Part Two: Plato’s Argument Against Artificial Intelligence
It is striking that thousands of years before the advent of “Artificial Intelligence” Plato should insist repeatedly and forcefully that mind (i.e., intelligence) without soul is impossible to find[i], that soulless intelligence can never come to be[ii], and that of all existing things only soul is fit to be possessed by mind[iii]. Similar arguments can be found in other writings of Plato[iv]. Though “artificial intelligence” in our sense was unknown in Plato’s time, it is remarkable that he would feel the need to insist that mind and intelligence can be found only in ensouled, i.e., living beings. What was he pushing against?
At any rate, what do these statements of Plato mean? Do they mean that soul is the cause for the existence of mind? Or, given that Plato in other locations[v] insists that mind is the cause of all things, that that the opposite is true and mind is the cause for the existence of soul? Or are mind and soul inseparable in some other way that awaits being understood.
There are deeper issues involved in any inquiry into how Plato views the relation between mind and soul, given that that he views mind as that by which we grasp timeless unchanging being whereas soul is the source of changing, becoming in time. Unresolved issues of how Plato sees the relation between rest and motion, being and becoming, the one and the many are involved in our inquiry into his view of the relation between mind and soul. We shall attempt it below anyway.
Apart from their poetic, theological and mystical allusions, none of the above statements would make any sense unless we can first ascertain what precisely it is that Plato means by “soul.” But once we have done that and have stripped the word “soul” of the baggage of all sorts of vague meanings and connotations that have attached themselves onto this word over the centuries and have thereby isolated exactly what Plato meant by “soul,” then we shall relate it to what he says he means by “mind” in the hope that his claims that “mind without soul is impossible to find” begin to make sense.
“Soul” for Plato is the cause and principle of self-motion and, by extension, of all motion. And insofar as it is also ruled by mind, it opposes random, inchoate motion. To deny the existence of ensouled mind, Plato argues, is the same as arguing that that our world is the chance result of the random motion of material particles. In such a world, mind (intelligence) would ultimately be the mechanical result, the artifact, created by human beings who themselves are the mechanical result of the random motion of material particles.
If the world was indeed created by the random motion of material particles, then matter precedes mind, and artificial (i.e., man-made) intelligence is the only intelligence possible. In a nutshell, according to Plato, precisely because the world is the created product of an intelligent creator force (i.e., is not “godless”), and specifically for this reason, artificial (man-made intelligence is impossible. For Plato, intelligence – mind – is God-made, and in this sense “natural” rather than artificial.
Conversely, according to Plato’s line of argumentation, the mistaken belief that artificial (man-made) intelligence is at all possible arises when society is seduced by the illusion that random material motion has caused our world (“godlessness”).
This will become clearer below when we follow Plato’s reasoning on this matter of “soul” and motion in some detail. Doing so will also provide additional insights into how the various operations of mind are to be understood in a manner that will help solve the difficulties in understanding the Parmenides dialogue.
For Plato soul is, strictly speaking, that-which-moves-itself. This and nothing else is the essence of soul and its definition. In his own words, the noun “soul” applies to an “entity” whose definition is “that which moves itself.” Everything else that he has to say about soul, whether literal, poetic, or allegorical, is rooted in this simple definition which, as far as Plato is concerned, is grounded in simple, common-sense interpretation of empirical data.
In the Phaedo, Plato may describe the soul as incorporeal, invisible, immortal, etc.; in the Theaetetus as the thing which senses sensible things through its bodily sense organs and grasps intelligible things through its own incorporeal mind without the aid of bodily organs; in the Philebus as the seat of all kinds of pleasures, pains, cognitions and other motivating powers in general[vi]; in the Timaeus as the prized creation of a loving Demiurge who fashioned it by mixing Sameness, Otherness and Being; in the Republic as the vast battlefield where the dialectic endeavors to secure the rule of the mind over the other parts of the soul; in the Symposium as the place where that “the zeal for immortality,” Eros, may give birth to immortal offspring; and in the Meno as the immortal repository of all knowledge from which we draw recollections and call them learning.
But what controls all these Platonic explorations into the soul is the core definition of its essence as “that-which-moves-itself.” In the Phaedrus, Plato gives a quick summary of his view of soul as “that which moves itself,” but later, in the Laws, he offers a complete and elaborate presentation of the argument that shows why this is the case.
