Posts by Cassius

On my first readings of DeWitt's references to the sorites ("heap") argument, I did not know whether to think DeWit was being accurate or exaggerating as to its reputation, but I see that Cicero goes on an on in Academic questions about its "viciousness" and therefore presumably its effectiveness in combating dialectical logic.

Quote

What is there that can be perceived by reason? You say that Dialectics have been discovered, and that that science is, as it were, an arbiter and judge of what is true and false. Of what true and false?—and of true and false on what subject? Will a dialectician be able to judge, in geometry, what is true and false, or in literature, or in music? He knows nothing about those things. In philosophy, then? What is it to him how large the sun is? or what means has he which may enable him to judge what the chief good is? What then will he judge of? Of what combination or disjunction of ideas is accurate,—of what is an ambiguous expression,—of what follows from each fact, or what is inconsistent with it? If the science of dialectics judges of these things, or things like them, it is judging of itself. But it professed more. For to judge of these matters is not sufficient for the resolving of the other numerous and important questions which arise in philosophy. But, since you place so much importance in that art, I would have you to consider whether it was not invented for the express purpose of being used against you. For, at its first opening, it gives an ingenious account of the elements of speaking, and of the manner in which one may come to an understanding of ambiguous expressions, and of the principles of reasoning: then, after a few more things, it comes to the sorites, a very slippery and hazardous topic, and a class of argument which you yourself pronounced to be a vicious one.

### XXIX.

What then, you will say; are we to be blamed for that viciousness? The nature of things has not given us any knowledge of ends, so as to enable us, in any subject whatever, to say how far we can go. Nor is this the case only in respect of the heap of wheat, from which the name is derived, but in no matter whatever where the argument is conducted by minute questions: for instance, if the question be whether a man is rich or poor, illustrious or obscure,—whether things be many or few, great or small, long or short, broad or narrow,—we have no certain answer to give, how much must be added or taken away to make the thing in question either one or the other.

But the sorites is a vicious sort of argument:—crush it, then, if you can, to prevent its being troublesome; for it will be so, if you do not guard against it. We have guarded against it, says he. For Chrysippus's plan is, when he is interrogated step by step (by way of giving an instance), whether there are three, or few, or many, to rest a little before he comes to the “many;” that is to say, to use their own language, ἡσυχάζειν. Rest and welcome, says Carneades; you may even snore, for all I care. But what good does he do? For one follows who will waken you from sleep, and question you in the same manner:—Take the number, after the mention of which you were silent, and if to that number I add one, will there be many? You will again go on, as long as you think fit. Why need I say more? for you admit this, that you cannot in your answers fix the last number which can be classed as “few,” nor the first, which amounts to “many.” And this kind of uncertainty extends so widely, that I do not see any bounds to its progress.

Nothing hurts me, says he; for I, like a skilful driver, will rein in my horses before I come to the end, and all the more if the ground which the horses are approaching is precipitous. And thus, too, says he, I will check myself, and not reply any more to one who addresses me with captious questions. If you have a clear answer to make, and refuse to make it, you are giving yourself airs; if you have not, even you yourself do not perceive it. If you stop, because the question is obscure, I admit that it is so; but you say that you do not proceed as far as what is obscure. You stop, then, where the case is still clear. If then all you do is to hold your tongue, you gain nothing by that. For what does it matter to the man who wishes to catch you, whether he entangles you owing to your silence or to your talking? Suppose, for instance, you were to say, without hesitation, that up to the number nine, is “few,” but were to pause at the tenth; then you would be refusing your assent to what is certain and evident, and yet you will not allow me to do the same with respect to subjects which are obscure.

That art, therefore, does not help you against the sorites; inasmuch as it does not teach a man, who is using either the increasing or diminishing scale, what is the first point, or the last. May I not say that that same art, like Penelope undoing her web, at last undoes all the arguments which have gone before? Is that your fault, or ours? In truth, it is the foundation of dialectics, that whatever is enunciated (and that is what they call ἀξίωμα, which answers to our word effatum,) is either true or false. What, then, is the case? Are these true or false? If you say that you are speaking falsely, and that that is true, you are speaking falsely and telling the truth at the same time. This, forsooth, you say is inexplicable; and that is more odious than our language, when we call things uncomprehended, and not perceived.

