4. Terminological Horizons
© 2022 Thea Potter, CC BY-NC 4.0 https://doi.org/10.11647/OBP.0266.04
ὁ ὁρος —in Logic, term of a proposition (whether subject or predicate) […] definition; defined as ἡ τοῦ ἰδίου ἀπόδοσις […] in pl., title of pseudo-Platonic work […] premiss of a syllogism […] Math., term of a ratio or proportion […] pl., terms, conditions.1
Neologisms are the bread and butter of lexicographers, providing novelty in an otherwise backward-looking field of study. One of the main differences between a lexicographer and a philosopher, who are both engaged in etymological studies about the relations between words and things and words and other words, is that the philosopher is in the habit of coming up with new terms. These may be new terms for new concepts or new terms for old concepts or new terms for concepts yet to be conceptualised or concepts resisting conceptualisation. The lexicographer, on the other hand, wields the axe over these terms, choosing which ones will be admitted into the annals of eternity by attributing them with an entry and deciding which ones will fade out of usage and be forgotten until another philosopher attempts a resuscitation of old terms.
Is the difference between a ‘term’ and a ‘word’ how deeply it is embedded in a language? A term still has the packaging, the slick of newness from the shop, while a word is ingrained within the language that it shapes and is shaped by. According to current dictionary entries, the difference between a term and a word is that the former is supposed to represent a concept in a particular field of study while a word is an element of language marked by a space to either side. In Ancient Greek philosophy the term horos stood in for both of these words, as well as the word for ‘concept,’ and in the ancient texts there are no spaces between words.
Aristotle states that whoever is engaged in defining things must not coin new terms (οὐ ποιήσει ὁ ὁριζόμενος) because it would lead to a failure to be understood, for words are common, and it is necessary that they apply to something else as well.2 To coin new terms on the one hand, and to embrace undiscovered forms on the other, oddly enough, presents the same picture. In bringing up the word ‘horos’ from its hiding place within the texts of ancient philosophy or buried in archaeological remains, I am not coining a new term nor suggesting a new philosophical concept to add to an already prohibitively enormous repertoire. And yet if this is, as I suggest, a rule common to the positive unconscious of ancient thought and remaining with us as the material basis for our institutions today, there is no doubt that this word is here being transformed into a conceptual term, burdened with a plethora of meanings, both historical and cultural. In its original setting, however, the horos was certainly not a concept, nor a conceptual tool, though it was a term that could assist conceptualisation if that was necessary.
Terminology, unlike other -logies (biology, archaeology, philology, for example) is not a full science; it is not even in the humanities, not properly anyway, at least not yet. It is the use of technical terms within specific fields of study, such that every field has its own special system of nomenclature, and this is called its terminology. Every university course on the different fields of study ought to begin with the distribution of a dictionary of such terms; it would save students a lot of time. Of course, the different fields of study did not always have different terminologies. Ancient Greek philosophy is an excellent example of a common terminology used to address many fields of knowledge, though the fields were not distinct then, at least not before Aristotle’s commentators came along and classified knowledge into separate books: The Physics, The Metaphysics, The Ethics, Economics, Poetics, Politics, and so forth.
As a science, the study of ‘terminology’ is considered to be a subsection or subcategory of linguistics where it finds its purpose in conformism, the attempt to get people to mean the same thing when they use the same term. ‘Terminography,’ on the other hand, finds its job description as the specialised field looking at the terms of specialised fields and then telling the lexicographer about it, who may or may not include it in the lexicon. A condemnation of an entire science out of hand is definitely imprudent; however, the one thing terminology fails to examine is the term itself. Terminology as a science is chiefly seen where it fails to express a common meaning: in biology seminars, in the stock exchange and in those illiterate manuals for electronic devices. But the truth is that the present use of terminology obscures its distinguished and notorious history.
