Editing History of logic (section)

===Logic in medieval Europe===
[[File:Britoquestionsonoldlogic.jpg|alt=Top left corner of early printed text, with an illuminated S, beginning "Sicut dicit philosophus"|thumb|[[Radulphus Brito|Brito's]] questions on the ''Old Logic'']]

"Medieval logic" (also known as "Scholastic logic") generally means the form of Aristotelian logic developed in [[Middle Ages|medieval Europe]] throughout roughly the period 1200–1600.<ref name="Boehner p. xiv"/> For centuries after Stoic logic had been formulated, it was the dominant system of logic in the classical world. When the study of logic resumed after the [[Dark Ages (historiography)|Dark Ages]], the main source was the work of the Christian philosopher [[Boethius]], who was familiar with some of Aristotle's logic, but almost none of the work of the Stoics.<ref name="Kneale198">Kneale p. 198</ref> Until the twelfth century, the only works of Aristotle available in the West were the ''Categories'', ''On Interpretation'', and Boethius's translation of the [[Isagoge]] of [[Porphyry (philosopher)|Porphyry]] (a commentary on the Categories). These works were known as the "Old Logic" (''Logica Vetus'' or ''Ars Vetus''). An important work in this tradition was the ''Logica Ingredientibus'' of [[Peter Abelard]] (1079–1142). His direct influence was small,<ref>Stephen Dumont, article "Peter Abelard" in Gracia and Noone p. 492</ref> but his influence through pupils such as [[John of Salisbury]] was great, and his method of applying rigorous logical analysis to theology shaped the way that theological criticism developed in the period that followed.<ref>Kneale, pp. 202–203</ref> The proof for the [[principle of explosion]], also known as the principle of Pseudo-Scotus, the law according to which any proposition can be proven from a contradiction (including its negation), was first given by the 12th century French logician [[William of Soissons]].

By the early thirteenth century, the remaining works of Aristotle's ''Organon'', including the ''[[Prior Analytics]]'', ''[[Posterior Analytics]]'', and the ''[[Sophistical Refutations]]'' (collectively known as the ''[[Logica Nova]]'' or "New Logic"), had been recovered in the West.<ref>See e.g. Kneale p. 225</ref> Logical work until then was mostly paraphrasis or commentary on the work of Aristotle.<ref>Boehner p. 1</ref> The period from the middle of the thirteenth to the middle of the fourteenth century was one of significant developments in logic, particularly in three areas which were original, with little foundation in the Aristotelian tradition that came before. These were:<ref>Boehner pp. 19–76</ref>

* The theory of [[Supposition theory|supposition]]. Supposition theory deals with the way that predicates (''e.g.,'' 'man') range over a domain of individuals (''e.g.,'' all men).<ref>Boehner p. 29</ref> In the proposition 'every man is an animal', does the term 'man' range over or 'supposit for' men existing just in the present, or does the range include past and future men? Can a term supposit for a non-existing individual? Some medievalists have argued that this idea is a precursor of modern [[first-order logic]].<ref>Boehner p. 30</ref> "The theory of supposition with the associated theories of ''copulatio'' (sign-capacity of adjectival terms), ''ampliatio'' (widening of referential domain), and ''distributio'' constitute one of the most original achievements of Western medieval logic".<ref>Ebbesen 1981</ref>
* The theory of [[Syncategorematic term|syncategoremata]]. Syncategoremata are terms which are necessary for logic, but which, unlike ''categorematic'' terms, do not signify on their own behalf, but 'co-signify' with other words. Examples of syncategoremata are 'and', 'not', 'every', 'if', and so on.
* The theory of [[Logical consequence|consequences]]. A consequence is a hypothetical, conditional proposition: two propositions joined by the terms 'if ... then'. For example, 'if a man runs, then God exists' (''Si homo currit, Deus est'').<ref>Boehner pp. 54–55</ref> A fully developed theory of consequences is given in Book III of [[William of Ockham]]'s work [[Summa Logicae]]. There, Ockham distinguishes between 'material' and 'formal' consequences, which are roughly equivalent to the modern [[Material conditional|material implication]] and [[logical implication]] respectively. Similar accounts are given by [[Jean Buridan]] and [[Albert of Saxony (philosopher)|Albert of Saxony]].

The last great works in this tradition are the ''Logic'' of John Poinsot (1589–1644, known as [[John of St Thomas]]), the ''Metaphysical Disputations'' of [[Francisco Suarez]] (1548–1617), and the ''Logica Demonstrativa'' of [[Giovanni Girolamo Saccheri]] (1667–1733).