In the course of arguing in the Phaedrus that the ultimate cause of all kinds of motion in the universe is the necessarily immortal “that-which-moves-itself,” Plato asserts that “anyone who says that self-motion is the essence and the very definition of soul will not be embarrassed[vii].” This being the case for all soul – cosmic, divine, and human – Plato then proceeds to describe allegorically the self-moving human soul as a two-horse self-moving chariot with mind as its charioteer, i.e., with mind as the controller of the eternally self-moving.
The Tenth Book of Plato’s Laws, in which the detailed argument of soul as “that-which-moves-itself” is found, addresses a socio-political situation very much reminiscent of what is transpiring in contemporary (1st quarter of the 21st century) western civilization: a dominant, sophisticated secular elite questions the merits of grounding lawmaking on the belief of the existence of gods. These elites, in Plato’s text, find the commitment of crimes that accompany godlessness preferable to legislation that anchors its effectiveness on belief in gods. The sophisticated secular elite demands persuasive argument, not legal compulsion, to support any belief in the existence and providence of gods.
To supply the persuasive argument demanded by the sophisticated secular elite, Plato must show that all observed lawful order in the cosmos derives from and continues to depend on a self-moving mover, on “that-which-moves-itself” which we just happen to refer to with the conventional name “soul.”
The argument in Laws X.889a4-896b3 unfolds as follows:
The Athenian Stranger is concerned with the sophisticated secular opinion which holds that the “natural” elements (fire, water, earth and air) owe their existence to random motion and “nature” (i.e., inherent natural properties of matter); and also that the greatest and finest things of the world – the earth, sun, moon and stars – also owe their existence to random notion and “nature”. Art and artifact came later, after random motion and “nature” resulted in living beings. Art that produces artefacts is the brainchild of these randomly produced living beings.
How does one refute this? If it can be shown that the world is itself an artifact and not the result of random motion, then it will be admitted that the world is an offspring of an artificer’s mind, i.e., of a soul. But – the secular sophisticate reminds us – soul does not precede the world but it emerges from the material world at a later stage (891c3-4).
This claim that soul emerges later, the Athenian Stranger replies, is based on a misunderstanding by nearly everyone of what the nature and function of soul really is (892a2-3). If it can be shown that soul is older than moving material particles then a refutation of the secular sophisticate’s theory might be found.
Before addressing the question of soul directly, the Athenian Stranger begins his inquiry with the question: “Do all things stand still, or do they all move, or do some stand still and some move?”
The common-sense consensus answer that some things move and some stand still then leads into an inquiry of how many kinds of motion/change there are in the world. An exhaustive list of ten kinds of motion is identified the most important of which is self-motion, “the motion that moves both itself and other things, suitable for all active and passive processes and truly called the source of change and motion in all things that exist.”[viii] Next in importance is the kind of motion which, though not self-moving, moves all other things. Then follow the other dependent kinds of motion: rotation, locomotion, change by combination, change by separation, increase, decrease, generation, and destruction. (893b-895a4).
The focus now is on the motion that is the cause of all kinds of motion, including its own: “that-which-moves-itself.” After some elaboration of the findings, the Athenian Stranger concludes: “That-which-moves-itself, then, is the origin of all motions, and is first among both things at rest and things that move, and we must say that it is the most ancient and the most powerful of all changes.”[ix]
Up to this point, the discussion is about “motion” and there is no step in the sequence of argumentation to which the sophisticated secularist need object. A consensus is possible on the question of motion between the Athenian Stranger and his interlocutor, the dominant atheist elite opinion of his time.
It is at this point that the Athenian Stranger returns to the topic of “soul” by pointing out that a thing that we call “alive” is a thing “which-moves-itself” and by “alive” we mean they have “soul.” Plato writes: “the entity which we all call ‘soul’ is precisely that which is defined by the expression ‘that-which-moves-itself.’[x]”
This concludes the argument in Laws X.889a4-896b3. The definition of soul as that which moves itself as well as that which causes all other types of motion and change to exist can now be used to inquire what Plato may mean by his claims, mentioned in the beginning of this report, that it is “impossible to find mind without soul” and “soulless mind can never come to be.” Does he mean by this that soul precedes mind as its principle and cause or that mind precedes soul? Or does he hint at a different soul-mind relation?
