Handout
Deductive vs. Inductive Arguments
Two Types of Reasoning
Think of individual cases of reasoning – a detective trying to solve a murder; a lawyer
trying to win a case; a philosopher trying to argue for free will; a student trying to solve a
math problem.
There are two general types of reasoning we can engage in:
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Deductive reasoning – necessary reasoning
Inductive reasoning – probabilistic reasoning
Definitions
Deductive Argument
A deductive argument involves necessary reasoning.
It is an argument in which it is thought that the conclusion necessarily follows from the
premises.
For example:
(P1) All men are mortal.
(P2) Socrates is a man.
Therefore,
(C) Socrates is mortal
Inductive Argument
An inductive argument involves probabilistic reasoning.
It is an argument in which it is thought that the conclusion probably follows from the
premises.
For example:
(P1) John’s DNA was found at the murder scene.
(P2) John’s blood was found on the murder weapon.
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(P3) The murder victim was John’s ex-wife.
Therefore,
(C) John committed the murder.
Common Misconceptions
Mistake #1: Deductive and inductive arguments cannot have false premises
This is false!

The labels “deductive” and “inductive” refer to the type of reasoning the
argument involves

An argument can still involve necessary reasoning or probabilistic reasoning even
if the premises are false
Example of a deductive argument with false premises:
(P1) All women are rich.
(P2) Socrates is a woman.
Therefore,
(C) Socrates is rich.
Example of inductive argument with false premises:
(P1) In my life, all the dogs I have witnessed are red.
Therefore
(C) All dogs are red.
Mistake #2: Deductive and inductive arguments must have “good” reasoning
This is false!

The labels “deductive” and “inductive” refer to the type of reasoning the
argument involves, not the quality of the reasoning

Think of it this way: a philosopher, mathematician, statistician, scientist, or
lawyer who makes an argument is still using a certain type of reasoning (of
necessity or probability) even if her reasoning is flawed.
Example of a deductive argument with bad reasoning:
(P1) a^2 + b^2 = c^2
(P2) a = 3
2
(P3) b = 4
Therefore,
(C) c = 6
Example of an inductive argument with bad reasoning:
(P1) After one day in Paris, all the people I’ve talked to have been snooty.
Therefore,
(C) All Parisians are snooty.
How to Determine if Deductive or Inductive
Method #1: Indicator Words
Indicator words sometimes give clues as to the type of reasoning the argument involves.
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Deductive indicators – “necessarily”, “must”, “certainly”, “absolutely”
Inductive indicators – “probably”, “plausible”, “likely”, “reasonable to conclude”
Warning – Watch out for arguers using indicator words for rhetorical effect
Method #2: Type of Reasoning
Sometimes it is useful simply to observe the strength by which the conclusion follows
from the premises.
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
Deductive if conclusion follows necessarily from premises
Inductive if conclusion follows probably premises
Warning – Watch out for bad deductive or inductive arguments in which conclusion does
not follow at all
Forms of Argument
Deductive Argument Forms
Deductive arguments involve using premises to arrive at a necessary conclusion. Below
are common types of arguments that fit this description.
1) Argument based on mathematics (except statistical arguments)
Arguments that use arithmetic or geometric computation to arrive at a conclusion
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2) Argument from definition
Arguments in which the conclusion is claimed to depend on the definition of a
word or phrase in the premise.
Example:
(P1) Claudia is mendacious.
Therefore,
(C) Claudia lies.
3) Categorical syllogism
Arguments with (1) two premises and a conclusion; (2) three categories; (3) A
universal or particular quantifier in front of each claim
Example:
(P1) All cats are cute animals.
(P2) Some lions are cats.
Therefore,
(C) Some lions are cute animals.
4) Hypothetical syllogism
Arguments that have a conditional in both of its premises
Example:
(P1) If the 49ers win, he will be happy.
(P2) If he is happy, he will celebrate.
Therefore,
(C) If the 49ers win, he will celebrate.
5) Disjunctive syllogism
Arguments that have a disjunction in one premise and a negation of a part of the
disjunction in the other premise
Example:
(P1) Either the butler committed the murder or the ex-husband did.
(P2) It was not the ex-husband.
Therefore,
(C) The butler committed the murder.
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6) Scientific arguments that applies a general law
Scientific arguments that arrive at a conclusion using a general scientific law
Example
(P1) Boyle’s law says that the pressure exerted by a gas on the walls of its
container is inversely proportional to the volume.
(P2) We reduced the volume of our sample by half
Therefore,
(C) The pressure exerted by the gas on the walls of our container will
double.
Inductive Argument Forms
Inductive arguments involve using premises to arrive at a probable conclusion. Below
are common types of arguments that fit this description.
1) Predictions
Arguments that make a claim about the future based on knowledge of the past
Example:
(P1) She stayed up all night.
(P2) She drank heavily and woke up with a hangover.
(P3) She did not eat breakfast.
Therefore,
(C) She will probably bomb the test.
2) Generalizations
Arguments that make a claim about all members of a group based on a sample
size of the group
Example:
(P1) The football players in my French class are of low intelligence.
Therefore,
(C) All football players in my school are of low intelligence.
3) Causal inference
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Arguments that make a claim based on knowledge of a cause and effect
relationship
Example:
(P1) The chicken at Pedro’s Restaurant was salty.
Therefore,
(P2) The chef at Pedro’s Restaurant must have put too much salt on the
chicken.
4) Argument from analogy
Arguments that depend on the existence of an analogy
Example:
(P1) Christina’s Porsche is a great handling car.
Therefore,
(P2) Angela’s Porsche must be a great handling car.
5) Argument from authority
Arguments that make a claim based on assertions of an expert or authority
Example:
(P1) Stephen Hawking says that the universe began with the big bang.
Therefore,
(P2) The universe began with the big bang.
6) Scientific arguments that use observation/experimentation
Arguments that arrive at a general law based on individual observations
Example:
(P1) Each time we dropped bodies of various weights from various
heights, the time to fall was approximately proportional to the square root
of the distance.
Therefore,
(C) The time required for a body to fall is proportional to the square root
of the distance through which it falls.
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