rivers other and still other waters flow upon themrdquo (ποταμοῖσι τοῖσιν αυτοῖσιν ἐμβαίνουσιν έτερα και
ετερα υδατο ἑπιρρεῖ Diels 12) Both versions were known to Plato (Cratylus 402) and Aristotle (Met
4 1010a) It is now accepted that Plutarch was using an intermediate source that had probably
developed from the work of Plato and Aristotle (and Cratylus) ldquoIt is obvious that [Plutarchrsquos] ποταμῷ
hellip τῷ αὐτῷ reproduces the Aristotelian form of Platorsquos paraphrase of the river statement and not (as
Bywater Diels Kranz and others believed) the original words of Heraclitusrdquo (See Kahn 1979 168
100 (18 392 B) The assertion ldquoOne cannot step into the same river twicerdquo does not entail that the
individual elements that make up the river ndash the drops of water ndash change their composition or state
they are just different drops of water (Obsieger 2013 318) This linear flux or flow can be contrasted
101 (18 392 B) The phrase ldquoit disperses and gathersrdquo is perhaps a fragment from Heraclitus
(Diels 91) Bernardakis and Babbitt construe this phrase as a continuation of the river fragment but
this has been challenged Fairbanks did not see it as a literal quotation but as another ldquocatchwordrdquo
phrase a shorthand to denote early philosophical doctrines where a word or two of the original has
been preserved although not the meaning (Fairbanks 1897 79) Fairbanksrsquos view is now the
professional consenus Given that Young Plutarch has just been quoting Plato Kahnrsquos comment that
these pairs of antithetical verbs are reminiscent of Heraclitean ldquostylerdquo is intriguing He suggests that
this pair could well be a ldquoPlutarchean interpolationrdquo inspired by the Strangerrsquos contrast (at Sophist 242
D-E) between the Ionian (Heraclitus) and Sicilian (Empedocles) philosophers (Kahn 1979 130)
102 (18 392 C) The phrase ldquothe death of fire is birth for air and the death of air is birth for
waterrdquo is the third fragment that Plutarch attributes directly to Heraclitus Fairbanks notes that it
seems to be given accurately by Maximus Tyr (414) ldquoFire lives the death of earth and air lives the
death of fire water lives the death of air earth that of waterrdquo But note that Maximus is the only writer
to use the word ldquoliferdquo Plutarch has given this allusion twice (Mor 392 C and Mor 949 A) in two
opposites let us see whether the saying holds good that ldquoThe death of fire is the
73
Nevertheless Kahn is right to note the use of the words ldquobirthrdquo and ldquodeathrdquo for the transformations of
the elements This vocabulary (which may be metaphoric) allows Ammonius to make the logical leap
to animate being in ldquoand it is clearer still in ourselvesrdquo That is the changes we undergo are little
births and deaths where for us neither birth nor death is a metaphor
Ammonius then presents an elaborate excursus on the ages of man Plutarch himself may not
have been entirely in agreement with this analysis since there is a lost dialogue entitled ldquoAs to our not
remaining the same while being is always in fluxrdquo attributed to him in an anonymous note (Classical
Review 32 [1918] 150-153) but I have been unable to find it mentioned elsewhere Plutarch presents
the opposite view (speaking as himself) in another dialogue that also took place at Delphi The point at
issue is whether a delay in divine retribution brings encouragement to wrong doers and distress to their
victims who do not see their aggressors duly punished Plutarch describes a city as an organism
having a continuous life and a stable and integrated unity so that its moral responsibility outlasts the
lives of its individual inhabitants He compares the life of the city with its core identity to the life of a
man and ends his argument with an acerbic allusion to Heraclitus
αλλ᾽ ἄνθρωπός τε λέγεται μέχρι τέλους εἷς απὸ γενέσεως πόλιν τε την αὐτην
ὡσαύτως διαμένουσαν ἐνέχεσθαι τοῖς ὀνείδεσι τῶν προγόνων αξιοῦμεν ᾧ δικαίῳ
μέτεστιν αὐτῇ δόξης τε της ἐκείνων καὶ δυνάμεως ἢ λήσομεν εἰς τὸν Ἡρακλείτειον
ἅπαντα πράγματα ποταμὸν ἐμβαλόντες εἰς ὃν οὔ φησι δὶς ἐμβηναι τῷ πάντα κινεῖν
καὶ ἑτεροιοῦν την φύσιν μεταβάλλουσαν
Yet a man is called one and the same from birth to death and we deem it only
proper that a city in like manner retaining its identity should be involved in the
disgraces of its forbears by the same title as it inherits their glory and power else we
shall find that we have unawares cast the whole of existence into the river of
Heraclitus into which he asserts no man can step twice as nature in its changes
shifts and alters everything (De ser num 15 559 C trans by Phillip H De Lacy
and Benedict Einarson)
Ildefonse (2006) draws out the implications She comments citing Sirinelli (2000 423) that although
these two passages contain the same fragment of Heraclitus and compare it to the ages of man the
attitude of the two speakers is very different She continues that the structure of De E contains three
separate ldquoPlutarchsrdquo at different stages of his life but the presiding intellect is that of one person not a
series of different entities Hershbell (1977 198) simply notes that Plutarch voices an opinion different
from the one held by Ammonius in De E Flaceliegravere is more pointed (1941 89 11)
Ces ideacutees nrsquoexpriment qursquoun aspect de la reacutealiteacute et comportement assureacutement une
grande part drsquoexageacuteration Cf Ricard dans sa note agrave ce passage [1884 60 -61] laquoLes
vicissitudes que nous eacuteprouvons dans nos gouts nos affections nos sentiments et
74
mecircme dans les traits de notre figure ne deacutetruisent ni lrsquouniteacute de notre individu ni la
reacutealiteacute de notre existence propre et individuelle raquo
These ideas express only one aspect of reality and certainly contain some
exaggeration See Ricardrsquos note to this passage [1884 60-61] The vicissitudes we
experience in our tastes our affections our feelings and even in our physical traits
destroy neither the unity of our personalities nor the reality of our own individual
existencerdquo
Plutarch makes another reference to the river fragment in his discussion of the different
nourishment for plants contained in rain-water and irrigation water
Is the reason that Aristotle gives the true one namely that the water that comes
down as rain is fresh and new while that of a marsh or pool is old and stale The
running waters of springs and rivers are fresh and new-bornmdashyou could not step
into the same rivers twice as Heraclitus says because the waters that flow upon you
are not the samemdashyet they too are less nourishing than rain-water (QN 912 A
trans by F H Sandbach)
This reference to Heraclitus is in my opinion no more than a rhetorical flourish Despite its mention
of ldquoriversrdquo it tells us little about the question of the actual words of Heraclitus and it seems to rely on
Aristotlersquos use of the aphorism It also provides another example where ldquoHeraclitus saysrdquo does not
mean that the quotation is taken directly or accurately from its source
The thirty-oared galley on which Theseus returned to Greece from Crete provides another
example of the idea of constant change but this time applied to an inanimate object (Theseus 23 1)
Whittaker (1969 190) calling the theme ldquoevidently a Middle Platonic commonplacerdquo provides a
similar example in Senecarsquos letter to Lucius (On Being 58 22)
103 (18 392 D) A model in wax or plaster from ἐκμάσσω ldquoto mould or adapt oneself tordquo
SECTION 19 COMMENTARY and NOTES
105 (19 392 E) Time is mobile and immaterial but discernible in conjunction with matter So
true Being is outside time Thus the timeless existence of god as perfect and complete contrasts with
the defective existence of individual mortal beings
106 (19 392 E) The description ldquoaccording to their connections with timerdquo might mean that
each entity is somewhere between birth and death and the place of each one is determined by its own
circumstances
SECTION 20 COMMENTARY and NOTES
75
107 (20 393 A) The reading in Obsiegerrsquos and Bernardakisrsquo Greek texts and the English is in
Goodwinrsquos translation is ldquoiacutet must be saidrdquo (χρη φάναι) In contrast Flaceliegravere has the conditional ldquoif it
needs to be saidrdquo (εἰ χρη φάναι) which appears as an interrogative in the French ldquoLa diviniteacute elle
existe (est il neacutecessaire de le dire)rdquo Babbitt notes that εἰ does not appear in the manuscripts but was
added by Eusebius (Preparatio evangelica 1111) and followed by Cyril of Alexandria (Adv Jul 8)
In any case Babbitt uses ldquoif there be need to say sordquo The emphatic ldquoit must be saidrdquo underlines the
distinction that Ammonius is at great pains to make that the god is not enmeshed in temporality I
have adopted Obsiegerrsquos text
108 (20 393 A) Forever (αἰών) can mean a long space of time an age (as our ldquoeonrdquo) ldquoeternityrdquo
or ldquoagesrdquo with no beginning or end Here it is opposed to χρόνος the same vocabulary pair that
appears in Timaeus 37 c-38 C) The notion of ldquoeternityrdquo points us to Iamblichus (Waterfield 1988
110) where the word is equivalent to the number of the decad There are other resonances of
Pythagoreanism in this section they are Ammoniusrsquo name his background the two appeals to ldquothe
ancientsrdquo ( possibly a reference to Neo-pythagorean doctrine) and the close relationship to Timaeus
(Whittaker 1969 188)
Whittaker asks if the Platonic Forms are eternal in the sense that they endure everlastingly or
if their eternity simply transcends duration He concludes that the answer depends on the interpretation
of αεiacute as used by Plato ndash one referring to time and consequently involving duration and the other
referring to eternity that transcends duration Mediaeval Latin distinguished between ldquoeternalrdquo (outside
time) and ldquosempiternalrdquo (lasting for endless eons)
109 (20 393 A) ἀνέγκλιτον (from κλίνω to make to lie back to lean to incline) meaning
ldquounchangingrdquo and ldquoorthogonalrdquo (LSJ) Plutarch also uses the word in the Life of Pericles (15)
αριστοκρατικην καὶ βασιλικην ἐντεινάμενος πολιτείαν καὶ χρώμενος αὐτῇ πρὸς τὸ
βέλτιστον ὀρθῇ καὶ ανεγκλίτῳ
he struck the high and clear note of an aristocratic and kingly statesmanship and
employing it for the best interests of all in a direct and undeviating fashion
Furthermore the OED defines ldquoto deviaterdquo as ldquoto turn aside from a course method or mode of action
a rule or standardrdquo Hence ldquoto deviaterdquo carries an extra nuance beyond ldquoto changerdquo to
include the notion of falling away from a standard Similarly ldquoorthogonalrdquo can mean a standard or
norm (it also means ldquoright-angledrdquo) A change can be for the worse or the better but to deviate for the
worse is a pleonasm and to deviate for the better a contradiction Perrin has found the mot juste in her
76
translation a translation that works just as well here Then I discovered that Babbitt had used
ldquodeviaterdquo in his translation Nevertheless like Plato and Anaxagoras I shall bear my embarrassment
and gratefully borrow the word from him
110 (20 393 A) The phrase ldquoneither future nor past neither olderhelliprdquo (οὐδὲ μέλλον οὐδὲ
παρῳχημένον οὐδὲ πρεσβύτερον) appears only in Eusebius (see Obsieger 346)
111 (20 393 B) On the ancients Whittaker (1969 186) makes the link to ldquothose coming to the
shrine in search of wisdomrdquo (τοὺς ἐν αρχῇ περὶ τὸν θεὸν φιλοσοφήσαντας (De E 1 385 A)
112 (20 393 B) The word ldquogodrdquo appears in both the masculine (ο θεὸς) and the neuter (τὸ θεῖόν)
which I translate a few lines below as ldquothe divine is not manifoldrdquo I have treated the masculine as a
gendered being and the neuter as an analytic construct
113 (20 393 C) Obsieger (2013 349) suggests that these ancients (who called all things chaste or
pure ldquophoebusrdquo) are Parmenides and Plato referring us to Adv Col (13 1114 C-F) where the
doctrine underlying Ammoniusrsquo argument ndash that true being remains always the same but our world is
fleeting and subject to change ndash also appears
114 (20 393 C) We have already seen these etymologies for Apollo as the not many and the one
and for Phoebus as the chaste (2 388 F) Whittaker identifying these as Pythagorean etymologies
gives instances in works by Clement of Alexandria Plotinus and Porphyry (Whittaker 1969 187) He
also links the name Ieius to the Pythagorean formula ldquothe one and onlyrdquo (εἷς καὶ μόνος and sometimes
ἔν καὶ μόνον) and sees it as derived from the epic adjective ἰός ία ἰόν (meaning εις μια ndash one)
115 (20 393 C) As Ildefonse says the parallel to Homer (Iliad 4 141 ff) is loose perhaps
explaining Ammoniusrsquo use of the qualifier πού The conflating of the two meanings of μιαίνω (to
ldquostain colour or dyerdquo and to ldquostain or sullyrdquo) may have been a commonplace in classical times (and
perhaps today) but the Homeric simile does not introduce the resonances of μίγνυμι (to mix mingle)
that appear in Plutarch Compare also QC 851 725 C where the question posed is ldquoWhy do sailors
draw water from the Nile before daybreakrdquo The partial answer is that during the day riverwater is
stirred up by animals and river traffic and hence polluted This mixing ldquoproduces conflict conflict
produces change and putrefaction is a kind of change
Serendipitously English has an analogous pair of homonymsmdashdiedyemdasha doublet that has
proved a fertile field for punning Shakespeare has a simile in the same Homeric mode
And like a troop of jolly huntsmen come
77
Our lusty English all with purple hands
Dyed in the dying slaughter of their foes (King John II 1 629)
SECTION 21 COMMENTARY and NOTES
116 (21 393 E) The phrase ldquorapture and transformationsrdquo (ἐκστάσεις δ᾽ αὐτοῦ καὶ μεταβολὰς
repeated a few lines later as ἐκστάσεως καὶ μεταβολης) is another of Plutarchrsquos doublets here
combining two close synonyms The first meaning of ἔκστασις is ldquodisplacementrdquo the second
ldquostanding aside and the third ldquoentrancement astonishmentrdquo The Greek word can be transliterated as
ldquoecstasyrdquo an English word closely related to one of the meanings of ldquorapturerdquo (compare the OED
ldquoecstasy an exalted state of feeling which engrosses the mind to the exclusion of thought rapture
transportrdquo) Ammonius is referring to the passage in section 9 where Young Plutarch uses the single
word ldquotransformationrdquo
For we hear the theologians sometimes in verse sometimes in prose asserting and
hymning that the god by his nature is deathless and immortal Yet as a result of the
destined order of cosmos he himself undergoes transformations [μεταβολαῖς]
Ammonius uses this doublet to emphasise that the phrase describes more than spatial displacement or
uncomplicated change He is also stressing that this change is not of Apollorsquos volition since
everything in the cosmos is subject to a logos beyond human or divine control The English word
ldquorapturerdquo captures the involuntary nature of these changes The ldquoTheologiansrdquo could certainly include
Heraclitus who wrote prose but intricate and poetic prose
Plutarch uses this doublet again in discussing the question ldquoWhether it is possible for new
diseases to come into being and from what causesrdquo and whether qualitative changes in a substance
can bring about a change into a new substance (a ldquosubstantialrdquo change) Plutarch comments that if
this is not possible then there is no difference between vinegar and sour wine or bitter and astringent
or wheat and darnel or between one kind of mint and another Yet all of these are very clearly
qualitative losses of identity and transformations (καίτοι περιφανῶς ἐκστάσεις αὗται καὶ μεταβολαὶ
ποιοτήτων εἰσίν QC 893 732 B)
117 (21 393 E) Those saying this are the Stoics or the theologians in the passage from Section 9
Flaceliegravere (1941 84) suggests that the names of the two periods in the religious calendar where satiety
or famine prevail and the earlier passage in De E are related to Diels fragment 65 of Heraclitus
118 (21 393 F) For the simile comparing Apollo and his deadly destruction with a thoughtless
little boy see Homer Iliad 15 362
78
119 (21 394 A) Here we have a balance sheet contrasting the names of Apollo and Hades and
their attributes and predilections Ammonius explores possible etymologies of these names
contrasting the one (A-pollo) with the many (Pluto from πλέος - full or perhaps from πλούτος -
wealth) Ammonius does not mention απόλλων (the future participle of απόλλυμι ldquoto destroyrdquo)
whence as Socrates explains some people wrongly derive his name (Cratylus 405e-406a) since that
abstract noun signifies ldquodestructionrdquo but not ldquodestroyerrdquo the agent of that destruction There are
other epithets of Apollo that do entail havoc if not destruction for example the Homeric epithet ldquothe
far shooterrdquo (Ἀπόλλων ἕκατος Iliad 783)
The name ldquoDelianrdquo describes someone born on the island of Delos as Apollo was but could
also denote clarity (δηλος - clear) which contrasts with Hades or Aiumldoneus that which is hidden in
the dark or invisible (in the Ionic dialect of Heraclitus the initial aspirate is missing and thus a-idēs
means ldquoinvisiblerdquo (Khan 1978 257) Plutarch has already cited Cratylus and clearly enjoyed its
anarchic approach to etymology and he must surely have been aware of the passage in Cratylus where
Socrates riffs on the names of the gods ldquoAs for Pluto he was so named as the giver of wealth
(πλοῦτος) because wealth comes up from below out of the earth And Hades ndash I fancy most people
think that this is a name of the Invisible (αειδής) so they are afraid and call him Plutordquo (Plato
Cratylus 403a) Indeed the section in Cratylus on divine names brings up another resonance with
Heraclitus These etymologies (from 401d to 411b) are organized around the theme of the Heraclitean
theory of flux (See Ademollo 2011 201 ff) We have already discussed the name Phoebus in