Display More

In Academic Questions XXVI, Cicero says that all the challenges against the possibility of knowledge fall into one of four categories about which the schools had split and been arguing for hundreds of years. Over time it would be good to develop some kind of chart explaining these and the Epicurean response to each:

Quote

However, to abridge the controversy, consider, I pray you, within what narrow bounds you are confined. There are four principles which conduct you to the conclusion that there is nothing which can be known, or perceived, or comprehended;—and it is about this that the whole dispute is. The first principle is, that some perceptions are false; the second, that such cannot be perceived; the third, that of perceptions between which there is no difference, it is not possible that some of them can be perceived and that others cannot; the fourth, that there is no true perception proceeding from the senses, to which there is not some other perception opposed which in no respect differs from it, and which cannot be perceived. Now of these four principles, the second and third are admitted by every one. Epicurus does not admit the first, but you, with whom we are now arguing, admit that one too,—the whole contest is about the fourth.

Voula Tsouna, in her "Ethics of Phildemus," says:

Quote

.... Section V deals with the issue of whether anger is a good or a bad thing. It elaborates Philodemus’
distinction between two kinds of anger, which he calls, respectively, ὀργή (translit. org¯e ) and θυμός (translit. thymos), as well as his contention that the Epicurean sage experiences the former kind of anger (org¯e ) but not the latter.

...

Quote

Epicurus makes the puzzling remark that the wise man is more susceptible than other men to some passions without this impeding his wisdom (D.L. X. 117), and he asserts that the gods feel neither anger nor gratitude (KD 1)—which might imply that lesser beings feel both. According to Philodemus, Epicurus also claims that the wise man will experience thymos; similar statements are found in the writings of Metrodorus and Hermarchus as well (De ir. XLV. 5–15). In general, ‘the Great Men’ appear to have held that some sort of anger is unavoidable,and that some sages are more prone to it than others. However, they evidently did not clarify just what kind of anger is ineradicable or whether the wise man is susceptible to every form of anger. Later Epicureans debate these issues, each group giving a different interpretation of the canonical texts and citing scripture to defend it. The position that Philodemus advocates in On Anger (probably also held by Zeno of Sidon and his school) is one such view: the sage never experiences an unnatural kind of anger, but is liable to feeling a natural kind of anger compatible with moral perfection. Thus, Philodemus can be perceived as striking a wise compromise between the Peripatetics and the Stoics, and also as holding a middle ground between competing Epicurean factions.²²

...

Quote

Since there is false reasoning of some sort induced by the word (sc. org¯e ), we do not make any simple pronouncement (sc. as to whether anger is a fine or an evil thing), but we claim that the emotion itself taken in isolation is an evil because it is painful or close to painful, whereas taken in conjunction with one’s disposition it can even be called a good, as we think. For it results from our understanding of the nature of things and from our holding no false beliefs in the matter of measuring the offences and of punishing the offenders. As a result, in the same way in which we called empty anger (cf. κ[ενὴν ὀρ]γήν: XXXVIII. 1) an evil because it arises from a thoroughly corrupt disposition and brings on countless troubles, we must call natural anger (cf. φυσική[ν]: XXXVIII. 6) not an evil—but, in so far as it is something biting,⁸⁰ [it lasts a very short time].
(XXXVII. 20–XXXVIII. 9)

Quote

[To call anger] a weakness (τὸ ἀσθενές) and then apply it to the wise man, sothat we also make him weak, is no great problem to us, as it is to some thinkers. They, writing against the Κύριαι ∆όξαι, maintained that it was extraordinary that anyone had dared to claim that anger, gratitude and all these sorts of things occur in weakness, since Alexander, the most powerful human being of all, was subject to frequent outbursts of anger and did favours to countless men. However, it is not the weakness opposite to the strong constitution of athletes and kings that the (Epicurean) argument is talking about. It is rather a natural constitution subject to death and pain, of which Alexander and indeed every other human being have their share, and perhaps most of all those who, like him, are called the most
powerful in that other sense of the word.
(XLIII. 14–41)⁹⁵

Quote

We shall tell our opponent that the sage will be profoundly alienated from, and indeed hates, the person who inflicts on him such great [injuries] or will obviously cause him [great] damage in the future—for this is a fitting consequence (ἀκ[όλο]υθον: XLII. 3–4)—but he does not suffer great mental disturbance. [Neither is any] external thing [all that important], since the sage is not even susceptible to great mental disturbance in the presence of great physical pain, let alone in the presence of angry feelings. For [to be in a state of dreadful suffering] derives from folly. So if one is a fool, this suffering can be [inevitable]. Indeed, there are infinite misfortunes both involved in his folly and consequent upon it, into which the wise man, having a completely clear vision of them (θεωρῶν: XLII. 19–20), would never fall.
(XLI. 39–XLII. 20)

Our material this week will start with Cicero discussing anger, and apparently taking the position that the wise man will never be angry.