Terminus was the Roman god of boundaries, and his worship was enshrined within the temple of Jupiter Optimus Maximus on the Capitoline Hill, the centre of ancient Roman religion, and an entire festival took its name from the god, the ‘Terminalia.’ If this is not glorification enough, turn to Aristotle, whose investigations, from the Physics through the Metaphysics (investigations into pretty much everything that is and is not), invariably feature as a guiding thread not only the question of the ‘term,’ horos, but an entire examination into the activity of the term, or, as he terms it horismos, the project of definition.
The horos is situated where definitions or determinations overlap, where words that are always composite (whether we place them in signifying chains or in dictionaries) cannot help but encroach upon another word’s territory. Aristotle calls this particular force that unites word and being the ‘chōriston,’ the ‘divider.’ However, if he listened to his own advice—not to coin new terms—he would perhaps have admitted that the same activity takes place in the horos. The horos simultaneously divides and unites, providing the (common) term and essential being of synonymity, where the crossover or overlap occurs between a word’s description (logos) as well as marking out its (substantial) difference from other words.
The translation of the Greek terms in Aristotle is something that I am never quite satisfied by, and therefore the translations used in the subsequent chapter unfortunately require something of a preface. The translation of Aristotle has become something of a terminological debate, in both senses. To begin with, many terms were mistranslated long ago, chiefly in being filtered through mediaeval Christianity and the dominance of the Latin language.3 Latin and Christian interpretations are largely responsible for slightly warped translations, such as ‘substance’ for ousia, which purposefully remove agency from anything other than a single divine creator. The problem is, however, that these translations have for the most part been canonised, and to alter them risks alienating, or at least confusing, readers. That said, I cannot help but agree with Owens’s explication of the absurdity of translating ousia as ‘substance.’4 However, his assumption that ‘words and concepts merely signify as best they can the truth contained in things,’ should not go unchallenged, specifically given the significance that this study places upon the precedence of the sign or writing.5 Also, his argument that Aristotle’s phrase to ti en einai is not to be understood as the articular infinitive but a novel coinage in which the einai is an infinitive of purpose (‘in order to be’) seems to me an unnecessary complication.
The frustrating fact is that it is not complicated in the original. The past tense of the third singular verb ‘to be’ is, according to Owens, supposed to ascribe timelessness to the verb. This would mean that the ‘is’ is not essentially present, but was and presumably, from the so-called infinitive of purpose, will continue to be. Owens translates to ti en as ‘what-IS-being,’ in his translation of Aristotle’s Metaphysics, Sachs modifies this to ‘what it is for it to be.’ Basically, I am convinced by Sachs’s argument for the translation of ousia as ‘thinghood,’ regardless of whether the word is derived from the feminine participle or the admittedly peculiar formation of an abstract noun from the neuter noun on, as he suggests in his introduction.6 However, I have used neither of these translations, instead using a phrase as immediately close to the original as possible and then always including the Greek or a transliteration of the Greek in parentheses. I do not see any other way around these problems, other than to keep close contact with the original language.
In the following I therefore depart from the English tradition of translating ousia as ‘substance.’ In an effort to remain as close to the Greek language as possible, and in order to hold onto the material of language, that is not just the ‘sense’ or the feeling of a word but its essential nature, the translation used will always be accompanied by a transliteration of the Greek, especially where the wordplay is significant. So, because this chapter is devoted to the concept of definition, the following translations will be observed: ousia is translated as ‘essence’ or ‘being,’ given that it is the feminine abstract participle of the verb ‘to be’; essence is also derived from the Latin participle for the verb to be ‘esse.’ Hypostasis is translated as ‘substance,’ for the simple reason that both words are composed of the same elements in their respective languages: In Greek, the prefix hypo- ‘under’ and stasis from the verb ‘to stand, support’; in Latin, the prefix sub- ‘under’ and stance from the verb ‘to stand, support.’ I believe the similarity is sufficient to support the translation. I recognise that these translations are contrary to traditional usage. But the fact that a convention is established, does not mean that we have to keep doing it. And it has to be said that traditional translations of Aristotle do not make it any easier for someone without a knowledge of Greek to understand what on earth is being said, so I do not believe there is too much to lose. As the following will make clear, definition and determination, that is, what words mean, and how they are explained, are not only sidelines to understanding philosophy; they are, or at least they were for Aristotle, the core of any philosophical investigation.
