There are more sophisticated and subtle ways of forming new logics. Hieronymous Pardus (often called “Pardo”) developed an interesting logic. He came from Spain and did some work in Paris between 1481 and 1502. John Longeway describes Pardo’s logic as
defending a wholistic account of the meaning of propositions rather than building up their meanings out of the independently established meanings of their parts.
Traditionally, we consider a proposition like “the chair has four legs” as having a meaning which is assembled by adding the meanings of individual words like “chair” and “four” and “legs” — but Pardo challenges us to grasp the entire proposition as a unit, as atomic, as simple not complex. Offering, however, a slightly different interpretation of Pardo, Professor Nuchelmans at the University of Leiden put it this way:
the signification of the whole complex was commonly held to be of a compositional nature and to be determined by the signification of its parts. As Pardo put it, only incomplex expressions have been given conventional meanings in a primary and immediate way; a propositional complex, such as Homo est animal, on the other hand, has been destined to signify its meaning only in a mediate, consequential and secondary manner, since its signification can be derived from the significations of the incomplex parts.
Let’s let Pardo speak for himself, then. He wrote:
For the truth of a proposition in which there is distribution is recognized by means of a conjunctive descent; and that of a proposition in which there is a term suppositing determinately is recognized by means of disjunctive descent; and of a term suppositing merely confusedly, by means of the disjunct or conjunct descent. For what else is it for a term to be distributed, but for it to be taken for its significata conjunctively, and for a term to supposit determinately, but for it to be taken for its significata disjunctively, and for a term to supposit merely confusedly, but for it to be taken for its significata disjunctly or conjunctly? Therefore, to explicate the way of taking the term (acceptionem explicare) is to descend. Thus, if descent is negated, nothing reliable remains for the cognition of the truth of a proposition on the basis of supposition.
These are murky waters: the reader is advised to re-read the above paragraphs several times slowly. In any case, there is sufficient evidence to show that Pardo was a powerful and creative thinker, capable of executing sophisticated and intricate maneuvers in the subtle landscape of systematic logic.
Sadly, this era of technical sophistication in logic and mathematics faded away: Longeway writes:
I found the excitement at an end when the Renaissance began.
Popular historians have often painted the Renaissance as a time a great intellectual activity. In reality, the natural and mathematical sciences both languished, and philosophy was reduced to trite slogans, during this era. Investigating logical theory during the Renaissance leaves Longeway with the suspicion
that there is little pioneering work to do. What bothered me was the lack of any real semantic theory in these thinkers. Nuchelmans does what he can by them, but despite every effort at respect, in the end he points out “the general neglect” in Renaissance thought “of those fundamental problems to which late-scholastic philosophers gave pride of place.”
Despite the intellectually vacuous Renaissance which constitutes the gap between them, Medieval and modern symbolic logic share a sophisticated subtlety, and have much to say to each other.
