Deductive and Inductive Arguments

A deductive argument is an argument in which it is thought that the
premises provide a guarantee of the truth of the conclusion. In a
deductive argument, the premises are intended to provide support for
the conclusion that is so strong that, if the premises are true, it
would be impossible for the conclusion to be false.

An inductive argument is an argument in which it is thought that the
premises provide reasons supporting the probable truth of the
conclusion. In an inductive argument, the premises are intended only
to be so strong that, if they are true, then it is unlikely that the
conclusion is false.

The difference between the two comes from the sort of relation the
author or expositor of the argument takes there to be between the
premises and the conclusion. If the author of the argument believes
that the truth of the premisesdefinitely establishes the truth of the
conclusion due to definition, logical entailment or mathematical
necessity, then the argument is deductive. If the author of the
argument does not think that the truth of the premises definitely
establishes the truth of the conclusion, but nonetheless believes that
their truth provides good reason to believe the conclusion true, then
the argument is inductive.

The noun "deduction" refers to the process of advancing a deductive
argument, or going through a process of reasoning that can be
reconstructed as a deductive argument. "Induction" refers to the
process of advancing an inductive argument, or making use of reasoning
that can be reconstructed as an inductive argument.

Because deductive arguments are those in which the truth of the
conclusion is thought to be completely guaranteed and not just made
probable by the truth of the premises, if the argument is a sound one,
the truth of the conclusion is "contained within" the truth of the
premises; i.e., the conclusion does not go beyond what the truth of
the premises implicitly requires. For this reason, deductive arguments
are usually limited to inferences that follow from definitions,
mathematics and rules of formal logic. For example, the following are
deductive arguments:

There are 32 books on the top-shelf of the bookcase, and 12 on the
lower shelf of the bookcase. There are no books anywhere else in my
bookcase. Therefore, there are 44 books in the bookcase.Bergen is
either in Norway or Sweden. If Bergen is in Norway, then Bergen is in
Scandinavia. If Bergen is in Sweden, the Bergen is in Scandinavia.
Therefore, Bergen is in Scandinavia.

Inductive arguments, on the other hand, can appeal to any
consideration that might be thought relevant to the probability of the
truth of the conclusion. Inductive arguments, therefore, can take very
wide ranging forms, including arguments dealing with statistical data,
generalizations from past experience, appeals to signs, evidence or
authority, and causal relationships.

Some dictionaries define "deduction" as reasoning from the general to
specific and "induction" as reasoning from the specific to the
general. While this usage is still sometimes found even in
philosophical and mathematical contexts, for the most part, it is
outdated. For example, according to the more modern definitions given
above, the following argument, even though it reasons from the
specific to general, is deductive, because the truth of the premises
guarantees the truth of the conclusion:

The members of the Williams family are Susan, Nathan and Alexander.
Susan wears glasses.
Nathan wears glasses.
Alexander wears glasses.
Therefore, all members of the Williams family wear glasses.

Moreover, the following argument, even though it reasons from the
general to specific, is inductive:

It has snowed in Massachusetts every December in recorded history.
Therefore, it will snow in Massachusetts this coming December.

It is worth noting, therefore, that the proof technique used in
mathematics called "mathematical induction", is, according to the
contemporary definition given above, actually a form of deduction.
Proofs that make use of mathematical induction typically take the
following form:

Property P is true of the number 0.
For all natural numbers n, if P holds of n then P also holds of n + 1.
Therefore, P is true of all natural numbers.

When such a proof is given by a mathematician, it is thought that if
the premises are true, then the conclusion follows necessarily.
Therefore, such an argument is deductive by contemporary standards.

Because the difference between inductive and deductive arguments
involves the strength of evidence which the author believes the
premises to provide for the conclusion, inductive and deductive
arguments differ with regard to the standards of evaluation that are
applicable to them. The difference does not have to do with the
content or subject matter of the argument. Indeed, the same utterance
may be used to present either a deductive or an inductive argument,
depening on the intentions of the person advancing it. Consider as an
example.

Dom Perignon is a champagne, so it must be made in France.

It might be clear from context that the speaker believes that having
been made in the Champagne area of France is part of the defining
feature of "champagne" proper and that therefore, the conclusion
follows from the premise by definition. If it is the intention of the
speaker that the evidence is of this sort, then the argument is
deductive. However, it may be that no such thought is in the speaker's
mind. He or she may merely believe that most champagne is made in
France, and may be reasoning probabilistically. If this is his or her
intention, then the argument is inductive.

It is also worth noting that, at its core, the distinction has to do
with the strength of the justification that the author or expositor of
the argument intends that the premises provide for the conclusion. If
the argument is logically fallacious, it may be that the premises
actually do not provide justification of that strength, or even any
justification at all. Consider, the following argument:

All odd numbers are integers.
All even numbers are integers.
Therefore, all odd numbers are even numbers.

This argument is logically invalid. In actuality, the premises provide
no support whatever for the conclusion. However, if this argument were
ever seriously advanced, we must assume that the author would believe
that the truth of the premises guarantees the truth of the conclusion.
Therefore, this argument is still deductive. A bad deductive argument
is not an inductive argument.

See also the articles on "Argument" and "Validity and Soundness" in
this encyclopedia.