philosophy and the sciences - phil. sci. course

Inductive Logic
Deductive and Inductive Logic
What is Reasoning?
Example: The first theorem Euclid’s
Elements
provides a good example of the kind of
reasoning that people admire.
Suppose we construct a triangle in the following way: 1. Draw a circle centered at point A.
Mark a point B on the circumference and draw a line from A to B. Draw a second circle
centered at B that passed through A. Mark one of the points at which the circles intersect as B
and draw lines from C to A and from C to B.
Theorem: All the sides of the triangle ABC are of equal length.
Proof: Let |AB| denote the length of the line segments AB, and so on.
Step 1: |AB| = |AC| because they are radii of the circle centered at A.
Step 2: |BA| = |BC| because they are radii of the circle centered at B.
Step 3: |AB| = |BA| because AB and BA denote the same line.
Step 4: |AC| = |BC| because they are each equal to the same thing (viz. |AB| ).
Step 5: Therefore, |AB| = |AC| = |BC| by steps 1 and 4.
Definition: An
argument
is a list of statements, one of which is the conclusion and the rest of
which are the premises.
The
conclusion
states the point being argued for and the
premises
state the reasons being
advanced in support the conclusion. They may not be good reasons. There are good and bad
arguments.
Tip: To identify arguments look for words that introduce conclusions, like "therefore",
"consequently", "it follows that". These are called

conclusion indicators
. Also look for
premise
indicators
like "because" and "since".
Remark: Each of the five steps in the proof to Euclid’s first theorem is an argument. The
conclusions in steps 1 to 4 are called
intermediate
conclusions, while the conclusion in step 5
is the
main
conclusion.
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Inductive Logic
Question: All arguments, or sequences of arguments, are examples of reasoning, but is every
piece of reasoning an argument? A perceptual judgment such as "I see a blue square", or the
conclusions of scientific experts reading in X-rays, or looking through a microscope, may be
examples of reasoning that are not arguments. They are derived from what Kuhn called tacit
knowledge, acquired through training and experience (e.g., knowing how to ride a bicycle). It
is not easily articulated, and is not stated in any language.
The Difference between Good and Bad Arguments
In logic, we assume that any reasoning is represented as an argument, and the evaluation of
an argument involves two questions:
1. Are the premises true?
2. Supposing that the premises are true, what sort of support do they give the conclusion?
Answers to question 2: Compare the following arguments.
1. All planets move on ellipses. Pluto is a planet. Therefore, Pluto moves on an ellipse.
2. Mercury moves on an ellipse. Venus moves on an ellipse. Earth moves on an ellipse.
Mars moves on an ellipse. Jupiter moves on an ellipse. Saturn moves on an ellipse.
Uranus moves on an ellipse. Neptune moves on an ellipse. Therefore, Pluto moves on

an ellipse.
Definition: An argument is
deductively valid
if and only if it is
impossible
that its conclusion is
false while its premises are true.
Examples: Argument 1 is deductively valid, while argument 2 is not.
Remark on terminology: The notion of deductively validity is such a central and important
concept in philosophy, that is goes by several names. When an argument is deductively valid,
we say that the conclusion
follows from
the premises, or the conclusion
is deduced from
, or
i
nferred from
, or
proved from
the premises. Or we may say that the premises
imply
, or
entail
,
or
prove
the conclusion. We also talk of deductively valid arguments as being
demonstrative
.
All these different terms mean exactly the same thing, so the situation is far simpler than it

appears.
What’s possible? The sense of "impossible" needs clarification. Consider the example:
3. George is a human being. George is 100 years old. George has arthritis. Therefore, George
will not run a four-minute mile tomorrow.
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Inductive Logic
Suppose that the premises are true. In logic, it
is
possible that George will run a four-minute
mile tomorrow. It is not
physically
possible. But logicians have a far more liberal sense of what
is "possible" in mind in their definition of deductive validity. Argument 3 is not deductively
valid on their definition. So, argument 3 is invalid.
Key idea: In any deductively valid argument, there is a sense in which the conclusion is
contained
in premises. Deductive reasoning serves the purpose of
extracting
information from
the premises. In a non-deductive argument, the conclusion ‘goes beyond’ the premises.
Inferences in which the conclusion
amplifies
the premises is sometimes called
ampliative

inference.
Therefore, whether an argument is deductively valid or not, depends on what the premises
are.
‘Missing’ premises?: We can always add a premise to turn an invalid argument into a valid
argument. For example, if we add the premise "No 100-year-old human being with arthritis

will run a four-minute mile tomorrow" to argument 3, then the new argument is deductively
valid. (The original argument, of course, is still invalid).
Definition: An argument is
inductively strong
if and only if it is
improbable
that its conclusion
is false while its premises are true.
Remember: This definition is the same as the definition of "deductively valid" except that
"impossible" is replaced by "improbable."
The
degree
of strength of an inductive argument may be measured by the probability of that
the conclusion is true
given
that all the premises are true.
The probability of the conclusion of a deductively valid argument given the premises is one, so
deductively valid arguments may be thought of as the limiting case of a strong inductive
arguments. Ampliative arguments have an inductive strength less than one.
The probability of the conclusion given the premises can change from person to person, as it
depends on the stock of relevant knowledge possessed by a given person at a given time.
Summary: In response to question 2, we may give answers like "the argument is valid", "the
arguments is inductively strong" or "the argument is inductively weak."
Exercise: Discuss the following examples (all statements are understood to refer to the year
1998):
4. There are multi-celled organisms living on Mars. Therefore, there is intelligent life on
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Inductive Logic
Mars.
5. There are multi-celled organisms living on Mars. Therefore, there are single-celled

