might consider the hypothesis that on. You might consider the hypothesis that perhaps the batteries are dead. You decide to test perhaps the batteries are dead. You decide to test whether this is true.whether this is true.

2.Given this hypothesis, you predict that the music 2.Given this hypothesis, you predict that the music player should work properly if you replace the player should work properly if you replace the batteries with new ones. batteries with new ones.

3. You proceed to replace the batteries, which is the 3. You proceed to replace the batteries, which is the “experiment” for testing the prediction.“experiment” for testing the prediction.

4. If the player works again, then your hypothesis is 4. If the player works again, then your hypothesis is confirmed, and you throw away the old batteries. confirmed, and you throw away the old batteries. If the player still does not work, the prediction was If the player still does not work, the prediction was false, and the hypothesis is disconfirmed. You false, and the hypothesis is disconfirmed. You might reject your original hypothesis and come up might reject your original hypothesis and come up with an alternative one to test, such as the with an alternative one to test, such as the batteries are fine but your music player is broken.batteries are fine but your music player is broken.

Hypothesis: Centripetal acceleration = velocityHypothesis: Centripetal acceleration = velocity22 / / radius (radius (a = a = ωω22rr))

Deducing consequences from hypothesis:Deducing consequences from hypothesis: If this hypothesis is correct, then the larger the radius of If this hypothesis is correct, then the larger the radius of

the circle traveled, the larger the centripetal acceleration.the circle traveled, the larger the centripetal acceleration.

Since the earth is a sphere, there are different sized radii Since the earth is a sphere, there are different sized radii an object travels.an object travels.

Thus, gravitational acceleration will be lowest at the Thus, gravitational acceleration will be lowest at the equator, the largest circle an object can travel on the equator, the largest circle an object can travel on the surface of Earth.surface of Earth.

Testing the consequencesTesting the consequences Cayenne experiment: Jean Richer (1630–Cayenne experiment: Jean Richer (1630–

1696), a French astronomer, measured the 1696), a French astronomer, measured the length of a seconds pendulum at Cayenne, length of a seconds pendulum at Cayenne, that is a pendulum with a half-swing of one that is a pendulum with a half-swing of one second, and found it to be 1.25 lignes (2.8 second, and found it to be 1.25 lignes (2.8 millimeters) shorter than at Paris.millimeters) shorter than at Paris.

Repeat Repeat ad nauseumad nauseum for all available evidence for all available evidence Conclude that the hypothesis Conclude that the hypothesis a = a = ωω22rr is well- is well-

supported/confirmed/justifiedsupported/confirmed/justified

If light is indeed a wave, we expect If light is indeed a wave, we expect that it will show the phenomenon of that it will show the phenomenon of interference. A beam of light is shot interference. A beam of light is shot at an opaque plate that has twoat an opaque plate that has two

Yong designed the following Yong designed the following experiment: A beam of light is shot experiment: A beam of light is shot at an opaque plate that has two at an opaque plate that has two open slits in it. Behind the plate, open slits in it. Behind the plate, there is a white screen where the there is a white screen where the light that passes through the slits is light that passes through the slits is recorded.recorded.

Figure 1: The setup of Young's famous double slit experiment

If light is indeed a wave, we expect that wave If light is indeed a wave, we expect that wave fronts emerge from each slit, propagate in fronts emerge from each slit, propagate in concentric circles, interfere with each other and concentric circles, interfere with each other and yield an interference pattern that is characteristic yield an interference pattern that is characteristic of a wave. Indeed, when both slits are open, we of a wave. Indeed, when both slits are open, we see such an interference pattern { a pattern of see such an interference pattern { a pattern of alternating light and dark bands on the screen alternating light and dark bands on the screen (see figure 1). (see figure 1).

Background assumptions and the hypothesis Background assumptions and the hypothesis under test work together to yield predictions that, if under test work together to yield predictions that, if vindicated, confirm the wave nature of light.vindicated, confirm the wave nature of light.

Einstein’s postulate was confirmed experimentally Einstein’s postulate was confirmed experimentally by Robert Millikan and Arthur Compton over the by Robert Millikan and Arthur Compton over the next two decades. Thus it became apparent that next two decades. Thus it became apparent that light has both wave-like and particle-like properties. light has both wave-like and particle-like properties. De Broglie, in his 1924 PhD thesis sought to expand De Broglie, in his 1924 PhD thesis sought to expand this wave-particle duality to all particles:this wave-particle duality to all particles:

When I conceived the first basic ideas of wave When I conceived the first basic ideas of wave mechanics in 1923-24, I was guided by the aim to mechanics in 1923-24, I was guided by the aim to perform a real physical synthesis, valid for all perform a real physical synthesis, valid for all particles, of the coexistence of the wave and of the particles, of the coexistence of the wave and of the corpuscular aspects that Einstein had introduced for corpuscular aspects that Einstein had introduced for photons in his theory of light quanta in 1905.photons in his theory of light quanta in 1905.