(Section 2) which also means radiant or shiningand is clearly opposed to darkness blindness and
Homerrsquos ldquodarkness of deathrdquo (σκότιος)
120 (21 394 A) Apollo with his lyre and his interest in geometry is easily linked with the Muses
and memory which is the polar opposite of oblivion
Pausanias (10244) describes a statue of Apollo Musagetes (leader of the Muses) at Delphi
Henry Middleton describes statues of Apollo Artemis and Latona standing in the eastern pediment of
the new temple built at Delphi after the fire of 548 BC He speculates ldquoa well-known series of statues
in the Vatican of Apollo Musagetes and the Muses though rather feeble works of Imperial date look
as if they were partly copies of some much earlier pediment sculpturerdquo (Middleton 1888 289 see also
footnote 11 2 385 C)
121 (21 394 A) Theoros is an observer or one who contemplates and Phanaean one who reveals
or who brings light (discussed in section 2) Phanaeos is also an epithet of Zeus Both epithets contrast
79
nicely with ldquoLord of night and sleeprdquo in the fragment that follows This fragment and indeed the
whole passage appears again in An recte dict (6 1130 A) For the fragment itself see Bergk 3 719
= Adespota 92 = Edmonds 3 452
122 (21 394 A) For the phrase ldquoof the gods the most hated by mortal menrdquo see Homer (Iliad 9
158-9)
Ἀΐδης τοι αμείλιχος ἠδ᾽ αδάμαστος
τοὔνεκα καί τε βροτοῖσι θεῶν ἔχθιστος απάντων
hellip For Hades gives not way and is pitiless
And therefore he amongst all the gods is most hateful to mortals (Tr Lattimore)
123 (21 394 B) Wyttenbach (1830) established δὲ θνατοῖς in ldquotowards mortals he has been
judged the gentlestrdquo (κατεκρίθη δὲ θνατοῖς αγανώτατος ἔμμεν) by comparison with De def 7 413 C
where this fragment appears word-for-word and in Non pos suav again word-for-word except for δὲ
124 (21 394 A) The Suppliants 975 a Chorus of Argive women mourning their slain sons
125 (21 394 B) A fragment in Bergk 3 p 224 = Stesichorus no 50 = Edmonds 2 58
126 (21 394 B) A fragment of Sophocles Nauck no 764
127 Ammonius has linked the E symbolising the expression ldquoYou arerdquo and an offering from the
seven Sages with the aphorism ldquoKnow yourselfrdquo He has demonstrated the uncrossable chasm between
mortal substance which is always becoming but never is and the god who is neither coming into being
nor passing into destruction The words and the views given to Ammonius might have come from
Plutarch himself Since Plutarch is both a participant in the dialogue and its narrator we could
interpret the dialogue as a comparison of Plutarchrsquos views and understanding as a young man and his
views as a mature man and priest
Lamprias reports that the original E was a gift from the seven Sages to Apollo putting it on a
par with their other well-known maxims This report is accepted without question by the other
participants There is only one other passage (that we know of) where the Delphic E appears (in
De def 22 422 F) just after Cleombrotusrsquo long description of the arguments for and against the
existence of exactly one world or a finite number of them We hear of the wonderful universe of
Petron of Himera containing 183 separate dancing worlds arranged in a triangle enclosing the Plain of
Truth (This long digression brings to mind the glancing attention paid by Young Plutarch to the
question of the number of possible worlds) Not surprisingly Cleombrotusrsquo description of these
80
theories and of the extraordinary man who spent his days by the Persian Gulf consorting with nymphs
and roving demigods was met with thorough scepticism by the participants Cleombrotus himself
introduces one of his more outrageous anecdotes by asking where else would he find such kindly
listeners to test out his stories The participants in De def set a low bar for acceptable and credible
philosophical discourse and were unanimous in agreeing that the question of possible worlds had
hardly met their threshold test Consequently when Philip remarked to Lamprias that plumbing the
controversy over the number of possible worlds was more important to him than understanding the
meaning of the E he banishes that dialogue (De E )in which Lamprias participated to the remote
bathybial regions of intellectual enquiry
εἰ δὲ τὸν θεὸν ἐκβιβάζομεν ἑνὸς κόσμου διὰ τί πέντε μόνων ποιοῦμεν οὐ πλειόνων
δημιουργόν καὶ τίς ἔστι τοῦ αριθμοῦ τούτου πρὸς τὸ πληθος λόγος ἥδιον ἄν μοι
δοκῶ μαθεῖν ἢ της ἐνταῦθα τοῦ εἶ καθιερώσεως την διάνοιαν
But if we rule out that the god made only one world then the question is why do we
restrict the god to creating just five and no more and then what is the relation of
the number five to the rest of the many numbers Personally I should rather
understand this than discover the meaning of the E dedicated here [in the temple]
(De def 31 426 F)
This is a turnaround from the enthusiasm with which the participants in De E carried out their
discussion We see that the characters in the dialogue have convincingly demonstrated the limits of the
search for the truth there have been a succession of clouded insights and the uncovering of half truths
And as with the Delian problem to search for the truth however hopeless is an ineluctable
instruction from the god The limits of human knowledge are encapsulated in maxims and
proclamations from the god including the two maxims that recur throughout the dialogue ldquoKnow
yourselfrdquo and ldquoNothing in excessrdquo
Ammonius is of the same opinion as Philip He responds by finding the truth by proclaiming
the absolute transcendence of divinity and coining his own aphorism or if you will mantra ldquoYou
arerdquo As he says these are the words that people use when they approach the god We can see the
parallel to Socratesrsquo solution to the Delian problem The E symbolises divine transcendence and the
phraserdquoYou arerdquo which does not require logic dialectic philosophy or even geometry to be
understood No mortal can cross the chasm from Becoming to Being not even through profound
diligence and learning but mortals can through faith and the mantra ldquoYou arerdquo apprehend the god
Thus Ammonius answers the riddle to those who seek answers through reason by saying that it is
through faith The votive E turns us outward to contemplate god as Being and the aphorisms of the
sages turn us inward to understand our own humanity
81
APPENDIX A PLUTARCH AND HERACLITUS
The history of electrical development begins long before the Christian era when
Thales Theophrastus and Pliny tell of the magic properties of electronmdashthe
precious substance we call ambermdashthat came from the pure tears of the Heliades
sisters of Phaethon the unfortunate youth who attempted to run the blazing chariot
of Phoebus and nearly burned up the earth
Nikola Tesla Manufacturers Record September 9 1915
From the little we can guess from the fragments from his lost book Heraclitus the Ephesian
drew on the cosmology of the Milesians wrote on theology and was probably what we now
call a public intellectual and in any case a visionary1 That book no longer exists and all that
remains of his philosophy is ldquoa handful of polished aphorisms scattered across the eastern
Mediterraneanrdquo (Lowry 1974 434) Quotations from his work were filtered and collected by
Theophrastus (in a work now lost) the Stoics the Christian Fathers Diogenes Laertius
Plutarch and others We may admire his prose but not so much the man2 He wrote a scornful
assessment of Hesiod Pythagoras Xenophanes and Hecataeus and thought that Homer and
1 Diogenes Laertius gives us the title On Nature and adds that Heraclitus deposited the book in the
Temple of Artemis in Ephesus (DL 95) Plutarch wrote a study (also lost) of Heraclitus ldquoOn the
Question of Heraclitusrsquo Beliefsrdquo listed as Lamprias 205 (Moralia LCL Vol 15)
2 Not everyone admires Heraclitusrsquo style Lucretius (De Rerum Natura 1638 44) objecting to his
extravagant imagery and sophomoric wordplay lambasted him for his obscurity and chastised those
who enjoyed his wordplayldquomistaking itrdquo for cogent reasoning
82
Archilochus should have been excluded from rhapsodic competitions at athletic games On
the other hand he approved of Bias of Priene apparently for his probity3 Bias one of the
seven Sages is known to us for his maxim ldquoMost men are badrdquo (πλεῖστοι ἄνθρωποι κακοί)
which Heraclitus himself borrowed He excoriated his fellow Ephesians for their stupidity
(Diels 121)4 and perhaps all humankind of whom (he said) most are bad and very few good
(Diels 104)
The ldquoartrdquo in the title of a collection of the fragments The Art and Thought of
Heraclitus (Kahn 1979) is apt since in the aphorisms form is as important as substance and
often the form is the substance The art in the aphorisms lies in their careful structure their
ambiguity and their use of literary ornament Consider for example the fragment used in the
epigraph to this thesis αρμονίη αφανης φανερης κρείττων (Diels 54) according to Kahn ldquothe
shortest and most beautifully designed of the fragmentsrdquo (Kahn 1979 202) The two central
words are the same adjective positive and privative and their central position presents the
opposition that holds the sentence together (and illustrates Heraclitusrsquo doctrine of the unity of
opposites) Kahn speculates that by placing αφανης before φανερης Heraclitus is affirming
3 Diogenes Laertius often seems to enjoy gossip and name-dropping Kahn (1979 10) calls Diogenesrsquo
Life of Heraclitus ldquoa tissue of Hellenistic anecdotes most of them obviously fabricated on the basis of
statements in the preserved fragmentsrdquo
4 The different numbering systems for identifying the fragments are distracting In this appendix the
Diels number of a fragment is always given Numbers from other systems are given when they may
help the reader find a particular fragment in a particular text It is possible to track through different
systems by using some combination of the following concordances in Kahn a one way concordance
(DielsKahn) and a triple one-way concordance (KahnDielsMarcovich) in Marcovich a one way
concordance(DielsMarcovich) and a triple-one way concordance (MarcovichDiels Bywater) Diels
cross references his fragments to Bywater
83
that ldquothe negative term is superior to the positive and he has expressed in a formal way the
dialectical re-evaluation of the negative principlerdquo but this may be going too far It is easy to
understand what the fragment says but it not so easy to know what it means If we think of an
ambiguity as any verbal nuance that leaves room for different reactions to the same syntagm
(Empson 1949 1) then Heraclitusrsquo use of three polysemic words allows us to read it in
several different ways I chose Keatsrsquos translation because he has given the fragment context
a poem with a title and a form (the ecphrasis) that nod towards classical Greek literature and
plastic art and then the oxymoron ldquounheard melodiesrdquo with the noun suppressed a direct
homage to Heraclitusrsquo appositional structure I like to think that Heraclitus would have
enjoyed the bad pun in the third line There is no ldquorightrdquo translation of the fragment but Keats
gives one that respects the thought living in the Greek and the art and artifice that we can
sense in Heraclitus
Bywater attributes this fragment (Diels 54 Bywater 47) to Plutarch and translates it
ldquoOf the soul however nothing is pure and unmixed nor remains apart from the rest for lsquothe
hidden harmony is better than the visiblersquo in which the blending deity has sunk variations and
differencesrdquo Bywater on the strength of Hippolytus also connects it to ldquowhatever concerns
seeing hearing and learning I particularly honourrdquo (Diels 55 Bywater 13) 5 Both these
fragments are credited to Hippolytus Bishop of Rome in the late second century AD In his
5 The Greek version ndash αρμονίη αφανης φανερης κρείττων ndash as given in the epigraph to this thesis is
consistent almost without exception across editions and quotations of the fragments Bywater (47)
has κρείσσων for κρείττων which is neither here nor there Plutarch inserts ldquoγαρrdquo (αρμονίη γαρ
αφανης φανερης κρείττων) The careful structure of poetry with its rhythms and rhymes and other
extra-semantic attributes simplifies memorization and protects against faulty recall Aphorisms such
as this one may be easier to recall and quote exactly than less dense prose structures
84
treatise The Refutation of All the Heresies he argues that the source of the Neotian heresy
could be found in the teachings of Heraclitus He is responsible for eighteen of our
Heraclitean frgaments Here is his exegesis of this fragment
Heraclitus honours in equal degree the seen and the unseen as if the seen and
the unseen were confessedly one For what does he say ldquoA hidden harmony
is better than a visiblerdquo and ldquowhatever concerns seeing hearing and learning
I particularly honourrdquo having before particularly honoured the invisible
(Hippolytus Refutation of All the Heresies 9910)
We could draw up a table of opposites to contrast Plutarch and Heraclitus the one
scabrous rude antisocial and misogynistic the other moderate in his views and in his
expression of them gentle in his humor and a participant in and host of elegant symposia
Their only similarities are their love of learning and writing One wonders what affinity
Plutarch could find for this strange man who lived half a millennium before him
Yet affinity there was and it is reflected in Plutarchrsquos attention to Heraclitusrsquo
philosophy and writings and his numerous allusions to him in his own work According to the
Lamprias catalogue of the 120 or so extant fragments of Heraclitus Plutarch cites thirty-two
and he is our sole authority for seven He has about fifty distinct citations of Heraclitus (some
are repeated) and seventy if one counts references to the testimonia6
Plutarch was known to his contemporaries for the breadth and depth of his reading
and to modern readers for the variety frequency and zest of his citations7 There are about
6 The testimonia are listed in section A of Diels and the quotations in section B This paper discusses
only the quotations and I have dispensed with the designation B for them
7 Annewies Van Den Hoek (1993) in her essay on Clement of Alexandriarsquos methods of citation
briefly discusses Plutarch on whom Clement often relied Discussing note taking by ancient authors
including Plutarch she describes the three ldquobookwormsrdquo (her term) ndash Clement Plutarch and Eusebius
85
7000 identified quotations and borrowings from 497 authors in Plutarchrsquos extant works
(Helmbold-OrsquoNeil) Even in one short piece such as De E the resonance of Plutarchrsquos
quotations and allusions and their fitness to the occasion delight the reader In De E we see
in almost every speakerrsquos contribution to the dialogue a mention of an interesting problem or
story that receives no more than a glancing remark accompanied by a succinct quotation or
allusion8 Plutarchrsquos three attributed fragments from Heraclitus in this dialogue are in this vein
ndash short but a direct contribution to the development of the narrative arc of the dialogue The
first is Young Plutarchrsquos use of the notion of exchange to describe the regularity and
periodicity of the pentad (Diels 90) and the second and third occur in Ammoniusrsquo argument
on the many and the one and the gulf between human-kind and the god (Diels 91 and 76)
These allusions to Heraclitus are not only an ornament to Plutarchrsquos prose but also a
contribution to the development of his ideas Before discussing these further it is important to
describe the structure and content of the fragments
THE HERACLITEAN FRAGMENTS
Heraclitusrsquo reputation for obscurity has probably been enhanced by the fragmentary nature of
his extant writings and by the filtering of those fragments through his different authorities
with their different agendas and points of view One puzzle for compilers has been how to
present the more than one hundred fragments (estimated to be about half of Heraclitusrsquo
ndash writers who reportedly loved books and libraries and who seeded their written works with the
harvest from their omnivorous reading and meticulous note-taking
8 For the sake of some examples consider the story of the seven Sages (3 385 D) the Delian problem
(6 386 E) the number of worlds (11 389 F) the divisions of the soul (13 390 F) the source of the
illumination of the moon (15 391 A) and musical theory (10 389 D)
86
original output) without imposing an extraneous ordering or logic upon them This question
arises in our attempt to confront Heraclitus through Plutarchrsquos presentation of him in De E I
do not discuss the testimonia nor descriptions of Heraclitus his life or his teachings
Ingram Bywater (Heracliti Ephesii Reliquiae Oxford 1877) produced a Greek-Latin
version of the fragments with an extensive review of the work of German philologists This
was quickly translated into English by G T W Patrick (Heraclitus of Ephesus on Nature
Baltimore N Murray 1889)9 Patrick presents Bywaterrsquos compilation as the culmination of a
century of scholarly study (mainly on the continent) beginning with the publication of
Friedrich Schleiermacherrsquos Herakleitos der Dunkle von Ephesos (1807) followed by the
Heraclitea of Jakob Bernays (1848) Bywaterrsquos work provides an excellent introduction to the
work of Heraclitus and Patrickrsquos translation made it available
to every man to read and judge for himself [the philosophy of Heraclitus]hellip The
increasing interest in early Greek philosophy and particularly in Heraclitus who is
the one Greek thinker most in accord with the thought of our century makes such a
translation justifiable and the excellent and timely edition of the Greek text by Mr
Bywater makes it practicable
Bywaterrsquos specialist work has been overtaken by the more general studies of Diels and Kranz
on the pre-Socratic philosophers nevertheless Bywater remains a reliable and lucid
9 The English title Heraclitus of Ephesus on Nature tells us as much about Bywater as it does about
