Chrysippus

Template:Short description Template:About Template:Good article Template:Use dmy dates Template:Infobox philosopher

Chrysippus of Soli (Template:IPAc-en;<ref>"Chrysippus". Random House Webster's Unabridged Dictionary.</ref> Template:Langx, {{#invoke:Lang|lang}}; Template:Nowrap Template:Nowrap) 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.<ref>Template:Harvnb</ref>

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 which 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.<ref name="Luhtala2000">Template:Harvnb</ref>

Of his several written works, none have survived except as fragments.Template:Efn In 2004, segments of some of his works were discovered among the Herculaneum papyri.Template:Efn

LifeEdit

Presumably of Phoenician descent,<ref>Template:Cite book</ref><ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> Chrysippus was the son of Apollonius of Tarsus, and he was born at Soli, Cilicia.<ref>Template:Harvnb, citing Diogenes Laërtius, vii. 179; Galen, Protreptic, 7; de Differentia Pulsuum, 10</ref> He was slight in stature,<ref name="laertius182">Diogenes Laërtius, vii. 182</ref> and is reputed to have trained as a long-distance runner.<ref name="laertius179">Diogenes Laërtius, vii. 179</ref> While still young, he lost his substantial inherited property when it was confiscated to the king's treasury.<ref>Diogenes Laërtius, vii. 181.</ref>Template:Efn Chrysippus moved to Athens, where he became the disciple of Cleanthes, who was then the head (scholarch) of the Stoic school.<ref>Diogenes Laërtius, vii. 179.</ref>Template:Efn He is believed to have attended the courses of Arcesilaus and his successor Lacydes, in the Platonic Academy.<ref name="laertius184">Diogenes Laërtius, vii. 184</ref>

Chrysippus threw himself eagerly into the study of the Stoic system. His reputation for learning among his contemporaries was considerable.<ref name="laertius179"/> He was noted for intellectual audacity and self-confidence and his reliance on his own ability was shown, among other things, in the request he is supposed to have made to Cleanthes: "Give me the principles, and I will find the proofs myself."<ref name="laertius179"/> He succeeded Cleanthes as head of the Stoic school when Cleanthes died, in around 230 BC.

Chrysippus was a prolific writer. He is said to rarely have gone without writing 500 lines a day<ref name="laertius181">Diogenes Laërtius, vii. 181</ref> and he composed more than 705 works.<ref name="laertius180">Diogenes Laërtius, vii. 180</ref> His desire to be comprehensive meant that he would take both sides of an argument<ref name="laertius184"/> and his opponents accused him of filling his books with the quotations of others.<ref>Diogenes Laërtius, vii. 181, x. 26–27</ref> He was considered diffuse and obscure in his utterances and careless in his style, but his abilities were highly regarded, and he came to be seen as a preeminent authority for the school.<ref name="davidson614">Template:Harvnb</ref>

File:Chrysippus of Soli - Delle Vite de Filosofi di Diogene Laertio 1606.png

Final moments in the life of Chrysippus. Engraving from 1606.

He died during the 143rd Olympiad (208–204 BC) at the age of 73.<ref name="dorandi1"/> Diogenes Laërtius gives two different accounts of his death.<ref name="laertius185">Diogenes Laërtius, vii. 185</ref> In the first account, Chrysippus was seized with dizziness having drunk undiluted wine at a feast, and died soon after. In the second account, he was watching a donkey eat some figs and cried out: "Now give the donkey a drink of pure wine to wash down the figs", whereupon he died in a fit of laughter.<ref>Template:Cite book</ref> His nephew Aristocreon erected a statue in his honour in the Kerameikos.<ref>Plutarch, De Stoicorum Repugnantiis; Diogenes Laërtius, vii. 183</ref> Chrysippus was succeeded as head of the Stoic school by his pupil Zeno of Tarsus.<ref>Eusebius, Praeparatio Evangelica, 15. 18; Diogenes Laërtius, vii. 35</ref>

