Head of Chrysippus, Roman copy of a Hellenistic original, Louvre
Chrysippos of Soloi (* 281/76 BC in Soloi in Cilicia ; † 208/4 BC probably in Athens ), usually cited in the short form Chrysippus , was a Greek philosopher who, after the death of his teacher Kleanthes 232 / 1 v. Became head of the Stoa school and renewed it as one of its most important representatives. His most famous disciples were Diogenes of Babylon and Zenon of Tarsus , who later directed the Stoa.
His teaching, which he laid down in 705 scrolls, was considered authoritative for generations. The stoic teaching was systematized by him in ethics , logic and physics . Together with Zeno von Kition , he created a materialistic epistemology based on perception . For him, concepts were generalizations of the objects contained in perception. He led logic beyond Aristotle through a clear distinction between object , meaning and linguistic designation . He emphasized what he believed to be an expedient, anthropocentric world through the Logos . Chrysippus was the first to formulate the ideal of the stoic wise man in ethics , who lives in freedom from affects such as fear , hate , love and lust , but in harmony with the (naturally expedient) laws of the world.
logic
Chrysipp's extensive grammatical logic is only very fragmentarily attested in commentaries by later Stoics or critics; the most detailed source comes from the skeptic Sextus Empiricus , who meticulously torn apart the stoic logic. Despite this bad tradition, Chrysipp's main ideas, with which he shaped the later Stoic logic, are certain. As a small core of his logic, he created the prototype of the two-valued axiomatic propositional logic. He defined statements as true or false and separated them from questions, commands, wishes and other non-statements. Essential logical components are the conjunction and , the negation not , the conditional if and the alternative either ... or . For them he gave two-valued semantics according to the method of Philo of Megara ; it can be translated into modern truth tables if you set 1 for true and 0 for false :
(In the vertical the values for A, in the horizontal the values for B, with A B)
This two-valued model still determines classical propositional logic today . With him Chrysipp could determine the validity of his axioms by inserting the truth values, namely the five unprovable , which he formulated with Greek ordinal number variables as follows:
Chrysippus' unprovable syllogisms
If the α ', the β'. Furthermore the α '. So the β '.
If the α ', the β'. Furthermore, not the β '. So not the α '.
Not the α 'and the β' at the same time. Furthermore the α '. So not the β '.
Either the α 'or the β'. Furthermore the α '. So not the β '.
Either the α 'or the β'. Also not the α '. So the β '.
He supplemented these axioms with four themes in the form of metalogical rules, of which the Stoic fragments only mention two explicitly, but possibly not in their original form. In any case, there is no doubt that Chrysippus formulated the first explicit logical calculation in an almost formalized form. However, it is not yet a complete classical calculus in the modern sense, although Chrysippus made a kind of claim to completeness that he could prove everything else with the five unprovable , which Sextus Empiricus skeptically classified as a dream and actually can only be proven with certain hypotheses.
The five unprovable syllogisms of Chrysipps have been known as hypothetical syllogisms since late antiquity (around the 2nd century) . Under this name they spread through Boëthius in medieval logic. However, its originator was forgotten early on, and its origin in the Stoa in general. Since then, the Chrysippian logic has been anonymously passed on to modern logic. The name hypothetical syllogisms says that it is a question of logical rules in the form of a syllogism made up of two premises and a conclusion, the first name hypothetically originally being a synonym for Chrysipp's designation Unprovable ; In modern terms this means that we are dealing with propositional axioms . Even in late antiquity, other hypothetical syllogisms were occasionally added to Chrysippus' list of axioms, so that today they are generally understood to be propositional syllogisms. The epithet hypothetical then became a general technical term for propositional expressions, so that this keyword refers to stoic influence.
swell
Diogenes Laertios : Lives and Opinions of Famous Philosophers 7, 179–201.
Karlheinz Hülser (Ed.): The fragments for the dialectic of the Stoics , volumes 3 and 4, Frommann-Holzboog, Stuttgart-Bad Cannstatt 1987/88.
literature
Richard Goulet, Pierre Hadot , François Queyrel: Chrysippe de Soles. In: Richard Goulet (ed.): Dictionnaire des philosophes antiques. Volume 2, CNRS Éditions, Paris 1994, ISBN 2-271-05195-9 , pp. 329-3365
Oskar Becker : Two studies on ancient logic (= Classical-philological studies 17, ZDB -ID 130711-3 ). Harrassowitz, Wiesbaden 1957.
Michael Frede : The stoic logic (= treatises of the Academy of Sciences in Göttingen, Philological-Historical Class. F. 3, No. 88). Vandenhoeck and Ruprecht, Göttingen 1974, ISBN 3-525-82354-1 (also: Göttingen, Univ., Habil.-Schr. 1972).
Josiah B. Gould: The Philosophy of Chrysippus. State University Press, Albany NY 1970, ISBN 0-87395-064-X .
Teun Tieleman: Chrysippus' On Affections. Reconstruction and interpretation (= Philosophia antiqua 94). Brill, Leiden et al. 2003, ISBN 90-04-12998-7 .
