Logic

(This is taken from St. George William Joseph Stock's A Guide to Stoicism.)

The Stoics had a tremendous reputation for logic. In this department they were the successors or rather the supersessors of Aristotle. For after the death of Theophrastus the library of the Lyceum is said to have been buried underground at Scepsis until about a century before Christ, So that the Organon may actually have been lost to the world during that period. At all events under Strato the successor of Theophrastus who specialized in natural science the school had lost its comprehensiveness. Cicero even finds it consonant with dramatic propriety to make Cato charge the later Peripatetics with ignorance of logic! On the other hand Chrysippus became so famous for his logic as to create a general impression that if there were a logic among the gods it would be no other than the Chrysippean.

But if the Stoics were strong in logic they were weak in rhetoric.  This strength and weakness were characteristic of the school at all periods. Cato is the only Roman Stoic to whom Cicero accords the praise of real eloquence. In the dying accents of the school as we hear them in Marcus Aurelius the imperial sage counts it a thing to be thankful for that he had learnt to abstain from rhetoric, poetic, and elegance of diction. The reader however cannot help wishing that he had taken some means to diminish the crabbedness of his style. If a lesson were wanted in the importance of sacrificing to the Graces it might be found in the fact that the early Stoic writers despite their logical subtlety have all perished and that their remains have to be sought for so largely in the pages of Cicero. In speaking of logic as one of the three departments of philosophy we must bear in mind that the term was one of much wider meaning than it is with us.  It included rhetoric, poetic, and grammar as well as dialectic or logic proper, to say nothing of disquisitions on the senses and the intellect which we should now refer to psychology.

Logic as a whole being divided into rhetoric and dialectic: rhetoric was defined to be the knowledge of how to speak well in expository discourses and dialectic as the knowledge of how to argue rightly in matters of question and answer. Both rhetoric and dialectic were spoken of by the Stoics as virtues for they divided virtue in its most generic sense in the same way as they divided philosophy into physical, ethical, and logical. Rhetoric and dialectic were thus the two species of logical virtue. Zeno expressed their difference by comparing rhetoric to the palm and dialectic to the fist.

Instead of throwing in poetic and grammar with rhetoric, the Stoics subdivided dialectic into the part which dealt with the meaning and the part which dealt with the sound, or as Chrysippus phrased it, concerning significants and significates. Under the former came the treatment of the alphabet, of the parts of speech, of solecism, of barbarism, of poems, of amphibolies, of metre and music—a list which seems at first sight a little mixed, but in which we can recognise the general features of grammar, with its departments of phonology, accidence, and prosody. The treatment of solecism and barbarism in grammar corresponded to that of fallacies in logic. With regard to the alphabet it is worth noting that the Stoics recognised seven vowels and six mutes. This is more correct than our way of talking of nine mutes, since the aspirate consonants are plainly not mute. There were, according to the Stoics, five parts of speech—name, appellative, verb, conjunction, article. ‘Name’ meant a proper name, and ‘appellative’ a common term.

There were reckoned to be five virtues of speech—Hellenism, clearness, conciseness, propriety, distinction. By ‘Hellenism’ was meant speaking good Greek. ‘Distinction’ was defined to be ‘a diction which avoided homeliness.’ Over against these there were two comprehensive vices, barbarism and solecism, the one being an offence against accidence, the other against syntax.

The famous comparison of the infant mind to a blank sheet of paper, which we connect so closely with the name of Locke, really comes from the Stoics. The earliest characters inscribed upon it were the impressions of sense, which the Greeks called “phantasies.” A phantasy was defined by Zeno as “an impression in the soul.” Cleanthes was content to take this definition in its literal sense, and believe that the soul was impressed by external objects as wax by a signet ring. Chrysippus, however, found a difficulty here, and preferred to interpret the Master’s saying to mean an alteration or change in the soul. He figured to himself the soul as receiving a modification from every external object which acts upon it just as the air receives countless strokes when many people are speaking at once. Further, he declared that in receiving an impression the soul was purely passive and that the phantasy revealed not only its own existence, but that also of its cause, just as light displays itself and the things that are in it. Thus, when through sight we receive an impression of white, an affection takes place in the soul, in virtue whereof we are able to say that there exists a white object affecting us. The power to name the object resides in the understanding. First must come the phantasy, and the understanding, having the power of utterance, expresses in speech the affection it receives from the object. The cause of the phantasy was called the “phantast,” e.  g. the white or cold object. If there is no external cause, then the supposed object of the impression was a “phantasm,” such as a figure in a dream, or the Furies whom Orestes sees in his frenzy.