As to the word ‘substance,’ given this study’s focus upon mattering and meaning it would appear careless not to use the word with an appropriate sense of gravity. According to Owens, ‘substance’ fails to express the direct relation with Being denoted by ousia (ουσία).7 The translation ‘substance’ has filtered down through a history of philosophy that rendered ideas quite foreign to Aristotle’s original setting. Substance denotes changeable things, the things that ‘stand under’ where solidity and extension seem to adhere to the definition; for example, Augustine struggles to attribute substantia to God. In this sense, substance is not being used as what is essential to all beings. But ousia describes the primary instance of being; for Aristotle that essentially means what something is before it is denoted by a word. Does this mean that ousia is a thought experiment? The word ‘essence’ does seem to go in the opposite direction to ‘substance,’ the one denoting the body of a thing, the other the soul, or at least something nonexistent. Ousia is not responsible for such binaries and they are not represented at all in the Greek.
In a sense the closest rendering of the word ousia might be ‘object,’ but only as the word is used by Harman to mean the being of anything, from a crystal to a war. At least here we can see how something’s ousia does not need to relate to either a tangible or a conceptual being, though that does not mean that it does not denote the matter of a thing. Harman suggests that we cannot ‘paraphrase an object, as if it were truly equivalent to a sum total of qualities or effects and nothing more.’8 It cannot be reduced to our knowledge of it, as either a material object or an active one. According to Aristotle, all things depend upon ousia, but ousia is not universal to all things or the same in all things; something’s ousia is peculiar to the thing itself and belongs to nothing else.9 Its ‘beingness’ or its ‘thinghood’ is always primary.
A Question of Definition
To study the terms a science employs is not just to question the given definitions but to question the way a science expresses itself, its language, and hence, the science as such, its ends or aims. The actual practice of terminology is therefore where ethics meets logic, at the intersection between purpose and form in which words are used. Aristotle states that the ‘essence’ of a thing must be sought and defined (ζητεῖν καὶ ὁρίζεσθαι) ‘not without matter’ (μὴ ἄνευ τῆς ὕλης).10 Are words twofold? Can a word be broken down to the matter of the word (sign), and the matter of what the word means (signifier and signified)? Is this what Aristotle means? Definition is one of the main tasks of Aristotelian philosophy because it is the first question asked, the question of a thing’s essence (ἔστι δ᾽ ὅρος μὲν λόγος ὁ τὸ τί ἦν εἶναι σημαίνων), ‘horos is a word that means what a thing is.’11 But this does not mean that philosophy has exclusively to do with matter, because the definition of a thing is also a word (ἐπειδὴ πᾶς ὁρισμὸς λόγος τίς ἐστιν).
Therefore, Aristotle finds his project located exactly in the margins between words and things, where ‘definitions pose questions of similarity and difference’ (καὶ γὰρ περὶ τοὺς ὁρισμούς, πότερον ταὐτὸν ἢ ἕτερον). ‘So’ Aristotle concludes, ‘let us simply call everything definitory (horika) that follows this method of defining (horismous) things’ (τὰ ὑπὸ τὴν αὐτὴν ὄντα μέθοδον τοῖς ὁρισμοῖς).12 In this section from the Topics, the horos appears in various guises (adjectival, nominal, verbal), and it is singly important for coming to an understanding of how to deal with words and the problem of meaning. Take, for example, the following statement from the Metaphysics.
ἀλλὰ μὴν δοκεῖ γε πᾶσι καὶ ἐλέχθη πάλαι ἢ μόνον οὐσίας εἶναι ὅρον ἢ μάλιστα: νῦν δ᾽ οὐδὲ ταύτης. οὐδενὸς ἄρ᾽ ἔσται ὁρισμός: ἢ τρόπον μέν τινα ἔσται τρόπον δέ τινα οὔ.13
But it seems to all, and was said a while ago, that being [ousia] is the only or main definition [horos]; but now it seems not even this is the so. Then there can be no definition of anything; or in a sense there can, and in a sense cannot.
