Inference:
In logic, the assertion of a conclusion, in general because one has already
asserted (and thus accepted) certain premisses one considers sufficient to
assert the conclusion. In natural language, there are terms that
mark conclusions and inferences: "therefore", "so", "since", "because",
"ergo", "it follows", "entails" and others. One important point to be clear about is that
in an inference one detaches the conclusion from
the premisses, and asserts the conclusion by itself because one considers the
premisses sufficient for its assertion. This is valid in deductive logic in
the sense that if the premisses are all true and the conclusion follows from
the premisses, then the conclusion is also true.
There are three basic kinds of inference,
that cover very many specific sorts of inferences:
1. Deductions: To find conclusions
that follow from given assumptions.
2.
Abductions:
To find assumptions from which given
given
conclusions
follows.
3.
Inductions:
To confirm or infirm
(support or undermine) assumptions by showing their conclusions do (not)
conform to the observable facts.
Normally in reasoning all three kinds are
involved: We explain supposed facts by
abductions; we check
the abduced assumptions by deductions of the facts they were to
explain; and we test the assumptions arrived by deducing consequences
and then revise
by inductions the probabilities of
the assumptions by
probabilistic
reasoning
when these consequences are verified or falsified.
In ordinary life, outside mathematics, logic or science, most conclusions
that are inferred are not deductively valid as they are given, either because
this would be difficult or needlessly pedantic or because there is no real
need for a deductively valid conclusion.
Even so, the fundamental checks of any conclusion one regards as important
are (1) whether one can supply a deductively valid argument for it and (2)
whether that argument has only true or only probable premisses.
The first check should guarantee one has, at least in principle, an ifthen
argument with the if made up of premisses and the then the conclusion, which,
since it is a deduction, has the property that if the premisses are true, then
the conclusion is true. The second check should make clear, at least in
principle, how good that ifthen argument is, for a deductive argument has the
property that its conclusion can not be less probable than the probability of
its premisses, and so the less probable the premisses one needed to deduce the
conclusion, the less probable that conclusion is, from those premisses.
(For if pr(QT)=1 then pr(Q&T)=pr(T), and that may be quite small and indeed
must be smaller than pr(S) for any S such that pr(ST)=1.)
Charles Sanders Peirce, who first saw this threesome of kinds of inference
formulated it once as follow, in terms of syllogistic logic
DEDUCTION:
Rule.All the beans from this bag are white.
Case.These beans are from this bag.
.·.Result.These beans are white.
INDUCTION:
Case.These beans are from this bag.
Result.These beans are white.
.·.Rule.All the beans from this bag are white
HYPOTHESIS [ABDUCTION]:
Rule.All the beans from this bag are white.
Result.These beans are white.
.·.Case.These beans are from this bag.
(CP 2.623, 1878)
