Lecture 7
Hypothetical Deductive Method
WANG Huaping
Philosophy Department, Shandong University
Contents
 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.
 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).
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.
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.

 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.
Initial observation
suggests
hypothesis
Prediction A
hypothesis
hypothesis
Prediction B
Prediction C
New observations
NO, falsify
hypothesis
Do new
observations match
predictions?
hypothesis
Prediction D
YES, repeat
attempts to
falsify
Multiple
failed
falsifications
“Accepted
truth”
 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.
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.
 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.
 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 wellsupported/confirmed/justified
 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
 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.

 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.
 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.


 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.
 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.
 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.

 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.
 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.
 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.
 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
 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
 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).
 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?
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.
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.
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
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
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.
Thanks！