29), and divisions into categorical and syncategorematic
His many books (14) and articles display an initial interest in and continuing concentration on formal logic, especially medieval logic, as witnessed by Elements of Formal Logic (Bobbs Merrill, 1965); William of Sherwood's Introduction to Logic (University of Minnesota Press, 1966); William of Sherwood's Treatise on Syncategorematic
Words (University of Minnesota Press, 1968); Paul of Venice: Logica Magna: Part One, On Terms (Oxford University Press for the British Academy, 1979) The Cambridge Translations of Medieval Philosophical Texts: Volume One: Logic and the Philosophy of Language, with Eleonore Stump (Cambridge University Press, 1988); The Sophismata of Richard of Kilvington: Text Edition, with Barbara E.
Accepting an infinity of things, but not infinite wholes, amounts, Leibniz goes on to say in the New Essays, to accepting a syncategorematic infinite but not a categorematic one.
It becomes clear, indeed, that to take the infinite plurality of things as a whole is, for Leibniz, to reverse the true order of precedence: the syncategorematic notion of infinity in fact derives from the hypercategorematic sense.
My concern in this essay is not, however, with Leibniz's notion of the absolute as infinite, but with the question of what room is left in Leibniz's metaphysics for the distinct idea of an indefinite, or syncategorematic, infinite.
64) Such infinities are indefinite or, to fall back on the Scholastic terminology to which Leibniz has recourse, syncategorematic.
expressions include the quantifiers, articles, copulae, truth-functional connectives, and nontruth functional connectives of a language.
This verbal form does not pertain to the verbal function within the dicisign as such (in contrast with the two prior syncategorematic linguistic elements), but rather adds to the language a represignificative element objectifying existence itself as something signified (existentia ut significata), often intending the so-called "real" existence of a physical or mind-independent being (existentia ut exercita).
If we add this new--or, more exactly, this now fully developed, explicit--convention to our scheme of "to be" as a verbal form, we get a third syncategorematic sense (Figure 2).