Mills methods Philosophy

Computer Science course philosophy

1. Mills Methods - Causation
Department of Computer Science,
Islamia College University Peshawar

2. Inductive Thinking
•Inductive arguments are those in which the
premises are intended to provide support, but not
conclusive evidence, for the conclusion.
•For example in deduction, we argue that “All fish
have gills, tuna are fish, therefore tuna have gills.”
•In induction we argue that “Tuna, salmon, cod,
sharks, perch, trout, and other fish have gills,
therefore all fish have gills.”

3. Inductive Thinking II
•To be even more precise, in using deductive
arguments we make explicit in the conclusion
what is implicit in the premises.
•In inductive arguments, we extend the premises
and make a claim beyond the cases that are given.
–Induction hazards an educated guess based on strong
but not on absolute proof about some general
conclusion that can be drawn from the evidence.
•However we characterize induction, we can see
that it is not nearly as reliable as deduction
because the conclusion is never certain.

4. Inductive Thinking III
•In the previous example, it is probably true that all
fish have gills, but we have not examined all
species of fish, so we never know that our claim is
true. The same can be said for the statement that
the sun will rise every day, which is based on all
recorded instances in the past but not on all
possible instances.
•Because inductive arguments do not guarantee that
their conclusions are true, we evaluate them
according to the strength of the support they
provide for their conclusion.

5. Causation
•One of the most basic, most common, and most
important kinds of knowledge we seek is
knowledge of cause and effect.
–Why didn’t my alarm clock go off when it was
supposed to?
–Why did I get a “D” in my exam?
•We want to know the cause of what happened. In
the absence of a good account, we will often
accept a bad one - as in the case of superstition
and mythology. E.g;
–Some people have believed that they can appease the
gods by sacrificing a virgin.
–Some people believe that if a black cat crosses their
path, bad luck will follow, and so forth.

6. Causation II
•In all of these cases, a false connection has been
established between two events such that we
assume that one event is responsible for the other
when they are actually unrelated.
•It can be difficult to recognize genuine causal
connections and distinguishing them from mere
temporal succession.
•In our reasoning we need to separate a necessary
train of happenings from an accidental one.

7. Causation III
•We can say that some events are subsequent,
meaning that they just happen to follow but with
no connection to the earlier event, while others are
consequent; they occur because of the earlier
event.
•We can, for example, justifiably assert that the
following causal sequences took place: the water
boiled because the temperature was raised to 212°
F; every time I let go of the chalk, the chalk falls
to the floor.
•In these cases the sequence was necessary, not
accidental; given one event, the other had to
happen.

8. Causation IV
•Obviously, the order in which things happen make a
difference here because the events are causally
related.
•It may not matter whether someone speak and then
smiles or smiles and then speaks, but when it comes
to a wound followed by a pain, the second must
occur after the first because it is a consequence of it.
•I forgot to buy snowshoes. Subsequently, it snowed
heavily.
•I bought snowshoes. Consequently, I didn't slip when
it snowed.

9. Mill’s Methods
•The nineteenth-century English philosopher John
Stuart Mill (11806-1873) considerably refined the
process of identifying causal connections.
•Mill specified 5 “methods” that can be used to
recognize cause-effect chains: that of agreement,
difference, agreement and difference, Method of
residue and concomitant variations.

10. Mill’s Method of Agreement
•The method of agreement is described by Mill as follows:
•If two or more instances of the phenomenon under
investigation have only one circumstance in common, the
circumstance in which alone all the instances agree, is the
cause (or effect) of the given phenomenon.
•For example, consider an individual doing research on why
some students are successful in an especially difficult subject,
say, mathematical logic. In reviewing the data, the researcher
finds many circumstances in which students are successful in
mathematical logic, such as instructors using particular
approaches to teaching the subject or assigning particular tests.
However, the researcher discovers that in all instances in which
students are successful they are highly motivated.

11. Mill’s Method of Agreement II
•High student motivation is the only condition that is common
to all instances of student success in mathematical logic. From
this observation, using the method of agreement, the
researcher concludes that the necessary condition for student
success in mathematical logic is high motivation.
A B C D E
All instances exhibit P (the phenomenon)
C1 C1 C1 C1 C1
C2 C6 C2 C4 C7
C3 C3 C4 C5 C6

12. Mill’s Method of Agreement III
•Although this method can be useful, it suffers from a
major defect: that there is very often more than one
common factor.
•For example a lot of students got ill after having
dinner last night:
– they may have drank from the same water fountain
–been to the same party the night before
–been exposed to someone with a contagious disease, and
so forth.
•This having been said, Mill’s methods are a form of
inductive reasoning.

