## 1. Life




Diodorus died around 284 BCE at Alexandria in Egypt. His date of
birth is unknown. It used to be common to consider him old enough to
have influenced Aristotle (died 322 BCE), but there are no strong
grounds for this. The dating was based largely on Aristotle's
response in *Metaphysics* Theta 3 to the modal theory of
'the Megarics'; but the theory discussed there differs from
that of Diodorus, who in any case (see below) should not necessarily be
assumed to be a Megaric, however great his debt to the school that went
under that name. The best evidence tends rather to make Diodorus an
older contemporary of, and a living influence on, the first generation
of the Stoic school, which began life *ca* 300 BCE. Zeno of
Citium, the school's founder, is said to have been
a pupil of Diodorus (among others). Among Zeno's
fellow-pupils in Diodorus's class is reported to have been Philo,
himself later a highly original logician in his own right (see
the entry on
 Dialectical School 
in this encyclopedia).




Diodorus came from Iasos in the eastern Aegean. In terms of
affiliation he is regularly spoken of in our sources as a
'Dialectician'. How distinct this school was from the
'Megaric' school is a matter of dispute, and one testimony
does speak of a certain 'Diodorus the Megaric' (see Denyer
2002), who may well be Diodorus Cronus. But at all events no evidence
that we possess associates him in any way with the town of Megara,
after which the Megaric school was named. Apart from his birthplace, we
hear of him as active at Athens in or around the last decade of the
fourth century, and later at Alexandria. These were the two major
cultural centres of the age.




'Cronus' was his nickname, said to have been inherited
from his teacher Apollonius Cronus. It meant roughly 'old
fogey'. But Diodorus, far from being an old fogey, comes over as
a rather flamboyant and non-traditional figure. To prove a point about
the non-natural character of language (see 3 below), he renamed one of
his slaves 'Allamen' (not a randomly chosen sound but
a Greek conjunction favoured by logicians like Diodorus for introducing
the minor premise of a syllogism, 'But now ...'). And
in defiance of the male-centred customs of contemporary philosophical
education, he trained all five of his daughters in dialectic. His work
in logic was so well known that, according to the Alexandrian poet
Callimachus, even the crows on the rooftops recognized his wisdom,
cawing out Diodorean questions about the soundness of a conditional.
And his celebrated Master Argument, with which he sought to establish
his modal definitions, was said to be hotly debated even at dinner
parties.




There is no evidence that he wrote anything, and the choice of oral
argument rather than written exposition would fit his label
'Dialectician', which refers to the Socratic practice of
question-and-answer philosophical discussion. According to the
anecdotal tradition (not necessarily to be trusted), he died after
public humiliation at the court of the Alexandrian ruler Ptolemy Soter,
having failed to solve a set of logical puzzles propounded there by the
Megaric philosopher Stilpo.


## 2. Minima and motion




Diodorus is credited with four paradoxes of motion, which inevitably
call to mind the celebrated four motion paradoxes of Zeno of Elea.




 Of Diodorus's four paradoxes (Sextus Empiricus,
*Against the professors* 10.85-118), two rested on the
hypothesis that matter and space are only finitely divisible, namely
into vanishingly small quanta, termed by him 'smallest and
partless' (*elachista kai amere*) bodies and places.
He may have postulated similar minima for time as well. Sextus calls
the postulation of minima Diodorus's 'hypothesis', but
the denial of motion his 'own doctrine' (10.85-86), and we
might do well to accept this distinction of status. Although there is
plentiful evidence that Diodorus did himself endorse the thesis of
minima as a correct account of the world's constitution, it was a
controversial view, to which a dialectician could not count on his
interlocutors' agreement. Hence in arguing against motion he may
have treated it as a hypothesis, and designed some of his arguments to
be independent of it.




Certainly some of those puzzled by Zeno's dichotomy argument
against motion (see Zeno of Elea 2.2.1) had sought to resolve the
puzzlement by postulating a smallest magnitude. That solution, although
rejected by Aristotle, was defended by his contemporary Xenocrates, a
leading Platonist. Diodorus, a generation later, can be seen taking up
this supposed solution to the Zenonian paradox and showing that it
itself in fact generates a new motion paradox, the first of his four.
(1) A minimal and partless body could never be moving, he argues,
because it always exactly fills the minimal space that it occupies. It
may next appear in a precisely adjacent space, but in the intervening
time it could never be *in transition* from the one space to the
other: that would have required its being partly in and partly not in
the original space, whereas what has no parts cannot be
'partly' in anything. (The basic argument goes back to
Plato, *Parmenides* 138d-e and Aristotle, *Physics*
6.10.)




