History of Logic from Aristotle to Gödel

by Raul Corazzon | e-mail: rc`@`

ontology.co

"Interest in medieval logic, and recognition of its significance as an original development of the formal logic founded by Aristotle, has arisen only within the past thirty-five
years [*written in 1966*]. For more than three centuries it had been assumed, by logicians and historians alike, that medieval logic was no more than a scholastic trivialization of
Aristotelian logic, its principal contribution being a fixation of terminology and invention of the mnemonic verse "Barbara", Celarent" etc., used in teaching the figures and moods of the syllogism.
[...] The rediscovery of medieval logic had to wait on the rediscovery of formal logic itself [...] Frege's Begriffschrift appeared in 1879, but its significance was not appreciated until the
beginning of the twentieth century when the Principia Mathematica of Whitehead and Russell gave the major impetus to the development of modern mathematical logic. On the contrary, the leaders of the
new movement claimed that nothing had been done to advance the subject between the time of Aristotle and that of Boole, Peirce, Peano and Frege. Two developments which have taken place during the
past thirty years have rescued medieval logic from oblivion and have stimulated a steadily increasing study of its content. First, the publication by Jan Lukasiewicz, in 1934, of a study which showed
that the logic of unanalyzed propositions, on which modern mathematical logic rests as its most fundamental part, had been discovered in antiquity by the Stoics, led to the further discovery that the
later medieval logicians, in their theory of Consequentiae, had independently developed this fundamental and non-Aristotelian part of logic. In the year 1935 J. Salamucha, a pupil of Lukasiewicz,
published a detailed study of the propositional logic of William of Ockham, and in that same year the present writer published (as his doctoral dissertation) the first modern study of Ockham's
logical writings as a whole. A second development, which has taken place during the past thirty years within modern logic itself, has been the extension of logical investigations into the fields of
semantics, modal logic, and philosophy of language, which turn out to be the areas in which the medieval logicians made their most interesting contributions. By reason of these developments, medieval
logic has received increasing study since 1935 by historically minded logicians and by logically educated historians, and fragments of medieval logical doctrine have become part of the stock in
trade, so to speak, of many contemporary logicians and philosophers of language.

"From "Ernest A. Moody - *The Medieval contribution to logic* - Studium Generale (Jahr. 19, Heft 8, Heidelberg 1966 - pp. 443-452; reprinted in: *Studies in Medieval
Philosophy, Science, and Logic* - University of California Press - Berkeley 1975: pp. 371-392 - notes omitted).

"As the name implies, the theory of properties of terms is intended to provide an account of the different rôles that words can have when they appear as terms in propositions. As a matter of fact these terms are commonly distinguished in Mediaeval logic into such terms as have meaning in their own right (termini significativi) and such as are only significant when joined to terms of the first sort (termini consignificativi).

The former are also named categorematic terms (termini categorematici), the latter syncategorematic terms (termini syncategorematici). However, there seems to be some confusion in so far as syncategorematic terms may be discussed as determining to some extent the actual signification or denotation (=supposition) of the categorematic terms to which they are joined, rather than taken in their own right. It must be borne in mind, then, that when those terms were only taken in their function of determining categorematic terms, Medieval logicians used to deal with them in the tracts on the properties of terms (namely, in the tract De distributionibus).

Whenever they were taken as having some kind of meaning (con-significatio) of their own, or when were determinants (functors) of phrases or of simple propositions, there were dealt with in special tracts, such as those entitled De syncategorematibus, and De consequentiis. Besides, there is another feature peculiar to the Medieval view of the properties of terms: Mediaeval logic apparently assumed that only those categorematic terms truly have significatio which signify forms (or: universal natures), either with the underlying substances of such forms or without. This assumption appears to have widespread in Medieval logic to such an extent, indeed, that the Medieval theory of the properties of terms was, in fact, reduced to a doctrine of significatio in its proper sense. This doctrine was concerned with significatio and its three functions: suppositio, appellatio, and copulatio."

From Lambertus Marie De Rijk, *Logica Modernorum. A Contribution to the History of Early Terminist Logic*, Assen: Van Gorcum & Co., 1967, vol. II, Part one: *The
Origin and Early Development of the Theory of Supposition*, (Chapter XVI: *The Grammatical Origin and Early Development of the Theory of Appellation and Supposition*, pp. 513-514).

(to be continued...)

Annotated Bibliographies on the medieval theories of supposition and mental language:

Annotated Bibliographies of:

On the website "Theory and History of Ontology" (www.ontology.co)