Heraclitus

Life and Works

Heraclitus, the weeping philosopher, was an aristocrat who lived in Ephesus perhaps circa 540-480 B.C., but little else is known about his life. According to one legend he inherited the title of king of the Ionians, and he rejected it. Known for his misanthropy and riddling manner of writing, [i] he wrote a book on the universe, politics and theology and dedicated it in the temple of Artemis. Some ancients believed that he wrote in an obscure manner in order that only educated aristocrats would be able to access his meaning,[ii] or to make his sayings similar to oracular utterances. One can see clearly why such an assemblage of declarations would be dedicated in an ancient temple; the gods gave advice as well as augury and many valuables were placed in temples. His book seems to have taken the form of a collection of aphorisms, in ancient Greek gnomai, which may have been gathered together by his followers or arranged by Heraclitus himself. It was divided into three parts – cosmology, politics and theology – though these topics are intertwined in Heraclitus. His seemingly theological [iii] musings on nature and its relationship to human beings survives in fragments taken from ancient quotes.

First Principles

Arguably a monist, Heraclitus claimed that there is an inherent structure to things, which must be understood through logos, a term ordinarily signifying “reason” or “word.”

It is a wise thing for those hearing not me but the logos to agree that all things are one. ( Fr. 50, Hippolytus Ref. IX, 9 I).

That logos exists forever men always come to be uncomprehending, both prior to hearing and having heard it. That all things have come about according to this logos they are like those with no experience, attempting to understand such words and deeds as I relate while I distinguish each thing according to its nature and declare how it exists; but as much as escapes the notice of some men what they do while awake just so much they forget while sleeping. (DK 1B, Fr. 1, Sextus adv. math. VII, 132).

Logos for Heraclitus signifies a specific kind of composition, not mere logic or even reasoning, but logic is a significant part of it. Logos seems to be for Heraclitus a process-structure that can be found in the universe, but it is also the order found in the reasoning mind. [iv] Human beings are able to access the order of the universe through reason. In other words, the universe is ordered in some way and reason allows us to apprehend the structure that is at the same time a process. What that order is Heraclitus partially explains, admitting that things are revealed to human beings even as they are concealed. Reason orders by assessing perception after the senses take in sights, sounds and understanding:

However-so-much things of which there is sight, hearing and learning I hold in high regard. (Fr. 55, Hippolytus Ref. IX 9, 5).

Yet, Heraclitus seems to have thought that the eyes and ears are deceptive; he understood that perception is necessary in order to assess the inherent order of things.

  • Bad witnesses are eyes and ears for human beings who possess minds foreign to understanding. (Fr. 107, Sextus adv. math. VII, 126).

The eyes and the ears of human beings are unable to interpret correctly what the senses tell them and so they are foreign to knowledge, which is directed by logos. According to Heraclitus, not many human beings use reason appropriately because instead of attempting to find the commonalities of the universe they employ logos in a private manner:

It is necessary to follow the general; while there exists a general logos the many live as if having a private thought. (Fr. 2, Sextus adv. math. VII, 133).

One is able to discern immediately a sense of what moderns may call objectivity in the notion that what is general in the universe is most important, while what is private – or perhaps subjective – Heraclitus disdained. [v] Again, logos is that which finds the inherent order of things and so reason finds universals, but perception deceives. Because perception deceives it needs to be ordered by the mind, or logos.

Causation and Cosmology

Such an inherent order was not straightforward, but a riddle; some scholars see Heraclitus' claim as a unity of opposites:

  • Sea is the most pure and most soiled water; for fish it is potable and preserving, for humans non-potable and destructive. (Fr. 61, Hippolytus Ref. IX, 10, 5).
  • A path up-down is one and the same. (Fr. 60, Hippolytus Ref. IX, 10, 4).
  • Sickness makes health sweet and good, as hunger does for satiety and toil for rest. (Fr. 111, Stobaeus Anth. III, I, 177).
  • The same thing exists within, the living and dead, the wakeful and sleeping, the young and old. For these things here having changed are those there and those there having changed again are here these. (Fr. 88, [Plutarch] Cons. ad Apoll. 10, 106E).