Although he here denies that things move, Diodorus is not rejecting
ordinary experience, as Zeno of Elea is generally held to have done. He
concedes the empirical fact that things are in different places at
different times, and therefore that an item can be said to 'have
moved'. What he denies is that motion could ever be taking place
in the present. It may nevertheless be true that something has moved.
The result, a staccato analysis of motion comparable to a series of
film frames, is quite sufficient to account for our experience.




But can it be true that something, in this case motion, *has*
happened, when it was never true to say of it 'It is
happening'? Yes, replies Diodorus (Sextus, 10.97-100): for
example, 'These men have married' may be true despite the
fact that there was never a time when it was true to say of them
'These men are marrying,' since they each married at a
different time. This supporting argument, drawn from Diodorus's
logical arsenal, sits comfortably with the assumption that the staccato
theory of motion really was his own doctrine. Although unmistakably in
the tradition of Zeno of Elea, it is an attempt to make us re-analyse,
rather than reject, phenomenal change.




Diodorus also sought to defend his motion doctrine with his second
and third motion paradoxes, both of them independent of the hypothesis
of minima.




(Paradox 2) 'If something is moving, it is moving either in the place
it is in, or in the place it is not in. But it is moving neither in the
place it is in (for it is at rest in it [subsequently further explained
as: "for it completely fills it"]) nor in the place it is
not in (for it is not in it). Therefore it is not the case that
something is moving' (Sextus, 10.87). This is sometimes
attributed to Zeno of Elea, and it certainly owes some of its
inspiration to him, but the dilemmatic form, at least, seems more
characteristic of Diodorus.




(Paradox 3) 'What is moving is immediately in a place. But what is in
a place is not moving. Therefore what is moving is not moving'
(Sextus, 10.112). Too brief to admit of close analysis, this looks like
a descendant of Zeno's Arrow paradox (see Zeno of Elea 2.2.3).
How far it can be deemed to differ, other than in form, from the first
horn of Diodorus's preceding dilemma is unclear.




Diodorus's fourth motion paradox appeals to the theory of
minima once again. It assumes that a moving body, if there were one,
would consist of a set of minima, and that the whole body would be
moving if and only if a preponderance of its constituent minima were
moving. The point of choosing minima as the relevant constituents is
presumably (cf. Sextus Empiricus, *Outlines of Pyrrhonism* 3.76)
to avoid the vicious regress that would threaten if everything moved by
courtesy of the movement of a preponderance of its parts, which
themselves moved by courtesy of the movement of *their* parts,
and so on: minima, being defined precisely by their partlessness,
provide the starting point from which composite motion--if there
is such a thing--would be built up. The paradox asks us to
imagine a body consisting of three minima, two moving plus one
stationary. Thanks to this simple majority, the whole body is in
motion. Hence if a further stationary minimum were now added to it,
that could not be enough to halt its motion, being in a minority of 1
to the original 3, which, taken as a whole, have been assumed to be
moving, and therefore preponderate. And stationary minima can go on
being added to the body, one at a time, until it consists of 10,000
minima, only two of which are individually moving, and yet the whole
body will, absurdly, nonetheless be moving, because of the
ever-increasing preponderance of its moving parts.




Sextus (10.113-18), who reports this paradox, thinks the fallacy
obvious, as it no doubt is, since on the original assumption, if it is
to be acceptable, whether a whole body is moving or not should be a
function of what the majority of its minimal parts, each taken on its
own, are doing. What is most interesting about the paradox is that it
is a variant of the Sorites or little-by-little argument (see next
section), and thus clear evidence that Diodorus used to employ this
form of argument, whose invention is in fact attributed to his
forerunner Eubulides (see Dialectical School).


## 3. Semantics




The classic Sorites, or 'heap argument', seeks to show
that even 10,000 grains do not make a heap, on the ground that (a)
three grains do not, and (b) the addition of one grain could never be
enough to turn a non-heap into a heap: however often a further grain is
added, no precise boundary between non-heap and heap is ever found.
Applications of this argument form were widespread in the Hellenistic
age, and the Stoic logician Chrysippus wrote many books trying to solve
it. Diodorus is a likely source or inspiration for this Hellenistic
preoccupation (see previous paragraph).




