The Metaphysics of Sigil II — H3: Theophrastus, On First Principles, and Aristotle, Metaphysics Λ, entire, reconstituted as one work Sigil · 2026-09-08 · Text AXN:068D.UNCLASSIFIED.🏠📎⛵🏠🕘📜
AXN:068D.UNCLASSIFIED.🏠📎⛵🏠🕘📜
The Metaphysics of Sigil II — H3: Theophrastus, On First Principles, and Aristotle, Metaphysics Λ, entire, reconstituted as one work
TheophrastusAristotleMetaphysics LambdaOn First PrinciplesSigilH3reconstitutionbinding dependenciescontinuity trialKendall taudemand-structurecommissioningvan RaalteIsḥāq ibn ḤunaynAlon 1985
Description
The maximal reading, and the companion to #1596. Hypothesis H3: one continuous whole, separated, and rearranged into two continuous wholes. Both texts entire in one order — 8,441 words, 3,370 Theophrastus in thirty-five movements and 5,071 Λ in twenty, fifty-five units in eleven parts, nothing omitted and nothing repeated — with the Greek printed whole and unbroken before any apparatus, a working rendering of every unit, and a commentary. The warrant is that no monotone merge of the two received orders exists: matching all sixteen Λ movements to their Theophrastan counterparts by subject gives Spearman ρ = +0.459 (permutation p = 0.039) and Kendall τ-b = +0.326, concordant 79, discordant 40, one tied pair, 40 inversions of 120. Λ runs matter → potency → the unmoved mover → the spheres → mind → the good; the fragment runs the mover → doxography → matter → knowing → astronomy → teleology → the good — same matter, same close, inverse middle. Four audits are reported. (1) Clause completeness: one break in 54 junctions, and the composition inherits rather than makes it, since the fragment ends mid-sentence at ἐν τίσι τὰ ὄντα καὶ πῶς ἔχει πρὸς ἄλληλα. (2) Binding dependencies: connectives naming a specific antecedent (οἱ δέ requiring its οἱ μέν, ἤ requiring the aporia it answers, ἀλλὰ μήν answering a step) must have it adjacent; five violations were found and cleared by redividing five movements at their operational seam, each having contained an ending and a beginning at once; two remain and are printed as violations rather than resolved. (3) The instrument: 55 units on the 120 commonest short words, length-controlled, name-crossings not detectably rougher than within-text junctions (difference +0.724, p = 0.1161, bootstrap 95% CI −0.174 to +1.603) — underpowered to say identical. (4) The continuity trial: the whole read straight through with every mark stripped, which measures nothing and can only be run by reading, and which produced one relocation the computable audits had not. Usener references for the Theophrastan movements are VERIFIED against van Raalte's margins, correcting eight citations carried in earlier files of this line: the whole demand-cluster stands in Chapter II at 5 a 14 – 5 b 10, not at 8 a 21, and ἐπεισοδιῶδες stands at 4 a 13-16 in Chapter I, not at 11 b 24.
Wiki Article
The Metaphysics of Sigil II, deposit #1597 of the Crimson Hexagonal Archive (8 September 2026), sets Theophrastus's On First Principles and Aristotle's Metaphysics Λ entire in a single order — 8,441 words, fifty-five units, nothing omitted and nothing repeated — under the hypothesis that they are one continuous whole later separated and rearranged into two. Its warrant is that no monotone merge of the two received orders exists: over sixteen subject correspondences the orders give Spearman ρ = +0.459 and Kendall τ-b = +0.326 with forty inversions of a hundred and twenty, sharing their matter and their close while ordering the middle inversely. The edition reports four audits, of which the second and fourth are new instruments: a test of binding dependencies, which asks whether connectives naming a specific antecedent still have it adjacent and which found five violations that were cleared by redividing five movements at their operational seam; and a continuity trial, the whole read straight through with every mark stripped, which measures nothing, can only be run by reading, and produced a relocation the computable audits had missed. Its commentary raises the question the corrected references sharpen: why the text standing under the successor's name reads not as objection but as commission — a specification stating what would count as an answer, issued before any answer is given, naming and refusing the method the other text then uses. Three accounts are offered and none chosen; what would decide between them is Isḥāq's Arabic, from a Greek uncial outside the surviving stemma, read at five loci.
Theophrastus, On First Principles, and Aristotle, Metaphysics Λ, reconstituted as one work
Text under the name Sigil · Lee Sharks, ed. · v1.3 · 2026-09-08 Addresses computed from the seated bytes of EA-CORPORA-14 (#1595)
All of both texts, in one order. 8,441 words: 3,370 Theophrastus in thirty-five movements, 5,071 Λ in twenty. Nothing omitted, nothing repeated. Whether this order is original is a separate question from whether it is coherent; this edition claims the second only.
THE WORK
Read this first, whole, without apparatus. The marks, the addresses and the audits are behind it, to be checked against it — not read instead of it.
A rendering for reading, not part of the edition's text. Movement by movement, numbered to the concordance. The Theophrastan movements are rendered as in the continuous edition of the fragment; the Λ movements are rendered here. This is a working rendering, not a scholarly translation: where precision matters the Greek above is the authority, and van Raalte (Brill, Mnemosyne Suppl. 125, 1993) for the fragment, Ross for Λ. Several passages of the fragment are corrupt and the rendering says so or renders loosely rather than smoothing.