Heraclitus Bywater Regius Professor of Greek at Oxford had a keen interest in the natural and
biological sciences He was instrumental in establishing a scholarship in biology at Exeter College
Oxford in 1872 and was a corresponding member to the Academy of Sciences in Berlin He was also
one of the academics involved in the organisation of the ldquoChallengerrdquo oceanic expedition (1872-76)
which circumnavigated the globe to gather information on the worldrsquos oceans His obituary appeared
in Nature 94 (1914) 455
87
introduction to the Heraclitean fragments 10 To my knowledge Arthur Fairbanks (1897) was
the first to analyse the records of Plutarchrsquos quotations from the early philosophers11 Using
Bywaterrsquos compilation (that of Diels was not yet in print) Fairbanks reviewed 228 fragments
from these philosophers12 In the case of Heraclitus he found forty-eight fragments cited by
Plutarch (of which seven are in De E)13 About half of these raised the suspicion of being
taken at second hand either from Plato and Aristotle or from some Stoic source others are
single phrases that were current and familiar (one in De E) Fairbanks winnows to four the
candidates that might have been quoted directly14
Diels built on Bywaterrsquos work but re-ordered the fragments alphabetically by the
name of the source (except for the first which looks very like a preamble to a treatise)
Amongst Dielsrsquos contemporaries John Burnet (1930) and H Gomperz (ldquoUumlber
10 Kahn comments favorably on Bywaterrsquos contribution ldquoin many respects [Bywaterrsquos compilation]
has remained the most useful edition of any detailed study of Heraclitus (ldquoA new look at Heraclitusrdquo
1979 189) Kahn sees Bywaterrsquos methodical arrangement of the fragments by topic as a valiant
attempt to interpret Heraclitusrsquo work as a coherent narrative argument
11 These were Heraclitus Empedocles Anaxagoras Parmenides and Xenocrates See Arthur
Fairbanks ldquoOn Plutarchs Quotations from the Early Greek Philosophersrdquo TAPA 28 (1897) 75-87
12 The precise numbers are Heraclitus 48 Empedocles 99 Anaxagoras 42 Parmenides 21 and
Xenocrates 18The number 48 apparently includes citations that Diels later included in his list of the
Testimonia There are fourteen testimonia listed in Helmbold-OrsquoNeil which with the 33 citations by
Plutarch sums (almost) to 48
13 They can be found in De E 8 388 C 8 388 E 9 389 C 18 392 A 18 392 C 18 392 D and 21
393 E Fairbanks counts seven allusions or quotations in DeE while Helmbold-OrsquoNeil restrict
themselves to the three signalled by a phrase meaning ldquoas Heraclitus saidrdquo
14 The four are fragments 11 12 130 and 126 in Bywater (93 92 127 and 128 in Diels) Plutarch
quotes the first three and Pseudo-Plutarch the last None is in De E
88
dieuumlrspruumlngliche Reihenfolge einiger Bruchstuumlcke Heraklitsrdquo Hermes 58 [1923 20])
disputed Dielsrsquos arrangement while Hermann Fraumlnkel argued persuasively that the care and
artifice exhibited in the construction of the extant fragments presupposed some larger
coherent composition Some later compilers (including Marcovich and Kahn) have arranged
the fragments by their personal conceptions of their subject matter Kirk restricts his analysis
to the ldquocosmicrdquo fragments those ldquodescribing the world rather than men in particularrdquo (1968
30) and included about half of the extant fragments Kathleen Freeman provided a handbook
to the whole of the Die Fragmente der Vorsokratiker following the Diels ordering whilst
allowing herself diversions back and forth to different fragments to suit her line of exposition
Eugen Fink and Martin Heidegger (Heraclitus Seminar 1979) taking a step away from the
linear ordering used the Diels numbering system to identify the fragments but eschewed any
significance to the order implicit in the numbers Thus at the opening of the seminar
Professor Fink on his own motion and authority simply declares ldquowithout further
preliminary considerations we shall proceed directly to the midst of the matter beginning our
interpretation with Fr 64 [τὰδὲ πάντα οἰακίζει κεραυνός]rdquo15 This free form approach leads to
a stimulating if discursive meander through 162 pages and forty-six fragments (some visited
more than once) Obviously to be productive this approach requires well prepared
15 The source for this fragment (Diels 64 Bywater 28 Kahn 119) is Refutation of All the Heresies
9107 Diels translates this into German as ldquoDas Weltall aber steuert der Blitzldquo (Diels 1906 71)
which Seibert translates as ldquolightning steers the universerdquo John Burnetrsquos translation is ldquothe
thunderbolt steers all thingsrdquo
89
participants who are familiar with the fragments as the participants in the Heraclitus Seminar
seem to have been16
Fink chose this fragment because it is a transparent expression with little of the
ldquolinguistic densityrdquo that appears in other fragments17 It consists of three words (ignoring the
particle δὲ) τὰ πάντα οἰακίζει and κεραυνός The English counterparts are ldquoall thingsrdquo
ldquosteersrdquo or ldquoguidesrdquo and ldquolightningrdquo or ldquothunderboltrdquo18 Heidegger commented that the
16 Martin Heidegger and Eugen Fink conducted this seminar at the University of Freiburg during the
school year 1966-67 The plan was to repeat the experiment but that did not come to pass We know
neither the names of the participants nor their number Heidegger himself described the procedure as
ldquoventuresomerdquo and ldquohazardousrdquo nevertheless reading the account of the seminar stimulates both the
mind and the imagination
17 Kahn describes two properties of the fragments linguistic density ldquothe phenomenon by which a
multiplicity of ideas is expressed in a single word or phraserdquo and resonance ldquothe relationship between
fragments by which a single verbal theme or image is echoed from one text to another [so that] the
meaning of each is enriched when they are understood togetherrdquo (1979 89) Kahn does not say so but
resonance must depend on some metric of distance The closer together two fragments are the easier it
is to ldquoseerdquo a relationship Closeness means that they are next to each other on the same page or share
common words or electronic links Dielsrsquos instincts were good when he tried to randomise the
fragments
18 Bywater gives the context ldquoAnd he [Heraclitus] says that a judgement of the world and all things
in it will take place by fire expressing it as follows lsquoNow lightning rules allrsquo that is guides it rightly
meaning by lightning everlasting firerdquo The ldquocontextrdquo for Bywater is the context given in the source
The source of this quotation is Refutation of All the Heresies 910 (Patrick Heraclitus on Nature 24
1888 91) Hippolytus is responsible for eighteen fragments (Diels 50-67) Similarly the twenty-seven
fragments cited by Plutarch appear in fragments 85-101 This classification creates anomalies for
instance in fragment 65 ldquoneed and satietyrdquo which lies within the range of Hippolytusrsquo citations but is
also cited in De E (9 389 C) and similarly fragment 47 is also quoted by Plutarch but attributed to
Hippolytus Plutarch died a few years before Hippolytus was born Two factors might explain this
90
sentence makes good sense in that one knows what it says but since each of the words is
multivalent not necessarily what it means19 The ship analogy in ldquosteersrdquo is a perennial
favorite that has persisted up to the present The notion of steering or governing resonates
throughout the fragments Lightning could be a transferred epithet for Zeus as Heidegger
commented ldquoI remember an afternoon during my journey in Aegina I saw a single bolt of
lightning after which no more followed and my thought was Zeusrdquo Finally the equating of
ldquoall thingsrdquo and ldquothe universerdquo is an adventurous but not an unreasonable or uncommon leap
Heidegger concludes this first chapter by noting that the opposition of the one (the lightning)
to the all is an opposition that preoccupied Heraclitus In Appendix C we see the
reconciliation of the one and the many in the tetractys a single entity identified with the
cosmos which is at the same time a collection of the all ndash the first ten numbers
Heidegger demonstrates how one can enter the maze of the fragments at any point in
this case via fragment 64 and still profit from reading them Kahn in a neat homage to
Heraclitus (see Diels 50 ldquoall things are one ldquoand Diels 10 ldquofrom all things one and from one
anomaly first as Fairbanks points out ldquoneed and satietyrdquo appears to have been a catch-phrase and
one that Plutarch did not describe as coming from Heraclitus and second Hippolytusrsquo citations are
contained in a span of 1000 words from Refutation of All the Heresies 991 to 9108 and their very
density within this passage would not spur a researcher to look for other earlier sources
19 Kahn makes precisely this point about the fragment ldquothe way up and the way down is one and the
samerdquo(Diels 60) which he says provides indirect evidence for a larger (coherent) structure since the
statement cannot be interpreted in isolation ldquoThe literal interpretation of this remark poses no
difficulties but taken in isolation it is so ambiguous as to be devoid of significance Everything turns
upon what kind of way is meant and that we could only learn from the context ndash from the sentences
that came before and afterrdquo
91
thing allrdquo) comments ldquoone might reasonably claim that all of Heraclitusrsquo fragments have
only one single meaning which in fact is the full semantic structure of his thought as a whole
of which any given phrase is but an incomplete fragmentrdquo (1979 95) 20
CITATIONS FROM HERACLITUS IN DE E
Having been shown the way by Heidegger we can enter the fragments with Plutarchrsquos
first explicit quotation from Heraclitus By giving Young Plutarch a quotation about circular
flow Plutarch is setting the stage for Ammoniusrsquo excursus on the theory of flux (πάντα ῥεῖ a
slogan from Cratylus 402) In section 8 even before he refers to Heraclitus Young Plutarch
proposes the hegemony of the pentad by describing the life cycle of wheat from the seed to
the plant and back to the seed ldquoso she [Nature] leads this work to its logical end and at the
end she displays its beginning ndash wheatrdquo (Diels 103) He then compares this to the cycle of
counting by fives where each number ends in either five or zero (5 10 15 20 25hellip) and
makes the imaginative analogical leap from these cycles to those of the cosmos being
20 We have mentioned Heraclitusrsquo syntax and the patterns he creates in his aphorisms these include
parallelism contrasts analogies and pairings Another is the pattern of the geometric mean
AB = BC which as the mean proportional provides a method for solving the Delian problem
Fraumlnkel in an elegant paper (ldquoA Thought Pattern in Heraclitusrdquo AJP 1938) demonstrates that
Heraclitus applied precisely this proportion to metaphysics He suggests that perhaps Heraclitus had
learned from the Pythagoreans about the correspondence between musical intervals and progressions
in geometry and algebrardquo
There is another correspondence to the Pythagorean tetractys The interior numbers of the
Platonic Lambda are the geometric means of the exterior numbers
92
continually created and destroyed in alternation and to the Heraclitean notion of balanced
exchange21
For the first principle preserves the cosmos and then out of the cosmos perfects
itself and as Heraclitus says ldquoall things are exchanged for fire and fire is exchanged
for all thingsrdquo just as ldquogold is for goods and goods for goldrdquo
This contains two different ideas one about the cosmos and the other about individual
exchange In quoting this Young Plutarch gives a version of Heraclitean theory of change ndash a
closed dynamic system autonomously maintaining its equilibrium This aphorism
memorable both for its content and for its artful chiasmus aptly reflects its connotations ndash
circularity reciprocity and fungibility Closed dynamic processes were explored much later in
European philosophy we see the same ideas of circularity in the ldquoinvisible handrdquo in The
Wealth of Nations of Adam Smith (1776) and in the Tableau eacuteconomique of Franccedilois
Quesnay (1758) Even the quotidian balance sheets of modern commercial book-keeping
reflect the idea
There is an ambiguity here whether ldquofirerdquo is one of the things in ldquoall thingsrdquo and
included in them or something apart The imagery suggests that fire possesses a unique and
universal value and is worth all the rest Kahn sees an echo of ldquofrom all things one and from
one thing allrdquo (Diels 10 Kahn 124) and links it to the cosmic cycle ldquoThe universal exchange
for fire is in one sense a fact of human experience we see all sorts of things go up in
flameshellip but the generation of all things from firehellip is a pure requirement of theory and
devoid of empirical supportrdquo (Kahn 1979 150)
21 Plutarch has lsquoπυρὸς τ᾽ ανταμείβεσθαι πάντα hellip lsquoκαὶ πῦρ απάντων ὅκωσπερ χρυσοῦ χρήματα καὶ
χρημάτων χρυσός (Diels 90 Marcovich 54 Kahn 40 Kirk 103 Bywater 22)
93
Young Plutarch speaks of the oneness of the unchanging Apollo and the
transformations of Dionysus adding ldquobut the periods of these cycles are not the same the
one that they call lsquosatietyrsquo is longer than the one they call lsquocravingrsquordquo (Diels 65) Young
Plutarch ends his discussion by defining the proportionate lengths of these ldquoas three is to one
so is the relation of the period of orderly disposition to that of fiery destructionrdquo Young
Plutarch has linked Apollo and Dionysus to the cosmos whose nature is one of underlying
law and order
[which] is not dependent on any divine purposeful will but all is ruled by an
inherent necessary ldquofaterdquo The elemental fire carries within itself the tendency
toward change and thus pursuing the way down it enters the ldquostriferdquo and war of
opposites which condition the birth of the world (διαχόσμησις) and experience that
hunger (χρησμoσύνη) which arises in a state where life is dependent upon
nourishment and where satiety (χόρος) is only again found when in pursuit of the
way up opposites are annulled and unity and peace again emerge in the pure
original fire (έχπύρωσις) This impulse of Nature towards change is conceived now
as ldquodestinyrdquo ldquoforcerdquo ldquonecessityrdquo ldquojusticerdquo or when exhibited in definite forms of
time and matter as ldquointelligencerdquo [Patrick 1889 39]
Nevertheless although the term ecpyrosis was not used by Heraclitus it was adapted
and elaborated by the Stoics in their theory of cyclical growth and destruction Young
Plutarch appears to be giving a Stoicised version of the Heraclitean notion of constant cosmic
change This change is regular confirming Heraclitusrsquo notion of measure and balance as both
Tarrant and Kahn emphasise Thus we see evidence of the cyclical rhythm at both the macro
and micro levels We can leave this here and await Ammoniusrsquo response when it is his turn to
speak
In section 18 Ammonius responds to Young Plutarch but gives short shrift to the
claim that the votary offering E is about numbers in general or the pentad He then cites two
fragments from Heraclitus which serve to contrast flux with circular flow
94
For it is not possible to step twice into the same river nor is it possible to encounter
a mortal being in one and the same state on two separate occasions For a being
changes its state so suddenly and swiftly that it both disperses and comes together
and disperses again or rather not again or later but all at once it is instantaneously
both coming together and departing is both lsquopresentrsquo and lsquoabsentrsquordquo
The authority for this quotation is Plutarch himself and whether it should be interpreted as an
accurate citation of Heraclitus or Plutarchrsquos own summary of a longer statement we cannot
say The detail ldquoyou cannot step twice into the same riverrdquo is even more contentious22 As I
discuss in section 18 some assert that this is no more than a loose paraphrase of ldquoas they step
into the same rivers other and still other waters flow upon themrdquo (Diels 12) Nevertheless the
river is quickly left behind as the subject of the argument and the mortal being who is both
coming together and departing and both present and absent comes to the fore Ammonius is
closing in on the focus of his argument the difference between mortal beings always in the
process of becoming and the god who is He has achieved this by disposing of the numbers
and their powers and lobbing back Young Plutarchrsquos Heraclitean simile with one of his own
Ammonius then takes Young Plutarchrsquos imagery of the seed and turns it to his own
advantage by describing the transformation of the seed as its ldquodeathrdquo and the transformation
into the embryo as a ldquobirthrdquo whence it is but a short step to another fragment a description of
the cosmic cycle ldquofor as Heraclitus said lsquothe death of fire is birth for air and the death of air
is birth for waterrsquordquo (Diels 76) with the afterthought ldquoand it is clearer still in ourselvesrdquo
22 The authenticity of the two river statements fragments (Diels 12 and 91) and their relationship to
each other is controversial There are three versions of Diels 12 Aristotle Meta1010a10-15 Cratylus
402a and De E 18 92 B The statement probably goes back to Heraclitus but Plato does not give it
verbatim Kahn (168) finds it ironic that the most celebrated saying of Heraclitus cannot be traced
directly to him Plutarchrsquos version appears to be derived from Aristotle and Plato
95
I discuss the Greek for these fragments in the notes to section 18 it suffices here to
note that ldquomortal substancerdquo includes animate beings and that in the second quotation we are
given the metaphor of birth and death for changes in elements that we usually do not consider