It could also be said that Socrates was as focused upon definition as Aristotle, as he was frequently posed by Plato asking questions about the meaning of words, or abstract concepts (the good, beautiful, justice and so forth). Perhaps where Aristotle’s project of definition differs from Socratic inquiry is the focus Aristotle places upon the matter of a thing, or rather, the coincidence between matter and word. It is not surprising then, to note the different usage of the word horos between Plato and Aristotle. Where in Plato the horos is firmly localised as the boundary-stone founded to maintain the law of a place (topos), for Aristotle the horos is the term that assists in his treatises on predication (topika) to talk about words as distinct from nouns or names (onoma) or logical phrases or arguments (logos). In Plato, it is the verbal form (horizein) that is pretty much exclusively used, while the noun horos is not identified with anything but the material (at least after avid searching I have not been able to find it to refer to anything other than actual boundary-stones in the land as in the Laws). In contrast, in Aristotle, horos is used frequently and in different contexts, and clearly means a ‘term’ or a ‘definition.’
Here we must make ourselves aware of a difference in terms that is not apparent in translation between horos (ὅρος) and horismos (ὁρισμός). Horismos is the noun formed from the aorist stem of the verb horizō, ‘to bound, mark out, define or determine, lay boundary-stones,’ etcetera. To raise the spectre of Heidegger we might say that the latter refers to the project of determination. We can see the difference between these two terms in a significant introductory definition of the definition (horos) in Aristotle’s Topics.
ἔστι δ᾽ ὅρος μὲν λόγος ὁ τὸ τί ἦν εἶναι σημαίνων. ἀποδίδοται δὲ ἢ λόγος ἀντ᾽ ὀνόματος ἢ λόγος ἀντὶ λόγου· δυνατὸν γὰρ καὶ τῶν ὑπὸ λόγου τινὰ σημαινομένων ὁρίσασθαι. ὅσοι δ᾽ ὁπωσοῦν ὀνόματι τὴν ἀπόδοσιν ποιοῦνται, δῆλον ὡς οὐκ ἀποδιδόασιν οὗτοι τὸν τοῦ πράγματος ὁρισμόν, ἐπειδὴ πᾶς ὁρισμὸς λόγος τίς ἐστιν. ὁρικὸν μέντοι καὶ τὸ τοιοῦτον θετέον, οἷον ὅτι καλόν ἐστι τὸ πρέπον. ὁμοίως δὲ καὶ τὸ πότερον ταὐτὸν αἴσθησις καὶ ἐπιστήμη ἢ ἕτερον· καὶ γὰρ περὶ τοὺς ὁρισμούς, πότερον ταὐτὸν ἢ ἕτερον, ἡ πλείστη γίνεται διατριβή. ἁπλῶς δὲ ὁρικὰ πάντα λεγέσθω τὰ ὑπὸ τὴν αὐτὴν ὄντα μέθοδον τοῖς ὁρισμοῖς. ὅτι δὲ πάντα τὰ νῦν ῥηθέντα τοιαῦτ᾽ ἀστί, δῆλον ἐξ αὐτῶν.14
A ‘definition’ [horos] is a phrase signifying a thing’s essence. It is rendered in the form either of a phrase [logos] in lieu of a word [onoma], or of a phrase in lieu of another phrase; for it is sometimes possible to define the meaning of a phrase as well. People whose rendering consists of a word only, try as they may, clearly do not render the definition [horismos] of the thing in question, because a definition is always a phrase of a certain kind [logos tis]. One may, however, use the word ‘definitory’ [horikο] also of a remark such as ‘the ‘becoming’ is ‘beautiful,’ and likewise also of the question, ‘are sensation and knowledge the same or different?,’ for argument about definitions is mostly concerned with questions of sameness and difference. We may simply call ‘definitory’ everything that follows the same method as definitions; and that all the above-mentioned examples are such is clear by example.