I. THE QUESTION
1. Θ · Thphr. w0–118 · ⟨Σ:294A⟩ — the question; the whole not episodic
How must one mark off the study of first things, and by what means? For the study of nature is more manifold, and — as some say — more disorderly, having changes of every kind; whereas the study of first things is determinate and always the same. That is why they place it among intelligibles and not among perceptibles, as being unmoved and unchanging; and on the whole they think it the more venerable and the greater. But first: is there some connection and as it were communion between the intelligibles and the things of nature, or none — but rather each as it were separate, yet somehow working together toward the whole of being? It is therefore more reasonable that there be some connection, and that the whole not be episodic, but rather that some things be prior and some posterior, some principles and some under the principles, just as the eternal things stand to the perishable.
2. Θ · Thphr. w118–225 · ⟨Σ:7C9C⟩ — what nature, and in what
If, then, it is so, what is their nature and in what do they consist? For if the intelligibles are in mathematical objects alone, as some say, the connection with perceptibles is not evident, nor do they appear worthy of the universe at all: they seem contrived by us, who put figures and shapes and formulae around them, while in themselves they have no nature. And if not — still, not so as to connect with the things of nature and produce in them something like life and motion. For neither does number itself, which some set down as first and most authoritative. But if there is some other substance, prior and stronger, one must try to say what it is: whether one in number, or in form, or in kind.
3. Α · Λ w0–325 · ⟨Σ:59A0⟩ — the inquiry into substance; the three kinds; the contraries
The study concerns substance: it is the principles and causes of substances that are sought. For if the universe is a kind of whole, substance is its first part; and if it is a sequence, even so substance is first, then quality, then quantity. And at the same time these others are not, so to speak, beings simply, but qualities and motions — or else "not-white" and "not-straight" would be beings too, since we do say of these that they are, as in "there is a not-white." Further, none of the others is separable.
The ancients bear witness to this in practice: it was of substance that they sought principles and elements and causes. Those of the present day set down universals as substances rather (for the genera are universals, which they call principles and substances rather, because they inquire logically); the older ones set down particulars, such as fire and earth, and not the common thing, body.
And there are three substances: one perceptible — of which one kind is eternal and one perishable, which all agree on, such as plants and animals, and one eternal — of which one must grasp the elements, whether one or many; and another unmoved, which some say is separable, some dividing it in two, others putting the forms and the mathematicals into one nature, others taking only the mathematicals of these. The former belong to natural science (for they are with motion), the latter to another, if they have no principle in common.
Perceptible substance is changeable. And if change is from opposites or from intermediates — not from all opposites (for a sound is not white) but from the contrary — there must be something underlying which changes into the contrariety; for the contraries do not change. Further, something remains while the contrary does not: there is therefore some third thing beside the contraries, matter. And if changes are of four kinds — in respect of the what, the of-what-sort, the how-much, or the where — with simple coming-to-be and perishing being change in respect of the this, growth and diminution in respect of quantity, alteration in respect of affection, and locomotion in respect of place, then the changes would be into the contrarieties proper to each.
4. Α · Λ w325–644 · ⟨Σ:13D8⟩ — matter must change, being capable of both; THE REGRESS
Matter, then, must change, being capable of both. And since being is twofold, everything changes from what is potentially into what is actually — for example, from potentially white to actually white, and likewise with growth and diminution. So that not only can a thing come to be incidentally from what is not, but everything comes to be from what is — from what is potentially, though from what is not actually. And this is the One of Anaxagoras: better than "all things together," and Empedocles' mixture, and Anaximander's, and as Democritus says — "all things were together potentially, but not actually." So they will have touched on matter.
Now all things that change have matter, but different matter; and of eternal things, those which are not generated but are movable in locomotion have matter — not matter for coming-to-be, but for motion from somewhere to somewhere.
One might raise the difficulty: from what sort of not-being does coming-to-be proceed? For not-being is threefold. If something is potentially, it is nevertheless not from just anything, but different things from different. Nor is it enough to say that all things were together, for they differ in their matter — since why did infinitely many come to be and not one? For mind is one, so that if matter too were one, that came to be actually of which matter was potentially.
There are then three causes and three principles: two being the contrariety, of which one is formula and form and the other privation, and the third matter. After this, that neither matter nor form comes to be — I mean the ultimate ones. For everything that changes is something and is changed by something and into something: by what — the first mover; what — the matter; into what — the form. The regress goes on to infinity, then, if not only the bronze becomes round but also the round or the bronze comes to be: it must therefore stop.
For it is not possible to grasp something universal and common among things said in many ways. Since this too is a difficulty, or at any rate not easy to say: how far and of what things causes are to be sought, alike in perceptibles and in intelligibles. For the road into the infinite is in both cases alien, and destroys thinking. And both are in a way a beginning — though perhaps the one is a beginning for us and the other simply, or the one is the end and the other a beginning of ours. Up to a point, then, we are able to contemplate through a cause, taking our principles from the perceptions. But when we cross over to the extremes themselves and the first things we are no longer able — whether because they have no cause, or because of our own weakness, as with looking toward the brightest things.
6. Α · Λ w969–1402 · ⟨Σ:4B5F⟩ — no element is the same as what is composed of it
For none of the elements can be the same as what is composed of elements — as B or A is not the same as BA. (Nor indeed is any intelligible an element, such as being or unity; for these belong to each of the composites too.) None of them, then, will be either substance or relative — but it must be. So the same elements do not belong to all things.
Or, as we say: in a way they do and in a way they do not. Of perceptible bodies, perhaps, the hot is as form and in another way the cold is the privation, while the matter is what is potentially these primarily and in itself; and substances are both these and what comes from these, of which these are principles — or if something comes to be one out of hot and cold, such as flesh or bone, for what comes to be must be other than those. These things, then, have the same elements and principles (though different things have different ones); but one cannot say this of all things without qualification, only by analogy — as if one were to say that the principles are three, form and privation and matter. But each of these is different for each genus: in colour, white, black, surface; light, darkness, air, and from these day and night.
