Lesson Six
Deduction and Induction
Objective:
• At the end of this topic, the student is expected to:
• know the meaning of induction and deduction.
• 2. be able to distinguish between the different kinds of inductive
and deductive arguments.
• 3. be adept at determining instances of deductive validity and
inductive strength.
Deduction and Induction
• Arguments are traditionally divided into two different types,
deductive and inductive.
• A deductive argument is one in which the conclusion follows
necessarily from the premises; in other words, the premises support
the conclusion in such a way that if they are assumed true, it is
impossible that the conclusion be false.
• An inductive argument is one in which the conclusion follows only
probably from the premises; in other words, the premises support the
conclusion in such a way that if they are assumed true, then, based
on that assumption, it is only probable that the conclusion be true
Three factors that bear upon the evaluation of an
argument as inductive or deductive are the following:
• a. the occurrence of special indicator words – If, in drawing a
conclusion the arguer uses words such as “probable,” “improbable,”
“plausible,” “implausible,” “likely,” “unlikely,” or “reasonable to
conclude,” the evaluator may take such indicators as reason for
considering the argument inductive.
• Neon has unstable isotopes. Therefore, since argon is similar in many
ways to neon, it probably follows that argon has unstable isotopes,
too.
• On the other hand, if the arguer uses words such as “necessarily,”
“certainly,” “absolutely” or “definitely,” the evaluator may consider
the argument deductive.
• If a substance is a noble gas, it is inert. Therefore, since argon is a
noble gas, it necessarily follows that it is inert.
• b. the nature of the inferential link between premises and
conclusion – If this link is such that the conclusion follows necessarily
from the premises, the argument is clearly deductive. To say that the
conclusion follows “necessarily” means that the premises support the
conclusion in such a way that if they are assumed true, it is absolutely
impossible that the conclusion be false.
• All teachers are patient. Ronald is a teacher. Therefore, he is patient.
• On the other hand, if the conclusion does not follow necessarily from
the premises but does follow probably, it is usually best to consider
the argument inductive.
• The vast majority of saleswomen are extroverts. Rose Liam is a
saleswoman. Therefore, Rose Liam is an extrovert.
• the character or form of argument the arguer uses – Sometimes it
happens that an argument contains no indicator words and the
conclusion follows neither necessarily nor probably from the
premises, that is, the premises provide no clear support for the
conclusion. This situation points out the need for the third factor to
be taken into account, which is the character or form of
argumentation the arguer uses.
Five Types of Deductive Arguments
argument based on
mathematics
An argument in which the conclusion depends on some purely arithmetic or
geometric computation or measurement.
A shopper may place two apples and three oranges into a paper bag and then conclude that the bag
contains five fruits. A surveyor might measure a square piece of land and, after determining that it
is 100 feet on each side, conclude that it contains 10,000 square feet.
argument
definition
from
An argument in which the conclusion is claimed to
depend upon the definition of some word or phrase used
in the premise or the conclusion.
Claudia is mendacious, so she tells lies. / This paragraph is prolix,
so it follows that it is excessively wordy.
categorical
syllogism
A syllogism in which each statement begins
with one of these quantifiers: “all”, “no,” “some.”
All lasers are optical devices. Some lasers are surgical
instruments. Therefore, some optical devices are surgical
instruments.
conditional
syllogism
A syllogism having a conditional statement for
one or both of its premises.
If quartz scratches glass, then quartz is harder than glass.
Quartz scratches glass. Therefore, quartz is harder than
glass.
disjunctive
syllogism
A syllogism having a disjunctive statement
(“either...or”) for one or both of its premises.
Either breach of contract is a crime or it is not punishable
by the state. Breach of contract is not a crime. Therefore,
it is not punishable by the state.
Inductive Arguments
• The following are typically inductive forms of argumentation.
Inductive arguments are such that the content of the conclusion is in
some way intended to go beyond the content of the premise. The
premises of such an argument typically deal with some subject that is
relatively familiar, and the conclusion then moves beyond this to a
subject that is less familiar or that little is known about
prediction
The premises deal with some known event in the present
or past, and the conclusion moves beyond this event to
some event in the relative future.
Because certain meteorological phenomena have been observed to
develop over a certain region in the Pacific, a storm will occur there
in the next several hours.
argument
analogy
from
An argument that depends on the existence of an analogy, or
similarity, between two things or state of affairs. Because of the
existence of this analogy, a certain condition that affects the better
known thing or situation is concluded to affect the similar lesser
known thing or situation.
From knowledge that his Mercedes car is an expensive car, I argue that your car,
being a Mercedes, is also expensive.
inductive
generalization
An argument that proceeds from the knowledge of a
selected sample to some claim about the whole group.
Because the members of the sample have a certain
characteristic, it is argued that all the members of the
group have the same characteristic.
One may argue that because three oranges selected from a certain
crate were especially tasty and juicy, all the oranges from that crate
are especially tasty and juicy.
argument from
authority
An argument in which the conclusion rests upon
a statement made by some presumed authority
or witness.
