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:
It follows: |
or in general an inference of the following form:
... | |
It follows: |
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.