We now turn to some relevant passages in the Philebus, Timaeus and Laws to see what Plato has to say about mind that might help us in this inquiry:
To set the stage for a discussion of the merits of mind vs. pleasure in the Philebus dialogue, Socrates reports on a piece of legendary wisdom handed down by “the ancients” according to which the “immutable entities” consist of the one and the many and have inherent in them the limit and the unlimited[xi]. This is subsequently (Philebus 16e3-19c) elaborated into an extensive exploration of the ontology of these “immutable entities” (referred to in other dialogues as eidē or ideas) that takes up a large portion of the dialogue. The purpose of that exploration is to show in what way these immutable entities, the eidē, are to be understood as “mixture of the limit and the unlimited.”
At some point in the discussion (Philebus 22c3-4) when the shortcoming of Socrates’s own mind come up, Socrates readily acknowledges the shortcoming of his individual mind but points out that this is not the case with the divine mind from which all individual minds are derived. This in turn launches a lengthy dialogue (Philebus 22c5-30e3) which culminates in the conclusion that “mind” is the cause of the “the mixture of the unlimited and the limit,”[xii] i.e., the cause of all these “immutable entities”[xiii]. It is in this context that Socrates hints at a peculiar aspect of the soul-mind relation that will be repeated in the Timaeus by the Eleatic philosopher of the same name: mind is that which supplies (παρέχει) soul to body[xiv].
In the Philebus Plato argues that “mind” is the cause of immutable, unchanging being; in the Laws he argues that “soul” is the cause of moving and changing becoming.
In the Timaeus, Plato subordinates “soul,” the cause of motion, to “mind,” the cause of being. Before he begins his “likely account” of the creation of the universe, Timaeus sets the stage by restating the Eleatic maxim that the operation of the mind, noesis, takes place in the domain of ungenerated, eternal entities[xv].
His actual account of the creation of the universe begins with in the passage 29d7-30c1, with the Craftsman “putting together” (that is, not “generating” or “creating”) mind inside soul and soul inside the body of the universe[xvi]. In the same passage, Timaeus argues that it is impossible for mind to be present in something that does not have soul.
With these difficult formulations Plato does not intend to imply that that the existence of mind depends on soul. On the contrary, Timaeus argues that there is a certain fundamental dependence of the soul on mind. Following the astonishing description of how the Craftsman “put together” the soul by forcibly mixing Sameness, Otherness and Being, and then dividing the mixture into the interval of the musical scale, Timaeus says that “the ‘putting together’ of the soul came about according to mind.”[xvii]
Moreover, to leave no doubt about the sovereignty of mind over soul, he concludes the discussion of the creation of the cosmic soul and all that comes in its train with the following: “most of what has been discussed so far has been a demonstration of what has been created by Mind. The birth of this world came about from the combination of Necessity and Mind, with Mind ruling over Necessity …”[xviii]
It is important to bear in mind, however, that although the soul is subordinated to the sovereignty of mind, it is given unlimited power over the physical world of matter and motion. We read in the Laws: “So soul, by virtue of its own motions, stirs into movement everything in the heavens and on earth and in the sea. The names of the motions of soul are: wish, reflection, diligence, counsel, opinion true and false, joy and grief, cheerfulness and fear, love and hate. Soul also uses all related or initiating motions which take over the secondary movements of matter and stimulate everything to increase or diminish, separate or combine, with the accompanying heat and cold, heaviness and lightness, roughness and smoothness, white and black, bitter and sweet.”[xix]
In a coda intended to shed light on the role the mind plays in the soul’s utilization of these various motions, the passage continues: “In employing these motions, when it rightly enlists divine mind, the godly soul always conducts everything to right and happy conclusions. When,by contrast, it is in league with mindlessness, it produces altogether opposite results.”[xx]
Thus, the relation of immutable mind to moving soul evokes the relation of a single, indivisible musical idea grasped in a single instant of time to the organized succession of the multitude of notes employed to communicate that idea by means of moving sounds; or of a single, indivisible poetic idea to the flood of words recited in succession in a way that is intended to convey that idea: when the unfolding in time of musical notes or of the words of a poem is organized by the soul in league with mind, the result is beautiful and “happy” and we marvel at the success of the composer in conveying to us, his audience, exactly the full weight of meaning of the musical or poetic idea as it was originally conceived in his mind at the single, original instant of “inspiration”.