organisms living on Mars.
6. There are multi-celled organisms living in Lake Mendota. Therefore, there is
intelligent life living in Lake Mendota.
7. There are multi-celled organisms living in Lake Mendota. Therefore, there are single-
celled organisms living in Lake Mendota.
Nevertheless, in logic, it is assumed that the answer to question 1 is relevant to the evaluation
of an argument. But it is a question that needs to be asked
in addition
to question 2. So, if the
premises of an inductively strong argument are false, then logicians are forced to say that the
argument is not a good one. It is confusing to say that an inductively strong argument is a
weak argument, but this is how the terms are
defined
.
Tip: Defined terms must be used as defined. You can’t use the term differently just because
you don’t agree with the definition.
Different Kinds of Ampliative Argument
Definition: Any argument that is not deductively valid, or deductively invalid, is called an
ampliative argument.
The term refers to the fact that the conclusion of such argument goes
beyond, or amplifies upon, the premises.
Remark on terminology: Again the notion of ‘invalid’ is so common and central, that it goes
by many names. Other terms commonly used are inductive and non-demonstrative. I prefer
‘ampliative’ because it reminds us that the conclusion ‘goes beyond’ the premises, and it does
not have the bad reputation that sometimes goes along with the word ‘induction.’
Here are a variety of examples of ampliative arguments:
Simple enumerative induction goes from a list of observations of the form "this A is a B"
to the conclusion "All A’s are B’s". The example Hume made famous is like this:
8. Billiard ball 1 moves when struck. Billiard ball 2 moves when struck. Billiard ball 3
moves when struck… Billiard ball 100 moves when struck. Therefore, all billiard balls

move when struck.
Some ampliative arguments go from general statements to general statements:
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Inductive Logic
9. All bodies freely falling near the surface of the Earth obey Galileo’s law. All planets
obey Kepler’s laws. Therefore, all material objects obey Newton’s laws.
Others go from general statements to specific statements:
10. All emeralds previously found have been green. Therefore, the next emerald to be
found will be green.
Conclusion: To understand empirical science we need to understand ampliative inference.
Two Kinds of Science? A Priori and Empirical?
1.
A priori
science, like Euclid’s geometry, is where the conclusions are deduced from
premises that appear to be self-evidently true.
2. In empirical science, like physics, conclusions are based on observational data.
● This is similar to the distinction between pure mathematics and applied mathematics.
The distinction is not always sharp.
Ever since Einstein rejected the use of Euclidean geometry in his new physics at the turn of
the 20
th
century, it seems that
a priori
sciences cannot tell us anything about the real world.
The focus of recent philosophy of science is on the empirical sciences.
● A priori sciences contain the strongest form of reasoning, at the expense of telling us
less about the real world.
Introduction to the Demarcation Problem
Definition: In philosophy of science, we refer to what we already know directly through
observation as the

empirical evidence
(we are open-minded about the possibility that some of
these ‘facts’ are mistaken). See Exercise 1.
All of empirical science uses ampliative arguments. Hume made the same point in a different
way. He pointed that in example 8, it is possible that the premises are true and the conclusion
is false. No matter how many instances of a generalization we observe, it does not prove that
the generalization is true.
What is the difference between science and pseudoscience? You often hear that
science is based on the ‘facts’ while pseudoscience is not. Or you say that religious belief is
based on faith, whereas scientific belief is not. Unfortunately, both scientific and non-scientific
reasoning go beyond the facts. So, can we tell them apart?
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Inductive Logic
Argument:
1. The demarcation between science and pseudoscience depends only the nature of the
reasoning used.
2. Genuine science involves ampliative inference.
3. Pseudoscience involves ampliative inference.
4. Therefore, there is no demarcation between science and pseudoscience.
The
problem of demarcation
is to say what is wrong with this argument. (Question: what are
the two things that can be wrong with an argument?)
Review of Central Definitions and Remarks on Terminology
Definition: An argument is
deductively valid
if and only if it is
impossible
that its conclusion is
false while its premises are true.

Remark: The notion of deductively validity is such a central and important concept in
philosophy, that is goes by several names. When an argument is deductively valid, we say that
the conclusion
follows from
the premises, or the conclusion
is deduced from
, or i
nferred from
,
or
proved from
the premises. Or we may say that the premises
imply
, or
entail
, or
prove
the
conclusion. We also talk of deductively valid arguments as being
demonstrative
. All these
different terms mean exactly the same thing, so the situation is far simpler than it appears.
Definition: Any argument that is not deductively valid, or deductively invalid, is an
ampliative
argument
. The term refers to the fact that the conclusion of such argument goes beyond, or
amplifies upon, the premises.
Remark: Again the notion of ‘invalid’ is so common and central, that it goes by many names.
Other terms commonly used are inductive and non-demonstrative. I prefer ‘ampliative’
because it reminds us that the conclusion ‘goes beyond’ the premises, and it does not have

the bad reputation that sometimes goes along with the word ‘induction.’
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Demarcation
Demarcation: Popper, Kuhn and Lakatos
Last modified on Friday, September 18, 1998.  Malcolm R. Forster, 1998
The Problem
The difference between science and non-science has practical ramifications for society:
● Parapsychology includes the study of such alleged phenomena as telepathy,
clairvoyance, and precognition. In 1969 the American Association for the Advancement
of Science (AAAS) admitted the Parapsychology association as an Affiliate member.
Should they have done that?
● In Arkansas, U. S. A., there were attempts to have the biblical story of creation taught
in schools alongside evolutionary theory (after earlier attempts to ban evolutionary
theory failed). They argued that creationism is a just as much a science, and therefore
deserves equal time.
● The
Merriam-Webster's Collegiate
®
Dictionary
defines creation science
n
(1979):
creationism;
also
: scientific evidence or arguments put forth in support of creationism.
Should an authoritative dictionary presuppose that creationism is a science?
● Freudian psychology has a poor reputation in scientific circles. Is it a pseudoscience?
● Immanuel Velikovsky and Erich van Daniken wrote best sellers
Worlds in Collision
and

Chariots of the Gods
, which angered many scientists. Are these examples of
pseudoscience.
● Thor Heyerdahl launched the Kon-Tiki expedition to support his theory that the
polynesians migrated from South America. Was he a pseudoscientist?
● Gould wrote a book called
The Mismeasure of Man
about the IQ debate, and
phrenology, which purported to predict the criminal nature of people from their skull
shape and other characteristics.
● IQ testing has been used to screen children from entering high school, or college, in
many countries for many years. Does it predict future academic performance reliably? Is
there really such a thing as intelligence?
● Chemistry grew out of alchemy. One’s a science and the other is not. What’s the
difference?
● The label 'science' carries a high degree of authority, and people need to understand
when the label, and the authority, are deserved. Is there any clear difference between
an unscientific study and a scientific one?
● More generally, an understanding of what science is carries us a step closer to telling
the difference between good and bad science, and the limits of good science. If we
understand how science works, we can be better and more informed use of scientific
expertise.
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Demarcation
If we wanted to know which subjects were generally
accepted
as science, we would probably
find a fairly sharp and clear division between two categories. But we are interested in more
than that! We want to understand the general characteristics of science that are different from
pseudoscience. That is actually surprisingly difficult and controversial.