One understands through perception only some incomplete part of material reality. Once one uses reason, one sees an interaction between or unity of opposites in common happenstance, which seems to be partly what Heraclitus means when he asks men to comprehend the general and not the private. Again, private things may here be linked to subjective interpretation, or to opinion. Heraclitus himself employs literary devices and hides a significant part of his meaning, but he seems to have been aware of the need to be more objective or rational in making assessments. Kirk and Raven [vi] point out four important ways that Heraclitus demonstrates the supposed “unity of opposites.” First, similar things produce opposing effects on differing classes of objects, as in the sea's affect on men and fish. Second, differing facets of the same thing elicit opposing descriptions, as in the differing directions being the same road.[vii] Third, things are recognizable as what they are only by means of comparison to their opposites, as in weariness making rest good. Fourth, some opposites are connected because they come after or are followed by each other, as in old age following youth; there is a unity in their opposition (see below). These are aspects of material reality that to Heraclitus seemed to be concrete, physical things and processes, again as in the water's affect on men and fish and weariness making rest more prominent. One is struck immediately by the relative relationship of the opposites. That is, the supposed continuum of opposites seems to be the same as the relative relationship of one opposing thing or happenstance to another. The south road and the north road being the same are not merely perspectives. They are absolutes that function in relation to one another, producing an apparent contradiction that encompasses the same thing. The dynamic is relative because of the relationship between things and contextualization, but Heraclitus describes it as an interaction between or a unity of opposites rather than a relative relation. Here he gives us a reference point and seems to comprehend and employ some element of relativism in his description of one thing being its own contradiction. The reference point is needed in order to determine if the road is the south road or the north road, and while these opposites seem to be absolute there is no way to determine the absolute answer to whether the road is north or south. There is no real, fundamental and eternal answer, other than the road north is the south road and vice versa. That is Heraclitus's point. Much of the unity of opposites in his thinking seems to stem from an insight into relativity, and so some part of relativity theory is inherent in his thought, but note also that he has observed first what seems to be a relative relationship. He then employs his reason, logos, in order to determine what is the deeper, or one may say higher, truth: the relationship of opposites that comprises a single happenstance. Within his way of comprehending things is a scientific framework: observation and later reasoning in order to bring out the inherent truth to the observations. Neither thought nor perception themselves suffice, and perception is taken to be decidedly inferior to thought combined with perception. Heraclitus may have taken much more concrete examples and used them to show the structure of their dynamic, rather than an abstraction made solid. If he did as much, it is possible that his thought possesses an empirical dimension worthy of mention. Yet, there are many kinds of opposites Heraclitus describes; a common way of understanding his insights comes from unity and plurality, a common topic among ancient thinkers:

A taking-together is whole and not-whole, a being-brought-together and separated, accorded-discorded. Out of all things is one and from one are all things. (Fr. 10, [Aristotle] de mundo 5, 396b20).

We do not know enough about Heraclitus's writing to make a definitive judgment of his meaning, and his literary manner along with his enigmatic expression inspire very various interpretations, but such a hermeneutic may have been Heraclitus' intention, since he asserts that things reveal and conceal themselves at once. It is important to remember that for Heraclitus the implicit structure beneath all rest and activity is that of opposition or perhaps tension. All things interact in an opposing way, even things that seem to have no opposition or even conflict at all, like the lyre:

They do not apprehend how a thing differing with itself agrees with itself; a stretched-back harmony [viii] exists, like the bow and the lyre. (Fr. 51, Hippolytus Ref. IC, 9, I).

The tension of the strings makes the lyre possible as a lyre. No music emerges, if the strings and tension are not present. Such a structure of conflict is needed for the instrument to be itself:

  • The thing setting itself against [itself] brings together and from different things the finest arrangement comes, [and all things have come to be through strife = B 80]. (Fr. 8 Eth. Nic. Q 2. 1155b4).
  • It is necessary to know that war is common to all and justice is strife. And all things have come to be through strife, it being necessary. (DK B80).

In this manner for Heraclitus conflict and strife compose the fundamental arena in which all things transpire:

War is the father of all things and of all things king, and on the one hand he put forth the gods and on the other human beings; some he made slaves and others free. (Fr. 53, Hippolytus Ref. IX, 9, 4).

What lies hidden is where the tension exists:

  • The growth of things is accustomed to conceal itself. (Fr. 123, Themistius Or. 5, p. 69).
  • An agreement unapparent is stronger than an apparent one. (Fr. 54 Hippolytus Ref. IX, 9, 5).