We'll need to contrast that with what Philodemus has to say as discussed in this thread:

Post

RE: Philodemus' "On Anger" - General - Texts and Resources

Couple more quotes from the Philodemus text:

From page 41 of the Armstrong book:

37.24–39: “the emotion itself, taken in isolation, is an evil, since it is painful or is analogous to something painful, but if taken in conjunction with one’s disposition, we think that it is something that may even be called a good. For it (anger) results from seeing what the nature of states of affairs is and from not having any false beliefs in our comparative calculations of our losses and in our…

Cassius

April 1, 2022 at 6:00 PM

Welcome to Episode 289 of Lucretius Today. This is a podcast dedicated to the poet Lucretius, who wrote "On The Nature of Things," the most complete presentation of Epicurean philosophy left to us from the ancient world.

Each week we walk you through the Epicurean texts, and we discuss how Epicurean philosophy can apply to you today. If you find the Epicurean worldview attractive, we invite you to join us in the study of Epicurus at EpicureanFriends.com, where we discuss this and all of our podcast episodes.

This week we continue our series covering Cicero's "Tusculan Disputations" from an Epicurean viewpoint.

Today we continue in Part 3, which addresses anger, pity, envy, and other strong emotions. We'll continue reading today with Section IX.

This is to provide a cross-reference to where the sorites argument is discussed in DeWitt's "Epicurus and His Philosophy"

DeWitt's References On The Sorites Question - Epicureanfriends.com

www.epicureanfriends.com

I agree Don....

Quote from Don

Cicero seems to equate pathē with ταραχή (tarakhē) "disturbance of mind; dis-ease" which is the opposite of αταραξία (a-taraksia) "lack of disturbance."

Which is not to say that Cicero was wrong as to the general usage of the term, if indeed that is what the other philosophers besides Epicurus were doing. I gather Cicero was correct about that, unless there is some reason in other literature to disbelieve him (?)

Also from Section XII the same issue of knowledge is explained by Cicero:

Quote

Then I replied — Arcesilas, as we understand, directed all his attacks against Zeno, not out of obstinacy or any desire of gaining the victory, as it appears to me, but by reason of the obscurity of those things which had brought Socrates to the confession of ignorance, and even before Socrates, Democritus, Anaxagoras, Empedocles, and nearly all the ancients; who asserted that nothing could be ascertained, or perceived, or known: that the senses of man were narrow, his mind feeble, the course of his life short, and that truth, as Democritus said, was sunk in the deep; that everything depended on opinions and established customs; that nothing was left to truth. They said in short, that everything was enveloped in darkness; therefore Arcesilas asserted that there was nothing which could be known, not even that very piece of knowledge which Socrates had left himself. Thus he thought that everything lay hid in secret, and that there was nothing which could be discerned or understood; for which reasons it was not right for any one to profess or affirm anything, or sanction anything by his assent, but men ought always to restrain their rashness and to keep it in check so as to guard it against every fall.

For rashness would be very remarkable when anything unknown or false was approved of; and nothing could be more discreditable than for a man's assent and approbation to precede his knowledge and perception of a fact. And he used to act consistently with these principles, so as to pass most of his days in arguing against every one's opinion, in order that when equally important reasons were found for both sides of the same question, the judgment might more naturally be suspended, and prevented from giving assent to either.

In this episode and next week as well we are dealing with questions about whether the wise man will experience grief, and whether the strong emotions should be considered to be a disease, topics on which the schools differed, and it's sometimes hard to tell Cicero's own views.

Here in Academic Questions is how Cicero explains the Stoic view (see especially the second paragraph):

Quote

X.