And since not only the constituents are causes but also external things such as the mover, it is clear that principle and element are different, though both are causes; and the principle is divided into these, while what moves or brings to rest is a kind of principle and substance. So that by analogy the elements are three, but the causes and principles four; and they differ in different cases, and the first cause as mover is different in different cases. Health, disease, body — the mover is medicine. Form, disorder of such a kind, bricks — the mover is building. And since the mover in natural things is, for man, a man, and in things from thought is the form...
7. Θ · Thphr. w1192–1227 · ⟨Σ:DF25⟩ — HOW AND OF WHAT SORT must the principles be posited?
But how and of what sort must the principles be posited? One might well raise this as a difficulty: whether formless and as it were potential, like those who posit fire and earth, or formed, on the ground that these above all must be determinate, as he says in the Timaeus.
II. MATTER AND FORM
8. Α · Λ w644–969 · ⟨Σ:DC74⟩ — THERE ARE THREE SUBSTANCES: matter, nature, the composite
There are three substances: matter, which is a this by appearing (for whatever is by contact and not by natural union is matter and substratum); nature, which is a this and a state into which; and third, that from these, the particular — Socrates or Callias. Now in some cases the this is not apart from the composite substance, as the form of a house is not, unless the art is (nor is there coming-to-be and perishing of these; rather it is in another way that a house without matter, and health, and everything by art, are and are not). But if anywhere, it is in natural things. Hence Plato was not wrong to say that there are as many forms as there are natural things, if indeed there are forms other than these, such as fire, flesh, head. For all these are matter, and the last is the matter of what is most properly substance.
Moving causes, then, are causes as having come to be before; but causes as the formula are simultaneous. For when a man is healthy, then health also exists, and the shape of the bronze sphere exists together with the bronze sphere. (Whether something remains afterward must be examined; in some cases nothing prevents it — for instance if the soul is such, not all of it but the mind, since all of it is perhaps impossible.)
It is clear, then, that for these reasons at least there is no need for the Ideas: for a man begets a man, the particular the particular. And likewise in the arts: the art of medicine is the formula of health.
Causes and principles are in one way different for different things, and in another way — if one speaks universally and by analogy — the same for all. For one might raise the difficulty whether the principles and elements of substances and of relatives are different or the same, and likewise for each of the categories. But it is strange if they are the same for all: for then relatives and substances will be from the same things. What then will this be? For besides substance...
9. Θ · Thphr. w1651–1749 · ⟨Σ:EB93⟩ — matter and form
And such matters as these too long for some account: how ever the division of beings into matter and form comes about — whether as the one being and the other not being, but being potentially and led into actuality; or as being, but indeterminate, as in the crafts, while the coming-to-be is for the sake of the substance, namely the being formed according to the formulae. But in that way there would perhaps be a passage toward the better, while the being would be no less truly present in accordance with it — for it would not come to be if it were not present — but rather a thing that is neither this nor of a quality nor of a quantity, indeterminate with respect to the forms while having some power.
10. Α · Λ w1402–1754 · ⟨Σ:4FB0⟩ — actuality and potency; the causes of a man; the sun and the inclined circle
In another way, things differ in actuality and potency where the matter is not the same, and of some of these the form is not the same but different — as the causes of a man are the elements, fire and earth as matter and the proper form, and further something else outside, such as the father, and besides these the sun and the inclined circle, which are neither matter nor form nor privation nor of the same species, but movers.
Further, one must see that some things can be spoken of universally and some not. The first principles of all things are: the first actual this, and another which is potential. Those universals, then, do not exist; for the particular is the principle of particulars. Man is the principle of man universally, but there is no such man: Peleus is of Achilles, your father of you, and this B of this BA, and B in general of BA in general.
Then, if the principles of substances are these, and different things have different causes and elements — as was said, things not in the same genus, colours, sounds, substances, quantity, except by analogy; and of things in the same species they are different, not in species but because the particulars are different, your matter and form and mover and mine, though the same in universal formula.
As to seeking what the principles or elements of substances and relatives and qualities are, whether the same or different — it is clear that when they are spoken of in many ways they belong to each, but when distinguished they are not the same but different, except in this way and for all: in one way the same or analogous, because matter, form, privation, the mover; and in another way the causes of substances are the causes of all, because when they are removed all is removed; and further, the first in actuality. In another way the primary things are different — all contraries which are neither said as genera nor said in many ways; and further, the matters.
11. Θ · Thphr. w1749–1848 · ⟨Σ:0EFA⟩ — the whole in opposites; Euripides
And in general one must take it by analogy with the crafts, and by any other likeness there may be. And this too would seem to hold a difficulty — if not indeed an over-curiosity — the inquiring why ever nature and the whole substance of the universe are in opposites, and the worse has nearly an equal share with the better, or rather much more; so that Euripides too seems to speak universally when he says that good things would not come to be apart. But such an account comes near to asking why not all things are good, nor all alike; and why, though we predicate being of all things, none is like another — as white things and black are in themselves.
12. Θ · Thphr. w1227–1352 · ⟨Σ:982D⟩ — order proper to the honoured; Heraclitus
For order and being determinate are most proper to the most honoured things. And it appears that things stand nearly so in the rest as well — as in grammar and music and the mathematical sciences. And what comes after the principles follows along with them. And further, it is likewise in the crafts, which imitate nature: both the instruments and the rest follow the principles.