13. Method of Difference
•The method of difference is described by Mill as follows:
•If an instance in which the phenomenon under
investigation occurs, and an instance in which it does not
occur, have every circumstance in common save for one,
that one occurring only in the former; then the
circumstance in which alone the two instances differ, is the
effect, or the cause, or an indispensable part of the cause,
of the phenomenon.

14. Method of Difference II
•In the previous example suppose that none of the
students became ill except for the one who ate
pumpkin pie for dessert. She had eaten the
appetizer and the main course just as the other
students did who did not become ill.
•Prior factors Effect
a, c, e, f, h no illness occurred
a, d, e, g, i no illness occurred
b, d, e, f, h no illness occurred
b, c, e, g, j illness occurred
Therefore j is the cause

15. Method of Difference III
•The problem with this approach is that, just as the
areas of agreement can be numerous, so can the
differences.
•Because of the number of variables involved, we
can never be sure when we have found the
consequential difference.
•Even though pumpkin pie may have been the
cause, it may not have been the cause. There
could have been additional variables. For
instance, she would have drunk alcohol the night
before, and so forth. The possibilities are
numerous.

16. Joint Method of Agreement and Difference
•To try and fill the gaps in both methods Mill
suggests a third approach called the joint method
of agreement and difference.
•Here we judge as the cause that element which all
preceding events have in common (agreement)
after factoring out any common elements that did
not result in the subsequent event (difference).
•We are then left with the one common element
present only in positive instances, and that is taken
as the cause.

17. Joint Method of Agreement and Difference II
•Prior factors Effect
a, c, e, f, h illness occurred
a, d, e, g, h illness occurred
b, d, e, f, h illness occurred
b, c, e, g, i no illness occurred
a, d, e, g, l no illness occurred
a, d, e, f, 1 no illness occurred
Therefore h is the cause

18. Joint Method of Agreement and Difference III
•Both e and h are present in cases where illness
occurred, but by extending the number of cases
further, e drops out as a possible cause. e is
present even when there is no illness, so it cannot
be the cause. H, on the other hand, is present only
(and always) when illness occurred, so it must be
the cause.
•So, as in the case of the method of difference,
when pumpkin pie appears to be the cause then
we can ask if there is anyone who ate pumpkin pie
that did not get sick. If we find such persons then
we can eliminate pumpkin pie as the cause of the
illness.

19. Method of Residue
•a process of elimination
•used when we remove from the phenomenon the
casual features that we already know, and what
remains (the residue) is (probably) causally
related.
•If a range of factors are believed to cause a range
of phenomena, and we have matched all the
factors, except one, with all the phenomena,
except one, then the remaining phenomenon can
be attributed to the remaining factor

20. Method of Residue
•Symbolically, the Method of Residue can be
represented as:
–A B C occur together with x y z
–B is known to be the cause of y
–C is known to be the cause of z
–Therefore A is the cause or effect of x.
ABC—xyz
B is the cause of y
C is the cause of z
A is the cause of x

21. Method of concomitant variations
•The last approach, the method of concomitant
variations, is usually employed when a continuous
flow of events is involved and we cannot control
for the negative occurrences.
•Here we try to establish causation by recognizing
a correlation in the way one set of event varies in
relation to another.
•That is, we see a correlation in degree and
regularity between two events, such that we infer
that the first must be causally related to the
second.

22. Concomitant graph
0
100
200
300
1 2 3 4
Heart attacks
b
lo
o
d
p
r
e
s
s
u
r
e
Series2
Series1

23. Method of concomitant variations II
•For example, people have observed that the height
of the tide depends upon the phases of the moon.
When the moon is full the tide is highest; a half-
moon is followed by a medium tide; and a low tide
seems to be related to a quarter or a crescent
moon.
•Because of the consistency and predictability of
the relation, we can infer a cause-effect link: the
larger the moon, the higher the tide.

24. Method of concomitant variations III
•suppose that various samples of water, each containing
both salt and lead, were found to be toxic. If the level of
toxicity varies with the level of lead, one could attribute
the toxicity to the presence of lead.
•Other examples are the age of a tree and its thickness; and
the darkness of our tan and the length of time we were in
the sun.

25. Thanks