The notion of “single, indivisible idea” at the instant of inspiration is represented in mythology by the legend of the goddess Athena erupting in an instant fully grown and fully armed from the mind of Zeus. It is most likely the case that great creative craftsmen experience their greatest inspirations in an elusive, timeless (i.e., “immutable”) instant as one perfect, complete and indivisible entity and afterward expend their great creative labors to transcribe that timeless, indivisibly one instant insight into the multitude of musical sounds, articulate speeches, painted shapes and colors, or architectural and sculptural volumes and shapes in the unfolding world of space-time. The instantaneous, timeless, immutable flash of creative insight is the work of mind; its transcription into unfolding space-time is the work of soul.
Differently equipped human beings receive and appreciate the works of creative craftsmen differently. All may receive identically the craftsman’s output as it unfolds in space-time: all hear the same notes of Mozart’s Requiem, the same words of Cavafy’s Barbarians; see the same colors in Rembrandt’s Prodigal Son and the same sculpted marble in Michelangelo’s Pieta. But not all understand what is meant behind these sound, words, colors, and shapes.
To reach the artist’s intended meaning, the viewer’s or listener’s mind must leap past the sounds, words and images transmitted by the creative craftsman’s soul to sensory organs of the listener/viewer through the medium of space-time, leap past these sensory indicators and reach that immutable entity which originally inspired the artist. Not all can do this. Those whose souls are absorbed in the moving world of matter and motion and do not enlist their “immutable” mind, invariably either misinterpret the artist’s intended meaning, or find it boring or incomprehensible or, worse, threatening. Those whose souls are allied with their “immutable” mind are likely to get nearer to the experience that the artist intended to convey with his work.
Moreover, the complete absence of mind, i.e., of intelligence in this Platonic sense precludes any entity that claims the title of “intelligence” – whether living or artificial – from even the possibility of grasping the meaning and intentions of the artist.
Criton M. Zoakos
July 2, 2023
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Appendix: An experiment with the Artificial Intelligence of ChatGPT
To test this, I conducted the following experiment: In a 2008 article in the Mathematical Intelligencer, mathematics professor A. Vardulakis of the Aristotelian University of Thessaloniki reported an earlier conjecture by another mathematician, the late A. Zachariou of the University of Athens, that a passage in Plato’s Laws V.737e1-738b1 contains a hidden theorem about the distribution of prime numbers. The conjecture was filed by Zachariou in the February 1982 issue of the Abstracts of the American Mathematical Society and, according to Vardulakis, the conjecture was first proven in 2004 by Peter Shiu of the University of Loughborough, UK. Plato’s “hidden theorem” states that
if 3<P<Q where P and Q are successive primes, then every integer r<Q divides P!
The implications of this theorem are enormous for the ongoing research about the distribution of prime numbers, the Holy Grail of modern Number Theory. Professor Vardulakis claims that Plato’s “hidden theorem” in Laws V.737e1-738b1 has implications for the 1859 Riemann Hypothesis about the Number of Prime Numbers Smaller than any Given Magnitude.
The discovery from the 160 words of this passage that Plato’s flash of creative insight was the hidden theorem described above was obviously the work of mind, specifically as mind is understood in the Platonic texts we have been discussing. To put contemporary artificial intelligence to the test, I submitted the passage from the Laws to ChatGPT, the flagship for the time being of the AI endeavors of state-of-the-art computer engineering, and asked ChatGPT if the text implies anything about prime numbers. ChatGPT answered that it does not. After some clever evasions, ChatGPT stated clearly that the passage “does not provide implicit information about the distribution of prime numbers that could be formulated into a theorem.”
Artificial Intelligence is not intelligence. It is an attempt to redefine what intelligence is:
MY QUESTION: What does the following statement in quotation marks imply about the distribution of prime numbers: “Let’s assume we have the convenient number of five thousand and forty farmers and protectors of their holdings, and let the land with its houses be divided up into the same number of parts, so that a man and his holding always go together. Divide the total first by two, then by three: you’ll see it can be divided by four and five and every number right up to ten. Everyone who legislates should have sufficient appreciation of arithmetic to know what number will be most use in every state, and why. So let’s fix on the one which has the largest number of consecutive divisors. Of course, an infinite series of numbers would admit all possible divisions for all possible uses, but our 5040 admits no more than 59 (including 1 to 10 without a break), which will have to suffice for purposes of war and every peacetime activity, all contracts and dealings, and for taxes and grants.”