animate It is not clear whether Ammonius means that the afterthought came from Heraclitus
or from himself He continues to describe the many deaths that we suffer during our lives23
Ammonius discussion leads up to the introduction of a god who ldquobeing one has with one
now filled foreverrdquo and he uses the sayings of Heraclitus to support his basic contention that
nothing of this world participates in true being
Ammonius treats the theories of cyclical change and flux as opposites but the
fragments do not bear this out Human beings in their temporal world may experience flux
from birth to death but many of the Heraclitean fragments are concerned with larger matters
23 Flaceliegravere (1941 89 fn 111) comments
Ces ideacutees nrsquoexpriment qursquoun aspect de la reacutealiteacute et comportement assureacutement une
grande part drsquoexageacuteration Cf Ricard dans sa note agrave ce passage [1884 60 -61] laquo
Les vicissitudes que nous eacuteprouvons dans nos gouts nos affections nos sentiments
et mecircme dans les traits de notre figure ne deacutetruisent ni lrsquouniteacute de notre individu ni
la reacutealiteacute de notre existence propre et individuelle raquo
Obsieger gives two other places where Plutarch explores this idea In the first (De ser Num
15 559 C) climaxes his argument that both man and city maintain some core of sameness with the
riposte ldquoelse we shall throw everything before we know it into the river of Heraclitus into which (he
says) no one can step twice since Nature by her changes is ever altering and transforming all thingsrdquo
In the second The Life of Theseus (231) explores the meaning when the idea is applied to an
inanimate object ndash in this case the thirty-oared galley on which Theseus returned to Greece from
Crete Whittaker (1969 190) provides a similar example in Senecarsquos letter to Lucius On Being (58
22) calling the theme of the ages of man ldquoevidently a Middle Platonic commonplacerdquo
96
ndash seasonality and periodicity starting with the cycle of human generations the sunrsquos annual
turnings between the tropics of Cancer and Capricorn and the Great Year when the sun moon
and planets return to their original relative positions after a lapse of 10800 years
My purpose in this brief discussion was to demonstrate that citations from Heraclitus
played a role in Plutarchrsquos construction of the dialogue After the discursive presentations of
the earlier speakers in De E these three fragments serve to focus the debate and provide a
comparison between the arguments of Young Plutarch and Ammonius Whether Heraclitus
meant to make the two sets of changes ndash circular flow and flux opposites as Ammonius
asserts is debatable It is certainly clear that Heraclitus was talking about cosmic order and
change not necessarily stages of a manrsquos life Furthermore Plutarch prefaces each of these
quotations with ldquoas Heraclitus saidrdquo so that we are in no doubt as to their source
The more one reads of Heraclitus and rereads De E the more one is struck by
Plutarchrsquos appreciation of Heraclitus in so far as we can tell from such scant evidence We
can only speculate on how many other resonances and allusions we might have found in the
complete works of Heraclitus (and the complete works of Plutarch) In footnote 13 I give the
seven allusions to Heraclitus in De E identified by Fairbanks The attentive reader will find
other resonances in this dialogue and of course there are others scattered throughout the
Moralia Expanding the focus to Plutarchrsquos use of Heraclitus in the Pythian Dialogues or
even in the whole Moralia could lead to fascinating insights
Nevertheless Ammonius has not reconciled Young Plutarchrsquos (and Heraclitusrsquo) notion
of circularity with his own (and Heraclitusrsquo) notion of flux which can be done I believe by
going beyond individual things (and goods) to the level of the cosmos As we noted earlier
(8 388 D) Heraclitus does not specify whether fire is a thing amongst ldquoall thingsrdquo or a thing
97
that encompasses all things but not fire itself (Russellrsquos and the Liarrsquos paradoxes) Ammonius
may have seen the truth but not the whole truth which would include not only the fates of
men and the gods but also the other truth that Heraclitus sought the truth about the cosmos
Finally I do not doubt that Heraclitus was a meteorologist and a cosmologist in fact a
scientist Kirk perceived the importance of this aspect of Heraclitusrsquo thinking when he
confined himself to the cosmic fragments Others have noticed this part of his philosophy and
his interest in science For example David Wiggins (2009) has cited the possible scientific
content of the fragment discussed earlier ldquothe lightning steers all thingsrdquo He compares fire
as Heraclitus conceived it and energy as conceived in eighteenth and nineteenth century
physics
Many plain men have scarcely any better idea of what energy is than Heraclitus had
of what fire was But most of us have some conception of energy The common idea
and the idea that holds our conception of energy in place and holds Heraclitus
conception of fire in place is the idea of whatever it is that is conserved and makes
possible the continuance of the world-orderrdquo
Fink saw in the fragment ldquoThe lightning steers all thingsrdquo a reference to the fire that
lightning often engenders and through that the idea of the fire that consumes all things But
that may be too literal an interpretation Lightning may engender fire but lightning s not fire
but the manifestation of the release of a force electrical energy Nikola Tesla another poet
and visionary saw in lightning one of the fundamental forces in our world ndash electricity or the
power that resides in the electron That force had been observed if not understood by the
ancients They knew of the static charge that develops in catrsquos fur and silk They also knew of
the magical properties of amber Indeed in lightning we see another instantiation of
Heraclitusrsquo fragment ldquothe hidden connection is more powerful than the visiblerdquo The other
fundamental force still not understood is that of gravity
98
In De E Plutarch the priest of Apollo writes of the golden-haired god who shares
space with Zeus Guide of Fate near the altar of Poseidon at Delphi Apollo god of the
electron flies with his musical swans to the magical islands of the north where amber grows
on trees Apollo as Phoebus Apollo is associated with the sun that burns with a heat greater
than anything on earth a heat generated not by the electrical energy but by another of the
fundamental forces in our world nuclear energy In the myth that is the heat that destroyed
Phaethon
99
APPENDIX B FREE INDIRECT DISCOURSE
Je ne suis pas toujours de mon avis
Madame de Seacutevigneacute (1626-1696)
In De E the transition from section 7 to section 8 contains an intriguing crux We have
reached the end of Eustrophusrsquo exposition on the E and are moving into Young Plutarchrsquos
This is described in two sentences where Plutarch declares
Eustrophus was not saying these things to us in jest but because I was at that time
devoting myself enthusiastically to my mathematics Nevertheless I was to observe
the maxim ldquoNothing in excessrdquo just as soon as I became part of the Academy
Section 8 Then I said that Eustrophusrsquo explanation had most gracefully resolved the
difficulty with Number ldquoForrdquo I continuedhellip
Since the narrator (Plutarch) is also a character in the story we must decide in each case of
the use of a first-person pronoun whether he is communicating his present thoughts or those
he had at the time of the event There are two possible referents for the six first-person
pronouns in these three English sentences Plutarch or Young Plutarch and if it is Plutarch
he may be narrating the story or as the author be addressing parenthetical remarks to
Sarapion For the first ldquoIrdquo Plutarch the narrator is commenting on young Plutarchrsquos interest in
mathematics In other words this is a self-reference to his younger self In the second and
third he is commenting in an aside on something that happened outside the time-frame of the
dialogue At the beginning of section 8 the last two pronouns ldquoIrdquo clearly refer to Young
Plutarch first as speech reported by the narrator then as the direct speech of Young Plutarch
Finally a first-person pronoun (ldquousrdquo) appears as an indirect object in the first sentence where
it entails another self-reference to the narrator as part of the group
100
This fussing over the grammar is not mere pedantry but an attempt to understand the
nature of the text that we are reading Up to this point in the dialogue we have seen a
straightforward reporting of different interpretations of the meaning of the E All seem to have
had the same philosophical weight all have been treated with mild scepticism by the listeners
and none has seemed persuasive Babbitt makes the interesting comment that these first
speakers are ldquosearching for an explanation of the unexplainablerdquo and that the dialogue
provides an engaging portrayal of the way in which a philosopher reacts when ldquoforced
unwillingly to face the unknowablerdquo A reader who expected or believed that this dialogue
was mere description or uncreative recounting of events that happened twenty years earlier
should be disabused by this point Plutarchrsquos self-referencing and shifting viewpoint suggests
that we are not going to get an answer to the question of the meaning of the E but will have to
settle for the insights into character and the intrinsic interest of the digressions into history and
philosophy that Plutarch provides Plutarch highlights the difficulty that the reader has in
identifying exactly what the dialogue is ldquoaboutrdquo1
Young Plutarch does not see the contradiction between his enthusiasm for
mathematics and the motto of the Academy because for him there is no contradiction The
irony can be enjoyed by the narrator Plutarch who surveys the whole timespan of the
anecdote To make this explicit we could rewrite the sentence putting the original into
reported speech and seeing that the irony has disappeared
Eustrophus did not say these things to those present in jest but because at that time
Young Plutarch was devoting himself enthusiastically to his mathematics But
1 In contrast to this account that given by Fink in The Heraclitus Seminar is a model of objective
rapportage No one could mistake that for a character study
101
Sarapion Young Plutarch did go on to observe the maxim ldquoNothing in excessrdquo just
as soon as he became part of the Academy
[Section 8] Then Young Plutarch said that Eustrophusrsquo explanation had most
gracefully resolved the difficulty with Number ldquoForrdquo he continued hellip
In this version the uninvolved narrator writes of all participants in the third person since
Plutarch as distinct from Young Plutarch is no longer a participant and he can replace ldquous
ldquowith ldquothose presentrdquo Young Plutarch a character in the narrative knows only the present
not that he will one day join the Academy
The technique of implicating the narrator in the story allows a character to appear in
two (or more) incarnations Both Young Plutarch and Plutarch appear within the same scene
and their simultaneous presence pulls us back to the present where Plutarch is writing to
Sarapion Thus three time periods are telescoped into one scene More generally time is fluid
in the dialogue where only two events in real time are given ndash the visits of Nero (1 385 C)
and Livia ldquothe wife of Caesarrdquo (3 386 A) ndash the first described by the narrator to Sarapion and
the second (in direct speech) by Lamprias to the group At the opening of the dialogue the
letter to Sarapion gives us three receding time periods The first is the ldquopresentrdquo where
Plutarch is writing to his friend Sarapion the second occurred ldquojust recentlyrdquo and involves
two of Plutarchrsquos teenage sons The remembered encounter with his sons and his conversation
about the E then conjures for Plutarch a meeting with Ammonius and several other friends
This meeting took place even earlier about twenty years ago and during the reign of Nero we
are told Then abruptly we are in a dialogue where Ammonius is introducing the subject to
Plutarch and his friends
The observations that Plutarch who as the author already has a presence inserts
himself into the narrative and that he scrambles time are not original to me I have seen three
other instances where commentators make essentially the same observation The first appears
102
in Flaceliegraverersquos translation of the Pythian Dialogues (1974) In his foreword to De def he notes
that the narrator in that dialogue has all the attributes of Plutarch and appears to be Plutarch
although later in section 8 he is identified as Lamprias Flaceliegravere in his discussion of this
passage (7 413 C-D) recounts the contretemps with the Cynic Planetiades and comments
Mais il y a lagrave un proceacutedeacute litteacuteraire un kunstgriff [artifice] comme dit Wilamowitz
que nous avons deacutejagrave signaleacute agrave propos de Theacuteon personnage du De Pyth Plutarque
se substituant par moments lui-mecircme agrave son personnage comme par inadvertance et
sans preacutevenir le lecteur (Flaceliegravere 1974 86-87)
Leaving aside for the moment Flaceliegraverersquos reference to Theon this dialogue De def begins as
did De E ndash an unnamed narrator relates the substance of a discussion at Delphi to a friend
The subject is the reason for the diminution and disappearance of many oracles in Greece
There are seven participants Lamprias Ammonius two eminent visitors Cleombrotus and
Demetrios and personnel from the temple including Heracleon (but not Plutarch) In the first
few sections the narrator remains outside the conversation relating the discussion between
Cleombrotus Demetrius and Ammonius in the third person These join another group who
invite them to join their philosophic discussion on which lambda the first or the second has
been lost in constructing the future tense of βάλλω At this point the narrator becomes part of
the conversation writing that ldquowerdquo joined their company and sat amongst them The careful
reader (or an adept at reading and decoding detective stories) will notice that the word ldquowerdquo
eliminates Plutarch as the narrator since he is not on the list of dramatis personae It is only
during the incident with the Cynic Didymus Planetiades that the name of the narrator is
revealed
The incident begins with the narrator explaining that Planetiades incensed by the
choice of the new topic for discussion (the disappearance of the oracles) claims (in indirect
103
speech) that there is so much evil in the world that Reverence (Αἰδὼς) and Divine Retribution
(Νέμεσις) have already fled the haunts of mankind and that it is no wonder that Divine
Providence (πρόνοια θεῶν) has gathered up her skirts and oracles and followed suit The
narrator adds that Planetiades would have said more but Heracleon intervened The narrator
in direct speech and using the pronoun ldquoIrdquo attempts to calm Planetiades The narrative then
continues with ldquowhatever I had said worked he [Planetiades] turned and went out the door
without another wordrdquo (ἐγὼ μὲν οὖν ταῦτ᾽ εἰπὼν τοσοῦτο διεπραξάμην ὅσον απελθεῖν διὰ
θυρῶν σιωπῇ τὸν Πλανητιάδην) Section 8 continues the narrative with ldquoIt became quiet for a
momentrdquo (ἡσυχίας δὲ γενομένης ἐπ᾽ ὀλίγον) and Ammonius ldquoaddressing himself to merdquo (ἐμὲ
προσαγορεύσας) in direct speech said ldquoSee what it is that you are doing Lampriashelliprdquo Thus
Lamprias is revealed as the narrator
Aside from that incongruous ldquowerdquo until this moment we have probably surmised that
Plutarch himself is the narrator Flaceliegravere bases his opinion on the narratorrsquos style and a
quotation from Pindar that appears three times in the Moralia But there is another cogent
reason for feeling that Plutarch may have inserted himself into the dialogue (se substituant par
moments lui-mecircme agrave son personnage) The wandering ldquoIrdquo allows the author (Plutarch) and
Lamprias (the narrator) to provide two different viewpoints The description by the narrator
that there was a moment of quiet juxtaposed with the intervention of Ammonius that
Lamprias ought to concentrate on the matter at hand suggests that the author sees a
contradiction between these ndash first that Lampriasrsquo self reported comments were not effective
and that Planetiadesrsquo abrupt departure has shocked the other participants into silence Plutarch
the author but not Lamprias himself is aware of the pain to Planetiades that Lamprias has
caused
104
Flaceliegravere refers us to Ulrich von Wilamowitzrsquos Der Glaube der Hellenen where
Wilamowitz too in precisely this passage identifies Plutarchrsquos tendency to blur the
boundaries between the narratorrsquos thoughts and words and those of his characters2 He does
not go beyond identification to an analysis of this device or trick [Kunstgriff] but simply
states that at 413 D the Cynic Planetiades is swiftly silenced by Plutarchrsquos brother Lamprias
whom Plutarch has made so much like himself that we might see Plutarch as the narrator of
the dialogue Wilamowitz then refers to his own Commentariolum Grammaticum III3 In that
document written in Latin he again describes the phenomenon of Plutarchrsquos appearing in his
own writings where one might not expect him He remarks on another example in De fac
where Lamprias is again one of the participants None of this needs to detain us except that in
the first sentence in the opening paragraph of the analysis of that dialogue he writes (and we
can see where he is going)
Sed redeo ad prosopopeian Plutarcheam
But back to Plutarchean personification (ie his charactersrsquo speeches)
Although in German Wilamowitz uses the generic Kunstgriff which could be a trick of any
sort and not necessarily literary in Latin he came up with the immensely appropriate Latin
borrowing from the Greek meaning mask face or personage with theatrical and dramatic
