ction does not depend merely upon
direct Induction.

(4) _Post hoc, ergo propter hoc_: to accept the mere sequence of
phenomena, even though often repeated, as proving that the phenomena are
cause and effect, or connected by causation. This is a very natural
error: for although, the antecedents of a phenomenon being numerous,
most of them cannot be its cause, yet it is among them that the cause
must be sought. Indeed, if there is neither time nor opportunity for
analysis, it may seem better to accept any antecedent as a cause (or, at
least, as a sign) of an important event than to go without any guide.
And, accordingly, the vast and complicated learning of omens, augury,
horoscopy and prophetic dreams, relies upon this maxim; for whatever the
origin of such superstitions, a single coincidence in their favour
triumphantly confirms them. It is the besetting delusion of everybody
who has wishes or prejudices; that is, of all of us at some time or
other; for then we are ready to believe without evidence. The fallacy
consists in judging off-hand, without any attempt, either by logic or by
common sense, to eliminate the irrelevant antecedents; which may include
all the most striking and specious.

(5) To regard the Co-Effects (whether simultaneous or successive) of a
common cause as standing in the direct relation of cause and effect.
Probably no one supposes that the falling of the mercury in his
thermometer causes the neighbouring lake to freeze. True, it is the
antecedent, and (within a narrow range of experience) may be the
invariable antecedent of the formation of ice; but, besides that the two
events are so unequal, every one is aware that there is another
antecedent, the fall of temperature, which causes both. To justify
inductively our belief in causation, the instances compared must agree,
or differ, in one circumstance only (besides the effect). The flowing
tide is an antecedent of the ebbing tide; it is invariably so, and is
equal to it; but it is not the cause of it: other circumstances are
present; and the moon is the chief condition of both flow and ebb. In
several instances, States that have grown outrageously luxurious have
declined in power: that luxury caused their downfall may seem obvious,
and capable of furnishing a moral lesson to the young. Hence other
important circumstances are overlooked, such as the institution of
slavery, the corruption and rapacity of officials and tax-gatherers, an
army too pow