Chrysippus of Soli (; , ; ) was a Greek Stoic philosopher. He was a native of Soli, Cilicia, but moved to Athens as a young man, where he became a pupil of the Stoic philosopher Cleanthes. When Cleanthes died, around 230 BC, Chrysippus became the third head of the Stoic school. A prolific writer, Chrysippus expanded the fundamental doctrines of Cleanthes' mentor Zeno of Citium, the founder and first head of the school, which earned him the title of the Second Founder of Stoicism.
Chrysippus excelled in logic, the theory of knowledge, ethics, and physics. He created an original system of propositional logic in order to better understand the workings of the universe and role of humanity within it. He adhered to a fatalistic view of fate, but nevertheless sought a role for personal agency in thought and action. Ethics, he thought, depended on understanding the nature of the universe, and he taught a therapy of extirpating the unruly passions that depress and crush the soul. He initiated the success of Stoicism as one of the most influential philosophical movements for centuries in the Greek and Roman world. The linguistic orientation of Chrysippus' work made it difficult for its students even within the Stoic school.
Of his several written works, none have survived except as fragments. Segments of some of his works were discovered among the Herculaneum papyri. to him, a conditional is true if denial of the consequent is logically incompatible with the antecedent. This corresponds to the modern-day strict conditional. which played the role of axioms, and four inference rules, called themata by means of which complex syllogisms could be reduced to these axioms. The forms of the five indemonstrables were:
{| class="wikitable" style="margin:1.0em auto;"
!colspan=2| Name
! Description
! Example
|-
|colspan=2| Modus ponens
|style="white-space:nowrap;"| If A, then B. A. Therefore, B.
| If it is day, it is light. It is day. Therefore, it is light.
|-
|colspan=2| Modus tollens
|style="white-space:nowrap;"| If A, then B. Not B. Therefore, not A.
| If it is day, it is light. It is not light. Therefore, it is not day.
|-
|rowspan=2| Modus ponendo tollens
|style="width:1.5em;text-align:center;"| i
|style="white-space:nowrap;"| Not both A and B. A. Therefore, not B.
| It is not both day and night. It is day. Therefore, it is not night.
|-
|style="text-align:center;"| ii
|style="white-space:nowrap;"| Either A or B. A. Therefore, not B.
| It is either day or night. It is day. Therefore, it is not night.
|-
|colspan=2| Modus tollendo ponens
|style="white-space:nowrap;"| Either A or B. Not A. Therefore, B.
| It is either day or night. It is not day. Therefore, it is night.
|}
Of the four inference rules (themata, θέματα), only two survived. One, the so-called first thema, was a rule of antilogism. The other, the third thema, was a cut rule by which chain syllogisms could be reduced to simple syllogisms. The purpose of Stoic syllogistic was not merely to create a formal system. It was also understood as the study of the operations of reason, the divine reason (logos) which governs the universe, of which human beings are a part. The goal was to find valid rules of inference and forms of proof to help people find their way in life.
Other logical work
Chrysippus analyzed speech and the handling of names and terms. In all, 28 works or 66 books were given over to puzzles or paradoxes. In the surviving evidence, Chrysippus frequently makes use of the categories of substance and quality, but makes little use of the other two Stoic categories (somehow disposed and somehow disposed in relation to something). It is not clear whether the categories had any special significance for Chrysippus, and a clear doctrine of categories may be the work of later Stoics. Diogenes Laërtius wrote: "If the gods use dialectic, they would use none other than that of Chrysippus." The logical work by Chrysippus came to be neglected and forgotten. Aristotle's logic prevailed, partly because it was seen as more practical, and partly because it was taken up by the Neoplatonists. It was not until the 20th century, with the advances in logic, and the modern propositional calculus, that it became clear that Stoic logic constituted a significant achievement. Chrysippus's theory of knowledge was empirical. The senses transmit messages from the external world, and their reports are controlled not by referring them to innate ideas, but by comparing them to previous reports stored in the mind. and this was interpreted literally by Cleanthes, who compared the impression on the soul to the impression made by a seal on wax. Chrysippus preferred to regard it as an alteration or change in the soul; True presentations are distinguished from those that are false by the use of memory, classification and comparison. In a context in which people are understood to be rational beings, reason is developed out of these notions.
Physics
right|thumb|A partial marble [[Bust (sculpture)|bust of Chrysippus that is a Roman copy of a Hellenistic original (Louvre Museum).]]
Chrysippus insisted on the organic unity of the universe, as well as the correlation and mutual interdependence of all of its parts. He said, the universe is "the soul and guide of itself." Following Zeno, Chrysippus determined fiery breath or aether to be the primitive substance of the universe. Objects are made up of inert formless matter and an informing soul, "pneuma", provides form to the undifferentiated matter. The pneuma pervades all of substance and maintains the unity of the universe and constitutes the soul of the human being. Fire first becomes solidified into air; then air into water; and lastly, water into earth. The process of dissolution takes place in the reverse order: earth being rarefied into water, water into air and air into fire. Individual souls are perishable; but, according to the view originated by Chrysippus, the souls of wise people survive longer after their death.