How then was the impression which had reality behind it to be distinguished from that which had not? “By the feel” is all that the Stoics really had to say in answer to this question. Just as Hume made the difference between sense-impressions and ideas to lie in the greater vividness of the former, so did they; only Hume saw no necessity to go beyond the impression, whereas the Stoics did.  Certain impressions, they maintained, carried with them an irresistible conviction of their own reality, and this, not merely in the sense that they existed; but also that they were referable to an external cause. These were called “gripping phantasies.” Such a phantasy did not need proof of its own existence, or of that of its object. It possessed self-evidence. Its occurrence was attended with yielding and assent on the part of the soul. For it is as natural for the soul to assent to the self-evident as it is for it to pursue its proper good. The assent to a griping phantasy was called “comprehension,” as indicating the firm hold that the soul thus took of reality. A gripping phantasy was defined as one which was stamped and impressed from an existing object, in virtue of that object itself, in such a way as it could not be from a non-existent object.  The clause “in virtue of that object itself” was put into the definition to provide against such a case as that of the mad Orestes, who takes his sister to be a Fury. There the impression was derived from an existing object, but not from that object as such, but as coloured by the imagination of the percipient.

The criterion of truth then was no other than the gripping phantasy.  Such at least was the doctrine of the earlier Stoics, but the later added a saving clause, “when there is no impediment.” For they were pressed by their opponents with such imaginary cases as that of Admetus, seeing his wife before him in very deed, and yet not believing it to be her. But here there was an impediment. Admetus did not believe that the dead could rise. Again Menelaus did not believe in the real Helen when he found her on the island of Pharos. But here again there was an impediment. For Menelaus could not have been expected to know that he had been for ten years fighting for a phantom. When, however, there was no such impediment, then they said the gripping phantasy did indeed deserve its name, for it almost took men by the hair of the head and dragged them to assent.

So far we have used “phantasy” only of real or imaginary impressions of sense. But the term was not thus restricted by the Stoics, who divided phantasies into sensible and not sensible. The latter came through the understanding and were of bodiless things which could only be grasped by reason. The ideas of Plato they declared existed only in our minds. Horse, man, and animal had no substantial existence but were phantasms of the soul. The Stoics were thus what we should call Conceptualists.

Comprehension too was used in a wider sense than that in which we have so far employed it. There was comprehension by the senses as of white and black, of rough and smooth, but there was also comprehension by the reason of demonstrative conclusions such as that the gods exist and that they exercise providence. Here we are reminded of Locke’s declaration: “’Tis as certain there’s a God as that the opposite angles made by the intersection of two straight lines are equal.” The Stoics indeed had great affinities with that thinker or rather he with them. The Stoic account of the manner in which the mind arrives at its ideas might almost be taken from the first book of Locke’s Essay. As many as nine ways are enumerated of which the first corresponds to simple ideas—

(1) by presentation, as objects of sense

(2) by likeness, as the idea of Socrates from his picture

(3) by analogy, that is, by increase or decrease, as ideas of giants and pigmies from men, or as the notion of the centre of the earth, which is reached by the consideration of smaller spheres.

(4) by transposition, as the idea of men with eyes in their breasts.

(5) by composition, as the idea of a Centaur.

(6) by opposition, as the idea of death from that of life.

(7) by a kind of transition, as the meaning of words and the idea of place.

(8)by nature, as the notion of the just and the good

(9)by privation, as handless

The Stoics resembled Locke again in endeavoring to give such a definition of knowledge as should cover at once the reports of the senses and the relation between ideas. Knowledge was defined by them as a sure comprehension or a habit in the acceptance of phantasies which was not liable to be changed by reason. On a first hearing these definitions might seem limited to sense knowledge but if we bethink ourselves of the wider meanings of comprehension and of phantasy, we see that the definitions apply as they were meant to apply to the mind’s grasp upon the force of a demonstration no less than upon the existence of a physical object.

Zeno, with that touch of oriental symbolism which characterized him, used to illustrate to his disciples the steps to knowledge by means of gestures. Displaying his right hand with the fingers outstretched he would say, “That is a phantasy,” then contracting the fingers a little, “That is assent,” then having closed the fist, “That is comprehension,” then clasping the fist closely with the left hand, he would add, “That is knowledge.”

A notion which corresponds to our word concept was defined as a phantasm of the understanding of a rational animal. For a notion was but a phantasm as it presented itself to a rational mind. In the same way so many shillings and sovereigns are in themselves but shillings and sovereigns, but when used as passage money they become fare.  Notions were arrived at partly by nature, partly by teaching and study. The former kind of notions were called preconceptions; the latter went merely by the generic name.

Out of the general ideas which nature imparts to us, reason was perfected about the age of fourteen, at the time when the voice—its outward and visible sign—attains its full development, and when the human animal is complete in other respects as being able to reproduce its kind. Thus reason which united us to the gods was not, according to the Stoics, a pre-existent principal, but a gradual development out of sense. It might truly be said that with them the senses were the intellect.

Being was confined by the Stoics to body, a bold assertion of which we shall meet the consequences later. At present it is sufficient to notice what havoc it makes among the categories. Of Aristotle’s ten categories it leaves only the first, Substance, and that only in its narrowest sense of Primary Substance. But a substance or body might be regarded in four ways—

(1) simply as a body

(2) as a body of a particular kind

(3) as a body in a particular state

(4) as a body in a particular relation.

