Stoic logic

[1] In contrast, Aristotelian propositions strongly affirm or deny a predicate of a subject and seek to have its truth validated or falsified independent of context.

Knowledge about Stoic logic as a system was lost until the 20th century, when logicians familiar with the modern propositional calculus reappraised the ancient accounts of it.

[10] Aristotle himself was familiar with propositions, and his pupils Theophrastus and Eudemus had examined hypothetical syllogisms, but there was no attempt by the Peripatetic school to develop these ideas into a system of logic.

[12] It was two dialecticians of this school, Diodorus Cronus and his pupil Philo, who developed their own theories of modalities and of conditional propositions.

[13] The logical writings by Chrysippus are, however, almost entirely lost,[12] instead his system has to be reconstructed from the partial and incomplete accounts preserved in the works of later authors such as Sextus Empiricus, Diogenes Laërtius, and Galen.

[13] To the Stoics, logic was a wide field of knowledge which included the study of language, grammar, rhetoric and epistemology.

[5] However, all of these fields were interrelated, and the Stoics developed their logic (or "dialectic") within the context of their theory of language and epistemology.

[17][18] A lekton can be something such as a question or a command, but Stoic logic operates on those lekta which are called "assertibles" (axiomata), described as a proposition which is either true or false and which affirms or denies.

[32] Logical connectives Assertibles can also be distinguished by their modal properties[b]—whether they are possible, impossible, necessary, or non-necessary.

[36] Chrysippus, on the other hand, was a causal determinist: he thought that true causes inevitably give rise to their effects and that all things arise in this way.

[31] A valid example of the fourth indemonstrable (strong modus tollendo ponens or exclusive disjunctive syllogism) is:[48] which, incorporating the principle of double negation, is equivalent to:[48] Many arguments are not in the form of the five indemonstrables, and the task is to show how they can be reduced to one of the five types.

[54] In the 2nd-century BCE Antipater of Tarsus is said to have introduced a simpler method involving the use of fewer themata, although few details survive concerning this.

In addition to describing which inferences are valid ones, part of a Stoic's logical training was the enumeration and refutation of false arguments, including the identification of paradoxes.

[59] The response of Chrysippus however was: "That doesn't harm me, for like a skilled driver I shall restrain my horses before I reach the edge ...

"[59] However, this mastery of logical puzzles, study of paradoxes, and dissection of arguments[60] was not an end in itself, but rather its purpose was for the Stoics to cultivate their rational powers.

[62] Its aim was to enable ethical reflection, permit secure and confident arguing, and lead the pupil to truth.

[60] The end result would be thought that is consistent, clear and precise, and which exposes confusion, murkiness and inconsistency.

[65] The logic of Chrysippus was discussed alongside that of Aristotle, and it may well have been more prominent since Stoicism was the dominant philosophical school.

[68] In the 18th-century Immanuel Kant declared that "since Aristotle ... logic has not been able to advance a single step, and is thus to all appearance a closed and complete body of doctrine.

"[69] To 19th-century historians, who believed that Hellenistic philosophy represented a decline from that of Plato and Aristotle, Stoic logic was seen with contempt.

[70] Carl Prantl thought that Stoic logic was "dullness, triviality, and scholastic quibbling" and he welcomed the fact that the works of Chrysippus were no longer extant.

The code happens to come from the nineteenth-century logician and mathematician George Boole, whose aim was to codify the relations studied much earlier by Chrysippus (albeit with greater abstraction and sophistication).

... his Aristotelian approach to the study and organization of argument-forms would have given his discussion of mixed hypothetical syllogisms an utterly unStoical aspect."

Shenefelt & White 2013, p. 288 e. ^ For a brief summary of these themata see Susanne Bobzien's Ancient Logic article for the Stanford Encyclopedia of Philosophy.

For a detailed (and technical) analysis of the themata, including a tentative reconstruction of the two lost ones, see Bobzien 1999, pp.