connotations
To return to the second example of Theon in De Pyth (nous avons deacutejagrave signaleacute agrave
propos de Theacuteon) Flaceliegravere claims that in that dialogue (409 B) Theon when he discusses
2 Ulrich von Wilamowitz-Moellendorff Der Glaube der Hellenen Berlin Weidenmannshe (1889 2
499)
3 Ulrich von Wilamowitz-Moellendorff Commentariolum Grammaticum Gottingen (1889 3 27)
105
the rites at the temple and the leader of ldquoourrdquo administration speaks as if he were Plutarch
Flaceliegravere repeats almost word for word what he had said earlier about Plutarch and Lamprias
in De def
Cependant il nrsquoest pas impossible que lrsquoon doive identifier malgreacute tout ce Theacuteon agrave
lrsquoami de Plutarque agrave condition drsquoadmettre que Plutarque a utiliseacute ici comme
ailleurs ce singulier proceacutedeacute litteacuteraire par lequel comme par inadvertance et sans en
preacutevenir le lecteur il se substitue soudain lui-mecircme agrave lrsquoun des personnages qursquoil met
en scegravene (Flaceliegravere 1974 43)
Flaceliegravere is correct that this sounds much like a priest of Delphi speaking This dialogue is
structured differently from both De E and De def As in the script of a drama each passage is
prefaced by the name of the speaker and at first it seems that all information will be conveyed
to us through the direct speech of the characters But by section 4 the author comes into focus
with remarks such as ldquosaid Diogenianusrdquo and ldquoTheon repliedrdquo and he turns into a participant
by using the pronoun ldquowerdquo ndash ldquowe urged him onhellip ldquowe accepted thisrdquo and so on Again
Plutarch is not listed amongst the dramatis personae so Flaceliegravere is correct that Plutarch has
once again inserted himself into the dialogue which has evolved from a script into a narrative
(with a narrator) Again the use of the first-person plural (ldquowerdquo) conflates the narrator with a
character in the dialogue
Finally Frieda Klotz (2011) describes how Plutarch recounts autobiographical
details4
4 See Freida Klotz ldquoImagining the past Plutarchrsquos Play with timerdquo eds Frieda Klotz and
Katerina Oikonomopoulou The philosopherrsquos banquet Plutarchs Table Talk in the Intellectual
Culture of the Roman Empire (Oxford Oxford University Press 2011) and ldquoPortraits of the
106
He shuffles his youth and development into an unexpected a-chronological structure
and although he beginshellip the book with scenes in which his own character is mature
and authoritative he ends with his teacher [Ammonius] playing the main role
This is also how Plato structures the Symposium with Socrates eventually ceding pride of
place to Diotima5 Klotzrsquos assessment is also an accurate description of the structure of De E
Plutarch follows the same scheme here with young Plutarch as a character and an Ammonius
who takes the stage at the end of the dialogue for his master class in ldquoGod isrdquo Klotz focusses
on the Table Talks but much that she says applies to the dialogues and it is certainly true in
De E that no one ever addresses Plutarch by his name She claims that this anonymity rather
than downplaying his importance has the opposite effect The unnamed shifting ego signifies
Plutarch as different from the other characters and draws our attention to him Klotz does not
make the connection to the use of personal pronouns and the authorrsquos use of first person or
third person narration which is discussed below in the continuation of the analysis of the
narration of De E
In De E the example given earlier on the transition from section 7 to section 8 is
extraordinary in that we confront the two Plutarchs on the same page The juxtaposition is not
just a literary flourish since their simultaneous presence presages Ammoniusrsquo argument on the
difference between Being and Becoming Every mortal being is always in the process of
ldquocoming-into-beingrsquo so that we get instantiations such as Young Plutarch and his older self
This is a fine illustration of the implications of Ammoniusrsquo assertion
Philosopher Plutarchrsquos Self-Presentation in the lsquoQuaestiones Convivalesrsquordquo Classical Quarterly 57
(2007) 650-67
5 See Daniel Babut ldquoPeinture et deacutepassement de la reacutealiteacute dans le Banquet de Platonrdquo Revue des
Eacutetudes Anciennes 82 (1980) 5-29
107
Other examples where Plutarch inserts himself in the dialogue occur in De E at the
points where one speaker hands over to another6 where the transition is usually accomplished
through an intervention from the narrator In section 2 Plutarch gives a summary of
Ammoniusrsquo analysis of Apollorsquos names and then allows Ammonius to continue without
interruption in direct speech Section 3 begins in the same way Plutarch says that Ammonius
has finished and introduces the next speaker Lamprias who continues without interruption7
Section 4 except for the last sentence is entirely in indirect discourse8
A different authorial intervention occurs in sections 6 and 7 There Plutarch
introduces parenthetical remarks addressed to Sarapion which serve to pull us out of the past
and remind us that this dialogue is indeed being reported in a letter In section 6 Plutarch
introduces ldquomy friend Theon whom you knowrdquo Theon is thus the friend of Young Plutarch
Plutarch and Sarapion and we know that he has survived the intervening twenty or so years
since the dialogue took place We have returned to the present when the letter was written and
6 These points are set out in the Schema Structure of the Dialogue page 16
7 The reader may have noticed that the section divisions track the changes of the speakers and
wonder why the section breaks do not provide sufficient sign-posting of the parts of the dialogue and
of the shift from one speaker to another Surely the division into sections says it all In answer I do not
believe that the section numbers are original to Plutarch although I have been unable to determine
their source They may have been created by Wyttenbach where they do appear They do not appear
in Amyot The place to look for an answer would be in the Aldine collection in the Rylands Library in
Manchester England If they did not exist then it is reasonable that Plutarch built in his own markers
within the narrative that separates direct speeches De Pyth begins with a formal dialogue with each
speaker named at the beginning of his particular speech but that soon evolved intothe system we have
here
8 See fn 21 in section 4
108
to Plutarch ndash the letter writer who can be distinguished from the narrator of the dialogue
when he addresses Sarapion directly (and us indirectly) This is confirmed at the beginning of
section 7 where Plutarch introduces the next speaker with ldquoit was I think Eustrophus the
Athenianrdquo (Εὔστροφον Ἀθηναῖον οἶμαι) Both the hesitation contained in ldquoI thinkrdquo and the
two pronouns require thought The hesitation suggests that Plutarch the letter writer is not sure
that his memory serves him (although he later repeats the name with confidence) So the
referent of the ldquoIrdquo is directing a parenthetical remark to his friend Sarapion apparently to
warn him that his memory may be faulty On the other hand the pronoun must include the
narrator the Plutarch of twenty years before who participated in the dialogue As discussed
earlier at the end of section 7 Plutarch again makes a parenthetical remark about joining the
Academy to Sarapion who no doubt enjoyed the joke about ldquoNothing in excessrdquo
The contributions of both Young Plutarch and Ammonius (sections 8-21) are
delivered almost entirely in direct speech Logically enough an intervention occurs at the
point where Young Plutarch cedes the podium to Ammonius The last sentence in section 16
and the first in section 17 read
[Section 16] τοιοῦτο μὲν καὶ ο τῶν αριθμητικῶν καὶ ο τῶν μαθηματικῶν ἐγκωμίων
τοῦ Ε λόγος ὡς ἐγὼ μέμνημαι πέρας ἔσχεν
Section 17 ο δ᾽ Ἀμμώνιος ἅτε δη καὶ αὐτὸς οὐ τὸ φαυλότατον ἐν μαθηματικῇ
φιλοσοφίας τιθέμενος ἥσθη τε τοῖς λεγομένοις
[Section 16] And that is as I remember how the discussion of the arithmetical and
mathematical encomia to the letter E came to its endhellip
Section 17 Ammonius in as much as he too believed that a not negligible part of
philosophy is found in the study of mathematics was pleased with the direction of
the discussion
The first sentence contains an aside to Sarapion and the second an authorial observation on
Ammoniusrsquo state of mind which can be interpreted also as an aside to Sarapion Thus the
109
referent of the ldquoIrdquo is Plutarch the letter writer and the sentence beginning section 17 is an
authorial intervention describing Ammoniusrsquo state of mind
ALThese interventions remind us of the temporal layers in the dialogue and its air of
nostalgia a nostalgia that is also obvious elsewhere in the Pythian dialogues Plutarchrsquos
references and allusions to thinkers of the past Homer the seven Sages Hesiod Heraclitus
and Pythagoras add to the effect In De E when we listen to the conversation of those seated
by the temple we are taken back to these philosophers who lived even before Cratylus Plato
and Aristotle In the introduction Plutarch describes to Sarapion the group at the temple at
Delphi and his own sons (1 385 A) an image mirrored by the group surrounding Ammonius
many years before (1 385 B) Plutarch goes even further by seeking from Sarapion reports of
similar discourses which reflects the image of these discourses into the future Plutarchrsquos self-
referencing goes beyond his implication in his own story to the implication of his own story in
a series of stories going back in time to the seven Sages and potentially forward into the
future Plutarch gives us no markers to his own time except for the references to Augustus
and Nero and we are lulled on gentle tides between the ldquopresentrdquo of the letter to Sarapion and
the implied future of return gifts from him the ldquorecentrdquo encounter between Plutarch and his
sons and the recollections of the mature Plutarch on the ldquopastrdquo where Young Plutarch his
brother Lamprias and their friends cavort under the intellectual guidance of Ammonius This
returns us to the reciprocal and reflexive giving of gifts described by the reversion from
Dichaearchus to Euripides to Archelaus in the opening lines of the dialogue The dialoguersquos
first word στιχίδιον announces and describes the dialoguersquos own structure The word
describes the whole just as Plutarch describes his own self within the dialogue
FLAUBERT AND AUSTEN LE DISCOURS INDIRECT LIBRE
110
To my knowledge only Flaceliegravere Wilamowitz and Klotz have commented on Plutarchrsquos
modes of speech and narration in the dialogues Their textual analyses suggest Plutarchrsquos skill
and sophistication but do not venture far into a literary analysis Only Klotz comments on the
fluid nature of time in much of Plutarchrsquos work which is I believe a direct result of his
narrative style The analysis of direct speech is straightforward the text gives us what the
character is supposed to have said in the characterrsquos own words The only caution is of
course that it is Plutarch the puppet-master who is putting these words into their mouths
Plato made a distinction between narration (diegesis) or authorial presentation on the one
hand and imitation (mimesis) on the other9 In direct discourse a writer speaks in the person
of another assimilating his style to that persons manner of speaking just as an actor does
when using voice and gesture he imitates the person whose character he assumes When a
writer uses direct speech for his characters it is the character who speaks to us but in indirect
discourse our understanding of the character is filtered through the thoughts of the writer
Lucianrsquos Metamorphoses has been analysed in much the same way by Andrew Laird
He contrasts the use of the first-person voice in discourse and the third in narration He finds
that ancient theorists did not often recognise the differences between literary expression in the
first and third persons He then analyses several examples of free indirect discourse in the
Metamorphoses which we need not go into but he finds the first and third persons used to the
9 Modern writers have explored the use of mimesis and diegesis in classical biography and fiction
Andrew Laird (ldquoPerson lsquoPersonarsquo and Representation in Apuleiusrsquos Metamorphosesrdquo Materiali e
Discussioni per LrsquoAnalisi dei Testi Classici (25 [1990] 129-64) explores the distinction between the
historical author and his (or her) fictional persona using Lucianrsquos Metamorphoses See also Tim
Whitmarsh ldquoAn I for an I reading fictional autobiographyrdquo in The Authorrsquos Voice in Classical and
Late Antiquity by Anna Marmodoro and Jonathan Hill Oxford 2013
111
same end that we discovered when reading De E Lairdrsquos description and interpretation of free
indirect discourse is like that which we saw in sections 7 and 8
The interesting quality of [these] instances of free indirect discourse in Apuleiuss
narrative is that they could be quotations of articulate thoughts of Lucius the
character made at the time described Or they can be discursive utterances given by
Lucius the narrator at the time of narration ndash probably this is how they would strike
a listener there are no declarative verbs of saying or thinking and the exclamations
are enclosed in pure narrative But we must really entertain both possibilities ndash a
synthesis of two voices character and narrator which respectively epitomise our
two modes namely narrative and discourse The quotation of the characters words
is the property of narrative the expression of the narratorrsquos current sentiment is the
property of discourse
The ldquoexpression of the narratorrsquos current sentimentrdquo in De E is contained in those
parenthetical remarks that I have described as being directed to Sarapion to whom Plutarchrsquos
letter is addressed Laird continues that the Metamorphoses combines elements of narrative
and discursive genres for its stylistic techniques such as apostrophe occupatio a specific
type of free indirect discourse and self reference He claims that none of these features were
conspicuous in prose fiction either Latin or Greek before Apuleius Laird may be right that
Apuleius was the first to use these figures so extensively Plutarch also uses them but no one
would describe Plutarchrsquos dialogues as ldquofictionrdquo nor would they unhesitatingly call them
ldquodiscoursesrdquo Plutarch writes in the first person as he would in a discourse but he also uses
the figures emblematic of fiction given by Laird and uses them with skill and sophistication
Narrative can also be varied by using correspondence inserted quotations and
flashbacks as well as changes in the scope of the voice of the narrator It can also be varied
by using free indirect discourse where there is no abrupt jump the from narrators
112
consciousness to the characterrsquos consciousness10 The two literary writers best known for their
use of this style and probably the most studied are Jane Austen and Gustave Flaubert This
paper is not about them but they must be mentioned On the other hand their work has been
analysed so often and so exhaustively that it is difficult to say anything fresh My only
contribution is that one can see a family resemblance between Plutarchrsquos insinuation of his
own persona into his writing and the more developed technique of Flaubert and Austen and
much modern experimental literature We can appreciate that even two millennia ago writers
such as Plato Aristotle and Plutarch were interested in the techniques of writing
Consider what is possibly the best known first sentence in an English novel ldquoIt is a
truth universally acknowledged that a single man in possession of a good fortune must be in
want of a wiferdquo (Pride and Prejudice 1813) Austen has defined the clause ldquothat a single man
in possessionhelliprdquo as a ldquotruerdquo statement (ldquoa truth universally acknowledgedrdquo) even as she
undermines it by subordinating it The truncated statement ldquoa single man in possession of a
good fortune must be in want of a wiferdquo as a complete sentence gives a different impression
If this were the opening sentence one would expect a different novel perhaps just a
10 I have consulted the following sources on the history and theory of discours indirect libre
P Hernadi Dual Perspective Free Indirect Discourse and Related Techniques Comparative
Literature (24 (1972) 32-43) Paul Hernadi Verbal Worlds between Action and Vision College
English (33 (1971)18-31) Norman Friedman Point of View in Fiction The Development of a
Critical Concept (PMLA 70 5 (1955) 1160-184) and Yun Lee Too The idea of ancient literary
criticism (Oxford New York Clarendon Press 1998) and Bernard Cerquiglini laquo Le style indirect
libre et la moderniteacute raquo in Langages 73 (1984) 7-16 Norman Friedman has associated Socrates
three styles of poetry with modern telling and showingrdquo and Paul Hernadi explores the dual roles
of literature as representation (mimesis) and presentation (narration)
113
romance11 Similarly at the end of section 7 in De E the irony arises from the two different
viewpoints contained in a compound sentence The sentence sets up a tension between the
narrator and those who might acknowledge the truth of the statement We the readers are left
to ponder the strength of ldquouniversallyrdquo and whether even if some find the statement true we
can go so far as to say this its truth is acknowledged by all Surely the author is taking too
much upon herself with such a categorical statement
Stephen Ullmann describes Flaubertrsquos mature use of indirect style in Madame Bovary
in statistical terms Flaubert has as many as five instances of the style to a page of the novel
more than Ullman has seen in other works Certainly the instances are more frequent than the
three that I have found in De E (which is certainly shorter than Madame Bovary) I give the