ChatGPT RESPONSE: The statement implies that the number 5,040 (referred to as “our 5040”) is significant in terms of its divisibility and consecutive divisors. The author suggests that this number is convenient because it can be divided evenly by many smaller numbers, from 1 to 10, without any gaps or breaks. The phrase “including 1 to 10 without a break” indicates that the number 5,040 has all the numbers from 1 to 10 as divisors. The author also mentions that this number has a total of 59 divisors, which is the largest number of consecutive divisors they could find within the range mentioned. The statement further suggests that having a number with a large number of consecutive divisors is desirable for legislative purposes, as it would be useful for various activities such as war, peacetime activities, contracts, dealings, taxes, and grants. In summary, the statement implies that the number 5,040 (5040) is a convenient choice due to its divisibility properties, particularly its consecutive divisors, making it useful for a wide range of practical applications.
MY QUESTION: So it contains no useful information about the distribution of prime numbers?
ChatGPT RESPONSE: Correct, the statement does not provide any specific information about the distribution of prime numbers. It focuses on the properties of the number 5,040 and its divisibility rather than providing insights into the distribution or characteristics of prime numbers themselves. The mention of consecutive divisors and divisibility by smaller numbers does not directly relate to prime numbers, which are numbers that are divisible only by 1 and themselves.
MY QUESTION: Does it imply anything about the distribution of prime numbers?
ChatGPT RESPONSE: Apologies for the confusion in my previous responses. Upon further analysis, the statement does imply certain aspects about the distribution of prime numbers. The statement mentions that the number 5,040 has 59 divisors, including the numbers from 1 to 10 without a break. This implies that the number 5,040 is not a prime number itself since it has divisors other than 1 and itself. However, it does not provide direct information about the distribution of prime numbers beyond that. It highlights the convenience and usefulness of the number 5,040 due to its divisibility properties, particularly its consecutive divisors, but it does not delve into the broader distribution patterns or characteristics of prime numbers in general. To gain insights into the distribution of prime numbers, you would need to explore other mathematical concepts, such as prime number theorems, sieves, or specific prime number distribution functions. The quoted statement, as it stands, does not provide explicit information about the distribution of prime numbers.
MY QUESTION:
OK I get it, no explicit information. But I am asking if it provides any implicit information about the distribution of prime numbers that could be formulated into a theorem.
ChatGPT RESPONSE:
I apologize for any confusion caused. Upon re-evaluating the statement, it does not provide implicit information about the distribution of prime numbers that could be formulated into a theorem.
The statement primarily focuses on the divisibility properties of the number 5,040 and its usefulness in practical applications. While it mentions consecutive divisors and the ability to divide the number by smaller integers, these properties do not directly relate to the distribution of prime numbers or offer insights that could be formulated into a theorem about prime number distribution.
To study and understand the distribution of prime numbers, mathematicians have developed various theorems and concepts such as the Prime Number Theorem, Sieve of Eratosthenes, or the Riemann Hypothesis. These theorems and concepts provide deeper insights into the distribution patterns and characteristics of prime numbers.
In summary, the quoted statement does not provide any implicit information about the distribution of prime numbers that could be formulated into a theorem. To explore the distribution of prime numbers, it is necessary to refer to established mathematical theorems and concepts specifically developed for that purpose.
.
[i] Timaeus 30 b4: “[I]t is impossible for mind to be found apart from soul” (“νοῦν δ’ αὖ χωρὶς ψυχῆς ἀδύνατον παραγενέσθαι”)
[ii]Philebus 30c9: “Wisdom and mind could never come into existence without soul.” (“Σοφία μὴν καὶ νοῦς ἄνευ ψυχῆς οὐκ ἄν ποτε γενοίσθην.”)
[iii] Timaeus 46d5-6: “τῶν γὰρ ὄντων ᾦ νοῦν μόνῳ κτᾶσθαι προσήκει, λεκτέον ψυχήν …»
[iv] Euthydemus 287c1-e1; Sophist 248e7-249a8; Laws XII.967a7-d1, and 961d1-11.
[v] E.g., Philebus 30e10-12.