Of his written works, none survived except as fragments quoted in the works of later authors like Cicero, Seneca, Galen, Plutarch, and others. In 2004, segments from Logical Questions and On Providence were discovered among the Herculaneum papyri.<ref name="fitzgerald">Template:Harvnb</ref> A third work by Chrysippus may also be among them.<ref name="fitzgerald"/>

StudyEdit

Chrysippus had a long and successful career of resisting the attacks of the Academy<ref name="ConEWP">"Chrysippus", J. O. Urmson, Jonathan Rée, The Concise Encyclopedia of Western Philosophy, 2005, pp. 73–74 of 398 pp.</ref> and hoped not simply to defend Stoicism against the assaults of the past, but also against all possible attack in the future. He took the doctrines of Zeno and Cleanthes and crystallized them into what became the definitive system of Stoicism.<ref name=ConEWP/> He elaborated the physical doctrines of the Stoics and their theory of knowledge<ref name="davidson614"/> and he created much of their formal logic.<ref name="barnes65">Template:Harvnb</ref> In short, Chrysippus made the Stoic system what it was. It was said that "without Chrysippus, there would have been no Stoa".Template:Efn

LogicEdit

Template:See also Chrysippus wrote much on the subject of logic and created a system of propositional logic. Aristotle's term logic had been concerned with the interrelations of terms such as "Socrates" or "man" ("all men are mortal, Socrates is a man, so Socrates is mortal"). Stoic logic, on the other hand, was concerned with the interrelations of propositions such as "it is day" ("if it is day, it is light: but it is day: so it is light").<ref name="sharples24">Template:Harvnb</ref><ref name="Mueller1978">Ian Mueller (1978) An Introduction to Stoic Logic Template:Harvnb</ref> Though the earlier Megarian dialecticians – Diodorus Cronus and Philo – had worked in this field and the pupils of Aristotle – Theophrastus and Eudemus – had investigated hypothetical syllogisms,<ref name="johansen466">Template:Harvnb</ref> it was Chrysippus who developed these principles into a coherent system of propositional logic.<ref name="johansen466"/><ref name="sharples2425">Template:Harvnb</ref>

PropositionsEdit

Chrysippus defined a proposition as "that which is capable of being denied or affirmed as it is in itself" and gave examples of propositions such as "it is day" and "Dion is walking."<ref>Diogenes Laërtius, vii. 65</ref><ref>Template:Harvnb</ref> He distinguished between simple and non-simple propositions, which in modern terminology are known as atomic and molecular propositions.<ref name="johansen466"/> A simple proposition is an elementary statement such as "it is day."<ref name="gould71">Template:Harvnb</ref> Simple propositions are linked together to form non-simple propositions by the use of logical connectives. Chrysippus enumerated five kinds of molecular propositions according to the connective used:<ref name="gould71"/>

Logical connectives
Type	Example
if	if it is day, it is light
and	it is day and it is light
either ... or	either it is day or it is night
because	because it is day, it is light
more/less likely ... than	more likely it is day than it is night

Thus several types of molecular propositions, familiar to modern logic, were listed by Chrysippus, including the conjunction, the disjunction, and the conditional,<ref name="johansen467">Template:Harvnb</ref> and Chrysippus studied their criteria of truth closely.<ref name="johansen467"/>

Conditional propositionsEdit

The first logicians to debate conditional statements were Diodorus Cronus and his pupil Philo. Writing five-hundred years later, Sextus Empiricus refers to a debate between Diodorus and Philo.<ref name="sextus1">Sextus Empiricus, Pyr. Hyp. ii. 110–112; Adv. Math. viii. 112–117</ref> Philo regarded all conditionals as true except those which with a correct antecedent had an incorrect consequent, and this meant a proposition such as "if it is day, then I am talking," is true unless it is day and I fall silent.<ref name="sextus2">Sextus Empiricus, Pyr. Hyp., ii. 110–112</ref> But Diodorus argued that a true conditional is one in which the antecedent clause could never lead to an untrue conclusionTemplate:Sndthus, because the proposition "if it is day, then I am talking" can be false, it is invalid.<ref name="sextus1"/> However, paradoxical propositions were still possible such as "if atomic elements of things do not exist, atomic elements exists."<ref name="sextus2"/> Chrysippus adopted a much stricter view regarding conditional propositions, which made such paradoxes impossible:Template:Efn to him, a conditional is true if denial of the consequent is logically incompatible with the antecedent.<ref name="johansen468">Template:Harvnb</ref> This corresponds to the modern-day strict conditional.<ref name="johansen468"/>

