The document discusses several methods of inductive argumentation described by John Stuart Mill for drawing general conclusions from specific observations or facts. These include the method of agreement, method of difference, joint method of agreement and difference, method of residues, and method of concomitant variations. Examples are provided to illustrate each method and how they can be used to infer causal relationships between phenomena based on commonalities and differences observed across multiple instances.

1. Classes of Argumentation:
Induction

2. Induction is the process of reasoning whereby
from the concurrence or conjunction of
particular instances or phenomena we draw a
general principle, rule o postulate.
In Induction, the mind starts from particular
phenomena, facts or instances; and from their
conjunction or concurrence it infers a general
truth.

5. “If two or more instances of a phenomenon under
investigation have only one instances in common , the
circumstances in which one alone all the instances
agree is the cause of the given phenomenon.”
The Method of agreement

6. Method of agreement

7. Example:
Some cities have markedly lower rates of tooth decay.
- Is there anything else these cities share in common?
• If so, that is the likely cause of lower rates
of tooth decay.

8. Four patients all show amnesia after brain injury:
- Patient 1--damage to the prefrontal cortex and the
hippocampus
-Patient 2--damage to the hippocampus and amygdala
-Patient 3--damage to the thalamus and hippocampus
- Patient 4--damage to the hypothalamus and hippocampus

9. The Method of difference
“If an instance in which the phenomenon under
investigation occurs, and instance in which it does not
occur, have every circumstance in common save one,
that one occurring only in the former; the circumstance
in which alone the two circumstances differ, is the
effect, or the cause or an indispensable part of the cause,
of the phenomenon.”

10. Example:
A B C D occur together with w x y z.
B C D occur together with x y z.
Therefore, A is the cause or the effect or an
indispensable part of the cause of W.

11. The Joint method of agreement and difference
“If two or more instances, in which the phenomenon
occurs, have only one circumstance in common, while
two or more instances in which it does not occur have
nothing in common save the absence of the
circumstance; the circumstance in which alone the two
sets differ is the effect, or the cause, or an indispensable
part of the cause of the phenomenon.”

12. Example:
Five factory workers are found to be inefficient relative
to others who are doing the same work.
The efficient workers and the inefficient workers were
found to be similar in all relevant ways except one: the
inefficient workers were not part of a profit sharing
plan.
Conclusion: profit sharing causes efficiency.

13. The Method of residues
“Sub duct from any phenomenon such part is known
by previous inductions to be the effect of certain
antecedents, and the residue of the phenomenon is
the effect of the remaining antecedents.”

14. Example:
A B C ----- 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 of x

15. The Method of concomitant variations
“Whatever phenomenon varies in any manner when
ever another phenomenon varies in some particular
manner is either a cause or an effect of the
phenomenon or connected with it’s through come fact
of causation.”

16. A B C ---- X Y Z
A + B C ---- X + Y Z
Therefore, A is always connected with X
Eating one fish meal a week reduced the risk of heart attack by
50%,
Eating just two fish a month reduced the risk of heart attack by
30%
Therefore, eating fish can reduce the risk of heart attack.

17. What is Mill saying?
Mill’s methods are useful in clarifying our
understanding of cause and how we test for
it.
one and only one factor is the cause, and it
is one you have considered.

18. Argument from Antecedent Probability

19. Antecedent Probability
Is an inference from a known cause to an
unknown effect. This type of argument is also
called an priori argument.
This is an argument from cause to effect.
To bring another fact.

21. Reference:
http//www.Science and Mill's Methods of Induction by Roberto
Ruiz on Prezi.com
Phil12_W10_Mill's_methods(2-22-2010).pdf
http://en.wikipedia.org/w/index.php?title=Inductive_reasoning&old
id=559982096
Deductive and Inductive Arguments", Internet Encyclopedia