All things are for Heraclitus in constant change. His famous river image [ix] gives the metaphor:

  • Upon those stepping into the same rivers different things and different waters do run. (Fr. B12, Arius Didymus ap. Eusebium P.E. XV, 20).
  • It scatters and collects, stands together and departs; it is nearby and away. (Fr. 91, Plutarch de E 18, 392B).

Perhaps he means that all things change constantly, as in even seemingly unchanging things are changing in imperceptible ways:

Somewhere Heraclitus says that all things make room for another and nothing remains still, and likening things existing to a rush of a river he says that twice into the same river you would not enter. (Plato Cratylus 402A).

  • And some say not that some of existing things move themselves and others do not, but all things move themselves and always do they do so, but that this escapes our senses. (Aristotle Phys. Q3, 253b9).[x]
  • Changing, it rests. (Fr. 84A, Plotinus, Enn, IV 8, 1 [n. B 60]).

What is interesting for us is the constancy of the interchange of opposites and change in general. The constant wrangling of the universe Heraclitus expresses in more than one metaphor, but his primary element of the universe seems to be fire.

All things are an exchange for fire and fire for all things – just as useful things for gold and gold for useful things. (Fr. 90, Plutarch de E 8 p. 388E).

Fire is commonly thought to be Heraclitus' first principle, but in his work fire is also at times a metaphor for change of various kinds; nonetheless it is also for Heraclitus a physical first element. So, fire is both a first principle and a metaphor for Heraclitus. Anaximander thought that there was vengeance between forces in the universe and some scholars believe that Heraclitus's sense of a constant give and take is a development of that thought, yet both thinkers seem to have thought change to be a part of a constant in the sense that there is an exchange of dominance without loss of activity or inherent ability. Thus, all powers of the universe are exchanging their ability to perform specific tasks, somewhat similar to our notion of the preservation of energy. Heraclitus' idea that the universe always has been and always will be, coupled with his assertions that opposites are at variance with one another and that they exchange forces, recall the first two laws of thermodynamics:

This order of the universe, the same for quite everything, neither some god nor some man made, but it always was and is and will be fire ever-living, flame-fixed in measures and squelched in measures. (Fr. 30 Clem. Strom. IV 105 [II 396, 10] [Plutarch d. anim. 5 p. 1014 A]).

The first law of thermodynamics is the law of conservation of energy. It states that all energy of an individual system is constant. Energy is not destroyed, but transformed from one kind of energy to another. Change in the internal energy of a system equals the heat supplied to that system minus the work done by that system on its surroundings. It is noteworthy that the first law of thermodynamics centers around heat and heat exchange. Heraclitus' notion of a closed system of constant change through fire, the entire universe, is similar in that the system always will be the same and yet constantly alters through the exchange of its fundamental process or element, fire. It itself is a closed system, and the change that physical objects undergo is that of heat, associated with fire, which can be interpreted as energy. The second law of thermodynamics states that all the entropy of an isolated system never diminishes because isolated systems alter into a thermodynamic equilibrium, the greatest entropy. Here is an equality similar to that of Heraclitus' notion. Fire for him is both a metaphor and an element; it is a constant change that alters constantly. In his universe the equilibrium is that of change itself, like the river metaphor. It is the running of the river that makes it constant. So, the very act of change is the remaining the same, a kind of equilibrium already balanced by the tension needed in order for something to be what it is. [xi] Heraclitus's universe, however, constantly changes and continues in the same manner. His universe would not suffer a heat death, so his way of thinking merely suggests these first two laws, and incompletely.

Argumentation

It is important to note a fundamental criticism of Heraclitus before we proceed to analyze a part of his argument.[xii] In logic there is a conception known as the principle of non-contradiction. It states that something cannot be true and not true in the same manner at the same time. [xiii] One immediately sees how scholars and thinkers may believe that Heraclitus is unaware of this logical principle, and perhaps he lacked understanding of it. Still, what he asserts is some ontology of the universe that seems to go beyond logical categorization. His unity of opposites may be a semi-rational way of delving into an inner working of the universe that itself is important to comprehend and yet beyond the conventions of human logic. Logic does not answer all questions, as the universe does not lend itself to mere human reason. It follows that thinking beyond reason benefits those attempting to comprehend the universe. In this sense, Heraclitus is more of a metaphysician than a scientist, but his status does not force him into the shape of a mere empirical observer. It seems that some part of his reasoning is as follows.