SyllogisticEdit

Chrysippus developed a syllogistic or system of deduction in which he made use of five types of basic arguments or argument forms called indemonstrable syllogisms,<ref>Diogenes Laërtius, vii. 79</ref> which played the role of axioms, and four inference rules, called themata by means of which complex syllogisms could be reduced to these axioms.<ref name="Kneale">Template:Harvnb</ref><ref>Susanne Bobzien, Stoic Syllogistic, Oxford Studies in Ancient Philosophy 14, 1996, pp. 133–192</ref> The forms of the five indemonstrables were:<ref>Diogenes Laertius, vii. 80-81; Sextus Empiricus, Hyp. Pyr. ii. 156–159; cf. Adv. Math. viii. 223ff.</ref><ref name="Mates">Template:Harvnb</ref>

NameTemplate:Efn		Description	Example
Modus ponens		If A, then B. A. Therefore, B.	If it is day, it is light. It is day. Therefore, it is light.
Modus tollens		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.
Modus ponendo tollens	i	Not both A and B. A. Therefore, not B.	It is not both day and night. It is day. Therefore, it is not night.
Modus ponendo tollens	ii	Either A or B. A. Therefore, not B.	It is either day or night. It is day. Therefore, it is not night.
Modus tollendo ponens		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),<ref name="L&S">Template:Harvnb, §36 HIJ</ref> 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.<ref name="Kneale2">Template:Harvnb</ref><ref>Template:Cite SEP</ref> 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.<ref name="sharples26">Template:Harvnb</ref> The goal was to find valid rules of inference and forms of proof to help people find their way in life.<ref name="johansen466"/>

File:New Guinea Singing Dog sniffing the ground.jpg

Chrysippus argued dogs reason.

According to Sextus Empiricus, Chrysippus held that dogs use disjunctive syllogism, such as when using scent to pick which path to run down. This was in contrast to a tradition since Aristotle, who saw reasoning (and reasoning deductively) as man's defining aspect.<ref>Sextus Empiricus, Outlines of Pyrrhonism, I.69</ref>

Other logical workEdit

Chrysippus analyzed speech and the handling of names and terms.<ref name="davidson614"/> He also devoted much effort in refuting fallacies and paradoxes.<ref name="davidson614"/> According to Diogenes Laërtius, Chrysippus wrote twelve works in 23 books on the Liar paradox; seven works in 17 books on amphiboly; and another nine works in 26 books on other conundrums.<ref name="barnes71">Template:Harvnb</ref> In all, 28 works or 66 books were given over to puzzles or paradoxes.<ref name="barnes71"/> Chrysippus is the first Stoic for whom the third of the four Stoic categories, i.e. the category somehow disposed is attested.<ref>Stephen Menn, "The Stoic Theory of Categories", in Oxford Studies in Ancient Philosophy: Volume XVII: 1999, 215–247.</ref> 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).<ref name="gould107">Template:Harvnb</ref> 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.<ref name="gould107"/>

Later receptionEdit

Chrysippus came to be renowned as one of the foremost logicians of ancient Greece. When Clement of Alexandria wanted to mention one who was master among logicians, as Homer was master among poets, it was Chrysippus, not Aristotle, he chose.<ref>Clement of Alexandria, Stromata, vii. 16</ref> Diogenes Laërtius wrote: "If the gods use dialectic, they would use none other than that of Chrysippus."<ref>Diogenes Laërtius, vii. 180.</ref> 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.<ref name="sharples26"/> As recently as the 19th century, Stoic logic was treated with contempt, a barren formulaic system, which was merely clothing the logic of Aristotle with new terminology.<ref name="otoole403">Template:Harvnb</ref> 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.<ref name="johansen466"/>