Exercise: Critically evaluate the following characterization of science (from the
Encyclopedia
Britannica
): any system of knowledge that is concerned with the physical world and its
phenomena and that entails unbiased observations and systematic experimentation. In
general, a science involves a pursuit of knowledge covering general truths or the operations
of fundamental laws.
Examples of Science and Pseudoscience
The key to understanding
Popper's demarcation criterion is to compare two examples. The
first, Popper thinks is typical of science, while the second is typical of pseudoscience.
Example (a): Einstein's prediction of the bending of star light. For over 200 years prior to
Einstein, Newtonian physics had enjoyed a period of unprecedented success in science. Many
scientists thought that Newton's theory was the end of science, and many philosophers not
only believed that Newton's theory was true, they thought that it was
necessarily
true. They
sought to explain why Newton's theory
had
to be true. All that began to change with Planck's
1900 introduction of the idea that energy comes in small discrete packages (the quantum
hypothesis) and Einstein's discovery of the special theory of relativity in 1905. Einstein's
special theory of relativity was a way of reconciling some inconsistencies between the wave
theory of light and Newtonian mechanics. Instead of modifying the wave theory, he modified
some of the fundamental assumptions used in Newtonian physics (like the assumption that
simultaneity did not depend on a frame of reference, and that the mass does not depend on
its velocity). However, Einstein's special theory of relativity said nothing about gravity.
Einstein's
general
theory of relativity was his theory of gravitation, which he had published by

1916. Many scientists were impressed by the aesthetic beauty of Einstein's principles, but it
was also important that it be tested by observation. For most everyday phenomena, in which
velocities are far smaller than the speed of light, there is no detectable difference between
Einstein's prediction and Newton's prediction. What we needed was a
crucial experiment
in
which Einstein and Newton made different predictions. In 1916, there were successful tests of
Einstein's special theory. But crucial tests of the general theory were harder to come by. One
such case was provided by the bending of starlight by the gravity of the sun. The period from
1900 to at least 1916 was a period of
revolution
in physics, and Eddington's confirmation of
Einstein's prediction in 1919 helped to complete the change in physics.
"The idea that light should be deflected by passing close to a massive body had been
suggested by the British astronomer and geologist John Michell in the 18th century. However,
Einstein's general relativity theory predicted twice as much deflection as Newtonian physics.
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Demarcation
Quick confirmation of Einstein's result came from measuring the direction of a star close to the
Sun during an expedition led by the British astronomer Sir Arthur Stanley Eddington to observe
the solar eclipse of 1919. Optical determinations of the change of direction of a star are
subject to many systematic errors, and far better confirmation of Einstein's general relativity
theory has been obtained from measurements of a closely related effect namely, the increase
of the time taken by electromagnetic radiation along a path close to a massive
body." (
Encyclopedia Britannica)
"The theories involved here were Einstein's general theory of relativity and the Newtonian
particle theory of light, which predicted only half the relativistic effect. The conclusion of this
exceedingly difficult measurement that Einstein's theory was followed within the experimental
limits of error, which amounted to +/-30 percent was the signal for worldwide feting of

Einstein. If his theory had not appealed aesthetically to those able to appreciate it and if there
had been any passionate adherents to the Newtonian view, the scope for error could well have
been made the excuse for a long drawn-out struggle, especially since several repetitions at
subsequent eclipses did little to improve the accuracy. In this case, then, the desire to believe
was easily satisfied. It is gratifying to note that recent advances in radio astronomy have
allowed much greater accuracy to be achieved, and Einstein's prediction is now verified within
about 1 percent." (Encyclopedia Britannica)
"According to this theory the deflection, which causes the image of a star to appear slightly
too far from the Sun's image, amounts to 1.75 seconds of arc at the limb of the Sun and
decreases in proportion to the apparent distance from the centre of the solar disk of the star
whose light is deflected. This is twice the amount given by the older Newtonian dynamics if
light is assumed to have inertial properties. If light does not have such properties, as is
generally accepted now, the Newtonian deflection is zero." (Encyclopedia Britannica)
Reconstruction of the example: Philosophers need a
general
characterization of the
example: Let
E
be a statement of the prediction made by Einstein's theory.
E
states the
direction that the starlight will be observed at the time at which the star was to be observed
by Eddington. Let
T
be a statement of the general principled in Einstein's general theory of
relativity. Let
A
be the conjunction of all auxiliary statements used to derive, or deduce,
E
from

T
. That is to say, the argument with
T
and
A
as premises, and
E
as the conclusion, is
deductively valid. Symbolically, we may write this as:
T
&
A
⇒
E
.
A
will include assumptions like "the sun is spherical ball of mass
M
", "there are no other bodies
close by to add to the sun's gravitational field," "If the sun were not present, then the star
would be seen in the direction such-and-such," "the effect of stellar aberration on the direction
of light is such-and-such," and so on.
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Demarcation
Example (b): Adler's 'individual psychology'. Compare the following two (hypothetical)
explanations of human behavior. (1)
E
1
: A man pushes a child into the water with the
intention of drowning it. (2)

E
2
: A man sacrifices his life in an attempt to save the child.
Popper claims that Adler's 'individual psychology' can explain both of these behaviors with
equal ease. Let
T
be Adler's theory, let
A
be the auxiliary assumption that the man suffered
feelings of inferiority (producing the need to prove to himself that he dared to commit some
crime). Then
T
&
A
1
⇒
E
1
. Let
A
2
be the auxiliary assumption that the man suffered feelings
of inferiority (producing the need to prove to himself that he dared to rescue the child). Now
T

