Articulating Medieval Logic

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referenced by John Lamont in his review of the draft history-of-logic paper "The Scholastics' Neglected Heritage"
also mentions Jean Poinsot (John of St. Thomas), e.g., p. 5fn6

Aquinas did not discuss general principles of logic much. A full set of views are laid out by his follower John of Saint Thomas (Jean Poinsot) in a very competent work from the early 1600s [Outlines of Formal Logic]; the logical doctrines laid out there mesh nicely with the ones [Parsons] discusse[s in this book]…

I would like to present Articulating medieval logic as theoutline of a research program for medieval logic scholars. The book canbe seen to belong to the first stage of a huge project: a seriousattempt at considering together two different logical paradigms (themedieval' and thepost-Fregean'), in the belief that they arecomparable. The first stage, represented here, is the development of anartificial language that can translate both, and (accompanied by thecorresponding semantics and deductive apparatus) can act as a mediumfor comparison.
Although the book might be used as a way of introducing medieval logicto non-experts (more specifically, to non-experts with a preference forcontemporary formal techniques), it might rather be seen as a way ofoffering medieval logic scholars (more specifically, medieval logicscholars with an interest in contemporary formal techniques) a tool ofanalysis that is adapted to the peculiarities of the medieval way ofdoing logic. In fact, by using this tool in his own research, theauthor intends to show the systematic character of the medieval logicaltradition (p. 1).
Of course, medieval logic is too vast and complex to be articulated asa whole. The author purposely ignores differences and disagreements'(p. 4), bases his work on published (and, mostly, translated intoEnglish) materials (p. 4), and selects a group of outstanding WesternEuropean figures to illustrate his points: from Peter of Spain to Paulof Venice, and even a bit further in the Appendix, to John Major (p.5). But it is the adoption of the point of view of the syllogisticdoctrine that imposes the main restriction: many of the developmentscharacteristic of logica modernorum (sophisms, exposition,obligations, insolubles, etc.) are intentionally left aside (p. 5). The articulation offered in this book contains: (a) a language oflogical forms provided with translating algorithms (Linguish); (b) asemantic apparatus for this language, which contains bothinterpretation for expressions and truth conditions for sentence-forms;(c) a rule system for categorical syllogisms. (a) Concerning language, the lack of variables to expressquantification is the main shortcoming of the logical languagedeveloped by medieval logicians. The artificial language proposed byParsons borrows from modern linguistics the devices for incorporatingvariables without losing the predicative structure of noun-phrases andverbs: Linguish usesmarkers' to make grammatical roles explicit, andadds indexes to allow cross-reference in the case of anaphoricpronouns.
(b) Concerning semantics, the theory of properties of terms (inparticular, the late medieval version of the theory of modes ofpersonal supposition) is given prominence as a semantic tool. Threeparticular devices developed by Parsons are worth mentioning. First,truth conditions are given by means of temporary names' as a way ofincorporating thesingulars' of a common term into a recursivesemantics (pp. 99–113). Second, the complications around propositionswith more than two terms are cleverly solved with the notion of globalquantificational import' (pp. 223–226). Finally, difficulties aboutanaphoric reference are solved by allowing the construction ofmolecular formulas with unfilled roles (pp. 244–251). (c) Concerning the rule system, a powerful extension of Aristotle'soriginal system is not only formally constructed, but also proven to becomplete (pp. 113–122). The structure of the book roughly reflects the development of theAristotelian-scholastic tradition of logic: first, the elements ofAristotelian syllogistics are presented, conveniently supplemented witha modern notion of validity and a formal version of Aristotle'sderivation rules (chapters 1 and 2); second, the late medievaltreatment of the four basic propositional forms is described, and thenarticulated in terms of Linguish and the corresponding semantic andinferential apparatuses (chapter 3 about quantified predicates,singular predicates, and negative terms and chapter 4 about the basicsyntax, semantics and derivation rules for Linguish, plus the firsthalf of chapter 7 about the modes of personal supposition); then, somefurther extensions of that basic logic are introduced, in order tocover propositions of any form and of any degree of complexity (chapter5 about new kinds of common terms, different kinds of complex terms,and new kinds of singular terms, plus the second half of chapter 7 withtheir respective modes of personal supposition, chapter 8 aboutanaphoric words, chapter 10 with some hints about tense and modality,and the Appendix on 16th-century artificial quantifiers). Chapter 6 illustrates three important aspects of the transformation ofAristotelian doctrines in late medieval times. First, the success indealing with relational expressions, and incorporating them into thesyllogistic system (pp. 160–164); second, the possibility of dealingwith multiple quantification without abandoning the predicativestructure of noun-phrases and verbs (pp. 164–173 and 176–183); third,the role of the doctrine of conversion as a trigger for the extensionof logical devices, making room, for example, for quantified predicatesand negative terms (pp. 173–176). These illustrations might serve toquieten the complaints of contemporary formal logicians against thepower of syllogistic logic, and (perhaps) to moderate their contemptfor natural language and the predicative structure that it reflects. Specially designed for people only trained in thepost-Fregean'tradition (and either ignorant of or hostile to the `medieval' one),chapter 9 contains proof that the two logical traditions arecomparable: it offers a translation of Linguish into first-order logic,and a translation of first-order logic into Linguish, plus a validationof the expressive power of Linguish, which consists in showing that (anextension of) Linguish can be used to formulate first-order arithmetic.
In sum, this book could serve as the starting point for an interestingline of research into the strengths and weaknesses of traditional logicin comparison with standard symbolic logic. In fact, Parsons encouragesadditional work in many places in the book: it would be excellent ifsome medieval logic researchers were to dare to follow him. Those whoare interested might want to have a look at the author's website,sites.google.com/site/tparsons5555/home/, which contains someuseful resources in connection with the book. Reviewed by Paloma Pérez-Ilzarbe