Zeno, then, was not at all a man like Theophrastus, to cut through the sinews of virtue; but, on the other hand, he was one who placed everything which could have any effect in producing a happy life in virtue alone, and who reckoned nothing else a good at all, and who called that honourable which was single in its nature, and the sole and only good. But as for all other things, although they were neither good nor bad, he divided them, calling some according to, and others contrary to nature. There were others which he looked upon as placed between these two classes, and which he called intermediate. Those which were according to nature, he taught his disciples, deserved to be taken, and to be considered worthy of a certain esteem. To those which were contrary to nature, he assigned a contrary character; and those of the intermediate class he left as neutrals, and attributed to them no importance whatever. But of those which he said ought to be taken, he considered some worthy of a higher estimation and others of a less. Those which were worthy of a higher esteem, he called preferred; those which were only worthy of a lower degree, he called rejected. And as he had altered all these things, not so much in fact as in name, so too he defined some actions as intermediate, lying between good deeds and sins, between duty and a violation of duty; — classing things done rightly as good actions, and things done wrongly (that is to say, sins) as bad actions. And several duties, whether discharged or neglected, he considered of an intermediate character, as I have already said. And whereas his predecessors had not placed every virtue in reason, but had said that some virtues were perfected by nature, or by habit, he placed them all in reason; and while they thought that those kinds of virtues which I have mentioned above could be separated, he asserted that that could not be done in any manner, and affirmed that not only the practice of virtue (which was the doctrine of his predecessors), but the very disposition to it, was intrinsically beautiful; and that virtue could not possibly be present to any one without his continually practising it.

And while they did not entirely remove all perturbation of mind from man, (for they admitted that man did by nature grieve, and desire, and fear, and become elated by joy,) but only contracted it, and reduced it to narrow bounds; he maintained that the wise man was wholly free from all these diseases as they might be called. And as the ancients said that those perturbations were natural, and devoid of reason, and placed desire in one part of the mind and reason in another, he did not agree with them either; for he thought that all perturbations were voluntary, and were admitted by the judgment of the opinion, and that a certain unrestrained intemperance was the mother of all of them. And this is nearly what he laid down about morals.

From Cicero's Academic Questions we see the same issue of the flux being too fast to be apprehended by the senses developed:

Quote from Cicero's Academic Questions Part 1

VIII.

The third part of philosophy, which is next in order, being conversant about reason and discussion, was thus handled by both schools. They said that, although it originated in the senses, still the power of judging of the truth was not in the senses. They insisted upon it that intellect was the judge of things. They thought that the only thing deserving of belief, because it alone discerned that which was always simple and uniform, and which perceived its real character. This they call idea, having already received this name from Plato; and we properly entitle it species.

But they thought that all the senses were dull and slow, and that they did not by any means perceive those things which appeared subjected to the senses; which were either so small as to be unable to come under the notice of sense, or so moveable and rapid that none of them was ever one consistent thing, nor even the same thing, because everything was in a continual state of transition and disappearance. And therefore they called all this division of things one resting wholly on opinion. But they thought that science had no existence anywhere except in the notions and reasonings of the mind; on which account they approved of the definitions of things, and employed them on everything which was brought under discussion. The explanation of words also was approved of — that is to say, the explanation of the cause why everything was named as it was; and that they called etymology. Afterwards they used arguments, and, as it were, marks of things, for the proof and conclusion of what they wished to have explained; in which the whole system of dialectics — that is to say, of an oration brought to its conclusion by ratiocination, was handed down. And to this there was added, as a kind of second part, the oratorical power of speaking, which consists in developing a continued discourse, composed in a manner adapted to produce conviction.

With the result that the "intellect" is the judge of things.

Episode 288 of the Lucretius Today Podcast is now available. Today our episode is entitled: "Will The Wise Man Feel Grief Or Other Strong Emotions?"

Yes Dave those are several of the most key references to prolepsis in the major texts. I would say that any good interpretation of prolepsis needs to be reconcilable with them. I don't find that DeWitt's choice of words is always the best, in that he sometimes comes close to calling them innate "ideas," but his list of the examples there is as I understand it correct.

I think it's very relevant to point out that Velleius pretty clearly divides the core attributes of blessedness and imlerishability from any other speculations, diving that from what the mind strives for further:

Quote

We have then a preconception of such a nature that we believe the gods to be blessed and immortal. For nature, which bestowed upon us an idea of the gods themselves, also engraved on our minds the belief that they are eternal and blessed. If this is so, the famous maxim of Epicurus truthfully enunciates that "that which is blessed and eternal can neither know trouble itself nor cause trouble to another, and accordingly cannot feel either anger or favor, since all such things belong only to the weak."

