Deduction and
Induction
Truth and Reasoning

All arguments have two basic elements:
statements and inferences.
 Statements
 Inferences
are true or false.
have to do with what “follows from”
a given set of statements.
The following argument (p.54) has a
reasoning problem:
P1: All cats are animals
P2: All dogs are animals
Con: All cats are dogs.
1. Each statement is, individually, true.
2. Since we know the conclusion is false, we know
there must be some problem with the reasoning in
this argument.
The following argument (p. 49) has a
truth problem:
P1: The vast majority of Rose Bowl
games have been played in freezing
cold weather.
Con: Probably the next Rose Bowl
game will be played in freezing cold
weather
Which is wrong with the following argument?
P1: If human rights are recognized, then civilization
flourishes.
P2: If equality prevails, then civilization flourishes.
Con: If human rights are recognized, then equality will
prevail.
Note: you might agree that the conclusion is true,
and maybe it is. But it’s truth does not follow from
the two premises.
Deduction and Induction are characteristics
of inferences.


In a good deductive
argument, the
conclusion follows
with certainty.
There is no
information in the
conclusion that is not
already in the
premises.


In a good inductive
argument, the
conclusion follows
with probability.
There is information
in the conclusion that
is not already in the
premises.
Some Examples of Deduction
Inferences from (non-statistical) math:
certain statements and operations entail
conclusions.
 Inferences from definition: the meaning of
words in the premises entails the truth of
the conclusion.
 Disjunctive syllogism: eliminating one of
two options leaves only the other.

Some Examples of Induction
Predictions: need I say more? 
 Generalizations: information in the
conclusion by definition is broader than
information offered in the premises.
 Causal inferences: these strive for, but
cannot achieve, necessity.

Two Common Confusions about Deduction and Induction
1. “Certainty” and “Probability” are meant logically, not
psychologically.
Psychological certainty is a state of mind; it
expresses something about your attitude toward a
statement.
Logical certainty is a characteristic of arguments; it
arises from a relationship between statements.
2. It is not essential that a deductive inference be
drawn from the general to the particular; nor is it
essential that an inductive inference be drawn from
particular to general.
Two Final Suggestions
1. Your only concern, in determining what
kind of inference is presented, is how the
conclusion follows from the premise(s).
Ignore questions of actual truth.
2. If you are still unsure about the nature
of the inference after applying the
“reasonable person” test, interpret the
inference as inductive.
The Language of
Logical Evaluation
Deductive and Inductive
Terminology
Content v. Inference
Only premises can be true or false
 Only inferences can be valid/strong or
invalid/weak.

 Logical terminology develops to reflect
this distinction between determining
truth and determining acceptable
reasoning.
In ordinary contexts, we say “good” arguments. In
logical contexts, we must clarify what kind of good
argument we mean.
A “Good” Argument
Sound Argument
Cogent Argument
Indicates a good
Indicates a good
deductive
inductive
argument
argument
In ordinary contexts, we say “good” arguments. In
logical contexts, we must also show that our kind of
argument passes the two essential tests of any
argument.
“Good” Argument =
Truth + Good
Reasoning
Sound Arguments
Cogent Arguments
Truth + Certainty
(all or nothing)
Truth + Probability
(degrees of acceptability)
Deductive Reasoning (Soundness)
1.
Valid arguments – If the premises were
true, then the conclusion must be true
2.
Sound arguments – the premises are,
actually, true; and the conclusion must
then be true
Inductive Reasoning (Cogency)
1.
Strong arguments – If the premises were
true, then the conclusion is probably true
2.
Cogent arguments – the premises are,
actually, true; so the conclusion is
probably true (although could always be
false).
Summary
All “good” arguments must have both true
premises and good reasoning.
 The standards for “good” reasoning differ
for deductive and inductive reasoning.

 Sound arguments = true premises and valid
deductive reasoning
 Cogent arguments – true premises and strong
inductive reasoning.