Stoic categories

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A bust of Zeno of Citium, considered the founder of Stoicism

Stoicism is a Hellenistic philosophy that flourished in ancient Greece and Rome. The Stoics believed that the universe operated according to reason, i.e. by a God which is immersed in nature itself. Of all the schools of ancient philosophy, Stoicism made the greatest claim to being utterly systematic.Template:Sfn

The Stoics provided a unified account of the world, constructed from ideals of logic, monistic physics, and naturalistic ethics. These three ideals constitute virtue, which is necessary for 'living a well-reasoned life', seeing as they are all parts of a logos, or philosophical discourse, which includes the mind's rational dialogue with itself.Template:Sfn Its logic focuses on reasoning through propositions, arguments, and the differentiation between truth and falsehood. Its ethics centers on virtue as the highest good, cultivating emotional self-control and rational judgment to attain eudaimonia, while viewing passions as misguided judgments to be mastered.

Stoicism was founded in the ancient Agora of Athens by Zeno of Citium around 300 BCE, and flourished throughout the Greco-Roman world until the 3rd century CE. Stoicism emerged from the Cynic tradition and was popularized through public teaching at the Stoa Poikile, a painted colonnade. Among its adherents was Roman Emperor Marcus Aurelius.

Along with Aristotelian term logic, the system of propositional logic developed by the Stoics was one of the two great systems of logic in the classical world. It was largely built and shaped by Chrysippus, the third head of the Stoic school in the 3rd century BCE. Chrysippus's logic differed from term logic because it was based on the analysis of propositions rather than terms. Stoicism experienced a decline after Christianity became the state religion in the 4th century CE, although Gnosticism lingered and incorporated pure elements of Stoicism and Platoism.

Since then, it has seen revivals, notably in the Renaissance (Neostoicism) and in the contemporary era. Its influence extended to Roman thinkers like Seneca and Epictetus and later influenced Christianity and the Renaissance Neostoicism movement. Stoicism shaped subsequent developments in logic and inspired modern cognitive therapies.

History

Template:Seealso The name Stoicism derives from the Stoa Poikile (Ancient Greek: ἡ ποικίλη στοά), or "painted porch", a colonnade decorated with mythic and historical battle scenes on the north side of the Agora in Athens where Zeno of Citium and his followers gathered to discuss their ideas, near the end of the fourth century BCE. Unlike the Epicureans, Zeno chose to teach his philosophy in a public space. Stoicism was originally known as Zenonism. However, this name was soon dropped, probably because the Stoics did not consider their founders to be perfectly wise and to avoid the risk of the philosophy becoming a cult of personality.

Zeno's ideas developed from those of the Cynics (brought to him by Crates of Thebes), whose founding father, Antisthenes, had been a disciple of Socrates. Zeno's most influential successor was Chrysippus, who followed Cleanthes as leader of the school, and was responsible for molding what is now called Stoicism. Stoicism became the foremost popular philosophy among the educated elite in the Hellenistic world and the Roman Empire to the point where, in the words of Gilbert Murray, "nearly all the successors of Alexander [...] professed themselves Stoics". Later Roman Stoics focused on promoting a life in harmony within the universe, within which we are active participants.

Scholars usually divide the history of Stoicism into three phases: the Early Stoa, from Zeno's founding to Antipater; the Middle Stoa, including Panaetius and Posidonius; and the Late Stoa, including Musonius Rufus, Seneca, Epictetus, and Marcus Aurelius. No complete works survived from the first two phases of Stoicism. Only Roman texts from the Late Stoa survived.

Logic

Chrysippus, the third leader of the Stoic school, wrote more than 300 books on logic. His works were lost, but an outline of his logical system may be reconstructed from fragments and testimony.

For the Stoics, logic (logike) was the part of philosophy which examined reason (logos). To achieve a happy life—a life worth living—requires logical thought. The Stoics held that an understanding of ethics was impossible without logic. In the words of Inwood, the Stoics believed that: Template:Blockquote

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

The Stoic tradition of logic originated in the 4th-century BCE in a different school of philosophy known as the Megarian school. It was two dialecticians of this school, Diodorus Cronus and his pupil Philo, who developed their own theories of modalities and of conditional propositions. The founder of Stoicism, Zeno of Citium, studied under the Megarians, and he was said to have been a fellow pupil with Philo.

However, the outstanding figure in the development of Stoic logic was Chrysippus of Soli (c. 279 – c. 206 BCE), the third head of the Stoic school. Chrysippus shaped much of Stoic logic as we know it, creating a system of propositional logic. The logical writings by Chrysippus are, however, almost entirely lost, instead his system has to be reconstructed from the partial and incomplete accounts preserved in the works of later authors.

Assertibles

The smallest unit in Stoic logic is an assertible (Template:Transliteration), a proposition which is either true or false and which either affirms or denies. Examples of assertibles include "it is night", "it is raining this afternoon", and "no one is walking." Assertibles have a truth-value such that they are only true or false depending on when it was expressed (e.g. the assertible "it is night" will only be true if it is true that it is night).Template:Sfn The Stoics catalogued these simple assertibles according to whether they are affirmative or negative, and whether they are definite or indefinite (or both).