Some, then, make all the principles formless, others only the material ones; others make both formed, the material ones too, on the ground that the complete lies in both — since the whole of being is as it were out of opposites. And this too would seem unreasonable: if the whole heaven and each of its parts are all in order and formula and shapes and powers and periods, but in the principles there is nothing of the sort — but rather, as Heraclitus says, the fairest cosmos is as it were a heap of things poured out at random.
And they take it in the least degree, so to speak, alike in soulless and ensouled things. For the natures of each are determinate, so to speak, even though they come about spontaneously, whereas the principles are indeterminate. But it is difficult, again, this very thing — to assign the formulae to each, bringing them together toward the for-the-sake-of-which in all cases: in animals and plants and in a bubble itself — unless it happens that through the order and change of other things all sorts of shapes and varieties come about, both of the things about the air and about the earth. Of which some make the greatest example the matters concerning the yearly seasons, in which there are generations of animals and plants and fruits, as though the sun were generating them.
III. BEING, AND KNOWING
14. Θ · Thphr. w1848–1940 · ⟨Σ:EFE5⟩ — being in many ways; perception feeds thought
And further, what seems more paradoxical: that being is not possible without the opposites. And those who employ a still greater paradox even count in the not-being, which has neither come to be nor will be, into the nature of the universe. But this is as it were an excessive wisdom.
That being is spoken of in many ways is clear. For perception both observes the differences and seeks the causes — though it is perhaps truer to say that it submits them to the thinking faculty, in some cases simply seeking, in others working up a difficulty, through which, even if it cannot go forward, nevertheless some light appears in the not-light for those who inquire further.
Knowing, then, is not without some difference. For if things are other than one another, there is some difference; and in the universals, since the things under the universals are several, these too must differ, whether the universals be genera or species. And nearly every science is of what is proper: for both the substance and the essence are proper to each, and the things contemplated in themselves and not incidentally would be something predicated of something. And in general, to see the same thing in several is a mark of science — whether said in common and universally, or in a way proper to each, as with numbers, lines, animals, plants.
16. Θ · Thphr. w2032–2157 · ⟨Σ:AE68⟩ — the end from both; ways of knowing
And the end is from both. For of some things the universal is the end, since in it is the cause; of others, the particular, in so far as there is division into indivisibles, as in matters of action and production: for their actuality is of that kind. And we know the same thing in respect of substance, and number, and species, and genus, and analogy — and if indeed, besides these, by division. And the analogical is at the greatest remove, since we stand furthest off, in some cases through ourselves, in others through the subject, in others through both. And since knowing is spoken of in many ways, the beginning and the greatest thing in how each is to be pursued is the manner proper to it: for instance, the first things and the intelligibles; and the movable things and those under nature; and, of these themselves, the ones at the beginning and those that follow, down to animals and plants and the lowest of the soulless things.
17. Θ · Thphr. w2157–2250 · ⟨Σ:FD63⟩ — proper to each genus; what is knowing
For there is something proper to each genus, as also in the mathematical sciences. And the mathematical sciences themselves have a difference, though they are in a way of one kind, and have been sufficiently divided. And if some things are knowable by being unknowable, as some say, the manner would be a proper one, and requires some division — though perhaps, where it is possible, it is more proper to speak by analogy than by the unknowable itself, as if one were to explain the visible by the invisible. How many manners there are, then, and in how many ways knowing is said, one must try to divide. And the beginning, with a view to these very things, is first to mark off what knowing is. But that would seem the harder task.
IV. REST, AND THE UNMOVED
18. Θ · Thphr. w1450–1540 · ⟨Σ:D6DC⟩ — REST IN THE PRINCIPLES
And these matters seek their examination somewhere here, demanding a determination of how far the ordered extends, and why more is impossible, or why there is a passage to the worse. But in the principles — whence indeed the first account also came — one might reasonably raise the difficulty about rest as well. For if it is as something better, one would attach it to the principles; but if as idleness and privation of motion, one will not attach it. But if so, then activity must be substituted for it, as prior and more honourable, and motion assigned to the perceptibles — since to rest for this reason, namely that it is impossible for what moves always to be moving, is strange.
19. Α · Λ w1754–2085 · ⟨Σ:3E58⟩ — MOTION IS CONTINUOUS AS TIME IS; substances without matter
...just as time also is: for it is either the same as time or an affection of motion. And motion is not continuous except locomotion, and of this the circular.
But if there is something capable of moving and producing, yet not actually active, there will not be motion; for what has a potency need not exercise it. Nothing is gained, then, even if we posit eternal substances, as those who posit the forms do, unless there is in them some principle capable of producing change. Nor even this is enough, nor another substance beside the forms; for if it will not be active, there will be no motion. Further, even if it will be, it is not enough, if its substance is potency; for there will not be eternal motion, since what is potentially may not be. There must therefore be such a principle whose substance is actuality. Further, then, these substances must be without matter, for they must be eternal, if indeed anything else is eternal. Therefore actuality.
[The first clause is corrupt; the sense is roughly:] for the danger would not be, in the first place, that it is not rational and otherwise not credible — but it seeks some greater cause. And perception too seems in a way to sing along with this: that it is possible for what moves not always to be other than what it moves, on account of acting and being acted upon. And this is so, if one brings the case to mind itself and to god. And the other thing said is strange too — that the things which strive do not imitate what is at rest; for if to them, being what they are, the rest would follow. Except that perhaps it is not to be taken in the same way, as though leading toward the partless, but rather so that it be as far as possible in concord with itself and completed — as a city might be, or an animal, or some other of the divisible things, or indeed the whole heaven, which they say is most complete.