Fate
For Chrysippus, all things happen according to fate: what seems to be accidental has always some hidden cause. The unity of the world consists in the chain-like dependence of cause upon cause. Nothing can take place without a sufficient cause. According to Chrysippus, every proposition is either true or false, and this must apply to future events as well:
<blockquote>If any motion exists without a cause, then not every proposition will be either true or false. For that which has not efficient causes is neither true nor false. But every proposition is either true or false. Therefore, there is no motion without a cause. And if this is so, then all effects owe their existence to prior causes. And if this is so, all things happen by fate. It follows therefore that whatever happens, happens by fate.</blockquote>
The Stoic view of fate is entirely based on a view of the universe as a whole. Individual things and persons only come into consideration as dependent parts of this whole. Everything is, in every respect, determined by this relation, and is consequently subject to the general order of the world. Becoming ill may be fated whatever happens but, if a person's recovery is linked to consulting a doctor, then consulting the doctor is fated to occur together with that person's recovery, and this becomes a complex fact. All human actionsin fact, our destinyare decided by our relation to things, or as Chrysippus put it, events are "co-fated" to occur:</blockquote>
Thus our actions are predetermined, and are causally related to the overarching network of fate, but nevertheless the moral responsibility of how we respond to impressions remains our own. The one all-determining power is active everywhere, working in each particular being according to its nature, whether in rational or irrational creatures or in inorganic objects. Every action is brought about by the co-operation of causes depending on the nature of things and the character of the agent. Moral responsibility depends only on freedom of the will, and what emanates from our will is our own, no matter whether it is possible for us to act differently or not.
Divination
right|thumb|[[Cleromancy in ancient Greece. Chrysippus accepted divination as part of the causal chain of fate.]]
Chrysippus also argued for the existence of fate based on divination, which he thought there was good evidence for. It would not be possible for diviners to predict the future if the future itself was accidental. There must be countless indications of the course of providence, for the most part unobserved, the meaning of only a few having become known to humanity. It is the guiding principle of the universe, "operating in mind and reason, together with the common nature of things and the totality which embraces all existence."
Chrysippus sought to prove the existence of God, making use of a teleological argument:
<blockquote>If there is anything that humanity cannot produce, the being who produces it is better than humanity. But humanity cannot produce the things that are in the universethe heavenly bodies, etc. The being, therefore, who produces them is superior to humanity. But who is there that is superior to humanity, except God? Therefore, God exists.</blockquote>
Chrysippus spoke of God and gods interchangeably. He interpreted the gods of traditional Greek religion by viewing them as different aspects of the one reality. Cicero tells us that "he further maintained that aether is that which people call Zeus, and that the air which permeates the seas is Poseidon, and that the earth is what is known by the name of Demeter, and he treated in similar style the names of the other gods."</blockquote>
Theodicy
In response to the question of how evil could exist in a good universe, Chrysippus replied "evil cannot be removed, nor is it well that it should be removed." Firstly, he argued, following Plato, that it was impossible for good to exist without evil, for justice could not be known without injustice, courage without cowardice, temperance without intemperance or wisdom without foolishness. Secondly, apparent evils exist as a consequent of nature's goodness, thus it was necessary for the human skull to be made from small and thin bones for reasons of utility, but this superior utility meant that the skull is vulnerable to blows. Thus evil is good under disguise, and is ultimately conducive to the best. Chrysippus compared evil to the coarse jest in the comedy; for, just as the jest, though offensive in itself, improves the piece as a whole, "so too you may criticize evil regarded by itself, yet allow that, taken with all else, it has its use."
Mathematics
thumb|right|The puzzle of Democritus. If a cone is sliced horizontally, are the surfaces produced equal or unequal?
Chrysippus regarded bodies, surfaces, lines, places, the void and time as all being infinitely divisible. He determined one of the principal features of the infinite set: since a man and a finger have an infinite number of parts as do the universe and a man, it cannot be said that a man has more parts than his finger, nor that the universe has more parts than a man.
Chrysippus also responded to a problem first posed by Democritus. If a cone is divided by a plane parallel to its base, are the surfaces of the segments equal or unequal? If they are equal, then the cone becomes a cylinder; if they are unequal, then the surface of the cone must be stepped. Chrysippus was, in effect, negating the law of excluded middle with respect to the equal and unequal, and thus he may have anticipated an important principle of modern infinitesimal calculus, namely, the limit and the process of convergence towards a limit. Chrysippus asserted that one had "magnitude one" (), although this was not generally accepted by the Greeks, and Iamblichus wrote that "magnitude one" was a contradiction in terms.]]
Chrysippus taught that ethics depended on physics. In his Physical Theses, he stated: "for there is no other or more appropriate way of approaching the subject of good and evil on the virtues or happiness than from the nature of all things and the administration of the universe." The goal of life, said Chrysippus, is to live in accordance with one's experience of the actual course of nature. A person's individual nature is part of the nature of the whole universe, and thus life should be lived in accordance with one's own human nature as well as that of the universe. Human nature is ethical, and humanity is akin to the Divine, emanating from the primal fire or aether, which, though material, is the embodiment of reason; and people should conduct themselves accordingly. People have freedom, and this freedom consists in emancipation from irrational desires (lust, riches, position in life, domination, etc.) and in subjecting the will to reason. Of things morally indifferent, the best includes health, and riches, and honour, and the worst includes sickness and poverty. Chrysippus accepted that it was normal in ordinary usage to refer to the preferred indifferent things as "good", The passions are like diseases which depress and crush the soul, thus he sought to eradicate them (apatheia). One cannot hope to eradicate the passions when one is in the heat of love or anger: this can only be done when one is calm. Therefore, one should prepare in advance, and deal with the passions in the mind as if they were present. By applying reason to passions such as greed, pride, or lust, one can understand the harm which they cause.