&
A
2
⇒
E

2
.
Definition: Let us say that a theory
T

predicts
an event
E
if and only if there are auxiliary
assumptions that have either been used successfully in other predictions, or are the simplest
and most obvious assumptions that one would make in the situation, and that
T
&
A
⇒
E
. If
there exists auxiliary assumptions such that
T
&
A
⇒
E
, where
A
is some
ad hoc
assumption
that is introduced in light of the evidence
E

itself, then theory
T

merely accommodates

E
.
In example (a), Einstein's theory predicts the observational evidence, while in example (b), the
theory is merely accommodates the evidence.
Popper describes the difference by claiming that Einstein's theory is
falsifiable, whereas Adler's
theory is not.
Remark: Popper also claims that the problem with Adler's theory is that it is too easily
verified: "the world was full of
verifications
of the theory." Adler may have seen it like that, but
was he right? My feeling is that mere accommodations do not count as verifications at all.
Hence, I think that a verificationist could account for the difference
between these two
examples
as well as, if not better than, a falsificationist.
Discussion Question: How does our previous distinction between ampliative inference and
deductive inference enter into these examples, if at all. Popperians tend to think that there is
no need for ampliative inference in science at all. Why might they think that? Are they right?
Popper's Path to his Demarcation Criteria
(Curd and Cover, pages 1-10) To understand a philosophical theory, like Popper's demarcation
criterion, it is useful to see why simpler alternative proposals do not work.
Proposal 1: Science is distinguished by its empirical method. That is, science is distinguished
from pseudoscience by its use of observational data in making predictions.
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Demarcation
Objection: Astrology appeals to observation, but is not a science.
Proposal 2: Scientific theories, like Einstein's, are more precise in their predictions that
Adler's psychology, or astrology.
Objection: While it is true that pseudosciences do often protect themselves from refutation
by making vague or ambiguous predictions, that is not always the case. The 'predictions' of
example (b) are precise enough for the purpose, and Einstein's prediction was not exact—it
had to allow for many errors of observation.
Proposal 3: Science is explanatory, whereas pseudoscience is not.
Objection: If you buy into the auxiliary assumptions in Adler's psychology, then the theory
explains
the phenomena perfectly well. It is true we have little reason to believe that the
explanation is correct, but that is a different issue.
Proposal 4: Science is distinguished from pseudoscience by its verifications, or confirmation.
Objection: Popper's objection is that "The world was full of verifications of those theories." I
have remarked that that does not ring true in examples (a) and (b). Nevertheless, there
seems to be some force behind Popper's point in other examples. For example, Einstein could
have pointed to all the verifications of Newton's theory for low velocities and claim these as
verifications for his own theory. Yet he did not. Why not? Because, says Popper, these were
not
risky
predictions. They were not potential falsifiers of Einstein's theory.
Popper’s Proposal: Every ‘good’ scientific theory is a prohibition: it forbids certain things to
happen.
The criterion of the scientific status of a theory is its falsifiability, or refutability, or
testability.
Note: Popper also anticipates a major objection to his criterion: namely, that
any
scientific
theory can be protected from refutation by introducing

ad hoc
auxiliary assumptions. His reply
is that the very use of
ad hoc
assumptions, in reducing the falsifiability of theory, also
diminishes its scientific status. The problem with Popper’s reply is that it is not always, if ever,
clear in advance that
ad hoc
auxiliary assumptions are needed to save the theory. This is
essentially Kuhn’s point.
Hypothetico-Deductivism
In the
first set of lecture notes, I introduced the demarcation problem as a problem about the
difference between good and bad kinds of ampliative inference. Popper rejects this
formulation of the problem. He thinks it is wrong to think of theories as being inferred from, or
induced from, the observational facts. Rather, the invention of theories is a question of
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Demarcation
psychology, which has nothing to do with the status of the theory as scientific. There are no
scientific or unscientific ways of inventing theories. They can come in a dream or they can be
constructed from the data—it does not matter. Rather, the essence of science is about how
predictions are deduced from the theories. This way of viewing science is known as
hypothetico-deductivism. The difference between science and pseudoscience rests solely on
the 'deductive' part of the process.
Kuhn’s Characterization of Science
Thomas Kuhn makes the following points against Popper (Curd and Cover, pages 11-19):
● The kind of examples Popper considers, like the 1919 test of Einstein’s theory of
gravitation, is an example of extraordinary science, or revolutionary science. These are
relatively rare in science.
● In non-revolutionary science, or

normal
science, the aim of research is to connect the
experimental data to the background theory, by inventing the appropriate auxiliary
assumptions. If a scientist fails, then scientist’s lack of ingenuity is blamed, not the
theory.
● It is for normal, not extraordinary, science that scientists are trained, and
● "If a demarcation criterion exists , it may lie in that part of science which Sir Karl
ignores."
Question: Kuhn concedes that "There is one sort of 'statement' or 'hypothesis' that scientists
do repeatedly subject to systematic test. I have in mind statements of an individual’s guesses
about the proper way to connect his own research problem with the corpus of accepted
scientific knowledge." Thus, thinks (a) a demarcation criterion should refer to normal science,
and (b) falsifiability does play a role in normal science. So, why doesn’t he apply a falsifiability
criterion to normal science, and say that an alleged science is genuinely scientific if and only if
its solutions to puzzles are falsifiable? As Kuhn says, this is not what Popper has in mind. But
does the new criterion work?
Central Concepts in Kuhn’s Account of Revolutionary Change in Science: Kuhn denies
that theories change by falsification in science, but he does not deny that theories are
sometimes
replaced
(revised). What is his own account of ‘theory replacement’? Here is very
brief summary of his positive account:
1. The process by which one paradigm is replaced by another is called
revolutionary
science
.
2. An
anomaly
is a violation of "the paradigm-induced expectations that govern normal
science" (Kuhn,