celebrated image of Emma as a good mother (1856 part ii 4 147) ldquoElle deacuteclarait adorer les
enfants crsquoeacutetait sa consolation sa joie sa folie et elle accompagnait ses caresses
drsquoexpansions lyriques qui agrave drsquoautres qursquoagrave des Yonvillais eussent rappeleacute la Sachette de
Notre-Damerdquo As Ullmann tells us ldquoGrammatically lsquocrsquoeacutetait sa consolation sa joie sa folie
might be the authors own words but the reader knows from the context that it is Emma not
Flaubert who is speaking and that she is not telling the truthrdquo (Ullman 109) We know that it
cannot be the narrator who tells us that Emmas little child was a joy and consolation for her
Rather reader and narrator share an ironic distance from the woman who tries to appear what
she is not ndash a devoted mother Ullmann does not quote the last part of the sentence where it is
not Emma who speaks but the narrator ldquoqui agrave drsquoautres qursquoagrave des Yonvillais eussent rappeleacute la
11 Laird cites this sentence saying ldquomoralizing such as we find in Jane Austen is discourse not
narrativerdquo (Laird ldquoPerson Personardquo 136)
114
Sachette de Notre-Damerdquo Here Flaubert uses an extravagant comparison to Sachette (from
The Hunchback of Notre Dame who idolised her baby daughter Esmeralda unfortunately
stolen by gypsies) to tell us that those who did not know Emma (ie those who did not live in
Yonville) might well be persuaded to see her as another doting mother Thus after letting
Emma convict herself out of her own mouth the narrator then steps into the minds of those
who do not know her and hypothesises on their reactions to her words if they could have
heard them A fine and intricate mixture of authorial commentary
The precise genre of De E has been the subject of debate some seeing it as a didactic
piece or as a discourse on religious themes By coincidence Appendix A led us to read and
consider Fink and Heideggerrsquos Heraclitus Seminar(1970) whose declared purpose was to
explore the thinking of Heraclitus
Our seminar is not concerned with a spectacular business It is however concerned
with a serious-minded work Our common attempt at reflection will not be free from
certain disappointments and defeats Nevertheless reading the attempts of an ancient
thinker we make the attempt to come into the spiritual movement that releases us
that releases us to the matter that merits being named the manner of thinking
There are echoes here of Ammoniusrsquo introduction to the interpretation of the E given two
millennia ago Plutarch is also engaged with a serious-minded work but not one that is
spectacular or portentous The subject of the E is not a showy or pressing philosophical
problem but it could through collegial debate and discussion lead to intellectually satisfying
ideas and conclusions The Heraclitus Seminar then proceeds into a dialogue on the
fragments just as De E proceeds into different interpretations of the E But there the similarity
ends the narrative style of the two seminars differs
The Heraclitus Seminar is written entirely in direct speech with each speaker
identified (as De Pyth began in the first two sections) although only Fink and Heidegger are
115
identified by name The other participants are called generically ldquoParticipantrdquo Fink
Heidegger and the participants are all on the same plane equal partners in the dialogue
There is no authorial presence and we could imagine that the report of the seminar is a
transcript by a court reporter or a transcript of a sound recording of the meeting The whole
thing is quite bloodless Professor Heidegger has the last word
At the close I would like the Greeks to be honoured and I return to the seven Sages
From Periander of Corinth we have the sentence he spoke in a premonition μελετα
το πᾶν ldquoΙn care take the whole as a wholerdquo Another word that comes from him is
this φυσεως καταγορια Hinting at making nature visible
Heideggerrsquos concept of a philosophical dialogue could be Plutarchrsquos or Ammoniusrsquo The
approach to truth and true understanding proceeds through stages of conversation thinking
and learning
Plutarchrsquos procedure is different He uses his literary skills to embellish his prose with
literary devices character sketches indirect discourse and through authorial interventions
that scramble discourse with narrative This makes for a richer mix than Heidegger gives us in
his exemplary but plain style We come away from Heraclitus Seminar with questions and
comments about the philosophy of Heraclitus but none about the comportment or
personalities of the participants at the seminar Whether one believes that questions such as
who Theon was is a disfigurement or an embellishment to the basic question of the meaning
of the E is entirely personal It suffices here to say that Plutarch has chosen to write a
dialogue that is more than a bare-bones discourse on a philosophical problem
116
APPENDIX C THE TETRACTYS
Live primrose then and thrive
With thy true number five
And woman whom this flower doth represent
With this mysterious number be content
Ten is the farthest number if half ten
Belongs to each woman then
Each woman may take half us men
Ormdashif this will not serve their turnmdashsince all
Numbers are odd or even and they fall
First into five women may take us all
mdash ldquoThe Primroserdquo John Donne (1572-1631)
The word ldquotetractysrdquo is not used in De E but its meaning is implicit in almost every
discussion of numbers there especially in sections 8 and 10 Young Plutarchrsquos exposition of
arithmology in section 8 focusses on the number five the pentad but the context is the decad
the system of the numbers between one and ten represented by the tetractys1 In section 10
1 Waterfield (1988 23) distinguishes arithmology from the hard science of mathematics (for example
Euclid) Jean-Pierre Brach asks how the two types of arithmetic mathematical and the analogical are
related and how such a relation can be justified philosophically and conceptually He finds that the
ldquothe rather disorderly and uncritical accounts in the few Hellenistic sources left to usrdquo leave those
questions unanswered These sources are Nicomachus of Gerasa Theology of Arithmetic (surviving
fragments in Photius Bibliothegraveque [cod 187] 40-48) Anatolius On the Decad and Iamblichus
Theology of Arithmetic (See ldquoMathematical Esotericism Some Perspectives on Renaissance
Arithmologyrdquo In Hermes in the Academy By Wouter J Hanegraaf and Joce Pijnenburg (eds)
Amsterdam University Press 2009 Pp 75-89
117
he advocates the highly mathematical approach to musical harmony developed by the
Pythagoreans where we recognize the commonality of the tetractys with the tetrachord
The OED dates the first use of the word to Dr Philemon Hollandrsquos 1603 translation of
De Is where he transliterates the word and yokes it to its Latin translation ldquothat famous
quaternarie [of the Pythagoreans] named Tetractysrdquo In the same passage Babbitt contents
himself with ldquothe so-called sacred quaternionrdquo Perhaps through inadvertence Holland uses
quaternerie for tetractys in De an procr where tetractys again appears2 The notion of
ldquofournessrdquo comes through in lsquoquarternaryrsquo but the Pythagorean understanding of the tetractys
is so foreign to our modern intuition of arithmetic that the similarly foreign looking Greek
word is probably preferable to the Latin then we can remember that it means something more
than ldquofourrdquo or a ldquoset of fourrdquo Figure 1 illustrates the notion of fourness in the tetractys and
its identification with the decad (and the universe) as the ldquofour is the tenrdquo according to
Pythagorean lore
Jean-PieRRe BRacHyancient arithmological writings including principally those of Varro Philo
Nicomachus Theon of Smyrna Anatolius the compilator of the Theologumena Arithmeticae
Chalcidius Macrobius Martianus Capella Favonius Eulogius and Johannes Laurentius Lydus
Θεολογούμενα αριθμητικης
2 OED sv ldquotetractysrdquo The word has four entries all associated with either Pythagoras or Plato The
1846 entry is a convoluted joke that will etch forever the meaning of the word in the readerrsquos mind In
the foreword to a collection of four works by Richard Baxter (an English Puritan church leader poet
hymnodist and theologian) Professor T W Jenkyn writes ldquoThose who understand what Tetractysm
was to the Pythagoreans will comprehend what Triadism was to Baxterrdquo Baxterrsquos Nachleben also
includes several spots on YouTube See ldquoThe Signs amp Causes of Depression - Puritan Richard
Baxterrdquo httpswwwyoutubecomwatchv=WJLd3vsVpc
118
Figure 1 The Pythagorean tetractys
This triangular figure in its completeness represents the unity of the decad and of the
cosmos It contains ten elements representing the first ten integers and four rows representing
the first four numbers In modern arithmetic we represent this as
1 +2+3 +4 = 10
It is not obvious from this equation that ten is a triangular number but it follows from
the arithmetic definition the sum of the first four integers Triangular numbers are formed
from the sum of a set of consecutive integers starting from one The first six triangular
numbers are 3 6 10 15 21 28 36
This appendix relies heavily on Waterfieldrsquos translation of Iamblichusrsquo Theology of
Arithmetic (τa θεολογουμενα της αριθμητικής) written after Plutarch lived and centuries after
the Pythagoreans were philosophising and arithmetising The manuscript was first edited in
1817 Thought to have been compiled by Iamblichus its chief sources are Anatolius and the
Theologoumena Arithmeticae of Nicomachus of Gerasa3 Keith Critchlow in his introduction
3 These names appear above in rough reverse chronological order For greater clarity I give their
generally accepted dates in chronological order Pythagoras (fl 540 BC) Nichomachus (fl100)
Plutarch (c 50-c 120) Anatolius of Alexandria (fl 269) Iamblichus (245 ndash c 325) Aetius (391-454)
On these dates it is not impossible that Plutarch knew of Nichomachusrsquo work but these dates may not
119
to Waterfieldrsquos translation quotes Aetius who relates Pythagorasrsquo description of numbers as
ldquothe first principlesrdquo and their interrelations as ldquoharmoniesrdquo (Waterfield 1988 9) Today we
might call such harmonies ldquothe structure of the number systemrdquo Furthermore these numbers
were not generated by a succession or a progression but rather represent a unity with ten
different qualities This structure is beautiful and harmony is indeed an apt description of it
Armand Delatte notes that in antiquity there was a pseudo-science of the numbers and
their properties that today we could not decently call ldquoarithmeticrdquo As to the coining of the
word ldquoarithmologyrdquo he adds4
It is found for the first time to my knowledge in a fragment of Codex Atheniensis
of the eighteenth centuryhellip Under the title Aριθμολγία ηθιχή (ethical arithmology)
the author has grouped series of numbers describing actions honest or dishonest
pious or impious found in the sacred writings of the Old Testament (Solomon
Sirach etc) (1915 139)
Waterfield has similar reservations about the enterprise of Pythagorean number theory For
the Pythagoreans ldquoGod manifests in the mathematical laws that govern everything and the
understanding of these laws and simply doing mathematics could bring one closer to Godrdquo
be right There is a story that Nichomachus was born a generation and a half later than the date given
above based on the belief that the cycle of Pythagorasrsquo regular reincarnations was 216 years
The story goes that Proclus the Neoplatonist (born 412) had a dream that he was a successor of
Pythagoras and hence his immediate predecessor must have died in the year 196 J M Dillon (A
Date for the Death of Nicomachus of Gerasa Classical Review 19 (1969) 274-75) traces out the
argument that led to identifying this person as Nicomachus of Gerasa Dillon then argues that
Nicomachus could have been born no earlier than 120 ndash too late to know Plutarch or for Plutarch to
know of him
4 My translation Delatte gives the reference for the codex (Bibliothegraveque de la Chambre n 65) f08
198a sq
120
(Waterfield 1988 24) Thus the name arithmology designates remarks on the structure and
importance of the first ten numbers where sober scientific thought and religious and
philosophical conjectures are mixed together
The Pythagorean tetractys contains the four basic musical intervals the fourth fifth
octave and double octave also the Platonic point line plane and solid it reflects the
understanding that the Greeks (and many) barbarians counted from one to ten and then started
again at one Pythagoras is said to have remarked ldquoWhat you suppose is four is really ten and
a perfect triangle and our oath5 The word ldquotetractysrdquo appears in two essays in the Moralia
De Is and several times in De an Procr
In De Is Plutarch is describing Egyptian religion to his friend Clea a priestess at
Delphi explaining that the Egyptians link the names of their kings to the numbers This
reminds him of similar properties in number theory where the Pythagoreans gave numbers
and geometric figures the names of the gods The number 36 (the sum of the first four odd
numbers and the first four even numbers) was called the holy tetractys and used for the most
sacred of oaths This number too resonates with the notion of ldquofournessrdquo6
Plutarch wrote De an Procr (14 1027 E 1019 A-B) to help his teenage sons
understand Platorsquos Timaeus Given its purpose Plutarch is not breaking new ground but
providing a teaching tool We are interested only in his construction of the third tectractys the
Platonic Lambda (see figure 3) Plutarch begins by paraphrasing Timaeus (35b 4) and then
5 Armand Delatte Eacutetudes sur la Litteacuterature Pythagoricienne (Paris Librairie ancienne Honoreacute
Champion 1915) 249-268
6Thirty-six is also a triangular number (the sum of the first eight numbers) a square number a perfect
number and the product of two square numbers (4 x 9) It is also an ErdősndashWoods number
121
explains the seven numbers the advantages of placing them in a lambda formation rather
than a straight line and finally how they are used in the composition of the soul (the last is not
pursued here)
Platorsquos Lambda (Timaeus 35b-c) can be presented as a type of tetractys one that still
displays ldquofournessrdquo but where numbers replace counters7
1
2 3
4 9
8 27
Figure 2 The Platonic Lambda
At the apex is the monad the non-spatial source of all number Moving down the rows the
two planar numbers (2 and 3) can be represented by dots in the shapes of plane figures an
oblong and a triangle) they are followed by two square numbers (4 and 9) and then two
cubic numbers (8 and 27)8 The sum of these is 54 Plato used these seven numbers in the
Timaeus to describe the creation of the world from the monad through the point the plane
7 Probably called lambda by Crantor of Soli one of Platorsquos students and an interpreter of the
Timaeus who contributed to the discussion of the world-soul interpreting its base number as 384 and
arranging its harmonic divisions in a lambda-shaped diagram rather than a straight line (See Harold
Tarrant Platorsquos First Interpreters (Ithaca New York Cornell University Press 2000 53-55)
8 In Timaeus these numbers are presented in the sequence 1 2 3 4 9 8 27 The placement of the
nine before the eight may seem odd but when the numbers are placed in a lambda the oddness
disappears the numbers are ordered down each leg of the lambda and numbers are not compared
across the horizontal
122
and then the third dimension The two legs represent the opposition between even (difference)
and odd (sameness) and the progression through the powers from the point to the square to the
cube
We then fill in the Lambda to make a Platonic tetractys using the patterning on each
of the arms 2 x 3 =6 and 2 x 6 = 12 similarly 3 x 2 = 6 and 3 x 6 = 18 Furthermore the
central number 6 serves to harmonise the odd and the even it is the geometric mean of (4 9)
(2 18) and (3 12)) Critchlow adds that these new numbers (6 1218) sum to 36 as do the
three apexes of the triangle (1 8 27) Waterfield remarks that this diagram ldquonow contains all
the factors of 36 which as our author [Plato in Timaeus] says sum to 55rdquo 9 As we see in
section 10 this tetractys provides a calculator for analysing musical harmony
1
2 3
4 6 9
8 12 18 27
Figure 3 The ldquofilled inrdquo Platonic Lambda or numbered Pythagorean tetractys
Plutarch notes that the three new numbers filling in the open positions in the Lambda turn the
figure into another tetractys that is another triangle (summing to another triangular number)
still representing unity but no longer the decad Waterfield adds
9 The sum of the two separate legs of the Lambda is also 55 Some numbers are perfect in that they
are equal to the sum of their factors One that we have already met is 6 (with factors 1 2 3) others are
28 496 and 8 128 The number 36 is not perfect (under the strict definition given above)
123
Even if Plato himself did not suggest the lambda form in the Timaeus yet because of
the convention of triangular numbering and the image of the tetraktys in four lines of
dots were completely familiar to the Pythagoreans of the day it would be inevitable
that they would make the comparison The idea of doing so is not new the pattern
we are about to investigate was in fact published by the Pythagorean Nicomachus
of Gerasa in the second century AD
The Pythagorean tetractys contains the first ten integers displayed with ten counters this
tetrad contains in its ten integers all the integers from one to ninety which can be produced
by judicious addition of the ten numbers in the tetractys The Platonic Lambda has several
attributes involving the number 6 the ldquomarriagerdquo number in Pythagorean theory (Waterfield
1988 29) The sum of each of the three geometric means is 36 (that is 6x6) and all eight of
the factors of 36 appear in the triangle Most fascinating of all if we ldquonestrdquo these geometric
