Editing History of logic (section)

==Rise of modern logic==
The period between the fourteenth century and the beginning of the nineteenth century had been largely one of decline and neglect, and is generally regarded as barren by historians of logic.<ref name="ReferenceA"/> The revival of logic occurred in the mid-nineteenth century, at the beginning of a revolutionary period where the subject developed into a rigorous and formalistic discipline whose exemplar was the exact method of proof used in [[mathematics]]. The development of the modern "symbolic" or "mathematical" logic during this period is the most significant in the 2000-year history of logic, and is arguably one of the most important and remarkable events in human intellectual history.<ref name="Oxford Companion p. 500"/>

A number of features distinguish modern logic from the old Aristotelian or traditional logic, the most important of which are as follows:<ref>Bochenski, p. 266</ref> Modern logic is fundamentally a ''calculus'' whose rules of operation are determined only by the ''shape'' and not by the ''meaning'' of the symbols it employs, as in mathematics. Many logicians were impressed by the "success" of mathematics, in that there had been no prolonged dispute about any truly mathematical result. [[Charles Sanders Peirce|C. S. Peirce]] noted<ref>Peirce 1896</ref> that even though a mistake in the evaluation of a definite integral by [[Laplace]] led to an error concerning the moon's orbit that persisted for nearly 50 years, the mistake, once spotted, was corrected without any serious dispute. Peirce contrasted this with the disputation and uncertainty surrounding traditional logic, and especially reasoning in [[metaphysics]]. He argued that a truly "exact" logic would depend upon mathematical, i.e., "diagrammatic" or "iconic" thought. "Those who follow such methods will ... escape all error except such as will be speedily corrected after it is once suspected". Modern logic is also "constructive" rather than "abstractive"; i.e., rather than abstracting and formalising theorems derived from ordinary language (or from psychological intuitions about validity), it constructs theorems by formal methods, then looks for an interpretation in ordinary language. It is entirely symbolic, meaning that even the logical constants (which the medieval logicians called "[[Syncategorematic term|syncategoremata]]") and the categoric terms are expressed in symbols.