Einstein’s postulate was confirmed experimentally Einstein’s postulate was confirmed experimentally by Robert Millikan and Arthur Compton over the by Robert Millikan and Arthur Compton over the next two decades. Thus it became apparent that next two decades. Thus it became apparent that light has both wave-like and particle-like properties. light has both wave-like and particle-like properties. De Broglie, in his 1924 PhD thesis sought to expand De Broglie, in his 1924 PhD thesis sought to expand this wave-particle duality to all particles:this wave-particle duality to all particles:

When I conceived the first basic ideas of wave When I conceived the first basic ideas of wave mechanics in 1923-24, I was guided by the aim to mechanics in 1923-24, I was guided by the aim to perform a real physical synthesis, valid for all perform a real physical synthesis, valid for all particles, of the coexistence of the wave and of the particles, of the coexistence of the wave and of the corpuscular aspects that Einstein had introduced for corpuscular aspects that Einstein had introduced for photons in his theory of light quanta in 1905.photons in his theory of light quanta in 1905.

Elementary particlesElementary particles

In 1927 at Bell Labs, Clinton Davisson and Lester In 1927 at Bell Labs, Clinton Davisson and Lester Germer fired slow-moving electrons at a crystalline Germer fired slow-moving electrons at a crystalline nickel target. The angular dependence of the nickel target. The angular dependence of the reflected electron intensity was measured, and was reflected electron intensity was measured, and was determined to have the same diffraction pattern as determined to have the same diffraction pattern as those predicted by Bragg for x-rays.those predicted by Bragg for x-rays.

Just as the photoelectric effect demonstrated the Just as the photoelectric effect demonstrated the particle nature of light, the Davisson-Germer particle nature of light, the Davisson-Germer experiment showed the wave-nature of matter, and experiment showed the wave-nature of matter, and completed the theory of wave-particle duality. completed the theory of wave-particle duality.

Neutral atomsNeutral atoms Experiments with Fresnel diffraction and specular Experiments with Fresnel diffraction and specular

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

Waves of moleculesWaves of molecules Recent experiments even confirm the relations for Recent experiments even confirm the relations for

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

Spatial Zeno effectSpatial Zeno effect

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

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

This observation raises an interesting question: This observation raises an interesting question: Why do the red blood cells appear smaller? Why do the red blood cells appear smaller? Here are two possible explanations:Here are two possible explanations:

1. Salt ions (Na+ and Cl-) push on the cell 1. Salt ions (Na+ and Cl-) push on the cell membranes and make the cells appear smaller.membranes and make the cells appear smaller.

2. Water molecules are attracted to the salt ions 2. Water molecules are attracted to the salt ions so the water molecules move out of the cells and so the water molecules move out of the cells and leave the cells smaller.leave the cells smaller.

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

A. the bag loses weightA. the bag loses weightB. the bag weighs the sameB. the bag weighs the sameC. the bag appears smallerC. the bag appears smaller

What result of the experiment would best show What result of the experiment would best show

that explanation II is probably wrong?that explanation II is probably wrong?

A. the bag loses weightA. the bag loses weight

B. the bag weighs the sameB. the bag weighs the same

C. the bag appears smallerC. the bag appears smaller

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

This observation raises an interesting question: Why This observation raises an interesting question: Why does the water rush up into the glass?does the water rush up into the glass?

Here is a possible explanation. The flame converts Here is a possible explanation. The flame converts oxygen into carbon dioxide. Because oxygen does not oxygen into carbon dioxide. Because oxygen does not dissolve rapidly into water but carbon dioxide does, the dissolve rapidly into water but carbon dioxide does, the newly-formed carbon dioxide dissolves rapidly into the newly-formed carbon dioxide dissolves rapidly into the water, lowering the air pressure inside the glass.water, lowering the air pressure inside the glass.

Suppose you have the materials mentioned above plus Suppose you have the materials mentioned above plus some matches and some dry ice (dry ice is frozen some matches and some dry ice (dry ice is frozen carbon dioxide). Using some or all of the materials, carbon dioxide). Using some or all of the materials, how could you test this possible explanation?how could you test this possible explanation?

1. Saturate the water with carbon dioxide and redo 1. Saturate the water with carbon dioxide and redo the experiment noting the amount of water rise.the experiment noting the amount of water rise.

2. The water rises because oxygen is consumed, so 2. The water rises because oxygen is consumed, so redo the experiment in exactly the same way to redo the experiment in exactly the same way to show water rise due to oxygen loss.show water rise due to oxygen loss.

3. Conduct a controlled experiment varying only the 3. Conduct a controlled experiment varying only the number of candles to see if that makes a difference.number of candles to see if that makes a difference.

4. Fill the glass with carbon dioxide, then turn it 4. Fill the glass with carbon dioxide, then turn it upside down and place it in the water.upside down and place it in the water.

What result of your test (mentioned in the What result of your test (mentioned in the previous question) would show that your previous question) would show that your explanation is probably right?explanation is probably right?

1. The water rises the same as it did before.1. The water rises the same as it did before.

2. The water rises less than it did before.2. The water rises less than it did before.

3. The water rises more than it did before.3. The water rises more than it did before.

UnderdeterminationUnderdetermination

One criterion for choosing two empirically One criterion for choosing two empirically equivalent hypotheses: choose the more equivalent hypotheses: choose the more falsifiable hypothesis.falsifiable hypothesis.HDM favors hypotheses that:HDM favors hypotheses that:

are simpler in one sense (e.g., are simpler in one sense (e.g., exceptionless laws)exceptionless laws)

tend to have more predictive and tend to have more predictive and explanatory powerexplanatory power

tend to be make more precise predictionstend to be make more precise predictions

Corroboration is not truthCorroboration is not truth

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

Disagreement need not be falsityDisagreement need not be falsity

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

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