means inside the Platonic Lambda we can continue to create as many new lambdas and
tetractyses as we please
First consider the tetractys created by Critchlow following the work of the Franciscan
friar Francesco Giorgi (1466-1540) Critchlow creates a new tetrad with the central number
36 by multiplying all the numbers in the tetractys in figure 3 by six10
10 This figure corresponds to Critchlowrsquos figure 14 see Critchlow (Waterfield 1988 18) For more
information on Giorgio and his work Critchlow (an architect himself) directs us to R Wittkowa
Architectural Principles in an Age of Humanism (W W Norton New York 1971) Another source is
Chapter Four ldquoThe Cabalist Friar of Venice Francesco Giorgirdquo in Yates (1979 33-42)
124
6
12 18
24 36 54
48 72 108 162
Figure 4 The tetractys of Francesco Giorgi
I offer an alternative derivation (which I have not seen elsewhere) relying on the generation
of the numbers in the Platonic tetractys from the two original numbers This motivates the
construction of Critchlowrsquos figures while staying true to the methods of the Pythagoreans I
give below a diagram of ldquonestedrdquo Platonic Lambdas all derived for the source of all number
the monad
1
2 3
4 6 9
8 12 18 27
24 36 54
48 72 108 162
144 216 324
288 432 648 972
Figure 5 Nested Platonic Lambdas The figure shows a sequence of stacked lambdas
(or inverted Vs) At the top of the stack is the familiar Platonic Lambda (in bold) Below it
lies a lambda (un-bolded) containing Critchlowrsquos numbers
At the apex of the pyramid is the monad or 20middot30 The identity n0 = 1 is consistent with and
sympathetic to the Greek understanding that the source of all number is the monad and it
vindicates the procedure of taking powers of the first two numbers (2 and 3) to generate the
125
table11 This table provides all the integers that have the numbers 2 and 3 as factors and it is a
limited application of the fundamental theorem of arithmetic (or the unique factorization
theorem) This theorem states that every integer greater than 1 is either is a prime number
itself or can be represented as the product of prime numbers and that moreover this
representation is unique except for the order of the factors This application is limited
because it uses only the first two prime numbers12
he family resemblance between this table Pascalrsquos triangle and the binomial theorem is
unmistakable
Keith Critchlow generates two tetractyses and asserts that one can build more for
which I have provided a template Theon of Smyrna may be the originator of this idea he
certainly understood it Asked how many tetractyses there are and what they signified he
replied first giving the Pythagorean oath ldquoI swear by the one who has bestowed the tetractys
the source of eternal nature upon coming generations and into our soulsrdquo and then listed
eleven tetractyses After the first and second tetractyses (the Pythagorean and Platonic) he
drifted into arithmology and I give only the last two the tenth is that of the seasons of the
year ndash spring summer autumn and winter and the eleventh is that of the ages childhood
11 Nested lambdas (and tetractyses) have an additional advantage the computational ease of
constructing new elements and new tetractyses
12 Gauss provides a statement and proof of the theorem using modular arithmetic (Disquisitiones
Arithmeticae 1801) Euclid set out the basic notion of the theorem in Elements Book VII
propositions 30 31 and 32 and continues the discussion in Elements Book IX proposition 14
126
adolescence maturity and old age13 All his constructions break into four parts but aside from
the first two they do not have the arithmetical inter-connectedness of the Pythagorean and
Platonic tetractyses The examples that he gives are often seen in arithmological discussion of
the properties of the tetrad (Waterfield 1988 55-63) His recital is like Young Plutarchrsquos
recital of the appearances of the pentad
Nested lambdas have an additional advantage the computational ease in constructing
them Professor Critchlow went to considerable trouble to demonstrate through their
properties as arithmetic geometric and harmonic means that 6 12 and 18 were the ldquoright
numbersrdquo to fill out the Platonic tetractys In the schema shown in figure 5 the pattern of the
powers of the two basic numbers (2 and 3) allows us to simply follow the progression in the
earlier rows and columns After the initial two rows a pattern is established of alternating
rows containing three and four elements In each row the sum of the powers of the two basic
numbers is constant and that constant increases by one is each successive row For example
the next (and ninth) row in the table will have three elements and the powers will sum to
eight The three elements will be 25middot33 24middot34 and 23middot35 and a quick calculation gives the
numbers 864 1296 and 1944
Other important numbers drop out of the tetractys I mention three the life span of the
hamadryads the number of the Great Year and Platorsquos number (5040)
13 See Theon of Smyrna Mathematics useful for understanding Plato translated from the 1892
GreekFrench edition of J Dupuis by Robert and Deborah Lawlor (San Diego Wizards Bookshelf
1979)
127
In De def or (11 415 F and 416 B) Lamprias (now grown up) reports on an old
riddle from Hesiod on calculating the lifespan of the hamadryads The discussion a ldquowitchesrsquo
brew of erudition and speculationrdquo (Kahn 1979 155) invokes many of the usual authorities
Zoroaster Homer Orpheus Plato Pindar Hesiod and Heraclitus The tetractys is not
mentioned but when Demetrios argues that fifty-four is the limit of the middle years of a
vigorous manrsquos life and explaining that fifty-four is the sum of ldquothe first number the first two
plane surfaces two squares and two cubesrdquo we know that we are in Pythagorean territory
These are the seven numbers in Platorsquos Lambda The interested reader can check that the
lifespans of crows stags vigorous men ravens phoenixes and hamadryads all the beings in
Hesiodrsquos riddle appear in figure 5
The Great Year comes every 10800 years when the sun the moon and the planets
having completed an integral (but different) number of revolutions return to the positions that
they were in at the beginning of this great cycle (Timaeus 39) Then according to the Stoics
the cycle culminates in the conflagration destruction and renewal of the cosmos One
derivation of the number 10800 is four seasons of three months each with 30 days in a
month yields the year (4 x 3x 30 =360) treating each day of the year as a human generation
of 30 years yields gives the Great Year (30 x 360=10800) This recalls the Heraclitean
fragment (Diels A 13)
There is a great year whose winter is a great flood and whose summer is a world
conflagration In these alternating periods the world is now going up in flames now
turning into water This cycle consists of 10800 years (Censorinus De Die
Natali 1811)
The careful reader will have noticed that 10800 does not appear in figure 5 although both 108
and 432 do (both factors of 10800) Not every interesting number in classical philosophy can
128
be computed from the Pythagorean and Platonic tetractyses The two tables are limited in that
they contain powers of only the first odd and the first even numbers The next step would be
to construct tables containing the next prime numbers (3 and 5) Then the number of the Great
Year can be computed from either of the two numbers shown in figure 5
432 x 25 = 432 x 5 x 5 = 10800
108 x 100 = 108 x 4 x 25 = 10800
Similarly to calculate Platorsquos number (Laws 737e1-3) from figure 5 we need the next
prime number seven The number can then be derived from 144 in the second last row in
Figure 5 5040 = 7 x 5 x 144
The number 5040 has many beguiling properties one of which is its appearance in Srinivas
Ramanujanrsquos list of highly composite numbers and it is indeed a ldquosuperior highly composite
numberrdquo14
The real charm of these numbers is that the world has come around at least in the
last two hundred years to the serious study of numbers and to a re-examination of ancient
number theory Many of the numbers that the ancients found pretty or intriguing are showing
14 Benjamin Jowett comments ldquoWriting under Pythagorean influences he [Plato] seems really to
have supposed that the well-being of the city depended almost as much on the number 5040 as on
justice and moderationrdquo (Platorsquos Laws translated by Benjamin Jowett 1871)
The number 5040 is a factorial (7) and one less than the square 5041 making (7 71) a Brown
number pair (and the largest of the three known pairs) a superior highly composite number a
colossally abundant number the number of permutations of four items out of ten choices (10 x 9 x 8 x
7 = 5040) and the sum of forty-two consecutive primes starting with the number 23 Given Plutarchrsquos
interest in the number 36 it is worth looking at the factors of 5040 We can write it as 36 x 2 x 70
which leads us back into the second row of figure 5
129
up in advanced mathematics Who could have imagined that after two and a half millennia
we would see the names of two of the modern greats in number theory Srinivas Ramanujan
and Paul Erdős appearing in the same paragraph as Plato and Pythagoras (the latter at least
implicitly) For example Jean-Pierre Kahane (2015) writes in his remembrance of Paul
Erdős
Jean-Louis Nicholas collaborated with Paul and wrote beautiful papers about him
As a detail let me mention their common interest in highly composite numbers a
term coined by Ramanujan for numbers like 60 or 5040 that have more divisors than
any smaller number My own interest was in the implicit occurrence of the notion in
Platorsquos Utopia 5040 is the best number of citizens in a city because it is highly
divisible (Laws 771c)
130
BIBLIOGRAPHY
EDITIONS AND TRANSLATIONS OF PLUTARCHrsquoS ldquoMORALIArdquo
This list includes both complete collections of the Moralia and editions of selected essays
that include De E Other selections without De E appear in the Select Bibliography below
For example Philemon Hollandrsquos 1603 translation of the complete works appears here but
not the reprint Plutarchs ldquoMoraliardquo Twenty Essays
Amyot Jacques Oeuvres morales et mesleacutees de Plutarque Paris Chez Barthelemy Maceacute au
mont S Hilaire agrave lEscu de Bretaigne 1572
Babbitt F C ed and trans ldquoThe E at Delphirdquo in Plutarchrsquos Moralia in Sixteen Volumes
Loeb Classical Library Vol 5 London and Cambridge Mass Harvard University
Press 1927-2004
Bernardakis G N ed and trans Plutarchi Chaeronensi Vol 3 Leipzig Teubner 1894
Bernardakis Panagiotes D and Henricus Gerardus Ingenkamp eds Plutarchi Chaeronensis
Moralia recognovit Gregorius N Bernardakis Editionem Maiorem Vols 1-7
Athens Academy of Athens 2008-2013
Dryden John ed Plutarchs Morals Translated from the Greek by several hands London
1684-94
Ducas Demetrios ed Plutarch Moralia Venice Aldus Manutius and Andreas Torresanus
1509
Estienne Henri [Henricus Stephanus] Plutarchi Chaeronensis Ethica sive Moralia Opera
Geneva 1572
131
Flaceliegravere Robert ed and trans Plutarque sur lrsquoE de Delphes Paris Les Belles Lettres
1941
mdashmdashmdash ed and trans Plutarque œuvres morales Dialogues Pythiques Vol 4 Paris Les
Belles Lettres 1974
Goodwin W W ed and trans Plutarchs Morals Translated from the Greek by several
hands with an Introduction by Ralph Waldo Emerson 5 vols Cambridge Little
Brown and Company 1878
Holland Philemon trans Plutarch The Philosophy Commonly Called the Morals 1603
Revised Corrected and Printed by George Sawbridge at the Sign of the Bible on
Ludgate-Hill 1657
Ildefonse Freacutedeacuterique trans Dialogues Pythiques Paris Flammarion 2006
Obsieger Hendrik De E apud Delphos Uumlber das Epsilon am Apolltempel in Delphi
Einfuumlhrung Ausgabe und Kommentar Stuttgart Franz Steiner Verlag 2013
Paton W R ed Plutarchi Pythici dialogi tres Berlin Weidmann 1893
Plutarchrsquos Moralia in Sixteen Volumes LCL with an English translation London and
Cambridge MA Harvard University Press 1927-2004
Plutarchi Moralia recensuerent et emendaverunt W Nachstaumldt W Sieveking and
J B Titchener Leipsig Teubner 1985
Prickard A O trans Selected Essays of Plutarch Vol 2 Oxford Clarendon 1918
Ricard Dominique trans Oeuvres morales de Plutarque Paris Lefegravevre 1844
Stephanus Henricus See Estienne Henri
Wyttenbach Daniel ed and trans Plutarchi Chaeronensis Moralia id est opera exceptis
vitis reliqua Graeca emendavit notationem emendationem et Latinam Xylandri
interpretationem castigatam subiunxit animadversiones explicandis rebus ac verbis
item indices copiosos adiecit D Wyttenbach Editio nova annotatione et indice aucta
tomi II pars II Leipzig 1828 (Reprinted in eight volumes in 1962 by Georg Olms
Verlag Hildesheim The last two volumes contain the Greek lexicon)
132
SELECT BIBILIOGRAPHY
This list is not a complete record of all the works and sources I have consulted It includes
most references found in the commentary and in the introductory material and appendices A
few references on topics that are of only passing interest for the dialogue appear with full
bibliographic information in the introductory material and appendices
Aalders G J D ldquoPolitical Thought in Plutarchs lsquoConvivium Septum Sapientiumrsquordquo
Mnemosyne 30 1 (1977) 28-39
Acerbi F ldquoOn the Shoulders of Hipparchus A Reappraisal of Ancient Greek
Combinatoricsrdquo Archive for History of Exact Sciences 57 (September 2003) 465-502
Ademollo Francesco The Cratylus of Plato A Commentary Cambridge Cambridge
University Press 2011
Afonasin E V John M Dillon and John F Finamore eds Iamblichus and the Foundations
of Late Platonism Leiden Boston Brill 2012
Alcock Susan E John F Cherry and Jas Elsner eds Pausanias travel and memory in
Roman Greece New York Oxford University Press 2001
Amandry Pierre La Mantique Apollinienne agrave Delphes Essai sur le fonctionnement de
lOracle Paris Arno Press 1950
Aulotte Robert Amyot et Plutarque La Tradition des ldquoMoraliardquo au XVIe siegravecle Genegraveve
Librairie Droz 1965
Babut Daniel ldquoPlutarque et le Stoiumlcismerdquo Paris Presses universitaires de France 1969
mdashmdashmdash ldquoPeinture et deacutepassement de la reacutealiteacute dans le Banquet de Platonrdquo Revue des Eacutetudes
Anciennes 82 (1980) 5-29
mdashmdashmdashBabut Daniel ldquoLa composition des Dialogues pythiques de Plutarque et le problegraveme
de leur uniteacuterdquo Journal des savants 2 (1992) 187-234
Balmer Josephine Piecing Together the Fragments Translating Classical Verse Creating
Contemporary Poetry Oxford Oxford University Press 2013
133
Barker Andrew ldquoEarly Timaeus Commentaries and Hellenistic Musicologyrdquo Bulletin of the
Institute of Classical Studies 46 (2003) 73-87
mdashmdashmdash The Science of Harmonics in Classical Greece Cambridge Cambridge University
Press 2007
Barrow R H Plutarch and his Times London Chatto and Windus 1967
Bastide Georges and Victor Goldschmidt ldquoLe paradigme dans la dialectique platoniciennerdquo
Revue des Eacutetudes Anciennes 50 (1948) 371
Baxter Timothy M S The Cratylus Platorsquos Critique of Naming Leiden New York Koumlln
Brill 1992
Stanford William Bedell Ambiguity in Greek Literature Studies in Theory and Practice
Oxford Basil Blackwell 1939
Berman K and L A Losada ldquoThe mysterious E at Delphi a solutionrdquo Z Papyrologie
Epigraphik 17 (1975) 115
Betz O ldquoConsiderations on the Real and the Symbolic Value of Goldrdquo In Prehistoric Gold
in Europe eds G Morteani and J P Northover 19-30 NATO ASI (Series E Applied
Sciences) vol 280 Dordrecht Springer 1995
Betz H D and Edgar W Smith Jr ldquoContributions to the Corpus Hellenisticum Novi
Testamenti Plutarch lsquoDe E apud Delphosrsquordquo Novum Testamentum 13 (1971) 217-
235
Boucheacute-Leclercq Auguste ldquoLe fonctionnement de lrsquooracle de Delphesrdquo Annales de lrsquoEacutecole
des Hautes Eacutetudes de Gand II (1938) 82-84
mdashmdashmdash Histoire de la Divination dans LAntiquiteacute 4 vols Paris Ernest Leroux 1879-1892
Bowie Ewen ldquoPlutarchrsquos Habits of Citation Aspects of Differencerdquo in The Unity of
Plutarchrsquos Work lsquoMoraliarsquo Themes in the lsquoLives Features of the Lives in the
Moralia ed Anastasios G Nikolaidis 143-158 Berlin New York Walter de
Gruyter 2008
mdashmdashmdash ldquoSage and Emperor Plutarch and Literary Activity in Achaea AD 107-117rdquo in
Plutarch Greek Intellectuals and Roman Power in the Time of Trajan eds
134
Philip A Stadter and L Van der Stockt 98-117 Leuven Leuven University Press
2002
Boyanceacute P ldquoNote sur la Teacutetractysrdquo Lantiquiteacute classique 20 (1951) 421-425
mdashmdashmdash ldquoSur la vie pythagoriciennerdquo Revue des Eacutetudes Grecques 52 (1939) 36-50
Brenk Frederick E In Mist Apparelled Religious Themes in Plutarchs Moralia Leiden
Brill 1997
mdashmdashmdash ldquoPlutarchrsquos Middle-Platonic God about to enter (or remake) the Academyrdquo in Gott
Und Die Gotter Bei Plutarch ed Rainer Hirsch Luipold 27-50 New York Berlin
Walter de Gruyter 2005
Brouillette Xavier and Angelo Giavatto Les Dialogues Platoniciens chez Plutarque
Strateacutegies et Meacutethodes Exeacutegeacutetiques Leuven Leuven University Press Ancient and
Medieval Philosophy ndash Series 1 43 2010-2011
Brouillette Xavier La Philosophie Delphique de Plutarque Lrsquoitineacuteraire des Dialogues
pythiques Paris Les Belles Lettres 2014
Brumbaugh Robert S Platorsquos Mathematical Imagination Bloomington Indiana University
Press 1977
Burkert Walter Lore and Science in Ancient Pythagoreanism trans Edwin L Minar Jr
Cambridge Mass Harvard University Press 1972
Burnet John Early Greek Philosophy 4th ed London A and C Black 1930
Chappell M ldquoDelphi and the Homeric Hymn to Apollordquo Classical Quarterly 56 (2006) 331-
348
Cherniss H ldquoThe Characteristics and Effects of Presocratic Philosophyrdquo JHI 2 (I951) 319-
355
mdashmdashmdash ldquoThe Sources of Evil according to Platordquo Proc Am Phil Soc 98 (1954) 23-30
Chlup Radek ldquoPlutarchs Dualism and the Delphic Cultrdquo Phronesis 45 (2000) 138-158