If we sought to attain nothing else beside piety in worshiping the gods and freedom from superstition, what has been said had sufficed; since the exalted nature of the gods, being both eternal and supremely blessed, would receive man's pious worship (for what is highest commands the reverence that is its due); and furthermore all fear of the divine power or divine anger would have been banished (since it is understood that anger and favor alike are excluded from the nature of a being at once blessed and immortal, and that these being eliminated we are menaced by no fears in regard to the powers above). But the mind strives to strengthen this belief by trying to discover the form of god, the mode of his activity, and the operation of his intelligence.

And later on he says:

XVIII. With regard to his form, we are directed partly by nature and partly by reason

"I can't find any arguments that would justify Epicurus' claims..."

To what claims are you referring? I see no claim other than that a god is a totally happy and totally deathless being. And I see examples of some things that are happier than others, and some things that love longer than others, all around me.

Now you may object to happy and death as being concepts, but those concepts arise from real particular examples whether I label them or not.

I would see prolepsis as an ability or disposition to pick out similars from among randomness.

Quote from sanantoniogarden

An analogy (imperfect at best) I use to describe prolepsis, which should be familiar to most these days, are the cameras on our phones. Say that your mind is like a camera constantly taking pictures of various things.

I agree this is useful. Like a camera, the eyes and other senses are continuously receiving stimulation and input. Something in our brains has to decide what inputs to pay attention to and to assemble into relevant connections before we start rationally evaluating them. We don't constantly state to ourselves in words what our senses are receiving. We act on and assemble relationships between data automatically, and then process those into words when appropriate.

Bryan will likely do better than me but I would say:

Quote from TauPhi

1) Prolepsis is a canonical faculty, knowledge is possible but prolepsis of gods is logically impossible (we know now that eidolas is a failed theory and images of gods do not reach human minds travelling from intermundia). That means Epicurus blundered with his description of gods being incorruptible and blessed. He had no input data to form prolepsis of gods and make any claims about gods, whatsoever.

I think according to your own reasoning, with which I agree, saying "prolepsis of gods" is improper. Eyes don't see gods or trees or birds or any other "object" either. Once you assign a word or name to what you are talking about you are selectively choosing from the inputs of the eye to the brain, and I would say the same applies to "gods." What we seem to be revolving around is seeing proplepsis as a form of automatic selectivity among the inputs provided by the sensations and feelings, by which the brain then in a separate step takes that selected raw data and then assembles the patterns into concepts and attaches names to them.

Quote from TauPhi

2) Prolepsis is a form of reasoning and cannot be considered canonical faculty or knowledge is impossible. That means Epicurus blundered with his description of canon or applied pure reasoning in his description of gods. Whether his reasoning is correct or incorrect remains forever undetermined as knowledge is impossible in this case and everything goes.

Same point as above. I would not see prolepsis as a form of "reasoning." Regardless of whether you pursue the "real" or "ideal" view of gods, the prolepsis that Velleius is talking about need not be anything more than the selective pattern-recognition of "blessed/happy" and "deathlessness." After those patterns are realized as applicable to life here, other observations about living beings here, that nature never makes a single thing of a kind, that the universe is eternal and filled with life, etc, would be enough to extend the concept through conceptual reasoning to conclude that such beings do in fact exist somewhere in the universe.

So in both cases I think your original point of reasoning - that prolepsis must be pre-rational and is never a "conclusion"- is the way forward. That original point just needs to be followed to its logical conclusion so that we rigorously separate the faculty of prolepsis from including "conclusions" or "ideas" of any kind.

And of course Heraclitus comes in for direct mention in Lucretius:

1-635 (continuing in following sections....)

Wherefore those who have thought that fire is the substance of things, and that the whole sum is composed of fire alone, are seen to fall very far from true reasoning. Heraclitus is their leader who first enters the fray, of bright fame for his dark sayings, yet rather among the empty-headed than among the Greeks of weight, who seek after the truth. For fools laud and love all things more which they can descry hidden beneath twisted sayings, and they set up for true what can tickle the ear with a pretty sound and is tricked out with a smart ring.

