NotaBene .


Mathematics of Quality, Preference Logic and the Rationality of Desire

This essay introduces and strives to show the untenability of the (somewhat unjustly named) dogma of Aristotelianism. (1) lists the principal tenets of the Aristotelian dogma and examines to what extent they are attributable to Aristotle, (2) analyzes the first part of the dogma the claim that mathematics is the study if quantity and hence is irrelevant to the study of qualitative structures, (3) reviews briefly the concept of semiorder and discusses the possibility to interpret it as the foundation of the mathematical treatment of qualities, (4) traces the genetic links between the algebraic theory of semiorders and the formal elaboration of the so-called preference logic, while (5) develops on this basis a somewhat controversial claim, relating to the last part of the Aristotelian dogma (ir)rationality of desire.
Keywords: philosophy of mathematics, semiorders, logic of preference, rationality.


What is this"?


The paper addresses the question of whether Strawsons claim that ordinary language has no exact logic entails a view according to which it is in ordinary languages nature to be illogical. It is first explained where the traditional idea of an exact, language-independent logic comes from, i.e. the idea of a logic which underlies ordinary languages and governs their logical use and which lack if Strawsons assumption is right would leave ordinary languages being illogical insofar as there would be nothing to eliminate their logical imperfections. Secondly, it is shown that it is inherent to language to human language in contrast to animal ones to be logical, because language games are typically introduced, explained, learned, and played out in a practice of giving and asking for reasons , which means, so to speak, in a logical space. Thus the fact that ordinary language has no exact logic in the sense that there is no one-to-one correspondence between its (grammatico-)syntactic and its (logico-)semantic sentence forms does not exclude the possibilities for it to be used in a logical manner.

Key words: metaphisics, thinking, framed feature model