as been vaguely conceived; the
extension of empirical laws beyond adjacent cases; the chief errors to
which the estimate of analogies and probabilities, or the application of
the principles of classification are liable; and the reliance upon
direct Induction where the aid of Deduction may be obtained, or upon
observation where experiment may be employed. As to formal fallacies
that may be avoided by adhering to the rules of logical method, this may
suffice.

Sec. 4. There remain many ways in which arguments fall short of a tolerable
standard of proof, though they cannot be exhibited as definite breaches
of logical principles. Logicians, therefore, might be excused from
discussing them; but out of the abundance of their pity for human
infirmity they usually describe and label the chief classes of these
'extra-logical fallacies,' and exhibit a few examples.

We may adopt Whately's remark, that a fallacy lies either (1) in the
premises, or (2) in the conclusion, or (3) in the attempt to connect a
conclusion with the premises.

(1) Now the premises of a sound argument must either be valid
deductions, or valid inductions, or particular observations, or axioms.
In an unsound argument, then, whose premises are supported by either
deduction or induction, the evidence may be reduced to logical rules;
and its failure is therefore a 'logical fallacy' such as we have already
discussed. It follows that an extra-logical fallacy of the premises must
lie in what cannot be reduced to rules of evidence, that is, in bad
observations (Sec. 5), or sham axioms (Sec. 6).

(2) As to the conclusion, this can only be fallacious if some other
conclusion has been substituted for that which was to have been proved
(Sec. 7).

(3) Fallacies in the connection between premises and conclusion, if all
the propositions are distinctly and explicitly stated, become manifest
upon applying the rules of Logic. Fallacies, therefore, which are not
thus manifest, and so are extra-logical, must depend upon some sort of
slurring, confusion, or ambiguity of thought or speech (Sec. 8).

Sec. 5. Amongst Fallacies of Observation, Mill distinguishes (1) those of
Non-observation, where either instances of the presence or absence of
the phenomenon under investigation, or else some of the circumstances
constituting it or attending upon it, though important to the induction,
are overlooked. These errors are implied in the Formal Fallacies of
Induction already treated