EpistemologyEdit

For the Stoics, truth is distinguished from error by the sage who possesses right reason.<ref name="hicks70">Template:Harvnb</ref> Chrysippus's theory of knowledge was empirical.<ref name="gould90">Template:Harvnb</ref> 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.<ref name="gould90"/> Zeno had defined impressions of sense as "an impression in the soul"<ref name="stock22">Template:Harvnb</ref> and this was interpreted literally by Cleanthes, who compared the impression on the soul to the impression made by a seal on wax.<ref name="zeller77">Template:Harvnb</ref> Chrysippus preferred to regard it as an alteration or change in the soul;<ref name="stock22"/> that is, the soul receives a modification from every external object that acts upon it, just as the air receives countless strokes when many people are speaking at once.<ref name="stock22"/>

In the receipt of an impression, the soul is purely passive and the impression reveals not only its own existence, but that also of its causeTemplate:Sndjust as light displays itself and the elements that are in it.<ref name="stock22"/> The power to name the object resides in the understanding. First must come the impression, and the understandingTemplate:Sndhaving the power of utteranceTemplate:Sndexpresses in speech the affection it receives from the object.<ref name="stock23">Template:Harvnb</ref> True presentations are distinguished from those that are false by the use of memory, classification and comparison.<ref name="gould90"/> If the sense organ and the mind are healthyTemplate:Sndand provided that an external object can be really seen or heardTemplate:Sndthe presentation, due to its clearness and distinctness, has the power to extort the assent that always lies in our power, to give or to withhold.<ref>Template:Harvnb</ref> In a context in which people are understood to be rational beings, reason is developed out of these notions.<ref name="hicks66">Template:Harvnb</ref>

PhysicsEdit

File:Chrysippus of Soli.jpg

A partial marble 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.<ref>Cicero, De Natura Deorum, ii, 19</ref> He said, the universe is "the soul and guide of itself."<ref>Plutarch, De Stoicorum Repugnantiis, 41.</ref> Following Zeno, Chrysippus determined fiery breath or aether to be the primitive substance of the universe.<ref>Template:Harvnb</ref> Objects are made up of inert formless matter and an informing soul, "pneuma", provides form to the undifferentiated matter.<ref name="otoole431">Template:Harvnb</ref> The pneuma pervades all of substance and maintains the unity of the universe and constitutes the soul of the human being.<ref name="otoole431"/>

The classical elements change into one another by a process of condensation and rarefaction.<ref name="stock79">Template:Harvnb</ref> 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.<ref name="stock79"/>

The human soul was divided by Chrysippus into eight faculties: the five senses, the power of reproduction, the power of speech, and the "ruling part" that is located in the chest rather than the head.<ref name="sharples67">Template:Harvnb</ref> Individual souls are perishable; but, according to the view originated by Chrysippus, the souls of wise people survive longer after their death.<ref name="sharples67"/> No individual soul can, however, survive beyond the periodic conflagration, when the universe is renewed.<ref name="sharples67"/>

There were no universals or abstract objects for Chrysippus, making him a kind of nominalist.Template:Efn

FateEdit

For Chrysippus, all things happen according to fate: what seems to be accidental has always some hidden cause.<ref name="zeller178">Template:Harvnb</ref> The unity of the world consists in the chain-like dependence of cause upon cause.<ref name="zeller176">Template:Harvnb</ref> Nothing can take place without a sufficient cause.<ref name="zeller175">Template:Harvnb</ref> According to Chrysippus, every proposition is either true or false, and this must apply to future events as well:<ref name="zeller174">Template:Harvnb</ref>

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.<ref>Cicero, On Fate, 20–21</ref>