There is also a lot of good discussion at the Internet Encyclopedia of Philosophy:

2. Theory of Knowledge

Heraclitus sees the great majority of human beings as lacking understanding:

Quote

Of this Word’s being forever do men prove to be uncomprehending, both before they hear and once they have heard it. For although all things happen according to this Word they are like the unexperienced experiencing words and deeds such as I explain when I distinguish each thing according to its nature and declare how it is. Other men are unaware of what they do when they are awake just as they are forgetful of what they do when they are asleep. (DK22B1)

Most people sleep-walk through life, not understanding what is going on about them. Yet experience of words and deeds can enlighten those who are receptive to their meaning. (The opening sentence is ambiguous: does the ‘forever’ go with the preceding or the following words? Heraclitus prefigures the semantic complexity of his message.)

On the one hand, Heraclitus commends sense experience: “The things of which there is sight, hearing, experience, I prefer” (DK22B55). On the other hand, “Poor witnesses for men are their eyes and ears if they have barbarian souls” (DK22B107). A barbarian is one who does not speak the Greek language. Thus while sense experience seems necessary for understanding, if we do not know the right language, we cannot interpret the information the senses provide. Heraclitus does not give a detailed and systematic account of the respective roles of experience and reason in knowledge. But we can learn something from his manner of expression.

Describing the practice of religious prophets, Heraclitus says, “The Lord whose oracle is at Delphi neither reveals nor conceals, but gives a sign” (DK22B93). Similarly, Heraclitus does not reveal or conceal, but produces complex expressions that have encoded in them multiple messages for those who can interpret them. He uses puns, paradoxes, antitheses, parallels, and various rhetorical and literary devices to construct expressions that have meanings beyond the obvious. This practice, together with his emphasis on the Word (Logos) as an ordering principle of the world, suggests that he sees his own expressions as imitations of the world with its structural and semantic complexity. To read Heraclitus the reader must solve verbal puzzles, and to learn to solve these puzzles is to learn to read the signs of the world. Heraclitus stresses the inductive rather than the deductive method of grasping the world, a world that is rationally structured, if we can but discern its shape.

For those who can discern it, the Word has an overriding message to impart: “Listening not to me but to the Word it is wise to agree that all things are one” (DK22B50). It is perhaps Heraclitus’s chief project to explain in what sense all things are one.

3. The Doctrine of Flux and the Unity of Opposites

According to both Plato and Aristotle, Heraclitus held extreme views that led to logical incoherence. For he held that (1) everything is constantly changing and (2) opposite things are identical, so that (3) everything is and is not at the same time. In other words, Universal Flux and the Identity of Opposites entail a denial of the Law of Non-Contradiction. Plato indicates the source of the flux doctrine: “Heraclitus, I believe, says that all things go and nothing stays, and comparing existents to the flow of a river, he says you could not step twice into the same river” (Cratylus 402a = DK22A6).

What Heraclitus actually says is the following:

Quote

On those stepping into rivers staying the same other and other waters flow. (DK22B12)

There is an antithesis between ‘same’ and ‘other.’ The sentence says that different waters flow in rivers staying the same. In other words, though the waters are always changing, the rivers stay the same. Indeed, it must be precisely because the waters are always changing that there are rivers at all, rather than lakes or ponds. The message is that rivers can stay the same over time even though, or indeed because, the waters change. The point, then, is not that everything is changing, but that the fact that some things change makes possible the continued existence of other things. Perhaps more generally, the change in elements or constituents supports the constancy of higher-level structures.As for the alleged doctrine of the Identity of Opposites, Heraclitus does believe in some kind of unity of opposites. For instance, “God is day night, winter summer, war peace, satiety hunger . . .” (DK22B67). But if we look closer, we see that the unity in question is not identity:

Quote

As the same thing in us is living and dead, waking and sleeping, young and old. For these things having changed around are those, and conversely those having changed around are these. (DK22B88)

The second sentence in B88 gives the explanation for the first. If F is the same as G because F turns into G, then the two are not identical. And Heraclitus insists on the common-sense truth of change: “Cold things warm up, the hot cools off, wet becomes dry, dry becomes wet” (DK22B126). This sort of mutual change presupposes the non-identity of the terms. What Heraclitus wishes to maintain is not the identity of opposites but the fact that they replace each other in a series of transformations: they are interchangeable or transformationally equivalent.