  • All subjective comprehensions are common apprehensions of things.
  • All perceptions of things are subjective comprehensions.
  • All perceptions of things are common apprehensions of things.

One can see a piece of his reasoning here in that perceptions, or private thoughts, are common thoughts at the same time. There is an objective aspect of an observation that may be used to comprehend a universal law. Modern physics does not, of course, claim that scientific law is universal, but only probable. Yet, the notion that an observation may prove to be a reliable general expectation is inherent in the notion that the subjective, private thought is also common. Reason for Heraclitus is able to make the distinction, and logos takes these private thoughts and makes them common. In other words, laws of nature come from seemingly subjective observations. Heraclitus argues thus for fit or unfit witnesses to truth:

  • All things misapprehended if taken privately are possible unfit witnesses of underlying truth.
  • All common apprehensions of things are things misapprehended if taken privately.
  • All common apprehensions of things are possible unfit witnesses of underlying truth.

The above argument is a warning that the common apprehensions can become unreliable, if logos is not properly applied. So, we must be careful what we do with our subjective assessments. If we find that they apply in at least a semi-regular manner, we may be justified in saying that they apply in most cases, or at least that they can be relied upon as probable expressions of truth. What Heraclitus seems to be saying is that observations made ought to be rigorously structured through reasoning. And here is one aspect of scientific reasoning. Much more paradoxical and revealing about Heraclitus' view of the structure of things is his argument that shows how his opposites operate:

  • All paths up are paths down.
  • All paths down are paths up.
  • All paths down are paths down.

One need not change the first two premises in order to come to another conclusion: All paths up are paths up. Still, here is the other configuration.

  • All paths down are paths up.
  • All paths up are paths down.
  • All paths up are paths up.

These two arguments seem to be a redundancy until one recognizes that the paths up and down, when these arguments are taken together, are the very same path that differs from itself. Their being the very same path is a spurious contradiction; it is a contradiction that does not contradict, if one may be inspired by Heraclitus's manner of expression. This contradiction is the implicit kind of order about which Heraclitus talks; the paths up are the paths up and the paths down are the paths down. One cannot say definitively which is the actual path, up or down, because they are the same, and that they are also radically different is one aspect of opposites that is part of a relative comprehension of what they are. If one begins with the reference point of paths down, then all paths down are paths up, and if one begins with the reference point of paths up, then all paths up are paths down. Recall the comment about the sea being unhealthy to men in some sense and healthy for fish. The aspects that make the sea both healthy and unhealthy are the same, and the very thing that elicits opposing description is the thing that has a different affect on differing things. What Heraclitus notices about these relationships is not the differences alone, but the similarities that lead to and sometimes themselves are the differences. Again, there is for him an absolute in each aspect of these things that leads to a shifting relationship between the different aspects that are the same. The path up becomes the path down and the unhealthy sea becomes the healthy one, yet not by changing into anything else but rather by changing into itself. Inherent in them is a constancy that is regular; it is also the result of a never-ending tension, which can be thought of as energy. It seems, then, that Heraclitus incorporated some aspects of what we call relativity and thermodynamic change into his insight about the apparent contradictions that compose things. His arguments are not those of conventional logic and they seem to be redundancies, but they reveal something about the nature of objects and processes; they are observations that have been reviewed and turned about by reason in order to find a more fundamental, general meaning. In this sense Heraclitus' thought is inductive; he proceeds from observations to general conclusions. He assumes that specific aspects of his observations are always true, and that is his most prominent flaw, yet he seems to be aware that the senses fool those who seek general truths and he attempts to eliminate perceptual illusion through reason, or logos. His arguments have an enigmatic soundness to them in that they have good form and they talk about things that actually exist in the world, yet they seem redundant or even trivial until one sees the depth to them. Heraclitus was no mathematician, and so no formula was used in order to discover insights about material reality. The significance of math in the ancient world really begins with the Pythagoreans. Heraclitus may have believed that fire was actually the material first element and principle of the universe, but it is advisable to take his fire as “fire.” Thus, fire for Heraclitus was a metaphor as well as an element. And here, of course, we may find some legitimate criticism of his cosmology. Naturally, fire is not an element at all, but a chemical process. Yet, if one takes fire as a metaphor, then Heraclitus' view applies still to our 21st century world. It is in part relativism, as we have seen. Heraclitus pointed out the strangeness and paradox of relative relationships between things. He claims that the universe is concealed and it seems as if he says the concealing is at the same time a revealing. His writing conceals and reveals in the same way, it seems, like his universe. And a part of his thought is consistent with commonly accepted scientific thought.