[vi] Philebus 47e: “[R]age and fear and longing and mourning and love and jealousy and malice” (“ὀργὴν καὶ φόβον καὶ πόθον καὶ θρῆνον καὶ ἔρωτα καὶ ζῆλον καὶ φθόνον”)
[vii] Phaedrus 245e2-4: “ … πεφασμένου τοῦ ὑφ᾽ ἑαυτοῦ κινουμένου, ψυχῆς οὐσίαν τε καὶ λόγον τοῦτον αὐτόν τις λέγων οὐκ αἰσχυνεῖται.” The full argument reads as follows (Phaedrus 245c5-246a2 Harold N. Fowler translation): “Every soul is immortal. For that which is ever moving is immortal but that which moves something else or is moved by something else, when it ceases to move, ceases to live. Only that which moves itself, since it does not leave itself, never ceases to move, and this is also the source and beginning of motion for all other things which have motion. But the beginning is ungenerated. For everything that is generated must be generated from a beginning, but the beginning is not generated from anything; for if the beginning were generated from anything, it would not be generated from a beginning. And since it is ungenerated, it must be also indestructible; for if the beginning were destroyed, it could never be generated from anything nor anything else from it, since all things must be generated from a beginning. Thus that which moves itself must be the beginning of motion. And this can be neither destroyed nor generated, otherwise all the heavens and all generation must fall in ruin and stop and never again have any source of motion or origin. But since that which is moved by itself has been seen to be immortal, one who says that this self-motion is the essence and the very idea of the soul, will not be disgraced. For every body which derives motion from without is soulless, but that which has its motion within itself has a soul, since that is the nature of the soul; but if this is true, that that which moves itself is nothing else than the soul, then the soul would necessarily be ungenerated and immortal.” (“ψυχὴ πᾶσα ἀθάνατος. τὸ γὰρ ἀεικίνητον ἀθάνατον· τὸ δ᾽ ἄλλο κινοῦν καὶ ὑπ᾽ ἄλλου κινούμενον, παῦλαν ἔχον κινήσεως, παῦλαν ἔχει ζωῆς. μόνον δὴ τὸ αὑτὸ κινοῦν, ἅτε οὐκ ἀπολεῖπον ἑαυτό, οὔποτε λήγει κινούμενον, ἀλλὰ καὶ τοῖς ἄλλοις ὅσα κινεῖται τοῦτο πηγὴ καὶ ἀρχὴ κινήσεως. ἀρχὴ δὲ ἀγένητον. ἐξ ἀρχῆς γὰρ ἀνάγκη πᾶν τὸ γιγνόμενον γίγνεσθαι, αὐτὴν δὲ μηδ᾽ ἐξ ἑνός· εἰ γὰρ ἔκ του ἀρχὴ γίγνοιτο, οὐκ ἂν ἔτι ἀρχὴ γίγνοιτο. ἐπειδὴ δὲ ἀγένητόν ἐστιν, καὶ ἀδιάφθορον αὐτὸ ἀνάγκη εἶναι. ἀρχῆς γὰρ δὴ ἀπολομένης οὔτε αὐτή ποτε ἔκ του οὔτε ἄλλο ἐξ ἐκείνης γενήσεται, εἴπερ ἐξ ἀρχῆς δεῖ τὰ πάντα γίγνεσθαι. οὕτω δὴ κινήσεως μὲν ἀρχὴ τὸ αὐτὸ αὑτὸ κινοῦν. τοῦτο δὲ οὔτ᾽ ἀπόλλυσθαι οὔτε γίγνεσθαι δυνατόν, ἢ πάντα τε οὐρανὸν πᾶσάν τε γῆν εἰς ἓν συμπεσοῦσαν στῆναι καὶ μήποτε αὖθις ἔχειν ὅθεν κινηθέντα γενήσεται. ἀθανάτου δὲ πεφασμένου τοῦ ὑφ᾽ ἑαυτοῦ κινουμένου, ψυχῆς οὐσίαν τε καὶ λόγον τοῦτον αὐτόν τις λέγων οὐκ αἰσχυνεῖται. πᾶν γὰρ σῶμα, ᾧ μὲν ἔξωθεν τὸ κινεῖσθαι, ἄψυχον, ᾧ δὲ ἔνδοθεν αὐτῷ ἐξ αὑτοῦ, ἔμψυχον, ὡς ταύτης οὔσης φύσεως ψυχῆς· εἰ δ᾽ ἔστιν τοῦτο οὕτως ἔχον, μὴ ἄλλο τι εἶναι τὸ αὐτὸ ἑαυτὸ κινοῦν ἢ ψυχήν, ἐξ ἀνάγκης ἀγένητόν τε καὶ ἀθάνατον ψυχὴ ἂν εἴη.”)