Thus, Heraclitus does not hold Universal Flux, but recognizes a lawlike flux of elements; and he does not hold the Identity of Opposites, but the Transformational Equivalence of Opposites. The views that he does hold do not, jointly or separately, entail a denial of the Law of Non-Contradiction. Heraclitus does, to be sure, make paradoxical statements, but his views are no more self-contradictory than are the paradoxical claims of Socrates. They are, presumably, meant to wake us up from our dogmatic slumbers.

I've moved this over to a new thread so that it will be easier over time to explore this precise relationship. In the meantime pending a better source of quotes, here is what Wikipedia says:

Quote

Little is known of Heraclitus's life. He wrote a single work, only fragments of which have survived. Even in ancient times, his paradoxical philosophy, appreciation for wordplay, and cryptic, oracular epigrams earned him the epithets "the dark" and "the obscure". He was considered arrogant and depressed, a misanthrope who was subject to melancholia. Consequently, he became known as "the weeping philosopher" in contrast to the ancient atomist philosopher Democritus, who was known as "the laughing philosopher".

The central ideas of Heraclitus's philosophy are the unity of opposites and the concept of change. Heraclitus saw harmony and justice in strife. He viewed the world as constantly in flux, always "becoming" but never "being". He expressed this in sayings like "Everything flows" (Greek: πάντα ῥεῖ, panta rhei) and "No man ever steps in the same river twice". This insistence upon change contrasts with that of the ancient philosopher Parmenides, who believed in a reality of static "being".

...

Heraclitus is said to have produced a single work on papyrus,^[a] which has not survived; however, over 100 fragments of this work survive in quotations by other authors.^{[note 5]} The title is unknown,^[20] but many later writers refer to this work, and works by other pre-Socratics, as On Nature.^[21][a]...

The opening lines are quoted by Sextus Empiricus:

Of the logos being forever do men prove to be uncomprehending, both before they hear and once they have heard it. For although all things happen according to this logos they are like the unexperienced experiencing words and deeds such as I explain when I distinguish each thing according to its nature and declare how it is. Other men are unaware of what they do when they are awake just as they are forgetful of what they do when they are asleep.^[x]

Display More

Also:

Diogenes Laërtius relays the story that the playwright Euripides gave Socrates a copy of Heraclitus's work and asked for his opinion. Socrates replied: "The part I understand is excellent, and so too is, I dare say, the part I do not understand; but it needs a Delian diver to get to the bottom of it."^[38]

There is one passage the relevance of which I think is underappreciated in the prolepsis discussion. This below from fragment 5 of Diogenes of Oinoanda gets referenced frequently in regard to Epicurus' canon in general, but I wonder if it not a specific reference to the function of prolepsis:

Quote

Fr. 5
....

Now Aristotle and those who hold the same Peripatetic views as Aristotle say that nothing is scientifically knowable, because things are continually in flux and, on account of the rapidity of the flux, evade our apprehension. We on the other hand acknowledge their flux, but not its being so rapid that the nature of each thing [is] at no time apprehensible by sense-perception. And indeed [in no way would the upholders of] the view under discussion have been able to say (and this is just what they do [maintain] that [at one time] this is [white] and this black, while [at another time] neither this is [white nor] that black, [if] they had not had [previous] knowledge of the nature of both white and black.

When you're living in an age when most every educated person would be aware that Heraclitus has said everything is in such flux and flows so fast that it is impossible to apprehend anything at all, you need a description of the process by which you DO apprehend things and make sense of them.

I wonder if prolepsis then might best be understood as Epicurus' answer not just to Plato and Aristotle, who were themselves apparently responding to Heraclitus by postulating that there are true forms or essences (neither of which exist).

Epicurus' prolepsis provides the foundation of an answer to Heraclitus' flux challenge in a natural faculty, just like pleasure and pain, to how we actually understand the things around us without reliance on forms or esences which do not exist, or on preexisting innate ideas from a time before birth. In providing a theory of understand the assembly of knowledge, it is parallel to atomism in providing a theory of physics.

Even as to the title we generally give to Lucretius' poem, how would we know what a "thing" is, or distinguish one "thing" from another, if we did not have a faculty which continuously organizes the raw data from the senses into something intelligible?

As I understand it there are not many reliable quotations from Heraclitus available, but those that do make it clear that this "flux" problem demanded a real-world answer.