Dalimier C Platon-Cratyle traduction ineacutedite introduction notes bibliographie et index
Paris Flammarion 1998
135
De Falco V ed Iamblichus Theologoumena Arithmeticae additions and corrections by
U Klein Stuttgart Teubner 1975
mdashmdashmdash Iamblichus Theologoumena Arithmeticae Leipzig Teubner 1922
De Wet B X ldquoPlutarchrsquos Use of the Poetsrdquo Acta Classica 31 (1988) 13-25
Delatte Armand Eacutetudes sur la litteacuterature pythagoricienne Geneva Slatkine 1974
Des Places Eacutedouard ldquoChronique de la philosophie religieuse des Grecs (1987-1991)rdquo
Bulletin de lAssociation Guillaume Budeacute Lettres dhumaniteacute 50 (1991) 414-429
Di Benedetto V 1990 ldquoAt the Origins of Greek Grammarrdquo Glotta 68 1 (1990) 19-39
Dillon John ldquoPlutarch and Platonist Orthodoxyrdquo Illinois Classical studies 13 (1988)
357-364
mdashmdashmdash ldquoPlutarch and God Theodicy and Cosmogony in the Thought of Plutarchrdquo in
Traditions of Theology Studies in Hellenistic Theology Its Background and
Aftermath ed Dorothea Frede and Andreacute Laks Leiden Boston Cologne Brill 2002
Dobson Marcia ldquoHerodotus 1471 and the Hymn to Hermes A Solution to the Test
Oraclerdquo AJP 100 (1979) 349-359
DOoge Martin Luther trans Nicomachus of Gerasa Introduction to Arithmetic Ann Arbor
University of Michigan Humanistic Series 16 London Macmillan 1926
Edmonds Radcliffe G III Redefining Ancient Orphism A Study in Greek Religion
Cambridge Cambridge University Press 2013
Einarson B and P de Lacy ldquoThe Manuscript Tradition of Plutarchrsquos Moralia 548A-612Brdquo
Classical Philology 46 (1951) 93-110
Empson William Seven Types of Ambiguity 2nd ed London Chatto and Windus 1949
Fairbanks Arthur ldquoHerodotus and the Oracle at Delphirdquo Classical Journal 1 (1906) 37-48
mdashmdashmdash ldquoOn Plutarchs Quotations from the Early Greek Philosophersrdquo TAPA 28 (1897)
75-87
Ficino Marsilio All Things Natural Ficino on Platos Timaeus trans Arthur Farndell
London Shepheard-Walwyn 2010
136
Flaceliegravere R ldquoPlutarque et la Pythierdquo Revue Des Eacutetudes Grecques 56 264265 (1943)
72-111
Fontenrose J The Delphic Oracle its responses and operations Berkeley University of
California Press 1978
Forshaw Peter J ldquoOratorium - Auditorium - Laboratorium Early Modern Improvisations on
Cabala Music and Alchemyrdquo Aries 10 (2010) 169-195
Fraumlnkel Hermann ldquoA Thought Pattern in Heraclitusrdquo AJP 59 (1938) 309-337
Franklin J C ldquoHarmony in Greek and Indo-Iranian Cosmologyrdquo Journal of Indo-European
Studies 30 (2002) 1-25
Frede Dorothea and Andreacute Laks eds Traditions of Theology Studies in Hellenistic theology
its Background and Aftermath Leiden Boston Koumlln Brill 2002
Freeman Kathleen Ancilla to the Pre-Socratic Philosophers Oxford Harvard University
Press 1957
Gee Emma Aratus and the Astronomical Tradition Oxford Oxford University Press 2013
Gerber Douglas E A Companion to the Greek Lyric Poets Leiden New York Koumlln Brill
1997
mdashmdashmdash Greek Iambic Poetry from the seventh to the fifth centuries BC Cambridge Mass
Harvard University Press 1999
Goldin Owen ldquoHeraclitean Satiety and Aristotelian Actualityrdquo The Monist 74 (1991) 568-
578
Goldschmidt Victor Le paradigme dans la dialectique platonicienne Paris Presses
Universitaires de France 1947
Grant Hardy ldquoMathematics and the Liberal Artsrdquo The College Mathematics Journal 30
(1999) 96-105
Gregory T E ldquoJulian and the last oracle at Delphirdquo GRBS 24 (1983) 355
Griffiths J Gwyn ldquoThe Delphic E A New Approachrdquo Hermes 83 (1955) 237-245
Guillon Pierre La Beacuteotie antique Paris Les Belles Lettres 1948
137
Gummere Richard M trans Seneca Ad Lucilium Epistulae Morales 3 vols Cambridge
Mass Harvard University Press London William Heinemann Ltd 1917-1925
Hadzsits George Depue Prolegomena to a Study of the Ethical Ideal of Plutarch and of the
Greeks of the First Century A D Cincinnati Ohio University of Cincinnati Press
1906
Hardie Alex ldquoPindarrsquos lsquoTheban Cosmogonyrsquo (The First Hymn)rdquo Bulletin of the Institute of
Classical Studies 44 (2000) 19-41
Heath Thomas History of Greek Mathematics 2 vols Oxford Clarendon 1921
mdashmdashmdash A Manual of Greek Mathematics Oxford Oxford University Press 1931 (Reprinted
by Dover New York 1968)
Heidegger Martin and Eugen Fink Heraclitus Seminar trans Charles H Seibert Evanston
Illinois Northwestern University Press 1993
Hershbell Jackson P ldquoPlutarch and Heraclitusrdquo Hermes 2 (1977) 179-201
Hodge A T ldquoThe mystery of Apollorsquos E at Delphirdquo AJA 8 (1981) 83-84
Holden H A ldquoPlutarchs Moraliardquo Classical Review 4 (1890) 306-07
Holland Philemon Trans Plutarchs ldquoMoraliardquo Twenty Essays London J M Dent amp
Sons 1911
Hunt A S and C C Edgar trans Private Documents Vol 1 of Select Papyri ed
Jeffrey Henderson Cambridge MA Harvard University Press 1932
Huxley George ldquoPetronian Numbersrdquo Greek Roman and Byzantine Studies 91 (Spring
1968) 55
Ilievski Petar ldquoThe Origin and Semantic Development of the Term Harmonyrdquo Illinois
Classical Studies18 (1993) 19-29
Imhoof-Blumer Friedrich and Percy Gardner lsquolsquoNumismatic Commentary on Pausaniasrdquo
Journal of Hellenic Studies 6 (1885) 50ndash 101 7 (1886) 57ndash 113 8 (1887) 6ndash 63)
Isenberg Meyer William ldquoThe Unity of Platos Philebusrdquo Classical Philology 35 (1940)
154-179
138
Jones C P ldquoPlutarchs Moraliardquo GampB 15 (1968) 130-146
mdashmdashmdash ldquoPausanias and His Guidesrdquo in Pausanias travel and memory in Roman Greece 33-
39 Edited by Susan E Alcock John F Cherry and Jas Elsner New York Oxford
University Press 2001
Jones Roger Miller The Platonism of Plutarch with an introduction by Leonardo Taraacuten
New York Garland Publications 1980
Kahane Jean-Pierre ldquoBernoulli convolutions and self-similar measures after Erdős A
personal hors doeuvrerdquo Notices of the American Mathematical Society 62 (2015)
136ndash140
Kahn Charles H ldquoA New Look at Heraclitusrdquo American Philosophical Quarterly 1 (1964)
189-203
mdashmdashmdash ldquoThe Greek verb lsquoto bersquo and the concept of beingrdquo Foundations of Language 2
(1966) 245-65
mdashmdashmdash The art and thought of Heraclitus an edition of the fragments with translation and
commentary Cambridge Cambridge University Press 1979
Kerenyi Karol Dionysos archetypal image of indestructible life Translated by Ralph
Manheim Princeton Princeton University Press 1976
Kingsley Peter In the Dark Places of Wisdom Inverness California The Golden Sufi
Centre 1999
Kirk G S ldquoNatural Change in Heraclitusrdquo Mind 60 237 (1951) 35-42
mdashmdashmdash Heraclitus The Cosmic Fragments Cambridge Cambridge University Press 1962
Korab-Karpowicz W Julian The Presocratics in the Thought of Martin Heidegger
New York Peter Lang 2017
Kouremenos Theokritos ldquoThe tradition of the Delian problem and its origins in the Platonic
corpusrdquo Trends in Classics 3 (2011) 341ndash364
Krappe Alexander H ldquoAΠOΛΛΩN KΥKNOΣrdquo Classical Philology 37 (1942) 353-370
139
Kurke Leslie ldquoAncient Greek Board Games and How to Play Themrdquo Classical Philology 94
(1999) 247-67
Laird Person Persona
Lamberton Robert Plutarch New Haven and London Yale University Press 2001
Lanzillotta L R ldquoPlutarch at the Crossroads of Religion and Philosophyrdquo in Plutarch in the
Religious and Philosophical Discourse of Late Antiquity edited by Lautaro Roig
Lanzillotta and Israel Muntildeoz Gallarte 1-21 Leiden Boston Brill 2012
Lawlor Robert and Deborah Lawlor Theon of Smyrna Mathematics useful for understanding
Plato translated from the 1892 GreekFrench edition of J Dupuis San Diego
Wizards Bookshelf 1979
Lernould Alain ldquoPlutarque sur lrsquoE de Delphes 390 B 6-8 et lrsquoexplication de la vision de
lsquoTimeacuteersquo 45 B-Drdquo Methodos 5 (2005) 1-19
mdashmdashmdash ldquoPlutarque E de Delphes 387 d 2-9 Une interpreacutetation philosophique de leacutepisode de
lenlegravevement du treacutepied par Heacuteraclegraves une erreur de jeunesserdquo Revue des Eacutetudes
Grecques 113 (2000) 147-171
Losada L A and K Morgan ldquoThe E at Delphi Again Reply to A T Hodgerdquo AJA 85
(1984) 115-117
Lowry S Todd ldquoThe Archaeology of the Circulation Concept in Economic Theoryrdquo Journal
of the History of Ideas 35 (1974) 429-444
Marcovich M Heraclitus Greek Text with a Short Commentary Merida Venezuela Los
Andes University Press 1967
mdashmdashmdash ldquoA New Poem of Archilochus lsquoP Colonrsquo inv 7511rdquo GRBS 16 (1975) 5ndash14
Martin Hubert Jr ldquolsquoAmatoriusrsquo 756 E-F Plutarchs Citation of Parmenides and Hesiodrdquo
AJP 90 (1969) 183-200
Mates Benson ldquoDiodorean Implicationrdquo The Philosophical Review 58 (1949) 234-242
Mates Benson ldquoStoic Logic and the Text of Sextus Empiricusrdquo AJP (1949) 290-298
140
Mathiesen Thomas J Apollos lyre Greek music and music theory in antiquity and the
Middle Ages Lincoln NE and London University of Nebraska Press 1999
Mathieu J M ldquoTrois notes sur le traiteacute De EI apud Delphos de Plutarque (384E 391F-393A
393D-Erdquo Kentron 7 (1991)
McClain Ernest G ldquoA new look at Platorsquos Timaeusrdquo Music and Man 1 (2000) 341-360
McNamee Kathleen and Michael L Jacovides ldquoAnnotations to the Speech of the Muses
(Plato Republic 546B-C)rdquo Z Papyrologie Epigraphik 144 (2003) 31-50
Meeusen Michiel Caroline ldquoPlutarch and the Wonder of Nature Preliminaries to Plutarchrsquos
Science of Physical Problemsrdquo Apeiron 47 (2014) 310-341
Merkelbach R and M L West ldquoEin Archilochos-Papyrusrdquo Z Papyrologie Epigraphik 14
(1974) 97-113
Merker Anne La vision chez Platon et Aristote Sankt Augustin Academia Verlag 2003
Michael D Bailey Fearful Spirits Reasoned Follies The Boundaries of Superstition in Late
Medieval Europe Ithaca Cornell University Press 2013
Middleton J Henry ldquoThe Temple of Apollo at Delphirdquo Journal of Hellenic Studies 9 (1888)
282-322
Miller Dana R ldquoPlatorsquos Argument for the Plurality of Worlds in De Defectu Oraculorumrdquo
424c10-425e7rdquo Ancient Philosophy 17 (1997) 375-394
Mueller Ian ldquoStoic and Peripatetic Philosophyrdquo Archiv fuumlr Geschichte der Philosophie 51
(1969) 173-186
Muumlller Alexander ldquoDialogic structures and forms of knowledge in Plutarchrsquos lsquoThe E at
Delphirsquordquo Studies in History and Philosophy of Science Part A 43 (2012) 245-249
Naber S A ldquoObservationes Miscellaneae ad Plutarchi Moraliardquo Mnemosyne 28 (1900) 85-
117+129-156+329-364
Nordgren Lars Greek Interjections Syntax Semantics and Pragmatics Berlin Boston
Walter de Gruyter 2015
141
ldquoNote on the Symposiacs and Some Other Dialogues of Plutarchrdquo Classical Review 32
(1918) 150-53
OBrien D ldquoDerived Light and Eclipses in the Fifth Centuryrdquo Journal of Hellenic Studies 88
(1968) 114-127
Oikonomides A N ldquoRecords of lsquoThe Commandments of the Seven Wise Menrsquo in the 3rd
century BCrdquo The Classical Bulletin 63 (1987) 67-76
Opsomer Jan Geert Roskam and Frances B Titchener eds A Versatile Gentleman
Consistency in Plutarchs Writing Leuven Leuven University Press 2016
mdashmdashmdash ldquoM Annius Ammonius A Philosophical Profilerdquo in The origins of the Platonic
system edited by M Bonazzi and J Opsomer 123-186 Louvain 2009
Palmer Richard E ldquoThe Postmodernity of Heideggerrdquo Boundary 2 4 ldquoMartin Heidegger and
Literaturerdquo (Winter 1976) 411-432
Parke H W and D E W Wormell The Delphic oracle 2 vols Oxford Blackwell 1956
Parker Robert ldquoThe Problem of the Greek Cult Epithetrdquo Opuscular Atheniensia 28 (2003)
174-183
Patrick G T W ed and trans The Fragments of the Work of Heraclitus of Ephesus on
Nature translated from the Greek text of Bywater Baltimore N Murray 1889
Pickard-Cambridge Arthur Wallace Sir Dithyramb Tragedy and Comedy Oxford
Clarendon Press 1927
Podlecki Anthony ldquoPlutarch and Athensrdquo Illinois Classical Studies 13 (1988) 231-43
Ramanujan S ldquoHighly Composite Numbersrdquo Proc London Math Soc 14 (1915) 347-409
mdashmdashmdash Collected Papers edited by G H Hardy P V S Aiyar and B M Wilson
Cambridge Cambridge University Press 1927
Riginos Alice Swift Platonica The Anecdotes Concerning the Life and Writings of Plato
Leiden Brill 1976
Robbins F E ldquoThe Lot Oracle at Delphirdquo Classical Philology 11 (1916) 278-292
142
mdashmdashmdash ldquoPosidonius and the Sources of Pythagorean Arithmologyrdquo Classical Philology 15
(1920) 309-22
mdashmdashmdash ldquoThe Tradition of Greek Arithmologyrdquo Classical Philology 16 no 2 (1921) 97-123
Robert Louis ldquoDe Delphes a lOxus Inscriptions grecques nouvelles de la Bactrianerdquo CRAI
(1968) 442-454
Robin Leacuteon La Penseacutee Grecque Paris Editions Albin Michel 1963
mdashmdashmdash Platon Paris Presses Universitaires de France 1968
Robins R H ldquoDionysius Thrax and the Western Grammatical Traditionrdquo Transactions of the
Philological Society 56 (1957) 67-106
Rodier Georges Eacutetudes de philosophie grecque Paris Librarie philosophique J Vrin 1969
Roskam Geert Review of Plutarch De E apud Delphos Uumlber das Epsilon am Apolltempel
in Delphi by Henrik Obsieger Antiquiteacute Classique 84 (2015) 314-320
Roux Georges Delphes son oracle et ses dieux Paris Les Belles Lettres 1976
Russell D A ldquoOn Reading Plutarchs Livesrdquo Greece and Rome 13 (1966) 139-154
mdashmdashmdash ldquoOn Reading Plutarchs Moraliardquo Greece and Rome 15 (1968) 130-146
mdashmdashmdash Plutarch London Duckworth 1973
Sandbach F H ldquoRhythm and Authenticity in Plutarchs Moraliardquo Classical Quarterly 33
(1939) 194-203
mdashmdashmdash ldquoPlutarch and Aristotlerdquo ICS 7 (1982) 207-232
Sansone David ldquoOn Hendiadys in Greekrdquo Glotta 62 (1984)16-25
Sedley D N ldquoThe Etymologies in Platorsquos lsquoCratylusrsquordquo Journal of Hellenic Studies 118
(1998) 140-154
mdashmdashmdash Platorsquos Cratylus Cambridge Cambridge University Press 2003
Shilleto A R Plutarchs Morals ethical essays London George Bell and sons 1888
Sirinelli Jean Plutarque de Cheacuteroneacutee Un philosophe dans le siegravecle Paris Fayard 2000
143
Soissons Jean-Pierre Jacques Amyot (1513-1593) Chaintreux Eacuteditions France-Empire
Monde 2013
Sosiades ldquoCommandments of the Seven Wise Men (Stobaeus Anthologium 31173)rdquo in
Stobei Anthologium edited by Curt Wachsmuth and Otto Hense Vol 3 Berlin 1894
125ff
Soury D La deacutemonologie de Plutarque essai sur les ideacutees religieuses et les mythes dun
platonicien eacuteclectique Paris Belles Lettres 1942
Spitzer Leo ldquoClassical and Christian ideas of World Harmony Prolegomena to an
Interpretation of the Word lsquoStimmungrsquo Part Irdquo Traditio 2 (1944) 409-464
Stanford William Bedell Ambiguity in Greek Literature Studies in Theory and Practice
Oxford Basil Blackwell 1939
Stanley Richard P ldquoHipparchus Plutarch Schroumlder and Houghrdquo American Mathematical
Monthly 104 (1997) 344-350
Taraacuten Leonardo ldquoThe River-Fragments and their Implicationsrdquo Elenchos Rivista di Studi
Sul Pensiero Antico 20 (1999) 9-52
Tarrant D ldquoColloquialisms Semi-Proverbs and Word-Play in Platordquo Classical Quarterly 40
(1946) 109-117
mdashmdashmdash ldquoMore Colloquialisms Semi-Proverbs and Word-Play in Platordquo Classical Quarterly
ns 8 (1958) 158-160
mdashmdashmdash ldquoGreek Metaphors of Lightrdquo Classical Quarterly 10 (1960) 181-187
Tarrant Harold Platorsquos First Interpreters Ithaca New York Cornell University Press 2000
Taylor Thomas trans Iamblichus Life of Pythagoras or Pythagoric Life London
J M Watkins 1818
Thompson E A The Last Delphic Oracle Classical Quarterly 40 (1946) 35-36
Trivigno Franco V ldquoEtymology and the Power of Names in Platorsquos lsquoCratylusrsquorsquorsquo Ancient
Philosophy 32 (2012) 35-75
144
Van Den Hoek Annewies ldquoTechniques of Quotation in Clement of Alexandria A View of
Ancient Literary Working Methodsrdquo Vigiliae Christianae 50 (1996) 223-243
Van Sickle John ldquoThe Doctored Text Translating a New Fragment of Archilochusrdquo MLN
90 (1975) 872-85
Vlastos Gregory ldquoOn Heraclitusrdquo AJP 76 (1955) 337-368
Waterfield A H ldquoPlato Philebus 52 c1 ndash d1 Text and Meaningrdquo Rheinisches Museum fuumlr
Philologie Neue Folge 129 (1986) 358-360
Waterfield Robin trans The Theology of Arithmetic On the Mystical Mathematical and
Cosmological Symbolism of the First Ten Numbers Attributed to Iamblichus
Foreword by Keith Critchlow Grand Rapids MI Phanes Press 1988
Waterfield Robin ldquoEmendations of Iamblichus Theologoumena Arithmeticae (De Falco)rdquo
Classical Quarterly 38 (1988) 215-227
Webster T B L ldquoPersonification as a Mode of Greek Thoughtrdquo Journal of the Warburg and
Courtauld Institutes 17 (1954) 10-21
West M L ldquoArchilochus Ludens Epilogue of the Other Editorrdquo Z Papyrologie Epigraphik
16 (1975) 217-19
mdashmdashmdash Ancient Greek music Oxford Clarendon Press 1994
mdashmdashmdash ldquoThe Eternal Triangle Reflections on the Curious Cosmology of Petron of Himerardquo
in Apodosis Essays Presented to Dr W W Cruickshank to Mark His Eightieth
Birthday (London St Paulrsquos School) 1992 105-110
Wiggins D ldquoHeraclitusrsquo Conceptions of Flux Fire and Material Persistencerdquo in Language
and Logos Studies in Ancient Greek philosophy Presented to G E L Owen eds M
Schofield and M Nussbaum 1-32 Cambridge Cambridge University Press 1982
Whittaker John ldquoAmmonius on the Delphic Erdquo Classical Quarterly 19 (1969) 185-192
mdashmdashmdash ldquoPlutarch Plato and Christianityrdquo in Neoplatonism and Early Christian Thought
Essays in Honour of AH Armstrong ed A H Armstrong H J Blumenthal and
R A Markus 50-63 Ann Arbor Variorum Publications 1981
145
mdashmdashmdash ldquoThe lsquoEternityrsquo of the Platonic Formsrdquo Phronesis 13 (1968) 131-144
Wilberding James ldquoEternity in Ancient Philosophyrdquo in Eternity ed Y Melamed 14-55
Oxford Oxford University Press 2016
Wright George T ldquoHendiadys and Hamletrdquo PMLA 96 (1981) 168-193
Yates Frances The Occult Philosophy in the Elizabethan Age London Routledge 1979
Zuntz G ldquoNotes on Plutarchrsquos Moraliardquo Rheinisches Museum fuumlr Philologie Neue Folge 96
Bd 3 (1953) 232-235