Webster's comparison of
words: infer [inference] suggests the arriving at
a decision or opinion by reasoning from known facts or evidence (from your
smile, I infer that you are pleased) deduce
[deduction] in strict discrimination, implies inference from a general
principle by logical reasoning (the method was deduced from earlier
experiments conclude strictly implies an inference that is
the final logical result in a process of reasoning (I must, therefore,
conclude that you are wrong) judge stresses the
careful checking and weighing of premises, etc, in arriving at a conclusion
gather is an informal substitute for infer or conclude (I
gather that you do not care)
Deduction:
A deduction is an
argument
or
theory
starting with
axioms or premises
and leading to a conclusion. The
argument or theory
explains
the
conclusion.
Deduction is used in
essays,
but not
usually in the formal way that it is when setting out a scientific
theory. An example of an essay that does use deduction
this way is James Mill's
Essay on
Government
(1820),
discussed in
Social Science History
chapter one.
John Stuart Mill
contrasted deductive
logic, the
established rules of reasoning dating back to ancient
Greeks like
Aristotle
, with
inductive
logic, the rules by
which one makes legitimate
inferences
from
empirical
data. Both, he said, are necessary for science. Deductive
reasoning is used to create
theories
and testable
hypotheses
for
empirical
research.
In natural science, these deductions will link universal
laws of nature to statements (
propositions)
about things that need explaining. In a paper published in
1948, Carl Hempel and Paul Oppenheim argue that a
form of argument they call deductive-nomological
explanations can be used to link universal laws to
statements - in way that can either explain or predict. If
the explanation predicts, it can be used to test the laws.
Deductive-nomological explanations show deductively
that the thing to be explained comes under certain
general laws. Nomos is a Greek word for law.
A Deductive-nomological explanation starts with Explans Sentences. These
are the sentences that can explain what needs to be explained. The
explanation will have two types of explans:
1) General Laws
2) Conditions (statements which make assertions about
relevant facts): These lead on to the Explanandum Sentences about the
thing to be explained.
For example:
General Law: The volume of a given quantity of any
gas will reduce in line with the pressure that it is under.
Conditions: An experiment that puts pressure on a
quantity of gas.
Explanandum: The volume of the gas decreases at the
same rate that the pressure it is under increases.
The general form of this is:
THE EXPLANS SENTENCES:
L1,L2,...Lr General Laws
C1,C2,...Ck Conditions
-----------
E: THE EXPLANANDUM SENTENCE
If the explans are hypothetical propositions that need
testing, the explanandum is not so much the thing to be
explained, but the thing predicted if the hypothesis is
correct. In other words, the example respecting gas
could be an explanation of why the volume of gas
decreases, if we accept the law; or a test of the law if
we regard it as a hypothesis. (This example is based on
Doyal and Harris 1986) (See
explanation)