What Aristotle is undertaking here is to provide the definition of definition, the boundary of the boundary, the limit of the limit. Is there any way to evade the inevitability of infinite regress?
Let us look closely at this definition. The first thing to note is that the word horos is placed in the foremost position and fails to reappear again. Henceforth, what Aristotle has to do with is not the noun horos but horismos, or the adjective (horiko) or different forms of the verb horizō. After positing horos as the signifying or indicative logos (to which we will return), Aristotle states that it pays its dues or is handed over and given away (apodidotai) as either a logos in place or instead of a name (noun or term) or a logos instead of a logos. Does this mean that the term of definition is given as a case of substitution, standing in for other descriptions where the determined place (horikon theteon) is only given in terms of a suspension of immediate meaning?
According to Agamben, in mediaeval philosophy a ‘term’ was ‘a word that did not signify itself (suppositio materialis) but instead stood for the thing it signified, referring to something (terminus supponit pro re, supposito personalis).’15 Is this what the horos is doing here? Does that mean that definition (horos) mediates signification, while it is itself an insignificant mediation of thought put into language? In a sense it is only qua logos as significant (sēmainōn) that horos can be defined. In defining a term an entire construct of language is required because otherwise, to simply place another word to explain the first word would not be a definition but mere metonymy. And within this construct, definition depends upon a relation between words that is based upon similarity and difference.
δυνάμενοι γὰρ ὅτι ταύτὸν καὶ ὅτι ἕτερον διαλέγεσθαι, τῷ αὐτῷ τρόπῳ καὶ πρὸς τοὺς ὁρισμοὺς ἐπιχειρεῖν εὐπορήσομεν· δείξαντες γὰρ ὅτι οὐ ταὐτὸν ἐστιν ἀνῃρηκότες ἐσόμεθα τὸν ὁρισμόν. οὐ μὴν ἀντιστρέφει γε τὸ νῦν ῥηθέν· οὐ γὰρ ἱκανὸν πρὸς τὸ κατασκευάσαι τὸν ὁρισμὸν τὸ δεῖξαι ταὐτὸν ὄν.16
For if we are able to argue that two things are the same or are different, in the same way we shall be able [euporēsamen] to undertake an argument about the definitions [orismous]: for when we have shown that they are not the same thing we shall have demolished the definition.
The definition is a complex of words embedded within and dependent upon the already fully structured existence of a language. What then can be said to be ‘logical’ about the horismos is the fact that it follows a method that is in essence the same as its name, coming about in terms of same or other (tauton/heteron), of what it is and what it is not but always in the same way. Definitions that do not depend on metonymy alone require the proximity of other words whose significations are similar and different. So, what is in fact going on here is that definition (horismos) is being defined as a grammatical complex within a language, and a definition of this type is ascribed to horos. What is essential to philosophy in this case would be the horismos, which is in a way a logos (logos tis), that helps us to understand the meaning of words and their relations with other words within a language that generates meaning, while the meaning of horos is deferred in the essence of the thing.
ὥστε τὸ τί ἦν εἶναί ἐστιν ὅσων ὁ λόγος ἐστὶν ὁρισμός. ὁρισμὸς δ᾽ ἐστὶν οὐκ ἂν ὄνομα λόγῳ ταὐτὸ σημαίνῃ (πάντες γὰρ ἂν εἶεν οἱ λόγοι ὅροι: ἔσται γὰρ ὄνομα ὁτῳοῦν λόγῳ, ὥστε καὶ ἡ Ἰλιὰς ὁρισμὸς ἔσται) ἀλλ᾽ ἐὰν πρώτου τινὸς ᾖ: τοιαῦτα δ᾽ ἐστὶν ὅσα λέγεται μὴ τῷ ἄλλο κατ᾽ ἄλλου λέγεσθαι.17
So what it is to be is such that the explanation [logos] is a definition [horismos]. It is not definition if the name [onoma] for the explanation signifies the same thing (for then all explanations [logoi] would be definitions [horoi]; for a name could be attributed to an explanation, so that even ‘the Iliad’ could be a definition), but only if it is something primary. These should not be said the one in place of the other.