[viii] Laws X. 894c4-7: “τήν τε ἑαυτὴν κινοῦσαν καὶ ἕτερον, ἐναρμόττουσαν πᾶσιν μὲν ποιήμασι, πᾶσιν δὲ παθήμασι, καλουμένην δὲ ὄντως τῶν ὄντων πάντων μεταβολὴν καὶ κίνησιν.”
[ix] Laws X. 895b3-6: “ἀρχὴν ἄρα κινήσεων πασῶν καὶ πρώτην ἔν τε ἑστῶσιν γενομένην καὶ ἐν κινουμένοις οὖσαν τὴν αὑτὴν κινοῦσαν φήσομεν ἀναγκαίως εἶναι πρεσβυτάτην καὶ κρατίστην μεταβολὴν πασῶν…”
[x] Laws X. 896a3-4: “τὸ ἑαυτὸ κινεῖν φῂς λόγον ἔχειν τὴν αὐτὴν οὐσίαν, ἥνπερ τοὔνομα ὃ δὴ πάντες ψυχὴν προσαγορεύομεν…”
[xi] Philebus 16c5-e2: “A gift of gods to men, as I believe, was tossed down from some divine source through the agency of a Prometheus together with a gleaming fire; and the ancients, who were better than we and lived nearer the gods, handed down the tradition that all immutable entities are sprung from one and many and have inherent in them the finite and the infinite. This being the way in which these things are arranged, [16d] we must always assume that there is in every case one idea of everything and must look for it—for we shall find that it is there—and if we get a grasp of this, we must look next for two, if there be two, and if not, for three or some other number; and again we must treat each of those units in the same way, until we can see not only that the original unit is one and many and infinite, but just how many it is. And we must not apply the idea of infinite to plurality until we have a view of its whole number [16e] between infinity and one; then, and not before, we may let each unit of everything pass on unhindered into infinity.” (“θεῶν μὲν εἰς ἀνθρώπους δόσις, ὥς γε καταφαίνεται ἐμοί, ποθὲν ἐκ θεῶν ἐρρίφη διά τινος Προμηθέως ἅμα φανοτάτῳ τινὶ πυρί: καὶ οἱ μὲν παλαιοί, κρείττονες ἡμῶν καὶ ἐγγυτέρω θεῶν οἰκοῦντες, ταύτην φήμην παρέδοσαν, ὡς ἐξ ἑνὸς μὲν καὶ πολλῶν ὄντων τῶν ἀεὶ λεγομένων εἶναι, πέρας δὲ καὶ ἀπειρίαν ἐν αὑτοῖς σύμφυτον ἐχόντων. δεῖν [16δ] οὖν ἡμᾶς τούτων οὕτω διακεκοσμημένων ἀεὶ μίαν ἰδέαν περὶ παντὸς ἑκάστοτε θεμένους ζητεῖν—εὑρήσειν γὰρ ἐνοῦσαν— ἐὰν οὖν μεταλάβωμεν, μετὰ μίαν δύο, εἴ πως εἰσί, σκοπεῖν, εἰ δὲ μή, τρεῖς ἤ τινα ἄλλον ἀριθμόν, καὶ τῶν ἓν ἐκείνων ἕκαστον πάλιν ὡσαύτως, μέχριπερ ἂν τὸ κατ᾽ ἀρχὰς ἓν μὴ ὅτι ἓν καὶ πολλὰ καὶ ἄπειρά ἐστι μόνον ἴδῃ τις, ἀλλὰ καὶ ὁπόσα: τὴν δὲ τοῦ ἀπείρου ἰδέαν πρὸς τὸ πλῆθος μὴ προσφέρειν πρὶν ἄν τις τὸν ἀριθμὸν αὐτοῦ πάντα κατίδῃ τὸν [16ε] μεταξὺ τοῦ ἀπείρου τε καὶ τοῦ ἑνός, τότε δ᾽ ἤδη τὸ ἓν ἕκαστον τῶν πάντων εἰς τὸ ἄπειρον μεθέντα χαίρειν ἐᾶν.”)
