Chain link

In traditional and modern logic, two different, but visually similar final figures (series of implications ) are referred to as chain links .

A chain link in modern logic

In modern logic is under chain circuit ( english chain inference a) propositional conclusion of the form called:

	${\ displaystyle A \ rightarrow B}$
	${\ displaystyle B \ rightarrow C}$
It follows:	${\ displaystyle A \ rightarrow C}$

or in general an inference of the following form:

	${\ displaystyle A_ {1} \ rightarrow A_ {2}}$
	${\ displaystyle A_ {2} \ rightarrow A_ {3}}$
	...
	${\ displaystyle A_ {n-1} \ rightarrow A_ {n}}$
It follows:	${\ displaystyle A_ {1} \ rightarrow A_ {n}}$

An example of a chain link in the modern sense is the following:

	When it rains, the road is wet.
	There is a risk of skidding when the road is wet.
It follows:	When it rains there is a risk of skidding.

Sorites, the chain link in traditional logic

The Sorites (short form of soriticus syllogismus, also cumulative closure, heaping closure, chain connection, syllogismos synthetos, coacervatio, soriticus syllogismus, English only sorites ) is a final form of traditional logic . It is a special abbreviated closing chain. The Stoics used the shortened conclusions (Epiballontes), in that they kept secret or omitted individual sentences in their conclusions (i.e. upper, lower and final clauses) .

The connection of the sentences follows the following scheme: The first sentence connects one term with another. The following sentence, in turn, connects this second term with a third. The next sentence in turn connects the third term with a fourth, and so on, and the final sentence in turn connects with the last term and the term introduced in the first sentence. A special case and example for Sorites is the syllogistic mode Barbara .

A distinction is made between the regressive Aristotelian and the progressive Goclenic Sorites.

Aristotelian Sorites: S is M ₁; M ₁ is M ₂; M ₂ is M ₃; ...; M _n-1 is M _n; M _n is P.; From this it follows: S is P
Goclenic Sorites: M _n is P.; M _n-1 is M _n; ...; M ₂ is M ₃; M ₁ is M ₂; S is M ₁; From this it follows: S is P
example: The stars are bodies; all bodies are mobile; everything movable is changeable; everything that is changeable is perishable: therefore the stars are perishable.

According to Prantl, Marius Victorinus used the Sorites first.

literature

Christian Thiel : Closing the chain. In: Jürgen Mittelstraß (Hrsg.): Encyclopedia Philosophy and Philosophy of Science. Metzler, Stuttgart 1996, ISBN 3-476-02012-6 , 2nd volume, p. 390.
Friedrich Kirchner : Dictionary of basic philosophical terms. Heidelberg 1890.
Rudolf Eisler: Dictionary of Philosophical Terms. Berlin 1904.
Carl Prantl: History of Logic in the Occident. Leipzig 1885.

Aristotelian Sorites

Eduard Zeller: The Philosophy of the Greeks. III, 13., p. 113.
Constantin Gutberlet: Logic and Knowledge Theory. P. 84 f.

Goclenic Sorites

Christian Wolff : Philosophia rationalis sive logica. Section 467.
Wilhelm T. Krug: logic or thought theory. P. 514.
Jakob F. Fries: System of Logic. P. 254 ff.
Hermann Lotze: Principles of Logic and Encyclopedia of Philosophy. P. 46.
Friedrich Kirchner: Catechism of Logic. P. 203.
Constantin Gutberlet: Logic and Epistemology. P. 84 ff.
Benno Erdmann: Logic I. 523 ff.
Christoph Sigwart: Logic. I2.

Web links

Wiktionary: sorites - explanations of meanings, word origins , synonyms, translations (English)