  • [i] For an insightful method on how to interpret Heraclitus's cryptic aphorisms, see Reames.
  • [ii] Diogenes Laertius IX, 5.
  • [iii] Herbert Granger correctly points out that “the theology of the early Greek philosophers goes hand-in-hand with their physics, since they had inherited a conception of divinity and nature that intertwines the two, and thus the study of the one topic brings along the other.” 163-4. For more, see Granger,
  • [iv] For a sense of logos in Heraclitus as objective reason and representative of universal law, see Hülsz. Hülsz believes that logos is representative of a measure of objective reality – itself a kind of proportion. Daniel Graham (2013) writes of logos as an expression of subjectivity and its implications, which is part and parcel to logos as measure of a private interpretation of a common universe. Emlyn-Jones claims that Heraclitus prefers images in place of logical explanations, and so logos may be interpreted as a kind of semi-metaphor. Wilcox points out that the Greeks made a direct connection between sight and knowing that compelled them to trust in perception too much. Heraclitus's logos seems to be a reaction and warning to that paradigm. Minar gives a review of logos and claims it signifies the proportionality, harmony and rhythm of the Pythagoreans. Thus, logos is variously interpreted, as Heraclitus seems to have intended.
  • [v] Ancient Greeks generally disdained the politically private in favor of the politically public, but here that inherent prejudice seems to take on an epistemological tone. The division between a more objective assessment and more subjective assessment seems obvious, but Heraclitus may have meant something other than objectivity entirely or he may have had a nascent awareness of objective reality. Also linked is the notion of opinion for ancient Greeks in general and Plato in particular. Opinions were unstable, unreliable private assessments that had no place in the comprehension of an ordered universe that had as its foundation universal elements or some kind of static basis.
  • [vi] The PreSocratic Philosophers, 190.
  • [vii] We must here be careful because in some ways the same thing elicits not merely different descriptions or characteristics, but the same thing actually is those different aspects. Opposites and their coincidence are part of Heraclitus' implicit structure of things and such structure is the whole object, not merely different aspects.
  • [viii] For a discussion on the unity of opposites as harmony, see Dilcher, Kahn. McIntosh-Snyder seems to think that unity comes from agreement, not so much tension, but the agreement may come only through the tension. Rabinowitz and Matson contend that Heraclitus expresses a “reality of pattern or order” and that is his “hidden attunement”. For Moravcsik claims that “to remain the same living thing requires constant change, and systematic replacement of parts, in order to remain the same entity” and he states that “Heraclitus...is challenging us to accept a radically new conception of reality in which the dynamic underlies even what on the surface looks like static.” 559. Moravcsik also believes Heraclitus to be a precursor to Plato. It is easy to see how Heraclitus sees a kind of motive attunement in things (and so he is not Aristotelian but Aristotle is Heraclitean), but that it is an underlying order like Plato's eidos seems suspect if only because Heraclitus suggests his conclusions; he does not develop his theory formally.
  • [ix] There are other so-called “river fragments”. B49: Into the same rivers we step and do not step, we are and are not. B91: (a) Into the same rive it is not possible to step twice. (b) It scatters things and again gathers them...and approaches and recedes. A6 (Plato, Cratylus 402a8-10): Heraclitus says, I think, that all things pass and nothing remains, and comparing things that exist to the running of a river, he claims that you cannot step twice into the same river.
  • [x] Aristotle also comments on static constancy through change at Politics 1276a34-39 and On Generation and Corruption 33 6b28-33.
  • [xi] Heisenberg claims that “modern physics is extremely near to the doctrine of Heraclitus. If we replace “fire” by the word “energy” we can almost repeat his statements word for word from our modern point of view. Energy is in fact that from which all elementary particles, all atoms,...are made; and energy is that which moves. ...Energy is a substance,.... Energy can be changed into motion, into heat, into tension. Energy may be called the fundamental cause for change in the world.” Haarhoff quotes Heisenberg further that “a little later he speaks of the transmutation into matter. Fragment 22 of Heracleitos reads: 'All things are exchanged for fire [i.e. energy] and fire for all things.' This idea of change and exchange, reminding us of the phenomena of radioactivity, is part of modern science. In the lecture referred to Heisenberg says: 'Energy is merely the force which keeps everything in perpetual motion; the “fire” of Heraclitus, the fundamental substance of which it consists.” 