David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Bulletin of Symbolic Logic 12 (2):219-240 (2006)
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 . Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski’s 1933 Convention T . 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 . Similarly, in first-order set theory, Zermelo’s second-order Separation Axiom is approximated by Fraenkel’s first-order Separation Schema . In some of several closely related senses, a schema is a complex system having multiple components one of which is a template-text or scheme-template, a syntactic string composed of one or more “blanks” and also possibly significant words and/or symbols. In accordance with a side condition the 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, called instances of 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.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
R. T. Cook (2012). The T-Schema is Not a Logical Truth. Analysis 72 (2):231-239.
Nikolaj Jang Lee Linding Pedersen & Marcus Rossberg (2010). Open-Endedness, Schemas and Ontological Commitment. Noûs 44 (2):329-339.
James S. Johnson (1973). Axiom Systems for First Order Logic with Finitely Many Variables. Journal of Symbolic Logic 38 (4):576-578.
Dale Jacquette (2010). Circularity or Lacunae in Tarski's Truth-Schemata. Journal of Logic, Language and Information 19 (3):315-326.
Christopher Gauker (2001). T-Schema Deflationism Versus Gödel’s First Incompleteness Theorem. Analysis 61 (270):129–136.
Agustin Rayo (1999). Toward a Theory of Second-Order Consequence. Notre Dame Journal of Formal Logic 40 (3):315-325.
Marco Mazzone (2011). Schemata and Associative Processes in Pragmatics. Journal of Pragmatics 43 (8):2148-2159.
Johannes Heidema (1990). An Axiom Schema of Comprehension of Zermelo–Fraenkel–Skolem Set Theory. History and Philosophy of Logic 11 (1):59-65.
J. O. Wisdom (1981). Schemata in Social Science. Part Two: Metatheoretical. Inquiry 24 (1):3 – 19.
Added to index2009-01-28
Total downloads69 ( #20,765 of 1,101,623 )
Recent downloads (6 months)10 ( #19,899 of 1,101,623 )
How can I increase my downloads?