A lawyer may argue that the criminal committed no
murder because an eyewitness testified to that effect
under oath.
argument
on signs
based
An argument that proceeds from the knowledge of a
certain sign to knowledge of the thing or situation that
the sign symbolizes.
When driving on an unfamiliar highway, one might see a sign
indicating that the road makes several sharp turns one mile ahead.
Based on this information, one might argue that the road does
indeed make several sharp turns one mile ahead.
causal inference
An argument that proceeds from knowledge of a cause to
knowledge of the effect or, conversely, from knowledge
of an effect to knowledge of a cause.
From the knowledge that a bottle of wine had been accidentally left
in the freezer overnight, someone might conclude that it had frozen.
(cause to effect) Or, after tasting a piece of chicken and finding
it dry and crunchy, one might conclude that it had been overcooked.
(effect to cause)
Deductive argument
• Although every argument involves the claim that its
premises provide evidence for the truth of its
conclusion, only a deductive argument involves the
claim that its premises provide conclusive evidence.
In the case of deductive arguments the technical
terms valid and invalid are used in place of correct and
incorrect.
• A deductive argument is valid when its premises, if
true, do provide conclusive evidence for its
conclusion, that is, when premises and conclusion are
so related that it is absolutely impossible for the
premises to be true unless the conclusion is true also.
Every deductive argument is either valid or invalid.
The task of deductive logic is to clarify the nature of
the relation between premises and conclusion in valid
arguments, and thus to allow us to discriminate valid
from invalid arguments.
Inductive Argument
• An inductive argument, on the other hand, involves the
claim, not that its premises give conclusive evidence for the
truth of its conclusion, but only that they provide some
evidence for it. Inductive arguments are neither valid nor
invalid in the sense in which those terms are applied to
deductive arguments. Inductive arguments may, of course,
be evaluated as better or worse, according to the degree of
likelihood or probability, which their premises confer upon
their conclusions.
Deductive Validity
• A deductive argument is one in which we expect the conclusion to
follow necessarily from the premises. If the conclusion does in fact
follow necessarily from the premises, the argument is said to be valid.
In other words, a valid deductive argument is an argument in which
the premises support the conclusion in such a way that if they are
assumed true, it is impossible that the conclusion be false.
Conversely, an invalid deductive argument is one in which the
conclusion does not follow necessarily from the premises; in other
words, a deductive argument such that if the premises are assumed
true, it is impossible that the conclusion be false.
• Two immediate consequences follow from these definitions. The first
is that there is no middle ground between valid and invalid. There are
no arguments that are “almost” valid or “almost” invalid. If the
conclusion does follow necessarily, the argument is valid; if not, it is
invalid. The second is that there is only an indirect relation between
validity and truth. For an argument to be valid, it is not necessary
that either the premises or the conclusion be true, but merely that if
the premises are assumed true, it is impossible that the conclusion be
false.
• Just as the occurrence of false premises and a false
conclusion does not prevent an argument from being
valid, so the occurrence of true premises and a true
conclusion does not guarantee validity. the question
is not whether the premises and conclusion are true,
but whether the premises support the conclusion in
such a way that if they are assumed true, it is
impossible that the conclusion be false.
Sound Argument
• A sound argument is a deductive argument that is valid and has true
premises. Both conditions must be met for an argument to be sound,
and if either is missing the argument is unsound. The qualification
that the premises must be true means that all the premises must be
true. Because a valid argument is one such that if the premises are
true it necessarily follows that the conclusion is true, and because a
sound argument does in fact have true premises, it follows that every
sound argument, by definition, will have a true conclusion as well. a
sound argument, therefore, is what is meant by a “good” deductive
argument in the fullest sense of the term.
• SOUND ARGUMENT = VALID ARGUMENT + TRUE PREMISES
Inductive Strength
• An inductive argument is an argument in which we expect the
conclusion to follow only probably from the premises. If the
conclusion does in fact follow probably from the premises, the
argument is said to be strong. In other words, a strong inductive
argument is an inductive argument such that if the premises are
assumed true, then based on that assumption, it is probable that the
conclusion be true. On the other hand, a weak inductive argument is
an inductive argument in which the conclusion does not follow
probably from the premises; in other words, an inductive argument
such that if the premises are assumed true, then, based on that
assumption, it is not probable that the conclusion be true.
•
• As with validity and invalidity, strength and weakness are only
indirectly related to truth and falsity. The central question in
determining strength or weakness is whether the conclusion would
probably be true if the premises were assumed true.
• Conversely, the fact that the premises of an inductive argument are
true and the conclusion probably true does not make the argument
strong.
• A cogent argument is an inductive argument that is strong and has
true premises, and if either condition is missing the argument is
uncogent. A cogent argument is the inductive analogue of a sound
deductive argument and is what is meant by a “good” inductive
argument without qualification. Because the conclusion of a cogent
argument is genuinely supported by true premises, it follows that the
conclusion of every cogent argument is probably true.
• COGENT ARGUMENT = STRONG ARGUMENT + TRUE
PREMISES
•