Detecting the Logical Content: Burley's 'Purity of Logic'

In one of his inaugural lectures Dov Gabbay demonstrated God’s providence as follows—I quote from memory. God had seen fit to send his revelation to mankind in a language with no verb tenses. (In classical Hebrew the verb forms are distinguished as perfective, imperfective, passive, reduplicative, etc., but not as past, present or future.) So there was a problem to explain how facts about a temporal world can be expressed in a language with no tenses. Logicians could not only solve this problem; they could also apply for research grants for solving it. Thus God ensured that logicians would not go short of spare cash. As a hardened atheist, what can I rescue from this story? Actually, quite a lot. In the history of logic we study texts that are written in a language generally quite different from our own, on subjects that supposedly have something to do with what we understand as logic. The links are often hard to make. One thing that historians of logic do is to describe the deductive practices of earlier thinkers. In this sense Netz’s [13] close study of Euclid’s procedures is an important contribution to the history of Greek logic. Here I try to make a small step in the same direction with a medieval logician. But reconstructing practices is not enough. Netz remarks [13, p. 216]:

[1]  L. Wittgenstein.  Tractatus Logico-Philosophicus , 2021, Nordic Wittgenstein Review.

[2]  Elly van Gelderen,et al.  A History of the English Language , 2000 .

[3]  Philotheus Boehner,et al.  De puritate artis logicae tractatus longior : with a revised edition of the Tractatus brevior , 1955 .

[4]  The distinction of actus exercitus/actus signifi-catus in medieval semantics , 1988 .

[5]  R. Montague,et al.  Logic : Techniques of Formal Reasoning , 1964 .

[6]  Lambertus Marie de Rijk,et al.  The origin and early development of the theory of supposition , 1970 .

[7]  Paul Vincent Spade,et al.  On the Purity of the Art of Logic: The Shorter and the Longer Treatises , 2000 .

[8]  Reviel Netz,et al.  The Shaping of Deduction in Greek Mathematics , 1999 .

[9]  Wilfrid Hodges,et al.  An Editor Recalls Some Hopeless Papers , 1998, Bulletin of Symbolic Logic.

[10]  Pauli Veneti,et al.  Logica Magna, Secunda Pars : Tractatus de veritate et falsitate propositionis et Tractatus de significato propositionis , 1980 .

[11]  E. Bos,et al.  Studies on the history of logic and semantics, 12th-17th centuries , 1996 .

[12]  Victor Sanchez,et al.  Studies on Natural Logic and Categorial Grammar , 1991 .

[13]  J. Locke,et al.  Some thoughts concerning education , 1989 .

[14]  L. D. Rijk.  On the twelfth century theories of fallacy , 1962 .

[15]  M. D. Rijk.  Some 14th Century Tracts on the Probationes Terminorum , 1982 .

[16]  P. Spade.  The Logic of the Categorical: The Medieval Theory of Descent and Ascent , 1988 .

[17]  Wilfrid Hodges.  The Laws of Distribution for Syllogisms , 1998, Notre Dame J. Formal Log..

[18]  Jan Van Eijck.  Syllogistics = Monotonicity + Symmetry + Existential Import , 2005 .