Schemata: The Concept of Schema in the History of Logic

Author:

Corcoran John

Abstract

AbstractSchemata have played important roles in logic since Aristotle'sPrior Analytics. The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 1927 von Neumann paper [31]. Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski's 1933 Convention T [42]. Mathematical logicians recognize the role of schemata in first-order number theory where Peano's second-order Induction Axiom is approximated by Herbrand's Induction-Axiom Schema [23]. Similarly, in first-order set theory, Zermelo's second-order Separation Axiom is approximated by Fraenkel's first-order Separation Schema [17]. In some of several closely related senses, a schema is a complex system having multiple components one of which is atemplate-textorscheme-template, a syntactic string composed of one or more “blanks” and also possibly significant words and/or symbols. In accordance with aside conditionthe template-text of a schema is used as a “template” to specify a multitude, often infinite, of linguistic expressions such as phrases, sentences, or argument-texts, calledinstancesof the schema. The side condition is a second component. The collection of instances may but need not be regarded as a third component. The instances are almost always considered to come from a previously identified language (whether formal or natural), which is often considered to be another component. This article reviews the often-conflicting uses of the expressions ‘schema’ and ‘scheme’ in the literature of logic. It discusses the different definitions presupposed by those uses. And it examines the ontological and epistemic presuppositions circumvented or mooted by the use of schemata, as well as the ontological and epistemic presuppositions engendered by their use. In short, this paper is an introduction to the history and philosophy of schemata.

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

Reference50 articles.

1. Gödel K. , The completeness of the axioms of the functional calculus of logic, In Heijenoort [22], 1967, pp. 582–591.

2. Encyclopedia Britannica, Chicago, London, Toronto, 1953.

Cited by 21 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Logical Hylomorphism Revisited: Aristotle, Tarski, and Corcoran;Studies in Universal Logic;2024

2. The Philosophy of Logic of John Corcoran;Studies in Universal Logic;2024

3. John Corcoran;History and Philosophy of Logic;2021-06-16

4. Schemata and creative thinking ability in cool-critical-creative-meaningful (3CM) learning;International Journal of Sustainability in Higher Education;2020-10-05

5. Absolutely general knowledge*;Philosophy and Phenomenological Research;2020-09-07

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3