, 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. In the words of Inwood, the Stoics believed that: To the Stoics, logic was a wide field of knowledge which included the study of
language,
grammar,
rhetoric 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. 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. The logical writings by Chrysippus are, however, almost entirely lost, 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 at night). 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 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"; 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". There was also a comparative (or dissertive): "more/less (likely) p than q".
Modal assertibles Assertibles can also be distinguished by their
modal properties—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 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. 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. Chrysippus's set of Stoic modal definitions was as follows:
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". In more general terms this argument would be: which all other arguments are reducible to: 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): "either [not p] or q; not [not p]; therefore q" which, incorporating the principle of
double negation, is equivalent to: "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. 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. which represented a challenge to the basic logical notions of the Stoics, such as truth or falsehood. One paradox studied by Chrysippus, known as the
Liar paradox, asked "A man says he is lying; is what he says true or false?"—if the man says something true then it seems he is lying, but if he is lying then he is not saying something true, and so on. Another, known as the
Sorites paradox or "Heap", asked "How many grains of wheat do you need before you get a heap?" In mastering these paradoxes, the Stoics hoped to cultivate their rational powers, to more easily enable ethical reflection, permit secure and confident arguing, and lead themselves to truth.
Categories The Stoics held that all
beings ()—although not all things (τινά)—are
material. Besides the existing beings, they admitted four incorporeals (asomata): time, place, void, and sayable. They were held to be just 'subsisting' while such a status was denied to universals. Thus, they accepted
Anaxagoras's idea (as did Aristotle) that if an object is hot, it is because some part of a universal heat body had entered the object. But, unlike Aristotle, they extended the idea to cover all
chance incidents. Thus, if an object is red, it would be because some part of a universal red body had entered the object. They held that there were four
categories: •
Substance (): The primary matter, formless substance, (
ousia) that things are made of •
Quality (): The way matter is organized to form an individual object; in Stoic physics, a physical ingredient (
pneuma: air or breath), which informs the matter •
Somehow disposed (): Particular characteristics, not present within the object, such as size, shape, action, and posture •
Somehow disposed in relation to something (): Characteristics related to other phenomena, such as the position of an object within time and space relative to other objects A simple example of the Stoic categories in use is provided by Jacques Brunschwig:
Epistemology According to the Stoics, knowledge can be attained through the application of reason to the impressions (
phantasiai) received by the mind through the senses. The mind can judge (συγκατάθεσις,
synkatathesis)—approve or reject—an impression, enabling it to distinguish a true representation of reality from one that is false. Some impressions can be assented to immediately, but others can achieve only varying degrees of hesitant approval, which can be labeled
belief or opinion (
doxa). It is only through reason that people gain clear comprehension and conviction (
katalepsis).
Certainty and true knowledge (
episteme), achievable by the Stoic sage, can be attained only by verifying the conviction with the expertise of one's peers and the collective judgment of humankind. == Physics ==