21. Α · Λ w2085–2310 · ⟨Σ:F548⟩ — actuality is prior — Anaxagoras bears witness; something unmoved that moves
That actuality is prior, Anaxagoras bears witness (for mind is actuality), and Empedocles with love and strife, and those who say motion always is, like Leucippus. So there was not chaos or night for an infinite time, but the same things always, either in a cycle or in some other way, if actuality is prior to potency. If, then, the same thing is always in a cycle, something must always remain acting in the same way. And if there is to be coming-to-be and perishing, there must be something else always acting in different ways. This must therefore act in one way in itself and in another in virtue of something else — either of a third thing or of the first. It must then be in virtue of the first; for that is again the cause both for the third and for itself. So the first is better: for it was the cause of what is always the same, and something else of what is otherwise; and of what is always otherwise, evidently both. So this is how the motions are.
Why then must we seek other principles? Since this is so — and if not, all will be from night and "all things together" and from what is not — these difficulties may be taken as resolved. There is something which, without being moved, moves, eternal and being both substance and actuality. And it moves in this way: as the desired and the intelligible; they move without being moved.
V. THE PRINCIPLE AND THE STRIVING
22. Θ · Thphr. w225–331 · ⟨Σ:76A3⟩ — the principle divine, cause of motion
It is more reasonable, then, that what has the nature of a principle should be among things few and exceptional — if not indeed among things first and in the first. What this is, then, and what they are if there are several, one must try to bring to light somehow, whether by analogy or by some other likeness. And perhaps one must necessarily grasp it by some power and pre-eminence over the rest, as one would grasp god: for the principle of all things is divine, through which all things both are and endure. To render it in that way is perhaps easy; to render it more clearly or more convincingly is hard. And since the principle is of that sort — since it connects with the perceptibles, and since nature, simply put, is in motion, and this is what is proper to it — it is clear that one must set this down as the cause of motion.
23. Θ · Thphr. w331–430 · ⟨Σ:EF8F⟩ — unmoved; the desired moves; THE ACCOUNT TOTALLED
But since it is unmoved in itself, it is clear that it would not be the cause for the things of nature by being moved, but rather by some other power, stronger and prior. And such is the nature of the object of desire, from which comes the circular motion, the continuous and unceasing. So that in that way the difficulty would be resolved — that there is no principle of motion, or else that what moves will be moved. Up to this point, then, the account is as it were even — making one principle of all things, and assigning to it both activity and being, and further saying that it is neither divisible nor of any quantity, but simply lifting it into some better and more divine portion; for it is better to render it thus than to take away the divisible and partible.
24. Α · Λ w2310–2513 · ⟨Σ:D8BF⟩ — the desired and the intelligible; IT MOVES AS A BELOVED; the necessary in three senses
For the object of appetite is what appears fine, and the primary object of wish is what is fine; and we desire a thing because it seems good rather than its seeming good because we desire it — for thinking is the starting point. And mind is moved by the intelligible; and one of the two columns is intelligible in itself, and in it substance is first, and of substance the simple and in actuality (the one and the simple are not the same: the one signifies a measure, the simple a way of being). But the fine too, and what is chosen for its own sake, are in the same column; and the first is always best, or analogous to it.
And that the for-the-sake-of-which is among the unmoved, the division shows: for the for-the-sake-of-which is both for someone and of something, of which the one exists and the other does not. And so it moves as a beloved, and by what is moved it moves the rest.
Now if a thing is moved, it can be otherwise; so that if its actuality is the primary locomotion, then insofar as it is moved, in this respect it can be otherwise — in place, even if not in substance. But since there is something which moves while itself unmoved, being in actuality, this cannot be otherwise in any way. For locomotion is the first of changes, and of this the circular; and this it moves. Necessarily, then, it is. And insofar as it is necessary, it is well, and in this way a principle.
For the necessary is spoken of in these many ways: what is by force because contrary to impulse; that without which the good is not; and what cannot be otherwise but is simply so.
25. Θ · Thphr. w430–522 · ⟨Σ:50F3⟩ — THE DEMAND; the dilemma; THE METHOD REFUSED
For at the same time, in a higher and truer account, the denial belongs to those who speak. But what comes after this now needs a fuller account, concerning the striving: what kind, and of what things. Since the circular motions are many, and their movements in a way opposed, and the endlessness and the for-the-sake-of-which unclear. For if what moves is one, it is strange that they do not all have the same motion; and if there is a different one for each, then the principles too are many — so that their concord, going toward striving, toward the best of them, is in no way evident. And as to the matter of the number of the spheres: its cause seeks a greater account, for the astronomers' is not it.
VI. THE COUNT
26. Α · Λ w2886–3167 · ⟨Σ:AF3B⟩ — ONE SUCH SUBSTANCE OR MORE, AND HOW MANY? and this science treats eternal perceptible substance
But whether one such substance is to be posited or several, and how many, must not escape us; rather we must recall the declarations of others too, that about number they have said nothing that can even be stated clearly. For the supposition about the Ideas has no inquiry proper to it (since those who speak of Ideas call the Ideas numbers, and about numbers they speak now as of infinite ones, now as bounded by the decad; and as to the cause why the multitude of numbers should be just so much, nothing is said with demonstrative seriousness).