Compound assertibles

Logical connectives
Name	Example
Conditional	if it is day, it is light
Conjunction	it is day and light
Disjunction	either it is day or night
Pseudo-conditional	since it is day, it is light
Causal	because it is day, it is light
Comparative	more likely it is day than night

Compound assertibles can be built up from simple ones through the use of logical connectives, which examine choice and consequence such as "if ... then", "either ... or", and "not both". Chrysippus seems to have been responsible for introducing the three main types of connectives: the conditional (if), conjunctive (and), and disjunctive (or). A typical conditional takes the form of "if p then q"; whereas a conjunction takes the form of "both p and q"; and a disjunction takes the form of "either p or q". The or they used is exclusive, unlike the inclusive or generally used in modern formal logic. These connectives are combined with the use of not for negation. Thus the conditional can take the following four forms: 1) "If p, then q" 2) "If not p, then q" 3) "If p, then not q" 4) "If not p, then not q." Later Stoics added more connectives: the pseudo-conditional took the form of "since p then q"; and the causal assertible took the form of "because p then q".Template:Ref label There was also a comparative (or dissertive): "more/less (likely) p than q".

Modal assertibles

Assertibles can also be distinguished by their modal propertiesTemplate:Ref label—whether they are possible, impossible, necessary, or non-necessary. In this, the Stoics were building on an earlier Megarian debate initiated by Diodorus Cronus. Diodorus had defined possibility in a way which seemed to adopt a form of fatalism. Diodorus defined possible as "that which either is or will be true". Thus, there are no forever unrealised possibilities, whatever is possible is or one day will be true. His pupil Philo, rejecting this, defined possible as "that which is capable of being true by the proposition's own nature", thus a statement like "this piece of wood can burn" is possible, even if it spent its entire existence on the bottom of the ocean. 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. But he was not a logical determinist or fatalist: he wanted to distinguish between possible and necessary truths. Thus, he took a middle position between Diodorus and Philo, combining elements of both their modal systems. Chrysippus's set of Stoic modal definitions was as follows:

Modal definitions
Name	Definition
possible	An assertible which can become true and is not hindered by external things from becoming true
impossible	An assertible which cannot become true or which can become true but is hindered by external things from becoming true
necessary	An assertible which (when true) cannot become false or which can become false but is hindered by external things from becoming false
non-necessary	An assertible which can become false and is not hindered by external things from becoming false

Arguments

In Stoic logic, an argument is defined as a compound or system of premises and a conclusion. A typical Stoic syllogism is: "If it is day, it is light; It is day; Therefore it is light". It has a non-simple assertible for the first premise ("If it is day, it is light") and a simple assertible for the second premise ("It is day"). Stoic logic also uses variables that stand for propositions to generalize arguments of the same form. In more general terms this argument would be: "If p, then q; p; Therefore q."

Indemonstrable arguments

Chrysippus listed five basic argument forms, called indemonstrables,Template:Ref label which all other arguments are reducible to:

Indemonstrable arguments
NameTemplate:Ref label	Description	Example
Modus ponens	If p, then q.  p.  Therefore, q.	If it is day, it is light. It is day. Therefore, it is light.
Modus tollens	If p, then q.  Not q.  Therefore, not p.	If it is day, it is light. It is not light. Therefore, it is not day.
Modus ponendo tollens	Not both p and q.  p.  Therefore, not q.	It is not both day and night. It is day. Therefore, it is not night.
Strong modus tollendo ponens	Either p or q.  Not p.  Therefore, q.	It is either day or night. It is not day. Therefore, it is night.
Strong modus ponendo tollens	Either p or q.  p.  Therefore, not q.	It is either day or night. It is day. Therefore, it is not night.

There can be many variations of these five indemonstrable arguments. For example the assertibles in the premises can be more complex, and the following syllogism is a valid example of the second indemonstrable (modus tollens): "if both p and q, then r; not r; therefore not: both p and q" Similarly one can incorporate negation into these arguments. A valid example of the fourth indemonstrable (strong modus tollendo ponens or exclusive disjunctive syllogism) is: "either [not p] or q; not [not p]; therefore q" which, incorporating the principle of double negation, is equivalent to: "either [not p] or q; p; therefore q."

Complex arguments

However, many other arguments are not expressed in the form of the five indemonstrables, and the task is to show how they can be reduced to one of the five types. A simple example of Stoic reduction is reported by Sextus Empiricus: "if both p and q, then r; not r; but also p; Therefore not q" This can be reduced to two separate indemonstrable arguments of the second and third type: "if both p and q, then r; not r; therefore not: both p and q; not: both p and q; p; therefore not q"

The Stoics stated that complex syllogisms could be reduced to the indemonstrables through the use of four ground rules or themata. Of these four themata, only two have survived. One, the so-called first thema, was a rule