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.