The Structure of Scientific Revolutions
, 1970, p.52).
3. A
crisis
in normal science occurs when puzzle-solving breaks down, either because no
solutions are found, or because the discrepancy corrected in one place shows up in
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Demarcation
another.
4. A paradigm is overthrown only if the paradigm is in crisis and there is a second
paradigm that shows equal or greater puzzle-solving potential.
Kuhn’s Demarcation Criterion: All of genuine science has a puzzle-solving tradition, while
pseudosciences do not.
Objection: Until Kuhn says what a puzzle-solving tradition is, his criterion is rather vague.
Why wouldn’t a research tradition that sought worked backwards from the fact to the auxiliary
hypotheses count as puzzle-solving. It seems that Kuhn needs to add something like
falsifiability.
Kuhn on Astrology:
1. Kuhn agrees that astrology is pseudoscience, but makes the point that it was not
obvious that it was pseudoscience in the century it was practiced most. That is because
its auxiliary assumptions, based on the configuration of the planets at the time of birth,
were subject to genuine doubt. Not everyone was sure of their exact date of birth in
any case. The problem is that similar arguments explaining away failed predictions are
regularly used today in medicine or meteorology.
2.
Astrology has no science to practice because practitioners had rules to apply, but no
puzzles to solve. Most difficulties "were beyond the astrologer’s knowledge, control, and
responsibility." In astronomy, however, if a prediction failed, a scientist "could hope to
set the situation right." There was a puzzle-solving tradition.
Final argument:

● For a long period of time, there was a sense in which Ptolemaic astronomy was
unfalsifiable by the means available (naked-eye observations). But that did not stop it
from being science at the time. Moreover, when it was finally falsified (by Galileo’s
observation of the phases of Venus, the moon’s of Jupiter, and Brahe’s observations of
comets), it had already been rejected.
Necessary and Sufficient Conditions
necessary condition: E.g., being enrolled in this course is a necessary condition for you
getting an A for the course. That is, you will not get an A if you are not registered. Or
equivalently, if you do get an A, then you are registered. In general: A necessary condition for
an event or state of affairs
X
is one that has to hold for
X
to be true. A necessary condition is
contrasted with a sufficient condition.
sufficient condition: E.g., getting an A in this course is a sufficient condition for passing this
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Demarcation
course. That is, it you get an A then you will pass. In general: A sufficient condition for an
event, or state of affairs
X
is one that enough to makes
X
true.
necessary and sufficient condition: A condition is necessary and sufficient for a
statement, or event,
X
if and only if it is necessary for
X
and sufficient for

X
. It is often
expressed by the phrase ‘if and only if’ or the abbreviation ‘iff’.
E.g.
, a necessary and sufficient
condition for passing this course is to receive a passing grade while being registered for the
course.
Popper says that the falsifiability is a necessary and sufficient condition for genuine science.
● Falsifiability is not a sufficient condition because astrology is falsifiable but not a
science. In the 1960s, Michael Gauquelin examined the careers and times of birth of
25,000 Frenchmen, and found no significant correlation between careers and either sun
sign, moon sign, or ascendant sign (see the Thagard reading). Gauquelin found some
statistically significant correlations between certain occupations and the positions of
certain planets at the time of their birth, but we can expect 1 in 20 random associations
will be statistically significant by chance alone. Also, studies of twin do not show the
correlation one would expect. These results cannot be explained away by supposing
that almost all assumptions in every case were false. Therefore, such a study falsifies
astrology in a sense that Popper would accept, and these studies were always possible,
which proves that astrology was always falsifiable.
● Falsifiability is not necessary for science. The example of Ptolemaic astronomy shows
this, because prior to the invention of telescope it was not falsifiable but it was still a
science.
Counterexamples: In order to show that a condition is not a sufficient condition for X, we
only need an example in which the condition holds, but X does not. In order to show that a
condition is not a necessary condition for X, we only need an example in which X holds but the
condition does not. In each case, the examples are called
counterexamples.
Astrology is a
counterexample for the sufficiency of falsifiability for science, and Ptolemaic astronomy is
counterexample to its necessity.

Here are some other arguments that make use of counterexamples.
● Astrology is not a science because it has mystical origins. Counterexample: Chemistry
had its origins in alchemy and medicine had occult beginnings.
● Astrology is not a science because people believe astrology for irrational reasons.
Counterexample: Many people believe in Einstein's theories for irrational reasons.
● Astrology is not a science because it assumes that gravitational influences of the planets
influence us, but they are too weak to do that. Counterexamples: The lack of a
physical foundation did not stop geologists from believing in continental drift, and we
(8 of 9) [08.04.2007 17:08:14]
Demarcation
have plenty of evidence to prove that smoking causes lung cancer with knowing the
details of the carcinogenesis.
(9 of 9) [08.04.2007 17:08:14]
Lakatos
Lakatos's Methodology of Scientific Research Programs
Last modified on Thursday, September 24, 1998, by Malcolm R. Forster
Points of Disagreement between Lakatos and Kuhn
1.
Subjective or objective?
Kuhn’s demarcation criterion appears to be subjective it
depends on what scientists do and what they believe (their psychology). In contrast,
Lakatos insists that "a statement may be pseudoscientific even if it is eminently
‘plausible’ and everyone believes in it." Belief that earth is flat may count as an example
of that. And "it may be scientifically valuable even if it is unbelievable and nobody
believes in it." Copernicus's theory that the sun moves like that, and very few believed
in evolution when Darwin introduced his theory.
2.
Sociology or logic?
Another point of disagreement between Kuhn and Lakatos is
whether a demarcation criterion should be talking about which

statements
are scientific
or pseudoscientific, or whether it should be saying which
community
is scientific or
unscientific. Lakatos, as a neo-Popperian, was raised in the tradition in which
logic
was
the main tool in philosophy of science, whereas Kuhn is more interested in the
sociology

of science.
3.
Religion or Science?
Kuhn compares science to religion, but Lakatos rejects this
comparison.
Main Point of Agreement between Lakatos and Kuhn
Any good science can be
practiced
in a pseudoscientific way. The demarcation between
science and pseudoscience refers to its method and not just what the theory says (its content).
● For example, some evolutionists may be tempted to fill in auxiliary assumptions in an
ad
hoc
way by working backwards from what is to be explained. For example, if see from
the fossil record that horses teeth become elongated, we may be tempted into using
evolutionary theory to infer that there was some change in the environment that made
shorter teeth less fit, and then explain the change by appealing to the law of natural
selection that "only the fittest survive."
● It would be equally easy for Newtonian mechanics to be practiced in a pseudoscientific

