A System of Logic: Ratiocinative and Inductive, 7th Edition, Vol. I — John Stuart Mill — John Shaqi
A System of Logic: Ratiocinative and Inductive, 7th Edition, Vol. I
John Stuart Mill · en
[4] Since this chapter was written, two treatises have appeared (or
rather a treatise and a fragment of a treatise), which aim at a further
improvement in the theory of the forms of ratiocination: Mr. De Morgan's
"Formal Logic; or, the Calculus of Inference, Necessary and Probable;"
and the "New Analytic of Logical Forms," attached as an Appendix to Sir
William Hamilton's _Discussions on Philosophy_, and at greater length,
to his posthumous _Lectures on Logic_.
In Mr. De Morgan's volume--abounding, in its more popular parts, with
valuable observations felicitously expressed--the principal feature of
originality is an attempt to bring within strict technical rules the
cases in which a conclusion can be drawn from premises of a form usually
classed as particular. Mr. De Morgan observes, very justly, that from
the premises Most Bs are Cs, most Bs are As, it may be concluded with
certainty that some As are Cs, since two portions of the class B, each
of them comprising more than half, must necessarily in part consist of
the same individuals. Following out this line of thought, it is equally
evident that if we knew exactly what proportion the "most" in each of
the premises bear to the entire class B, we could increase in a
corresponding degree the definiteness of the conclusion. Thus if 60 per
cent of B are included in C, and 70 per cent in A, 30 per cent at least
must be common to both; in other words, the number of As which are Cs,
and of Cs which are As, must be at least equal to 30 per cent of the
class B. Proceeding on this conception of "numerically definite
propositions," and extending it to such forms as these:--"45 Xs (or
more) are each of them one of 70 Ys," or "45 Xs (or more) are no one of
them to be found among 70 Ys," and examining what inferences admit of
being drawn from the various combinations which may be made of premises
of this description, Mr. De Morgan establishes universal formulæ for
such inferences; creating for that purpose not only a new technical
language, but a formidable array of symbols analogous to those of
algebra.