128-9. Daniel Graham states that “if measures or portions of the world are alternately being kindled and being quenched, the world is not fire in the sense of having the properties of fire. What happens of course is that the world is constantly changing, and in that sense it is firelike. But Heraclitus calls the world fire, as if to identify the nature of the world with its leading component; and in B31a he talks of the turnings of fire, as though it were fundamental in a way the other stuffs in the series are not.” 145-6. Graham continues by saying that “in summary, the evidence we have seen so far allows us to view Heraclitus as construing the transition from one substance to another in the series of basic substances as instances of generation. On this view there is no continuing element or subtratum, but a change of identity in which one substance dies as another is born. The relationship between the two is not a strict identity but an equivalence of value in which a given quantity of the first substance corresponds to a different, but proportionate, quantity of the second. As a quantity of the first substance turns into the second, a proportionate quantity of the second turns into the first. On the other hand, B30 and B31a give a pride of place to fire, and seem to assert that it remains when all else changes. Is there indeed an underlying reality that is preserved through all changes? Heraclitus's analysis of elemental changes tells us that there is not. Fire is fundamental just by being symbolic of the constant change that the elements undergo.” Graham further states that “the basic substances of the world are constantly undergoing reciprocal transformation in a lawlike way: i. Each portion of a given basic substance that turns into another substance is replaced by an equivalent portion form another basic substance which turns into the first substance, ii. Hence the total amount of each basic substance in the world remains constant. We have the beginnings of a law of conservation, not precisely of mass or of matter, but of material proportions. 167-8. Karl Popper articulates it a bit differently but with a similar understanding. He claims that “in reality a material thing is like a flame; for a flame seems to be a material thing, but it is not: it is a process; it is in flux; matter passes through it; it is like a river. Thus all the apparently more or less stable things are really in flux; and some of them – those which indeed appear stable – are in invisible flux.” 387 G.S. Kirk articulates the same kind of concept when he defends the unity of opposites theory. He states that “the unity depends not only on [opposites] alteration one into the other, but also on the quantitative regularity of this alteration. If the total amount of old age in the world begins greatly to exceed the total amount of youth, then the succession will eventually fail. If the total amount of heat and dryness I summer begins to out-weigh the total amount of cold and wetness in winter, or vice versa, first the crops will fail and eventually the earth will be overcome by one of those catastrophes of fire or flood. If the balance of processes is destroyed then the underlying unity of the cosmos fails, and this, for Heraclitus, was unthinkable. And this balance depends on metron.” 37 Finally, Vlastos adds that “for Anaaximander's equilibrium of elements he (Heraclitus) substitutes equilibrium of processes of change.” 359 For more see Haarhoff, Graham, Popper, Kirk, Moravcsik, and Vlastos (1955).
  • [xii] According to Daniel Graham there are five doctrines that form the ancient tradition of Heraclitus interpretation: (1) Fire is the origin and ruler, material cause, of the universe, (2) The universe periodically is consumed and then reborn, (3) All is in flux, (4) Heraclitus's opposites are identical and (5) Heraclitus violates the law of non-contradiction. Modern interpretation assaults all of these interpretations. For arguments against (2), (4) and (5), see Burnet. For arguments against all five, see Reinhardt, Kirk and Marcovich. For arguments for flux theory, see Vlastos, Popper, Mondolfo, Guthrie, Jones, Stokes and Barn es. Graham claims that Kahn, Mackenzie and Wiggins attempt “to break out of the limits of previous interpretations. Moravcsic looks at the history of interpretation. Kahn talks of identity preserved through alteration (168). Graham has the most comprehensive and thought-provoking interpretation, in the humble opinion of this text.
  • [xiii] Aristotle criticizes Heraclitus for this reason in Metaphysics IV, 1005b 17-20 and Metaphysics A6, 1015b 36. Plato discusses corollaries related to this issue at Theatetus 152 c-e.
  • © 2018 Kirk Shellko All rights reserved.

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