way. After all, Newton’s law of inertia says that a body continues in a straight line with
uniform velocity until acted on by a force, and then defines a force as anything that
diverts a body from uniform motion in a straight line.
Lakatos on Popper’s Demarcation Criterion
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Lakatos
1. Lakatos argues that ‘falsifiable’ already refers to how science is
practiced
. He interprets
Popper as demanding that scientists "specify in advance a crucial experiment (or
observation) which can falsify it, and it is pseudoscientific if one refuses to specify such
a ‘potential’ falsifier.’ If so, Popper does not demarcate scientific statements for
pseudoscientific ones, but rather scientific method from non-scientific method."
2. While Popper’s criterion does focus on practice, it is still wrong because it "ignores the
remarkable tenacity of theories." Scientists will either invent some rescue hypothesis
(accommodate the theory) or ignore the problem and direct their attention to other
problems. For example, some problems may be too hard (nobody rejected Newtonian
mechanics because it couldn’t predict all the properties of turbulent fluid flow, or the
chaotic motion of a physical pendulum).
A Puzzle about Prediction
Earlier, we saw that Popper's two examples, Adler's theory at one extreme, and Einstein's
theory at the other, illustrated a difference between accommodation and prediction. Adler's
theory merely accommodated the facts because it worked backwards from the evidence
E
to
the auxiliary assumption
A
needed so that the theory
T
entailed

E
(
T
&
A
⇒
E
). At the other
extreme, if intellectual honesty requires that a scientist specify a ‘potential’ falsifier’ in
advance, then they must specify
A
in advance. That is a
sufficient
condition for the theory to
make a prediction. But is it necessary?
Lakatos’s Picture of Science
The typical unit of science is not an isolated hypothesis, but rather a
research

programme
,
consisting in a
hard core
(theory),
protective belt
(auxiliary assumptions) and a
heuristic
.
Lakatos quote: A
heuristic

is a "powerful problem solving machinery, which with the help of
sophisticated mathematical techniques, digests anomalies and even turns them into positive
evidence. For instance, if a planet does not move exactly as it should, the Newtonian scientist
checks his conjectures concerning atmospheric refraction, concerning propagation of light in
magnetic storms, and hundreds of other conjectures that are all part of the programme. He
may even invent a hitherto unknown planet and calculate its position, mass and velocity in
order to explain the anomaly." (Lakatos, 1977, p. 5)
● In Kuhn's terminology: Heuristics are hints about how to solve normal science puzzles.
● In my terms: A heuristic is a hint about how to change the auxiliary assumptions so that
the theory better fits the facts.
The
negative heuristic
forbids scientists to question or criticize the hard core of a research
programme. "The
positive heuristic
consists of a partially articulated set of suggestions or hints
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Lakatos
on how to change, develop the 'refutable variants' of the research programme, how to modify,
sophisticate, the 'refutable' protective belt." (Lakatos, 1970, p.135).
Example:
Le Verrier and Adams were faced with the following problem in Newton's theory of
planetary motion. There were discrepancies (unpredicted wobbles) in the motion of the
outermost planet known at the time (Uranus). They postulated that these might be caused by
a hitherto unknown planet. Based on that conjecture they recalculated the solutions to
Newton's equations, and fit the solutions to the known data for Uranus. That fit even predicted
the position of the postulated planet, whereupon Neptune was seen for the first time once
telescopes were pointed in that direction (actually, it was later discovered that it had been
seen before, but mistaken for a comet).
● In this example, the positive heuristic used was something like this: "If there is an

anomaly in Newton's theory on the assumption that there are
n
planets, then try
assuming that there are
n+
1 planets."
The Role of Background Evidence
We have identified auxiliary assumptions with Lakatos's protective belt. That is, we are
assuming that auxiliary assumptions are always provisional in some sense. However, we must
now decide whether to count statements of background evidence, prior observations, and
data, as auxiliary assumptions. They are auxiliary in the sense that they are needed in order to
make predictions. In the Le Verrier-Adams example it would be impossible to predict the
position of the postulated planet without making use of the observed positions of Uranus, and
the other planets. Let use refer to this
background data
by the letter
D
('D' for data). We now
replace the previous pattern of inference (
T
&
A
⇒
E
) by the pattern:
T
&
A
&
D

⇒
E
.
We still refer to
A
as the auxiliary assumption, but with the explicit understanding that it
excludes
the background observational evidence or data
D
.
Models
It may be useful at this point to introduce the concept of a
model. A
model
is theoretical
statement, (often in the form of an equation) usually deduced from a
theory with the aid a
auxiliary assumptions. That is, a model
M
is equal to a theory
T
combined with an auxiliary
assumption
A
(which will be long list of assumptions in most cases). That is,
M
=
T
&
A

.
Example: In the LeVerrier-Adams example, there was first a Newtonian model of planetary
motion that assumed that there are only 7 planets. There were discrepancies between the
(3 of 8) [08.04.2007 17:08:43]
Lakatos
predictions of this model and the observed motions of Uranus. Therefore, the model was
replaced by one that assumed the existence of 8 planets. Not only did that accommodate the
anomalous motion of Uranus, but it predicted position of the eighth planet, whereupon
Neptune was discovered.
Remarks:
1. A model
M
is falsified when
M
&
D
⇒
E
because
D
is not blamed for the failed
prediction. Therefore,
models are falsifiable
, or
refutable
, even though theories are not.
2. The notion of a 'model' corresponds to Lakatos's notion of a 'refutable variant of a
theory'. If a Lakatosian heuristic defines an ordered list of auxiliary assumptions,
A
0

