Distribution and proportion (Q1346218)

The author's aim is to defend the Aristotelian concept of distribution against Geach's criticism (see section IV) by applying it to extended syllogistic systems. Section I deals with ``fractional'' syllogistics containing statements of the form ``more than 1/2 of the \(S\) are \(P\)'' or ``at least 7/8 of \(S\) are not \(P\)''. Section II discusses arguments with more than two premisses and three terms, and with additional quantifiers (e.g. ``exactly 3/4 of \(S\) are \(P\)'' or ``at most 3/4 of \(S\) are at least 1/2 of \(P\)''). Section III outlines systems with rational \(x/y\)- quantifiers \((1> x/y> 0)\). From this, according to the author, may arise ``a new approach to the foundations of mathematics''.