Theory: Set of
statements that is supposed to
explain a set
of statements of supposed observable fact. To be minimally
adequate, the theory
must be consistent and
deductively entail what it is supposed to
There are, of course, other possible stipulative
definitions of what a theory is, but normally these comprise that a
theory is a set of statements.
The criterion of minimal adequacy is added to dismiss inconsistent
theories and non-deductive theories. The motivations are as follows.
That inconsistency is an undesirable property for a theory is based
on the fact that in standard logic anything whatsoever follows from an
inconsistent set of statements.
That non-deductiveness is an undesirable property for a theory is
based on the fact that in standard logic a theory that is supposed to
explain whatever it explains in a non-deductive manner does not permit a
deductive step of what a theory is to what it is supposed to explain,
nor indeed a deductive step to the falsehood of the theory if it has a
The consistency requirement removes all manner of theories that
deductively entail consequences known to be
false, and the deductiveness
criterion removes all manner of stories that may be suggestive but don't
really explain deductively.
The relations between a theory, its predictions, and the observations
it explains can be sketched as follows:
Here explanation is a
deduction from a theory, as prediction
is, while expectation is a deduction from a
prediction, and test a
deduction about a prediction based on an
observation. Abduction and
induction are principles of
It should be noted also, since this is often
missed, that any testable theory goes beyond the known facts, for if it
does not it cannot be tested.
The six relations of
inference indicated by arrows in the
above picture may be somewhat more fully explained as follows:
An abduction is the inference of a
Theory to account for a (presumed) Observation. This inference is
normally not deductively valid, and indeed a theory cannot be tested
independently if it does not deductively imply statements that go
beyond the known evidence. A
Theory is a set of statements that has been inferred to account for (a)
presumed observation(s) and has been assigned some probability or
degree of belief (if only tentatively, in some cases).
An explanation is the
inference of a (presumed) observation
from a theory. This inference must be deductively valid to be a proper
explanation. The theory that is presumed may be any theory one has,
and as just indicated good testable theories always go beyond the
known evidence (and therefore never can be
deduced from the evidence).
prediction is the inference of a
presumed statement of fact from a Theory. This presumed statement of
fact is called Prediction (capital P), and a proper Prediction is not
known to correspond to observational fact when it is made. It should
follow deductively from a Theory.
induction is the inference of a new
probability or degree
of belief for a Theory when a new Observation verifies or
falsifies an earlier Prediction. Inductions follow deductively from
the fact that a new Observation that verifies or falsifies an earlier
Prediction has been made together with the rules and assumptions of
An expectation is the inference of a
presumed Observation from a
Prediction. The presumed Observation should not have been made or
refuted when expected, and the degree of its expectation depends on
the probability of or degree of belief in the Theory that allowed the
A test is the inference that a Prediction is true
or false from the fact that the expectation has been found to be true
or false by observation.
Note that in the above outline of only theories are non-deductively inferred, though it also should be added that
inductions can be
inferred deductively only with the help of the assumption of probability
theory and some further assumption.