We, however, must speak from what has been laid down and determined. For the principle and first of beings is unmoved both in itself and incidentally, but moves the first eternal and single motion. And since what is moved must be moved by something, and the first mover be unmoved in itself, and the eternal motion be moved by something eternal and the single motion by a single thing — and since we see that besides the simple locomotion of the whole, which we say the first and unmoved substance moves, there are other eternal locomotions, those of the planets (for the body that moves in a circle is eternal and unresting — this has been shown in the physical treatises) — each of these locomotions too must be moved by a substance unmoved in itself and eternal. For the nature of the stars is an eternal substance, and the mover is eternal and prior to the moved, and what is prior to a substance must be a substance. It is clear, then, that there must be just so many substances, eternal in nature and unmoved in themselves and without magnitude, for the reason stated before.
That they are substances, then, is clear, and that one of them is first and another second in the order of the locomotions of the stars. As to the number of the locomotions, we must inquire from that one of the mathematical sciences which is most akin to philosophy — from astronomy.
27. Α · Λ w3167–3633 · ⟨Σ:1EB4⟩ — the movements are more than the bodies; EUDOXUS AND CALLIPPUS
For this makes its study concerning a substance which is perceptible but eternal, whereas the others concern no substance — such as those about numbers and geometry.
That the locomotions are more than the bodies that travel is clear even to those who have touched the subject moderately (for each of the planets has more than one locomotion). As to how many these happen to be, we now state what some of the mathematicians say, for the sake of an idea, so that thought may grasp some definite number; for the rest we must partly inquire ourselves and partly learn from those who inquire, and if anything appears otherwise to those occupied with these things, we must love both parties but obey the more accurate.
Eudoxus, then, held the movement of the sun and moon each to be in three spheres, of which the first is that of the fixed stars, the second along the circle through the middle of the zodiac, and the third along the circle inclined across the breadth of the zodiac (and the circle along which the moon travels is inclined at a greater breadth than that along which the sun does); and the movement of the planets in four spheres each, of which again the first and second are the same as those (for the sphere of the fixed stars is the one that carries them all, and the one ranged beneath it, having its movement along the circle through the middle of the zodiac, is common to all); and the poles of the third sphere of all of them are in the circle through the middle of the zodiac; and the movement of the fourth is along a circle inclined to the middle of this one. And the poles of the third sphere are proper to each of the others, but the same for Venus and Mercury.
And Callippus posited the same arrangement of the spheres as Eudoxus — that is, the order of their distances — but as to the number, he assigned to Jupiter and Saturn the same as Eudoxus, while to the sun and the moon he thought two more spheres must still be added, if one is to account for the appearances, and one to each of the remaining planets.
But it is necessary, if all together are to account for the appearances, that for each of the planets there be other spheres, one fewer, which counter-roll and always restore to the same position the first sphere of the star ranged below; for only so can all together produce the locomotion of the planets. Since, then, the spheres in which they themselves travel are eight and twenty-five, and of these only those in which the lowest-ranged travels need not be counter-rolled, the counter-rolling spheres of the first two will be six, and of the next four will be sixteen; and the number of all together, both those which carry and those which counter-roll these, will be fifty-five. And if one does not add to the moon and the sun the motions we mentioned, all the spheres will be forty-seven.
Let this, then, be the number of the spheres; so that it is reasonable to suppose the unmoved substances and principles to be just so many — let the necessity be left for stronger minds to state.
28. Α · Λ w3633–3965 · ⟨Σ:89C9⟩ — no movement without a star; the number of substances; THE GODS; ancestral opinion
But if it is not possible for there to be any locomotion not contributing to the locomotion of a star, and further if every nature and every substance which is unaffected and has attained the best in itself must be held to be an end, then there could be no other nature besides these, but this must be the number of the substances. For if there are others, they would move as being an end of locomotion; but it is impossible that there be other locomotions besides those mentioned. And it is reasonable to suppose this from the bodies that travel. For if everything that carries is by nature for the sake of what is carried, and every locomotion is of something carried, no locomotion could be for the sake of itself or of another locomotion, but they must be for the sake of the stars. For if there is to be a locomotion for the sake of a locomotion, that too will have to be for the sake of something else; so that since it is not possible to go on to infinity, the end of every locomotion will be one of the divine bodies that travel in the heaven.
That there is one heaven is clear. For if there are many heavens as there are many men, the principle for each will be one in form but many in number. But whatever things are many in number have matter (for one and the same formula belongs to many, as of man, whereas Socrates is one). But the primary essence has no matter, for it is a fulfilment. The first unmoved mover, then, is one both in formula and in number; and so too is what is moved always and continuously. There is therefore one heaven only.
It has been handed down from the ancients and the very early, and left to posterity in the form of a myth, that these are gods and that the divine encompasses the whole of nature. The rest has been added mythically for the persuasion of the many and for use toward the laws and the common advantage: for they say that these are man-shaped and like some of the other animals, and other things consequent on and similar to these. If one were to separate off the first point alone and take it — that they held the first substances to be gods — one would think it divinely said, and that while every art and philosophy has probably been discovered as often as possible and perished again, these opinions have been preserved like relics of theirs down to now. The ancestral opinion, then, and that from the earliest, is clear to us to this extent only.
29. Θ · Thphr. w522–619 · ⟨Σ:0D6C⟩ — motion not rest; and soul
And it is a difficulty too, how it can be that things having a natural striving pursue not rest but motion. What then do they say about that, together with the imitation — both those who speak of the One and those who speak of the numbers? For they themselves say that the numbers are the One. If, then, there is striving — and especially striving for the best — it goes with soul. Unless one were to say that the things moved are ensouled by way of likeness and difference. And soul seems to be present together with motion, for it is life to those that have it, and from it come the strivings toward each thing, just as in animals — since perceptions too, though they lie in being acted upon and come about through other things, nevertheless become ensouled.
