INDUCTION
Induction is a method of reasoning that moves from specific instances to a
general conclusion. Also called inductive reasoning.
In an inductive argument, a rhetor (that is, a speaker or writer) collects a
number of instances and forms a generalization that is meant to apply to all
instances. (Contrast with deduction.)
Examples and Observations
"Induction operates in two ways. It either advances a conjecture
(inference/ assumption) by what are called confirming instances, or it
falsifies a conjecture by contrary or disconfirming evidence. A common
example is the hypothesis that all crows are black. Each time a new
crow is observed and found to be black the conjecture is increasingly
confirmed. But if a crow is found to be not black the conjecture is
falsified."
(Martin Gardner, Skeptical Inquirer, Jan.-Feb., 2002
"If you have trouble remembering the difference
between inductive and deductive logic, consider their roots. Induction
comes from Latin for 'to induce' or 'to lead.' Inductive logic follows a
trail, picking up clues that lead to the end of an
argument. Deduction (both in rhetoric and expense accounts) means 'to
take away.' Deduction uses a commonplace to pull you away from your
current opinion."
(Jay Heinrichs, Thank You for Arguing: What Aristotle, Lincoln, and
Homer Simpson Can Teach Us About the Art of Persuasion. Three Rivers
Press, 2007
"Inductively valid, or correct, arguments, unlike deductively valid ones,
have conclusions that go beyond what is contained in their premises.
The idea behind valid induction is that of learning from experience. We
often observe patterns, resemblances, and other kinds of regularities in
our experiences, some quite simple (sugar sweetening coffee), some
very complicated (objects moving according to Newton's laws—well,
Newton noticed this, anyway)...
"Here is a simple example of an inductively valid argument of the kind
sometimes called induction by enumeration:
I loaned my friend $50 last November and he failed to pay me back.
(Premise) I loaned him another $50 just before Christmas, which he
hasn't paid back (Premise), and yet another $25 in January, which is still
unpaid. (Premise) I suppose it's time to face facts: He's never going to
pay me back. (Conclusion)
"We use inductive reasoning so frequently in everyday life that its
nature generally goes unnoticed."
(H. Kahane and N. Cavender, Logic and Contemporary Rhetoric, 1998)
Characteristics of Induction
In deductive argument, the conclusion necessarily follows from the premises.
The premises demonstrate the truth of the conclusion as they imply it.
On the other hand induction deals with those inferences which derive
universal conclusions from instantial premises. Hence inductive arguments
are not to be classified as valid or invalid which is a characteristic feature of
deductive arguments.
But inductive arguments are characterized as probable, and there are degrees
of probability. Again it should be noted that inductive logic does not formulate
arguments, but studies the nature of inductive arguments with a view to
laying bare the structure and procedure of generalizations.
Further it was noticed that the basis of primary induction is observation of
particular instances. That is by observation or experiment of facts we are able
to make inductive generalizations. Thus observation and experiment provide
the material basis of induction.
Again inductive leap is a very important feature of induction. Without
inductive leap no inference can be characterized as truly inductive. Therefore
having an inductive leap is considered as an essential feature of inductive
generalization.
Further because of the leap involved in induction an inductive argument is
considered probable. Since all inductions are about propositions relating to
matters-of-fact such propositions lack analytical certainly.
Any such proposition is contingently true and its opposite is also a possibility.
So probability is another important characteristic of an inductive
generalization.
Thus having been based on observation of facts, having an inductive leap and
having been about the world of facts and thereby being probable are the
significant characteristics of induction proper.
In absence of any of these characteristics no inference can be considered as
induction proper. Hence any process of inference can be characterized as
inductive if its conclusion is based on observation of instances, possesses an
inductive leap, i.e. passes from some to all or observed to unobserved and is a
real proposition which is only contingently true.
There are three such kinds of inference and they are scientific induction,
unscientific induction analogy.
There are some simulating forms which give the appearance of being
induction but are not inductions at all. Any inference that does not possess the
essential features of induction is not an induction.
In some of the text books induction by complete enumeration, parity of
reasoning and colligation of facts are named as induction-improperly-so-
called. But since they are not to be classed as inductions calling them as
induction is misleading. In induction by complete enumeration the conclusion
does not possess any inductive leap for it is established after exhaustive
enumeration.
The conclusion here is a universal proposition based on observation of all
facts connected with this induction. After individually verifying all the cases
and subsuming them under one proposition a universal proposition is formed.
So perfect induction by complete enumeration is more of a deductive
argument than an inductive argument.
To make assertions like ‘every month of English calendar has less than thirty
two days’, ‘every planet rotates round the sun’, ‘each student in a particular
class knows English’ etc. are examples of this type of induction. Similarly in
parity of reasoning the conclusion is a mathematical assertion deductively
drawn from some theories or axiom.
Here it is taken that what-ever reasoning holds in a single case the same
reasoning will apply in every other similar case. For example, after proving
that the interior angles of a triangle are equal to two right tangles we
generalize that the same reasoning will apply in case of every other triangle.
So there is a generalization that the interior angles of every triangle will make
two right angles. But such an inference is not at all inductive for it is not based
on any observation of facts. Since it is not based on any observation of facts,
the conclusion reached here is not a real proposition.
The conclusion is a mathematical proposition which is necessarily true. So
most of the important characteristics of induction are lacking in induction by
parity of reasoning. Similarly in colligation of facts a set of observed
phenomena is brought under a notion or a class name. After going round a
building one forms the idea that it is an educational institute.
In this form of reasoning new concepts are formed by binding together many
observed facts. But no inductive leap is involved in this process of thinking.
Thus induction by complete enumeration, parity of reasoning and colligation
of facts are not considered as induction and therefore are not discussed in this
chapter which deals with induction as a form of inference.
