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
For instance, to return to that much debated question
about the arrangement of the stars, there can hardly be any
doubt that what Mitchell,--who started the discussion,--had
in view was the decision between Chance and Design. He
says (_Trans. Roy. Soc._ 1767) "The argument I intend to
make use of... is of that kind which infers either design or
some general law from a general analogy and from the greatness
of the odds against things having been in the present
situation if it was not owing to some such cause." And he
concludes that had the stars "been scattered by mere chance
as it might happen" there would be "odds of near 500,000
to 1 that no six stars out of that number [1500], scattered at
random in the whole heavens, would be within so small a
distance from each other as the Pleiades are." Under any
such interpretation the controversy seems to me to be idle.
I do not for a moment dispute that there is some force in
the ordinary teleological argument which seeks to trace signs
of goodness and wisdom in the general tendency of things.
But what do we possibly understand about the nature of
creation, or the designs of the Creator, which should enable
us to decide about the likelihood of his putting the stars in
one shape rather than in another, or which should allow any
significance to "mere chance" as contrasted with his supposed
all-pervading agency?
22. Reduced to intelligible terms the two following
questions seem to me to emerge from the controversy:--
(I.) The stars being distributed through space, some of
them would of course be nearly in a straight line behind
others when looked at from our planet. Supposing that
they were tolerably uniformly distributed, we could calculate
about how many of them would thus be seen in apparent
close proximity to one another. The question is then put,
Are there more of them near to each other, two and two,
than such calculation would account for? The answer is that
there are many more. So far as I can see the only direct
inference that can be drawn from this is that they are _not_
uniformly distributed, but have a tendency to go in pairs.
This, however, is a perfectly sound and reasonable application
of the theory. Any further conclusions, such as that
these pairs of stars will form systems, as it were, to themselves,
revolving about one another, and for all practical purposes
unaffected by the rest of the sidereal system, are of
course derived from astronomical considerations.[10] Probability
confines itself to the simple answer that the distribution is
not uniform; it cannot pretend to say whether, and by what
physical process, these binary systems of stars have been
'caused'.[11]
Public-domain text, read in full here on John Shaqi.
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