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.<ref name="zeller177">Template:Harvnb</ref> Everything is, in every respect, determined by this relation, and is consequently subject to the general order of the world.<ref name="zeller176"/>

If his opponents objected that, if everything is determined by destiny, there is no individual responsibility, since what has been once foreordained must happen, come what may, Chrysippus replied that there is a distinction to be made between simple and complex predestination.<ref name="zeller181">Template:Harvnb</ref> 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.<ref name="kenny195">Template:Harvnb referencing Cicero, On Fate, 28–29</ref> All human actionsTemplate:Sndin fact, our destinyTemplate:Sndare decided by our relation to things,<ref name="zeller182">Template:Harvnb</ref> or as Chrysippus put it, events are "co-fated" to occur:<ref name="kenny195"/>

The non-destruction of one's coat, he says, is not fated simply, but co-fated with its being taken care of, and someone's being saved from his enemies is co-fated with his fleeing those enemies; and having children is co-fated with being willing to lie with a woman. ... For many things cannot occur without our being willing and indeed contributing a most strenuous eagerness and zeal for these things, since, he says, it was fated for these things to occur in conjunction with this personal effort. ... But it will be in our power, he says, with what is in our power being included in fate.<ref>Diogenianus in Eusebius, Praeparatio evangelica, vi. 8, quoted in Template:Harvnb</ref>

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.<ref>Template:Harvnb</ref> 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.<ref name="zeller179">Template:Harvnb</ref> Every action is brought about by the co-operation of causes depending on the nature of things and the character of the agent.<ref name="zeller179"/> Our actions would only be involuntary if they were produced by external causes alone, without any co-operation – on the part of our wills – with external causes.<ref name="zeller179"/> Virtue and vice are set down as things in our power, for which, consequently, we are responsible.<ref name="zeller180">Template:Harvnb</ref> 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.<ref name="zeller180"/> This rather subtle position, which attempts to reconcile determinism with human responsibility, is known as soft-determinism, or as compatibilism.<ref>Template:Harvnb</ref>

DivinationEdit

File:Kleromanteia.jpg

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.<ref name="gould144-5">Template:Harvnb</ref> It would not be possible for diviners to predict the future if the future itself was accidental.<ref name="zeller175"/> Omens and portents, he believed, are the natural symptoms of certain occurrences.<ref name="hicks947">Template:Harvnb</ref> 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.<ref name="hicks947"/> To those who argued that divination was superfluous as all events are foreordained, he replied that both divination and our behaviour under the warnings which it affords are included in the chain of causation.<ref name="hicks947"/>

GodEdit

The Stoics believed that the universe is God, and Chrysippus affirmed that "the universe itself is God and the universal outpouring of its soul."<ref name="cicerodenati15">Cicero, De Natura Deorum, i. 15</ref> 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."<ref name="cicerodenati15"/> Based on these beliefs, physicist and philosopher Max Bernhard Weinstein identified Chrysippus as a Pandeist.Template:Efn

Chrysippus sought to prove the existence of God, making use of a teleological argument:

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 universeTemplate:Sndthe 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.<ref>Cicero, De Natura Deorum, iii. 10. Cf. ii. 6 for the fuller version of this argument</ref>

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."<ref name="cicerodenati15"/> In addition, the universe exists for the benefit of the universal god:

We should infer in the case of a beautiful dwelling-place that it was built for its owners and not for mice; we ought, therefore, in the same way to regard the universe as the dwelling-place of the gods.<ref name="cicerodenatiii10">Cicero, De Natura Deorum, iii. 10</ref>

TheodicyEdit

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."<ref>Plutarch, De Stoicorum Repugnantiis, 1051 B</ref> 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.<ref name="gelliusvii1">Aulus Gellius, vii. 1</ref> 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.<ref name="gelliusvii1"/> Thirdly, evils are distributed according to the rational will of Zeus, either to punish the wicked or because they are important to the world-order as a whole.<ref>Plutarch, De Stoicorum Repugnantiis, 1050 E; De Communibus Notitiis, 1065 B</ref> 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."<ref>Plutarch, De Communibus Notitiis, 1065 D</ref>

