Inductive Reasoning
DEDUCTIVE reasoning:
If the premises are true,
the conclusion MUST be true.
So, this is the more certain kind of
reasoning.
But…
It almost always depends on some kind of
INDUCTIVE reasoning:
If the premises are true,
the conclusion is, at best, probably true.
Note: Even if the premises are true,
the conclusion might not be true at all.
It’s
our best guess after weighing the
evidence.
Purpose
The purpose of induction is
to recognize patterns!
When we’re looking for patterns, we begin with
a sample.
A sample is a subset of a population.
A population is the whole group that is being
studied.

These guys are
gathering a
sample of fish
from this creek in
order to find out
something about
this creek’s fish in
general, i.e., the
creek’s fish
population.
Is the sample large enough?
Is it representative?
A sample can either be
Uniform
(all the same)
or
Varied
(different)
The conclusion drawn from the sample
can either be
general (universal)
or
particular
(Think of the Square of Opposition here.)
1. ENUMERATIVE INDUCTION
uniform sample  general conclusion
2. ANALOGICAL INDUCTION
uniform sample  particular conclusion
3. STATISTICAL INDUCTION
varied sample  similarly varied population
ENUMERATIVE INDUCTION
If I see one black crow…
ENUMERATIVE INDUCTION
And then I see a couple more
crows that are black...
ENUMERATIVE INDUCTION
And then we see a few more…
We begin to recognize a pattern, and may
come to the conclusion that
All crows are black.
Uniform sample  General Conclusion
(Universal)
Discovering a pattern this way is
called “Induction by Enumeration”
hint: conclusion is that ALL of the rest are that way
one white crow
William James
“If you wish to upset the law
that all crows are black,
you mustn't seek to show
that no crows are;
it is enough if you prove
one single crow to be white.”
All it takes is one white crow
to prove they’re not all black.
REASONING BY ANALOGY
A has properties x and y
B has properties x and y
A also has property z
B probably has property z as well
ANALOGICAL INDUCTION
uniform sample  particular conclusion
Finding a pattern this way is called an
“Analogical Induction.”
example: All the crows I’ve seen have been
black, so my hypothesis is that
the next crow I see will probably
be black also.
STATISTICAL INDUCTION
Varied Sample  Varied Population
Day 1, Day 2, Day 3, Day 4, Day 5, Day 6, Day 7, Day 8…
every day for x amount of time
Higher Level Induction
We can learn from higher level inductions.
All Cars
My Car
effect to cause
cause to effect
Mill’s Methods
Method of Agreement
Whenever A occurs, B is there.
John Stuart Mill
Method of Difference
Whenever I take B away, A stops happening.
Joint Method
Whenever A occurs, B is there, and
whenever I take B away, A stops happening.
Method of Concomitant Variation
Whenever A increases or decreases,
B increases or decreases proportionately.
Method of Residues
A occurs, and B is the only known potential cause left
after eliminating all the other known possible causes.
III. Scientific Method
1. define the issue
2. gather evidence
3. form hypothesis
4. test
5. evaluate (3 main options)
not looking for verification, but falsification
1. accept
2. reject and revise
(In a testing situation, if you reject, the next step is to REVISE)
3. or suspend judgment
The Problem of Induction
There are no necessary connections
between past events and future events.
David Hume
Scottish Philosopher
1711-1776
How can you be certain?
Stephen Hawking
British theoretical physicist
“No matter how many times the results of
experiments agree with some theory, you
can never be sure that the next time the
result will not contradict the theory.”