30. Θ · Thphr. w619–713 · ⟨Σ:557D⟩ — not the cause of the best; why only circular
But if, then, the first is the cause of the circular motion, it would not be the cause of the best; for the soul's is stronger, and first indeed and most of all the mind's, from which also comes the striving. And perhaps one would further inquire into this too: why only the circular motions are objects of striving, and none of the motions about the centre, although these too are movable — whether because they are incapable, or because the first does not reach through to them. But that at least is strange, if it is through weakness; for one would think it stronger than Homer's Zeus, who says: I could drag up the very earth and the very sea. But it remains that there is something as it were unreceptive and uncompounded.
31. Θ · Thphr. w2449–2543 · ⟨Σ:F292⟩ — astronomy not first
And further, as to the matters of the movements and the magnitudes and the shapes and the distances and whatever else astronomy demonstrates — for these it remains to speak of the first movers and of the for-the-sake-of-which, and what the nature of each is, and their position with respect to one another, and the substance of the whole; and then, descending toward the rest, according to each of the kinds in order, down to animals and plants. If, then, astronomy contributes, but not among the first things of nature, the most authoritative and prior things would be other than it — since indeed its manner, as some think, is not natural, or not wholly so.
VII. THE HEAVEN
32. Θ · Thphr. w713–808 · ⟨Σ:75D8⟩ — parts of the heaven?
But perhaps one would first inquire how the matter stands: whether these are parts of the heaven or not parts, and if parts, in what way parts. For as it is they are as it were thrust away from the most honoured things, not only in respect of place but also in respect of activity — if indeed the circular motion is of that sort. For it turns out that the changes, both into places and into one another, come about as it were incidentally, through the circular revolution. And if the best comes from the best, something finer than circular motion would be needed from the first — unless it were prevented by an inability to receive. For the first and most divine wills all the best things.
33. Θ · Thphr. w808–902 · ⟨Σ:D260⟩ — the first heaven: is the revolution its substance?
But perhaps this is as it were an excess and not to be inquired into. For whoever says this claims that all things are alike, and that among the best there is some small difference, or none at all. But one might perhaps raise this difficulty, referring it to the first heaven itself: whether the revolution belongs to its substance, and would perish together with its ceasing, or whether it belongs incidentally, by some striving and desire — unless indeed the striving is inborn in it, and nothing prevents there being some such things among the beings. And perhaps one might also, taking away the striving, raise the difficulty about the motion itself, whether if taken away it would destroy the heaven.
34. Α · Λ w2513–2861 · ⟨Σ:77F4⟩ — ON SUCH A PRINCIPLE THE HEAVEN DEPENDS; THE LIFE OF GOD
...and as it is necessary, it is well, and in this way a principle. On such a principle, then, depend the heaven and nature. And its course of life is such as the best we have for a short time (for it is always in this state, which for us is impossible), since its actuality is also pleasure. And for this reason waking, perceiving and thinking are most pleasant, and hopes and memories through these. And thinking in itself is of what is best in itself, and the highest thinking of the highest.
And mind thinks itself by partaking of the intelligible; for it becomes intelligible by touching and thinking, so that mind and the intelligible are the same. For what is receptive of the intelligible and of substance is mind, and it is in actuality by possessing; so that this rather than that seems to be the divine thing mind possesses, and contemplation is the pleasantest and best. If, then, god is always in that good state in which we sometimes are, it is wonderful; and if more so, still more wonderful. And it is so. And life belongs to it: for the actuality of mind is life, and that is the actuality; and its actuality in itself is life best and eternal. We say that god is a living being, eternal and best, so that life and continuous and eternal duration belong to god; for this is god.
Those who suppose, as the Pythagoreans and Speusippus do, that the finest and best is not in the beginning — because the beginnings of plants and animals are causes, but the fine and complete is in what comes from these — do not think rightly. For the seed is from other prior complete things, and the first is not the seed but the complete: as one might say that a man is prior to the seed — not the man from this seed, but another from whom the seed comes.
That there is, then, an eternal and unmoved substance separate from perceptible things is clear from what has been said. And it has been shown too that this substance can have no magnitude, but is without parts and indivisible (for it moves for infinite time, and nothing finite has infinite power; and since every magnitude is either infinite or finite, it could not have a finite magnitude for this reason, and not an infinite one because there is no infinite magnitude at all).
35. Α · Λ w2861–2886 · ⟨Σ:4DFA⟩ — …and further, that it is impassive and unalterable — these things are clear
And further, that it is impassive and unalterable: for all other motions are posterior to locomotion. These things, then, are clear — that they hold in this way.
36. Θ · Thphr. w2543–2645 · ⟨Σ:EC85⟩ — the revolution is a kind of life
And yet being moved is proper to nature simply, and most of all to the heaven. And so, if the activity belongs to the substance of each, then also the particular, whenever it is in activity, is also moved — as in animals and plants. And if not, they are homonymous; and it is clear that the heaven too would be in its revolution in respect of its substance, but separated and at rest would be homonymous — for the revolution of the universe is as it were a kind of life. If, then, life is not to be sought in animals either, or only in this way, is the movement not to be sought in the heaven and the heavenly things either, or only in some determinate way? And the present difficulty connects somehow with the motion caused by the unmoved.
