The Logic of Chance, 3rd edition: An Essay on the Foundations and Province of the Theory of Probability, With Especial Reference to Its Logical Bearings and Its Application to Moral and Social Science and to StatisticsVenn, John
Philosophy
The Logic of Chance, 3rd edition: An Essay on the Foundations and Province of the Theory of Probability, With Especial Reference to Its Logical Bearings and Its Application to Moral and Social Science and to Statistics
Venn, John
Chance; Logic, Symbolic and mathematical; Probabilities; Science -- Methodology
In the first place, it will be seen that in Probability _time_
has nothing to do with the question; in other words, it does
not matter whether the event, whose probability we are discussing,
be past, present, or future. The problem before us,
in its simplest form, is this:--Statistics (extended by Induction,
and practically often gained by Deduction) inform us
that a certain event has happened, does happen, or will
happen, in a certain way in a certain proportion of cases.
We form a conception of that event, and regard it as possible;
but we want to do more; we want to know _how much_ we
ought to expect it (under the explanations given in a former
chapter about quantity of belief). There is therefore a
sort of relative futurity about the event, inasmuch as our
knowledge of the fact, and therefore our justification or
otherwise of the correctness of our surmise, almost necessarily
comes after the surmise was formed; but the futurity
is only relative. The evidence by which the question is to
be settled may not be forthcoming yet, or we may have it by
us but only consult it afterwards. It is from the fact of the
futurity being, as above described, only relative, that I have
preferred to speak of the conception of the event rather than
of the anticipation of it. The latter term, which in some respects
would have seemed more intelligible and appropriate,
is open to the objection, that it does rather, in popular estimation,
convey the notion of an absolute as opposed to a
relative futurity.
2. For example; a die is thrown. Once in six times
it gives ace; if therefore we assume, without examination,
that the throw is ace, we shall be right once in six times.
In so doing we may, according to the usual plan, go _forwards_
in time; that is, form our opinion about the throw beforehand,
when no one can tell what it will be. Or we might go
_backwards_; that is, form an opinion about dice that had
been cast on some occasion in time past, and then correct
our opinion by the testimony of some one who had been a
witness of the throws. In either case the mental operation
is precisely the same; an opinion formed merely on statistical
grounds is afterwards corrected by specific evidence. The
opinion may have been formed upon a past, present, or future
event; the evidence which corrects it afterwards may be our
own eyesight, or the testimony of others, or any kind of inference;
by the evidence is merely meant such subsequent
examination of the case as is assumed to set the matter at
rest. It is quite possible, of course, that this specific evidence
should never be forthcoming; the conception in that
case remains as a conception, and never obtains that degree
of conviction which qualifies it to be regarded as a 'fact.'
This is clearly the case with all past throws of dice the results
of which do not happen to have been recorded.
Public-domain text, read in full here on John Shaqi.
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