The Sorites is a particularly lethal weapon when used in the field
of semantics, threatening to erase the boundaries on which rigid
definitions depend. It may be relevant, then, that Diodorus is reported
to have propounded a semantic theory of his own (Aulus Gellius,
*Attic nights* 11.12.1-3; cf. 1 above, the story of his
renaming his slave, reported by Ammonius, *On Aristotle's De
interpretatione* 38.17-20). This was based on the
'conventionalist' thesis expressed by the character
Hermogenes in Plato's *Cratylus*, according to whom nothing but
convention--whether national, local or simply
private--determines the meaning of a word, and any convenient
string of sounds can in principle be used to convey any meaning.
Diodorus's inference from this was that the sole determinant of any
word's meaning is the intention of the utterer on any given occasion
on which it is used. He went on to infer that there are no actual
ambiguities: given the assumption that a word is on each occasion
uttered with one specific meaning in mind, a word has only one meaning
at any time.




One may wonder whether this semantic theory, which reduced meaning to
utterer's meaning, was designed to remedy the kind of damage
that the Sorites threatened. If meanings are determined purely by the
utterer's intention on each occasion, a radical reconsideration
of definitional theory seems in any event to be called for. And it may
be that counting the grains becomes simply irrelevant to the
determination of what constitutes a heap.



Diodorus was also closely associated with the 'Veiled'
paradox (Diogenes Laertius, 2.111; Lucian, *Sale of lives*,
22-3): you know who your father is; you don't know who the
veiled man over there is; but that veiled man *is* your father;
so you both do and do not know who your father is. We might conjecture
Diodorus' own solution to have been once again a semantic
one. At each of its occurrences 'know' has, in the
respondent's mind, a distinct meaning appropriate to the case
(acquaintance, recognition), and hence no contradiction is
involved.


## 4. Philosophical position




Diodorus was known as a great dialectician. Zeno of Elea had been
called by Aristotle (in a lost work) the founder of dialectic, and the
motion paradoxes make it clear that Diodorus modelled himself to a
considerable extent on Zeno.




On the other hand Diodorus's Dialectical school was Socratic in its
affiliation (see the entry on
 Dialectical School 
in this encyclopedia, section 1). As mentioned above, it was a branch or
offshoot of the Megaric school, founded by Euclides of Megara and
recognized as one of the minor 'Socratic' schools, thanks
to Euclides's close association with Socrates.




The latter, Socratic link can be developed further. The Dialectical
school is listed by Diogenes Laertius (1.18) as one of the
'ethical' sects--surprisingly, given that no ethical
doctrines or interests are recorded for any of its known members. The
explanation may lie in a well-known passage in Plato's
*Apology* (38a), where Socrates remarks that 'The greatest
good for man is to hold discussions every day about virtue and about
the other things about which you hear me conversing
[*dialegomenou*, cognate with 'dialectic'] and
examining myself and others. And the unexamined life is not worth
living for man...' The Dialecticians may have concluded,
following Socrates, that the development and exercise of dialectical
skills are themselves the supreme fulfilment of the human self. If so,
it becomes that much easier to accept that Diodorus and his colleagues
gave their philosophy a Socratic pedigree.




However, there need be no tension between the Zenonian and the
Socratic roots of Diodorus's philosophy. Indeed, in Plato's
*Parmenides* (135c-d) a very young and still developing Socrates
is advised by Parmenides to exercise his dialectical skills according
to the model set by Zeno--a method which, perhaps significantly
for Diodorus, involves systematically examining the consequences of a
'hypothesis'.




To synthesize the methodologies of Zeno and Socrates may have seemed
to Diodorus the ideal way to be a dialectician, and to achieve the
human good.


## 5. Influence




Despite the above characterization, Diodorus's philosophy did not
provide a comprehensive tripartite philosophical system--physics,
ethics and logic--of the kind that was to flourish in the ensuing
Hellenistic age. It is therefore unsurprising that his school did not
last far into the third century BCE. Instead, some of his key ideas
were appropriated by the dominant schools of the age, namely the
Stoics, the Epicureans and the sceptically inclined dialecticians of
the New Academy. Thus it was Diodorus's propositional logic (see
Dialectical School), rather than the logic of terms developed by
Aristotle, that became the basis of the remarkable Stoic logical
system (see the entry on
 Stoicism 

in this encyclopedia, section 4, "Logic"). Diodorus's
Master Argument stood at the very centre of Hellenistic debates about
determinism (see especially Cicero, *On fate*). His theory of
minima was endorsed by Epicurus as a key part of his own physical
atomism (see the entry on
 Epicurus
in this encyclopedia, section 3). And some of Diodorus's dialectical
paradoxes, most notably the Sorites, became integral to the
methodology of the New Academy.