,
A
1
,
A
2
,
A
3
, then it also defines an ordered list of models
M
0
,
M
1
,
M
2
,
M
3
,
3. This use of the term 'model' differs from two other uses that are common in the
philosophy of science. (a) A 'model' as in a model airplane. Such models do appear in
science, such as in the 'model of the DNA molecule' Watson and Crick used, which was
made of wooden balls joined with sticks. (b) 'Model' in the sense used by
mathematicians in model theory. There it has a rather technical meaning, which
corresponds roughly to what logicians call an
interpretation of a language
(an

assignment of objects to names, set of objects to properties, a set of object pairs to
relations, and so on).
4. Scientists use the term 'model'
all the time
, and it very rarely fits sense (a) and
absolutely never fits sense (b). Our use of the term best fits the standard scientific
usage.
Solution to the Puzzle about Prediction
If a heuristics exists, then a scientist has an ordered list of suggested models
M
0
,
M
1
,
M
2
,
M
3
, Now the theory
T
is no longer falsifiable in Popper's methodological sense, for if a
scientist tries makes the prediction
E
0
from model
M
0
and

E
0
proves to be false, then the
scientist does not blame
T
, but instead moves to
M
1
, because it is next on the ordered list,
and so on. Scientists now predict
E
1
because
M
1
&
B
⇒
E
1
. And so on. There is no falsifiability
of the theory, but
it can still make predictions
. Thus, the idea of a heuristic may save the
distinction between accommodation and prediction, and thereby providing a weaker sufficient
condition for prediction.
● Note that the research program makes a different set of predictions at different times.
This allows Lakatos to introduce the idea of
novel
predictions new predictions not make

before.
When Should One Model Supercede Another?
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Lakatos
Lakatos does not believe that falsification is important in science, but like Kuhn, he does
recognize that theories, or paradigms, are superceded in science. He objects to Kuhn's
description of this process, of scientific revolutions, as being a like a religious conversion, or a
social revolution. Lakatos things that the process is more objective. Here is his view.
Thesis: A model
M¢
supercedes a model
M
if and only if (1)
M¢
has excess empirical content
over
T
: that is, it predicts
novel
facts, that is, facts improbable in light of, or even forbidden
by
M
; (2)
M¢
explains the previous success of
M
, that is, all the unrefuted content of
M
is
contained (within the limits of observational error) in the content of

M¢
; and (3) some excess
content of
M¢
is corroborated. (see Lakatos, 1970, p. 116; the phrase "should supercede" is
my paraphrase, and I have replaced 'theory' by 'model'.)
● This is Lakatos's account of normal science.
Lakatos introduces some new terminology to help formulate his theory of science.
1. A
problemshift
is a series of models
M
1
,
M
2
, such that (i) each can explain the
empirical success of its predecessor, and (ii) each can explain at least some of the
emprical failure of it predecessor as well. In other words, a Lakatosian problemshift
occurs whenever a Kuhnian solution to a normal science puzzle is found, since to be a
solution is must remove the anomaly with creating new one. Note that a problemshift
does not have to make novel predictions.
2. A
theoretically progressive
problemshift is a problemshift that predicts some novel facts.
3. A problemshift is
empirically progressive
if it is theoretically progressive and some of the
novel predictions have been corroborated.
Note: In Lakatos's original writings, Lakatos uses the word 'theory' instead of 'model', but

only because he fails to make the distinction. I think that he models in mind.
Definition: A problemshift is
progressive
if it is theoretically and empirically progressive.
Otherwise the problemshift is
degenerating
. The idea of a
degenerating problemshift

corresponds to Kuhn's notion of crisis.
Example 1: The LeVerrier-Adams discovery of Neptune is a great example of a problemshift
that was progressive, because (1) it led to novel predictions (the position of Neptune), which
(2) were then corroborated.
Example 2: Ptolemaic astronomy was degenerating not because it failed to be theoretically
progressive (Ptolemaic astronomers had the option of adding more epicycles) but because it
was not empirically progressive. That is, adding an epicycle would lead to novel predictions,
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Lakatos
but they were not corroborated (confirmed).
Lakatos on Revolutions
What is Lakatos's theory about when one
theory
should supercede another? In fact, Lakatos
does not provide such a criterion. Not even when one research program is degenerating and
another is progressive does Lakatos say that scientists do or should only work on the
progressive one, because like the stock-market, they may change their status over time.
●
The methodology of scientific research programmes does not offer instant rationality.

It is not irrational for a scientist to work on a young research programme if she thinks it shows

potential. Nor is it irrational for a scientist to stick with an old programme in the hope of
making it progressive. Thus, Lakatos appears to agree with Kuhn that theory change is a
rather fuzzy phenomenon. But he does insist that it depends on the assessment of
objective

facts the
future
progressiveness or degeneration of research programs. The decision of
scientists, however, must rely of their subjective predictions of the future course of science.
Unlike Kuhn, Lakatos does
not
think that the uncertainty makes these decisions irrational.
Example 3: Prout's program. Prout, in 1815, claimed that the atomic weights of all pure
elements were whole numbers. He knew that the experimental results known at the time did
not confirm his theory, but he thought that this arose because chemical substances as they
naturally occurred were impure. Thus, there ensued a program of research whereby chemical
substances were purified
by chemical means
. This program led from one failure to the next.
The program at this stage was
degenerating
. However, Rutherford's school explained this
failure by the fact that different elements can be
chemically identical
(as explained by the
periodic table). They proposed that the substances should be purified by physical means
(powerful centrifuges), whereupon the program made a progressive shift. Lakatos (1970,
pp.138-140) uses this as an example of why it would be wrong to advise scientists to instantly
abandon a degenerating research program.
Question: We have talked about Lakatos's view of normal science and revolutionary science.

