science and logic) means "to derive by reasoning, to lead to something
as a conclusion, or inference, to suggest or imply," and induction "as
the process of inferring a general law or principle from observation
of particular instances." Another version is the "adducing (pulling
together) of a number of separate facts, particulars, etc. especially
for the purpose of proving a general statement."
My 1967 edition of the Encyclopedia Britannica (E. Brit.) gives two
versions by John Stuart Mill: "the operation of discovering and
proving general propositions" or "that operation of the mind by which
we infer that what we know to be true in a particular case or cases
will be true in all cases that resemble the former in certain
assignable respects."
A paraphrase of Francis Bacon's view (also from the E. Brit.) is "a
selective process of elimination among a number of alternative
possibilities." The E. Brit. in a separate entry defines primary
induction as "the deliberate attempt to find more laws about the
behavior of the thing that we can observe and so to draw the
boundaries of natural possibility more narrowly" (that is, to look for
a generalization about what we can observe), and secondary induction
as "the attempt to incorporate the results of primary induction in an
explanatory theory covering a large field of enquiry" (that is, to try
to fit the generalization made by primary induction into a more
comprehensive theory).
E. Mayr in his Growth of Biologic Thought [6] offers this definition:
"inductivism claims that (we) can arrive at objective unbiased
conclusions only by...recording, measuring, and describing what we
encounter without any root hypothesis...."
Deduction.
Sherlock Holmes' "Elementary, my dear Watson!" has made deduction
common knowledge a more familiar feature than induction in problem
solving. The OED definition of to deduce is "to show or hold a thing
to be derived from etc..." or "to draw as a conclusion from something
known or assumed, to infer"; deduction thus is "inference by reasoning
from generals to particulars," or "the process of deducing from
something known or assumed..."
Both terms define systems of logic the purpose of which is to solve
problems, in the one case by looking for a general characteristic
(generalization, conclusion, conjecture, supposition, inference, etc.)
in a set or group of observations, in the other to identify a
particular instance through its resemblance to a set or group of known
instances or observations. Popper's ridicule of induction was based on
the premise that induction requires the observation of every instance
of a given phenomenon for the generalization to be true-an obvious
impossibility; the fact that all known crows are black, for example,
doesn't prove that no white crows exist. Of course it is ridiculous
when looked at in this way, but what really matters is that most if
not all crows are black, and even if a white one should show up and
prove to be a crow and not another kind of bird, most crows would
still be black. His argument can also be used to make deduction
useless for it, too, is based on an incomplete set of known facts.
Even if the identified fact resembles the members of the set, how can
we be sure that every possible feature of either the unknown or the
members of the set itself has been considered? As we will see in what
follows, in many of the examples of the way science is practiced,
induction is as much a part of this practice as is deduction or any
system of logic that serves the purpose of advancing knowledge.
Induction and deduction are two, usually different but never
contradictory, approaches to problem solving. The problem must be
solved by testing the validity of the conclusion or inference, etc.
reached from either direction. Induction and deduction are thus
valuable, often complementary, tools that facilitate problem solving.
http://www.ssr.org/Induction.html