MathematicsEdit

File:Kegelstumpf.png

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.<ref name="gould116">Template:Harvnb</ref> 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.<ref name="gould117">Template:Harvnb</ref>

Chrysippus also responded to a problem first posed by Democritus.<ref>Plutarch, De Communibus Notitiis, 1079F</ref> 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.<ref name="gould117"/> The reply of Chrysippus was that the surfaces are both equal and unequal.<ref name="gould118">Template:Harvnb</ref> 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.<ref name="gould118"/>

Chrysippus was notable for claiming that "one" is a number. One was not always considered a number by the ancient Greeks since they viewed one as that by which things are measured. Aristotle in his Metaphysics wrote, "... a measure is not the things measured, but the measure or the One is the beginning of number."<ref name="heath69">Template:Harvnb</ref> Chrysippus asserted that one had "magnitude one" (Template:Langx),<ref>Iamblichus, in Nicom., ii. 8f; Syrianus, in Arist. Metaph., Kroll 140. 9f.</ref> although this was not generally accepted by the Greeks, and Iamblichus wrote that "magnitude one" was a contradiction in terms.<ref name="heath69"/>

EthicsEdit

File:Medeia child Louvre K300.jpg

Greek amphora depicting Euripides' Medea. Chrysippus regarded Medea as a prime example of how bad judgments could give rise to irrational passions.<ref>Galen, On The Doctrines of Hippocrates and Plato, iii.3.13–22, iv.2.27, iv.6.19–27.</ref>Template:Efn

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."<ref name="stock13">Template:Harvnb</ref> The goal of life, said Chrysippus, is to live in accordance with one's experience of the actual course of nature.<ref>Template:Harvnb</ref> A person's individual nature is part of the nature of the whole universe,<ref name="laertius87">Diogenes Laërtius, vii. 87</ref> and thus life should be lived in accordance with one's own human nature as well as that of the universe.<ref name="laertius88">Diogenes Laërtius, vii. 88</ref> 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.<ref name="davidson615">Template:Harvnb</ref> 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.<ref name="davidson615"/> Chrysippus laid the greatest stress on the worth and dignity of the individual, and on the power of will.<ref name="davidson615"/>

The Stoics admitted between the good and the bad a third class of thingsTemplate:Sndthe indifferent (adiaphora).<ref name="kenny282">Template:Harvnb</ref> Of things morally indifferent, the best includes health, and riches, and honour, and the worst includes sickness and poverty.<ref name="zeller284">Template:Harvnb</ref> Chrysippus accepted that it was normal in ordinary usage to refer to the preferred indifferent things as "good",<ref name="kenny282"/> but the wise person, said Chrysippus, uses such things without requiring them.<ref name="zeller284"/> Practice and habit are necessary to render virtue perfect in the individualTemplate:Sndin other words, there is such a thing as moral progress, and character has to be built up.<ref name="davidson615"/>

On PassionsEdit

{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}} The Stoics sought to be free of the unruly emotions, which they regarded as being contrary to nature. The passions or emotions (pathe) are the disturbing element in right judgment.<ref name="davidson615"/> Chrysippus wrote a whole book, On Passions (Template:Langx), concerning the therapy of the emotions.<ref name="gould186">Template:Harvnb</ref> The passions are like diseases which depress and crush the soul, thus he sought to eradicate them (apatheia).<ref name="gould186"/> Wrong judgements turn into passions when they gather an impetus of their own, just as, when one has started running, it is difficult to stop.<ref name="sharples68">Template:Harvnb</ref> 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.<ref name="gould187">Template:Harvnb</ref> Therefore, one should prepare in advance, and deal with the passions in the mind as if they were present.<ref name="gould188">Template:Harvnb</ref> By applying reason to passions such as greed, pride, or lust, one can understand the harm which they cause.<ref name="gould188"/>