# Formal System

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## Formal System

an uninterpreted calculus such that (1) the class of its expressions, or formulas, is usually defined inductively through the specification of primitive (elementary, atomic) formulas and rules for the formation (construction) of formulas and (2) the subclass of provable formulas (theorems) is defined through the specification of a system of axioms and of rules for the derivation of theorems from axioms and already proved theorems (seeRULE OF INFERENCE).

The term “formal system” has many synonyms, which, however, are sometimes used to refer to concepts related to, but not identical with, formal systems. Examples of these synonyms are “formal theory,” “formal mathematics,” “formalism,” “formal calculus,” “abstract calculus,” “syntactic system,” “axiomatic system,” “logistic system,” “formal language,” “formal logic,” “codification,” and “deductive system.”

References in periodicals archive ?
Es en el libro III del System of Logic, el lugar donde Mill desarrolla en completitud su teoria sobre la induccion, aunque en los libros I y II nos entrega ya bastantes lineamientos generales.
But the 'System of Logic' supplies what was much wanted, a text-book of the opposite doctrine--that which derives all knowledge from experience, and all moral and intellectual qualities principally from the direction given to the associations."
One constructs any system of logic by stipulating a small but adequate number of logical operators, such as intersection (or conjunction or ^ or AND), union (or disjunction or v or OR), and negation (or ~ or [logical not] or NOT).
Among his most well-known and significant are A System of Logic (1843); Principles of Political Economy (1848); On Liberty (1859), and Utilitarianism (1863).
In A System of Logic, published in 1843, John Stuart Mill declares that his aim is to attempt a correct analysis of the intellectual process called Reasoning or Inference, and of such other mental operations as are intended to facilitate this: as well as ...
Although A System of Logic is concerned in part with logic, its scope is much broader, most of its voluminous contents being devoted to what Mill called "induction," or scientific method.
The Kal Ve-Chomer system of logic and the Hebrew language, although not unique in this respect, assume that words and sentences could have multiple meanings.
Frege, after deep thought, realized that his system of logic could not handle the contradiction, so that he found his project worthless at the moment of completion.
Ancient Chinese thought boasts no system of logic like that of Aristotle in the West.
Carlyle, pamphlets, Past and Present; Mill, System of Logic
In schools first established under the Carolingians and usually attached to monasteries or cathedrals, the Schoolmen, as distinct from the practicing clergy, were involved in trying to synthesize a Christian system of logic and philosophy based on Aristotle and other ancient scholars.
His effort to bring Hegel's daunting System of Logic into dialogue with recent debates from Quine to Kuhn and beyond on "conceptual change" and paradigms is a very interesting contribution.

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