[xii] Philebus 30d10-e2: “ὅτι νοῦς [30e] ἐστὶ γένους τῆς τοῦ πάντων αἰτίου λεχθέντος [τῶν τεττάρων, [ὧν] ἦν ἡμῖν ἓν τοῦτο].”
[xiii] Philebus 16c9: “… ὡς ἐξ ἑνὸς μὲν καὶ πολλῶν ὄντων τῶν ἀεὶ λεγομένων εἶναι …”
[xiv] Philebus 30b1-3: “τοῦτο ἐν μὲν τοῖς παρ᾽ ἡμῖν ψυχήν τε παρέχον καὶ σωμασκίαν ἐμποιοῦν καὶ πταίσαντος σώματος ἰατρικὴν …”
[xv] Timaeus 27d6-28a1: “τὸ ὂν ἀεί, γένεσιν δὲ οὐκ ἔχον … νοήσει … περιληπτὸν”
[xvi] Timaeus 30b1-5: “λογισάμενος οὖν ηὕρισκεν ἐκ τῶν κατὰ φύσιν ὁρατῶν οὐδὲν ἀνόητον τοῦ νοῦν ἔχοντος ὅλον ὅλου κάλλιον ἔσεσθαί ποτε ἔργον, νοῦν δ’ αὖ χωρὶς ψυχῆς ἀδύνατον παραγενέσθαι τῳ. διὰ δὴ τὸν λογισμὸν τόνδε νοῦν μὲν ἐν ψυχῇ, ψυχὴν δ’ ἐν σώματι συνιστὰς τὸ πᾶν συνετεκταίνετο”
[xvii] Timaeus 36d8-9: “… κατὰ νοῦν τῷ συνιστάντι πᾶσα ἡ τῆς ψυχῆς σύστασις ἐγεγένητο …”
[xviii] Timaeus 47e3-48a3: “Τὰ μὲν οὖν παρεληλυθότα τῶν εἰρημένων πλὴν βραχέων ἐπιδέδεικται τὰ διὰ νοῦ δεδημιουργημένα δεῖ δὲ καὶ τὰ δι᾽ ἀνάγκης γιγνόμενα τῷ λόγῳ παραθέσθαι. μεμειγμένη γὰρ οὖν ἡ τοῦδε τοῦ κόσμου γένεσις ἐξ ἀνάγκης τε καὶ νοῦ συστάσεως ἐγεννήθη: νοῦ δὲ ἀνάγκης ἄρχοντος τῷ πείθειν αὐτὴν …”
[xix] Laws X. 896e8-897b1: ἄγει μὲν δὴ ψυχὴ πάντα τὰ κατ᾽ οὐρανὸν καὶ γῆν καὶ θάλατταν ταῖς αὑτῆς κινήσεσιν, αἷς ὀνόματά ἐστιν βούλεσθαι, σκοπεῖσθαι, ἐπιμελεῖσθαι, βουλεύεσθαι, δοξάζειν ὀρθῶς ἐψευσμένως, χαίρουσαν λυπουμένην, θαρροῦσαν φοβουμένην, μισοῦσαν στέργουσαν, καὶ πάσαις ὅσαι τούτων συγγενεῖς ἢ πρωτουργοὶ κινήσεις τὰς δευτερουργοὺς αὖ παραλαμβάνουσαι κινήσεις σωμάτων ἄγουσι πάντα εἰς αὔξησιν καὶ φθίσιν καὶ διάκρισιν καὶ σύγκρισιν καὶ τούτοις ἑπομένας θερμότητας ψύξεις, βαρύτητας κουφότητας, σκληρὸν καὶ μαλακόν, λευκὸν καὶ μέλαν, αὐστηρὸν καὶ γλυκύ, καὶ πᾶσιν οἷς ψυχὴ χρωμένη,
[xx] Laws X. 897b1-3: νοῦν μὲν προσλαβοῦσα ἀεὶ θεὸν ὀρθῶς θεοῖς, ὀρθὰ καὶ εὐδαίμονα παιδαγωγεῖ πάντα, ἀνοίᾳ δὲ συγγενομένη πάντα αὖ τἀναντία τούτοις ἀπεργάζεται.
Leto Postscripts 