Deductive and Inductive Reasoning
What is the difference between deductive reasoning and inductive
reasoning? The former is a matter of applying formal logic to
premises to arrive at a conclusion. When used properly, and when
the premises are correct, the conclusion is necessarily correct.
"Inductive logic," as it is sometimes called, is perhaps
not true logic at all. It is simply the process of drawing conclusions
based on repeated patterns of observation or experience. Even
when the premises are correct, when using induction the conclusions
might be false.
Let's look at some examples. Using deductive reasoning, we
might start with the premises that all life forms have carbon
atoms, and that a given bacterium is a life form, and from there
deduce that the bacterium has carbon atoms. As long as the premises
are correct, the conclusion must be.
Notice that the fallibility of deductive logic is in the possibility
of the premises being wrong. In fact, the premises themselves
are often arrived at using induction. For example, where did
we get the premise that all life forms have carbon atoms? From
the following inductive reasoning: the life forms we have examined
have carbon atoms, therefore all must have them.
Philosopher David Hume denied the logical admissibility of
deductive reasoning. Europeans saw only white swans for centuries,
and so by induction assumed that all swans were white. Then it
was discovered that there were black swans in Australia. This
demonstrates the primary problem with inductive reasoning: It
is impossible to examine all particulars as they are potentially
infinite in number, thus we cannot logically make a valid generalization
in this way.
More than one person has pointed out that inductive reasoning
is almost identical to superstitious reasoning. We note several
instances where someone says "everything is going great,"
followed by everything going wrong, and we "learn"
that it is dangerous to "tempt fate" by saying such
things. That is superstition, but it is also induction. Some
go as far as to say that inductive reasoning is just superstition
dressed up as science.
This criticism is a bit severe, though. Examples of inductive
reasoning are usually classified as "weak induction"
and "strong induction." Superstitions are at best weak
induction. They rely on relatively few particulars and a willingness
to selectively focus on confirming evidence while ignoring anything
that contradicts the given belief. At least when people believed
all swans were white it was based on many thousands of examples
over many centuries, making it strong induction even if it was
later proved false.
Interestingly, although Hume said it is impossible to justify
inductive reasoning (except by induction, making it a circular
argument), he did not dismiss its necessity. He advocated practical
skepticism and common sense that allows for the inevitability
of induction. He pointed out, for example, that in our experience
bread nourishes us, and although that does not logically prove
it always will do so, we have to accept the inductive conclusion
that it will. He added that a person who waited for sound deductive
justifications for everything would starve.
Many philosophers accept this common sense skepticism as the
most appropriate approach to knowledge in general. Both deductive
reasoning and inductive reasoning can fail after all, and yet
we need to reason in some manner. In fact, deductive arguments
are not generally considered true or false, but only valid or
invalid, and sound or unsound. A valid deduction is one in which
the conclusion must be true provided that the premises are true.
A sound deductive argument is one in which we have a high degree
of confidence in the truth of the premises.
It is important to note that outside of closed systems of
mathematics, virtually all deductive arguments rely on inductively-arrived-at
premises, making all claims of knowledge worthy of a bit of skepticism.
If we agree that more carbon dioxide in the air must lead to
a warmer climate, and that we are adding more carbon dioxide
to the air, it is valid to say we are contributing to global
warming. Notice, though, that we only arrive at the first premise
by way of induction: we note that higher carbon dioxide levels
coincided with higher temperatures in the past and assume that
it must always be that way. This isn't an argument against human-caused
global warming, but it does suggest the possibility of our being
To repeat, as powerful and useful as deductive reasoning is,
it is difficult to find an example (again, outside of mathematics)
that does not have much weaker inductive reasoning somewhere
in its foundations. But this doesn't suggest that total skepticism
is called for. For myself, I'll still accept the deductive logic
in the reasoning which says, "gravity acts on all objects,
and I am an object, therefore I shouldn't step off a cliff if
I don't want to fall." I'll also use my own experiences,
and including seeing others fall, to form a similar conclusion
through induction. In other words, I won't be too skeptical of
On the other hand, there is nothing wrong with acknowledging
that the premise of gravity operating on all objects is based
simply on our observations thus far. It is not outside the realm
of the possible that we will someday discover objects which are
not affected by gravity. An open and honest mind requires that
we use deduction and induction, and also that we allow for the
potential fallibility of all the ways in which we reason.