It should be observed that the cogency of the proof depends entirely
upon its tending to show the unconditionality of the sequence A-_p_, or
the indispensability of A as a condition of _p_. That _p_ follows A,
even immediately, is nothing by itself: if a man sits down to study and,
on the instant, a hand-organ begins under his window, he must not infer
malice in the musician: thousands of things follow one another every
moment without traceable connection; and this we call 'accidental.' Even
invariable sequence is not enough to prove direct causation; for, in
our experience does not night invariable follow day? The proof requires
that the instances be such as to show not merely what events _are_ in
invariable sequence, but also what _are not_. From among the occasional
antecedents of _p_ (or consequents of A) we have to eliminate the
accidental ones. And this is done by finding or making 'negative
instances' in respect of each of them. Thus the instance
A D E
_p s t_
is a negative instance of B and C considered as supposable causes of _p_
(and of _q_ and _r_ as supposable effects of A); for it shows that they
are absent when _p_ (or A) is present.
To insist upon the cogency of 'negative instances' was Bacon's great
contribution to Inductive Logic. If we neglect them, and merely collect
examples of the sequence A-_p_, this is 'simple enumeration'; and
although simple enumeration, when the instances of agreement are
numerous enough, may give rise to a strong belief in the connection of
phenomena, yet it can never be a methodical or logical proof of
causation, since it does not indicate the unconditionalness of the
sequence. For simple enumeration of the sequence A-_p_ leaves open the
possibility that, besides A, there is always some other antecedent of
_p_, say X; and then X may be the cause of _p_. To disprove it, we must
find, or make, a negative instance of X--where _p_ occurs, but X is
absent.
So far as we recognise the possibility of a plurality of causes, this
method of Agreement cannot be quite satisfactory. For then, in such
instances as the above, although D is absent in the first, and B in the
second, it does not follow that they are not the causes of _p_; for they
may be alternative causes: B may have produced _p_ in the first
instance, and D in the second; A being in both cases an accidental
circumstance in relation to _p_. To remedy this shortcoming by the
method of Agreement itself, the only course is to find more instances of
_p_. We may never find a negative instance of A; and, if not, the
probability that A is the cause of _p_ increases with the number of
instances. But if there be no antecedent that we cannot sometimes
exclude, yet the collection of instances will probably give at last all
the causes of _p_; and by finding the proportion of instances in which
A, B, or X precedes _p_, we may estimate the probability of any one of
them being the cause of _p_ in any given case of its occurrence.
Public-domain text, read in full here on John Shaqi.
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