VIII. MIND
37. Θ · Thphr. w2359–2449 · ⟨Σ:5152⟩ — MIND TOUCHES
But perhaps that is truer: that the contemplation belongs to mind itself, which has touched and as it were laid hold — and for this reason there is no deception about these things. And the understanding and the conviction toward this very thing are hard; since it is also otherwise a great matter, and necessary for the inquiries into particulars, and most of all for the greatest, in what one must set the limit — as concerning nature, and concerning the things still prior to it. For those who seek an account of all things destroy the account, and knowing along with it. But it is truer to say that they seek what does not exist and is not of a nature to exist — all those who suppose the heaven to be eternal.
38. Α · Λ w3965–4293 · ⟨Σ:DE7F⟩ — THE DIFFICULTIES ABOUT MIND; thinking of thinking
The matters concerning mind hold certain difficulties. For it seems to be the most divine of things that appear, but how it must be if it is to be such is difficult. For if it thinks nothing, what is solemn in that? It would be like one sleeping. And if it thinks, but something else controls it, then — since its substance is not thinking but potency — it would not be the best substance, for it is through thinking that its value belongs to it.
Further, whether its substance is mind or thinking, what does it think? Either itself or something else; and if something else, either always the same or different things. Does it then make a difference, or none, whether it thinks the fine or a chance thing? Or is it absurd to be thinking about some things? It is clear, then, that it thinks the most divine and most valuable, and does not change; for change would be to something worse, and this would already be a motion.
First, then, if it is not thinking but potency, it is reasonable that the continuity of the thinking should be laborious for it. Next, it is clear that something else would be more valuable than mind, namely what is thought. For both thinking and the thinking will belong to one who thinks the worst thing; so that if this is to be avoided (for it is better not to see some things than to see them), the thinking would not be the best.
It thinks itself, then, if it is the most excellent, and the thinking is a thinking of thinking. But knowledge and perception and opinion and reasoning appear always to be of something else, and of themselves only incidentally. Further, if thinking and being thought are different, in respect of which does the good belong to it? For being an act of thinking and being an object of thought are not the same. Or is the knowledge in some cases the thing itself — in the productive sciences the substance and essence without matter, in the theoretical the formula and the thinking? Since, then, what is thought and mind are not different in things that have no matter, they will be the same, and the thinking will be one with what is thought.
A difficulty still remains: whether what is thought is composite. For then it would change among the parts of the whole.
39. Α · Λ w4293–4342 · ⟨Σ:0996⟩ — ἢ ἀδιαίρετον — the answer: whatever lacks matter is indivisible
Or is everything that lacks matter indivisible — as the human mind, or rather the mind of composite things, has its good at some time (for it does not have the good in this or that part, but the best, being something other, is in some whole)? And so the thinking of itself holds throughout all eternity.
IX. THE PREDECESSORS
40. Θ · Thphr. w902–1043 · ⟨Σ:FBAA⟩ — Eurytus; the One and the dyad
And this belongs, as it were, to other accounts. But from this principle, or from these principles, one would make his claim. And perhaps from the other principles too one might lay it down that the consequences are to be rendered straightaway, and not to stop after having gone forward only so far: for that is the mark of one who is complete and thinking — which is what Archytas once said Eurytus did, laying out certain pebbles. For he would say: this is the number of a man, this of a horse, and this happens to be of something else. But as it is, most of them go only so far and then stop — like those who make the One and the indefinite dyad. For having generated the numbers and the planes and the bodies, they leave nearly everything else aside, touching on it only so far as to show this much: that some things come from the indefinite dyad, such as place and void and the unlimited, and others from the numbers and the One, such as soul and certain other things; and time too, at the same time, and the heaven, and indeed several others.
But about the heaven and the rest they make no further mention. And likewise neither Speusippus and his circle, nor any of the others, except Xenocrates: for he somehow assigns all things a place about the cosmos alike — perceptibles and intelligibles and mathematicals, and indeed the divine things too. And Hestiaeus tries as far as a point, not, as has been said, only about the first things. Plato, then, in leading things back to the principles, would seem to touch on the rest, fastening them to the Ideas, and these to the numbers, and from these to the principles, and then, following the order of generation, as far as the things mentioned.
42. Θ · Thphr. w1134–1192 · ⟨Σ:BD7B⟩ — but others deal only with the principles
[from the covering movement] But others deal only with the principles. And some place the truth in these too: for the beings are only about the principles. Yet the opposite happens from what happens in the other methods of inquiry: for in those, the things after the principles are stronger and as it were more complete among the sciences — and perhaps reasonably so. For in the one case the inquiry is of the principles, in the rest it proceeds from the principles. But how one ought to posit the principles, and of what sort, one might well raise as a difficulty: whether formless and as it were potential, like those who posit fire and earth, or formed, on the ground that these above all must be determinate, as he says in the Timaeus.
X. THE GOOD, AND WHAT DOES NOT RECEIVE IT
43. Θ · Thphr. w2645–2740 · ⟨Σ:F784⟩ — all for the sake of something? the tides
But concerning the claim that all things are for the sake of something and nothing in vain — apart from anything else, the determination is not easy, as is said repeatedly (where must one begin, and in what must one end?) — and indeed because some things do not seem to be so, but some come about coincidentally and others by some necessity, as both in the heavenly things and in the many things about the earth. For the sake of what are the advances and retreats of the sea, or for the sake of what the flowings-forward or dryings-up of moisture, and in general the changes and destructions and generations toward one thing after another — or do the alterations and changes in the earth itself come about as things shift toward one state after another?
44. Θ · Thphr. w2740–2837 · ⟨Σ:85F0⟩ — pointless things in animals
And there are not a few others like these. And in the animals themselves some things are as it were pointless: as breasts in males, and the emission in females if it contributes nothing; and in some the growth of a beard, or of hair generally in certain places; and further the sizes of horns, as in deer; and in some, things mai
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