However, this is separate from the demarcation issue. Popper thinks that the essence of
science lies in the nature of revolutions, but Kuhn thinks that the essence of science lies in the
nature of non-revolutionary science. Where does Lakatos stand on this issue?
Lakatos's Demarcation Criterion
Lakatos is not explicit about his demarcation criterion in the passage we read, but he is explicit
about in his 1970 article: "We '
accept
' problemshifts as 'scientific' only if they are at least
theoretically progressive; if they are not, we '
reject
' them as 'pseudoscientific.'" (1970, p. 118)
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Lakatos
Presumably, therefore, a research program is
scientific
if and only if it is at least theoretically
progressive. Note that it is possible for a research program to be scientific at one time, but not
at another. It is even that a program practiced by one group is scientific, while the practice of
another group is pseudoscientific. This is how Lakatos is agreeing with Kuhn's point that even
a good theory can always be
practiced
in a pseudoscientific was. Thus, Adler's theory (about
inferiority complexes) might potentially be a good theory, but the fact is that it was being
practiced
in a pseudoscientific way (if Popper's account is correct).
● Lakatos is agreeing with Kuhn, against Popper, that the essence of science lies in the
nature of
normal
science.
Example 4: Astrology. Astrology has no theoretically progressive problemshifts, and therefore

no empirically progressive problemshifts. That is, it made no
novel
predictions, despite that
fact that it made predictions. Therefore, astrology was not a science.
Example 5: Prout's program. While Prout's program was degenerating, it was still
theoretically progressive, and hence scientific.
Example 6:
Jeane Dixon was a self-proclaimed psychic who predicted that JFK's
assassination. She made over 200 predictions each year (most of them wrong of course). Did
her method count as scientific? It would be by Popper's criterion, but not by Kuhn's or
Lakatos's demarcation criteria. Like astrology, there was no Kuhnian puzzle solving, and no
theoretically progressive problemshifts.
Musgrave's Criticisms of Lakatos
In an article called "Method or Madness" (in Cohen, R. S., Feyerabend, P. K and Wartofsky,
M. W. (eds)
Essays in Memory of Irme Lakatos
, Dordrecht, Holland, D. Reidel), Alan Musgrave
(1976) raises some interesting objections to Lakatos's theory of science, which I have
expanded upon in places.
1. Is the negative heuristic needed? Before 1850, Newtonian seldom treated Newton's
law of gravitation as part of the hard core. Therefore, scientists did not follow Lakatos's
methodology and render Newton's laws unfalsifiable by fiat. And why should scientists
have to specify
in advance
not to modify or renounce them in the face of difficulties.
Surely, it is enough that it is harder to produce theoretically problemshifts by changing
central assumptions because it is then harder to explain all the successes of the
superceded model. But there is no reason to rule it out in advance.
2. Are positive heuristics always specified in advance? Where was the positive
heuristic in the example of Prout's program? No-one tried physical separation of

chemical substances as soon as the chemical methods failed. They kept trying to
improve the chemical methods. It was only after the discovery of chemical similarities
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Lakatos
that the hint or suggestion appeared.
3. Why not compare one research program against another? Musgrave thinks that
Lakatos is overcautious in not recommending any rule for choice between competing
research programs. Why not say, that on the whole, the scientific community should
devote more resources to progressive as opposed to degenerating research programs?
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Evolution
Evolutionary Theory
Last modified on Friday, October 02, 1998, by Malcolm R. Forster
(Extracted in part from "Philosophy of Biology" by James G. Lennox)
Fact versus theory:
Fact of evolution = the fact that evolution has occurred.
Theory of evolution = an explanation about how and why evolution has occurred.
Note: Darwin did help establish the
fact
of evolution. However, the fact of evolution was
already accepted by some prominent biologists prior to Darwin, so this is not his most
important claim to fame.
● It is possible to accept the fact of evolution, but to seriously disagree with (or even
misunderstand) Darwin’s theory of how the fact of evolution come about.
Darwin’s theory of evolution is roughly as follows:
1. The struggle for survival: Biological organisms have more offspring than can possibly
survive.
2. Inheritability: Biological organisms
inherit
some of their traits from their ancestors

and
pass them on
to their descendents.
3. Variation: The inheritable traits of biological organisms vary, even within the same
species.
4. Differential fitness: Some inheritable traits will be more advantageous than others in
the struggle for survival.
Therefore, there has been and will continue to be, on average, a (natural) selection of those
organisms that have advantageous traits that will lead to the evolution of species.
This is what Lakatos would call the hard core of Darwin’s research program.
The radical nature of Darwin’s theory
The fact of evolution is radical enough, especially in light of the extremely recent arrival of
homo sapiens
. It questions the primacy of our place of the universe. However, the Darwin’s
theory is even more radical than that. Darwin delayed publication of his theory for many
years; in fact he only published when he discovered that Wallace was about to publish the
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Evolution
same theory. The probable reason for his delay was a fear of the controversy his
theory
would
provoke.
1. Darwin’s theory undermines one of best theological arguments for the
existence of God: If you come across a watch, and observed its intricate design, then
it is reasonable to infer the existence of a watchmaker. If you come across a biological
organism that has an even more intricate design, then it is reasonable to infer the
existence of a Creator. This is called the argument from design. Evolutionary theory
provides an alternative explanation. Moreover, the imperfection of many designs is
evidence for evolution and against design.
2. Darwin’s theory does not imply that evolution is progressive. Evolution has no

predetermined direction. The direction of evolutionary change depends on the
local

environment at the time. There is no progression from inferior to superior organisms
implied by the theory. In fact, immoral traits like ruthlessness and violence are often
rewarded in evolution. In particular, there is no implication that
homo sapiens
is
superior to other species. There is no
final cause
directing evolutionary change.
Evolution is not teleological or goal directed.
3. Darwin’s theory supports a materialistic world view (nothing to do with
materialism in the consumer sense). The view that humans have souls, while animals do
not, finds no place in Darwin’s theory. It supports the view that the only things in the
universe are material things.
The protective belt: Darwin’s theory predicts (or postdicts) that evolution has occurred.
However, the theory, by itself, does not say which traits are inheritable, nor how they vary, or
the way in which resources are limited, or how the different traits aid in survival, or how all
these factors change over time.
A
model
of a particular episode or instance of evolutionary change will add specific details to
the hard core assumptions, concerning:
a. the range of inheritable traits in a biological population(s).
b. the environment, and how it changes over time.
c. the relative benefit that these traits confer to the members of the populations
possessing them in the various environments (fitness values).
Accommodation versus prediction: Some of these details may be introduced as
parameters (e.g., fitness parameters), which are inferred backwards from facts to be

explained. But if all of these details are inferred from the facts to be explained, then the
theory is merely
accommodating
the facts, and there are no predictions (or postdictions). In
that case, evolutionary theory would be pseudoscientific according to Lakatos’s demarcation
criterion.
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