 

Hence result the four Stoic categories of—

substrates

suchlike

so disposed

so related

 

But the bodiless would not be thus conjured out of existence. For what was to be made of such things as the meaning of words, time, place, and the infinite void? Even the Stoics did not assign body to these, and yet they had to be recognized and spoken of. The difficulty was got over by the invention of the higher category of somewhat, which should include both body and the bodiless. Time was a somewhat, and so was space, though neither of them possessed being.

In the Stoic treatment of the proposition, grammar was very much mixed up with logic. They had a wide name which applied to any part of diction, whether a word or words, a sentence, or even a syllogism.  This we shall render by “dict.” A dict, then, was defined as “that which subsists in correspondence with a rational phantasy.” A dict was one of the things which the Stoics admitted to be devoid of body.  There were three things involved when anything was said—the sound, the sense, and the external object. Of these the first and the last were bodies, but the intermediate one was not a body. This we may illustrate after Seneca, as follows: “You see Cato walking. What your eyes see and your mind attends to is a body in motion. Then you say, ‘Cato is walking’.” The mere sound indeed of these words is air in motion and therefore a body but the meaning of them is not a body but an enouncement about a body, which is quite a different thing.

On examining such details as are left us of the Stoic logic, the first thing which strikes one is its extreme complexity as compared with the Aristotelian. It was a scholastic age, and the Stoics refined and distinguished to their hearts’ content. As regards immediate inference, a subject which has been run into subtleties among ourselves, Chrysippus estimated that the changes which could be rung on ten propositions exceeded a million, but for this assertion he was taken to task by Hipparchus the mathematician, who proved that the affirmative proposition yielded exactly 103,049 forms and the negative 310,962. With us the affirmative proposition is more prolific in consequences than the negative. But then, the Stoics were not content with so simple a thing as mere negation, but had negative arnetic and privative, to say nothing of supernegative propositions.  Another noticeable feature is the total absence of the three figures of Aristotle and the only moods spoken of are the moods of the complex syllogism, such as the modus penens in a conjunctive.  Their type of reasoning was—

If A, then B

But A

B

 

The important part played by conjunctive propositions in their logic led the Stoics to formulate the following rule with regard to the material quality of such propositions: Truth can only be followed by truth, but falsehood may be followed by falsehood or truth.

Thus if it be truly stated that it is day, any consequence of that statement, e.g. that it is light, must be true also. But a false statement may lead either way. For instance, if it be falsely stated that it is night then the consequence that it is dark is false also. But if we say, “The earth flies,” which was regarded as not only false but impossible [Footnote: Here we may recall the warning of Arago to call nothing impossible outside the range of pure mathematics] this involves the true consequence that the earth is.  Though the simple syllogism is not alluded to in the sketch which Diogenes Laertius gives of the Stoic logic, it is of frequent occurrence in the accounts left us of their arguments. Take for instance the syllogism wherewith Zeno advocated the cause of temperance—

One does not commit a secret to a man who is drunk.

One does commit a secret to a good man.

A good man will not get drunk.

The chain argument which we wrongly call the Sorites was also a favorite resource with the Stoics. If a single syllogism did not suffice to argue men into virtue surely a condensed series must be effectual. And so they demonstrated the sufficiency of wisdom for happiness as follows----

The wise man is temperate

The temperate is constant

The constant is unperturbed

The unperturbed is free from sorrow

Whoso is free from sorrow is happy

The wise man is happy

 

The delight which the early Stoics took in this pure play of the intellect led them to pounce with avidity upon the abundant stock of fallacies current among the Greeks of their time. These seem—most of them—to have been invented by the Megarians and especially by Eubulides of Miletus a disciple of Eucleides but they became associated with the Stoics both by friends and foes who either praise their subtlety or deride their solemnity in dealing with them.  Chrysippus himself was not above propounding such sophisms as the following—

Whoever divulges the mysteries to the uninitiated commits impiety

The hierophant divulged the mysteries to the uninitiated

The hierophant commits impiety

Anything that you say passes through your mouth

You say a wagon

A wagon passes through your mouth

 

He is said to have written eleven books on the No-one fallacy. But what seems to have exercised most of his ingenuity was the famous Liar, the invention of which is ascribed to Eubulides. This fallacy in its simplest form is as follows. If you say truly that you are telling a lie, are you lying or telling the truth? Chrysippus set this down as inexplicable. Nevertheless he was far from declining to discuss it. For we find in the list of his works a treatise in five books on the Inexplicables an Introduction to the Liar and Liars for Introduction, six books on the Liar itself, a work directed against those who thought that such propositions were both false and true, another against those who professed to solve the Liar by a process of division, three books on the solution of the Liar, and finally a polemic against those who asserted that the Liar had its premises false. It was well for poor Philetas of Cos that he ended his days before Chrysippus was born, though as it was he grew thin and died of the Liar, and his epitaph served as a solemn reminder to poets not to meddle with logic—

Philetas of Cos am I
‘Twas the Liar who made me die
And the bad nights caused thereby. 

Perhaps we owe him an apology for the translation.