The definition is not the name but something essential about the being of what is said. Therefore, substituting another name that has a similar meaning or explanation (logos) is not sufficient to provide a definition. According to Aristotle, these words should not be used interchangeably: explanation and homonymy are not the same thing.
Does that mean that horos is the boundary between every word, not as its definition but as the essential difference between words? Is it the meaningful boundary between same and other upon which the subsequent project of definition (horismos) works to bring difference and similarity together?
In the Topics, the ‘signifying word,’ logos sēmainōn, does not merely point to a sign but a method, reverting immediately from the simple horos to the horismos; as if the horos receded into its Aristotelian ‘definition’ as a project of definition, of the signifying word, or the alterity of creating meaning in process. Reading Hegel, Derrida suggests that it is semiopoetics that draws opposites together in more than a point of confrontation, in a resolution. This is something like, in Derrida’s words, ‘the resolution of the sign in the horizon of the non-sign.’ For semiopoetics
is a Mittelpunkt: both a central point on which all the rays of opposites converge, a middle point, a middle in the sense of element, of milieu, and also the medium point, the site where opposites pass one into the other. 18
For Hegel this Mittelpunkt of sign-making is the ‘productive imagination,’ where what is one’s own (das Eigene) and what is found along the way (Gefundensein), the universal and Being, become one.19 But we must not forget through all this that the horos is still localised and material and is not merely a sign. So, what if this site (topos) of definition can only maintain its path (meth-odos) and keep producing more definitions by virtue of already proposing a limit that is also a question of productivity as such?
Aristotle gives us a definition where signifying or meaning cannot emerge from anything but the problem, or more precisely the raising of the question of what was there before, what being was. He said that horos is a phrase that means ‘what it is to be’ to ti ēn einai (ἔστι δ᾽ ὅρος μὲν λόγος ὁ τὸ τί εἶναι σημαίνων). It is not quite what ‘it is’, but rather what ‘it was’ (ἦν), third-person singular imperfect. Though it could also be from the verb ‘to say’ (φημί), and in this case maybe it was ‘what it said it was,’ though this is unlikely. The point is that it is not that clear that it is what we thought it was, and in fact it might have been something else altogether. As Aristotle said before, when it comes to definitions, mostly we rub up against the different and the same (διατριβή).
The horos thus becomes a limit, a terminus ad quem, which proposes the question of what essence meant before it was localised in the horos. And indeed, what was being before it could be defined in language, before it could be put into question by the logos? Any search for essential beginnings, for principles (archai) and for a sure foundation, presumes exactly that something was (τι ἦν) before language and before the question of being. In the tradition of Heidegger, we could say that something began as revealed, only to be concealed and come into question later. However, what is significant about the horos is that, beginning only in division, it never fully began, not as a whole archē. Its principal meaning is always divided. It was nothing but the problem, as such and in itself, of the definition of essence (einai, ‘to be’; ousia, ‘being’) at the same time as indicating the essence of the question itself. It draws up that first line of division that is necessary for us to ask the question of definition, to distinguish between word and essence (the ‘being’ of a thing, esse is the Latin form of the verb to be, einai). But in doing so, horos also resists its own definition because its essence is that point of difference between words, and the similarity to the material, both word and stone.
Before the logos came along and started meaning something, did the horos mean nothing? That is to say, was the horos nothing but the matter of the sign, signifying nothing, meaningless? And is this what matter or substance is, that is, definition without further meaning—brute stone?
For this reason, nothing is discovered by asking, ‘what does horos signify?,’ ‘what does horos mean?’ because, as Derrida explains about the question of the signification of signification, ‘the very question would have brought us to the external border of its closure.’20 And then there we are back on the boundary, immersed in rock assuming it does not matter at all. But of course the border cannot help but matter, even if that is all it does. The question itself, the ‘what means,’ ‘what is’ or even the why of metaphysics is already taking place within the confines, on the basis, that is, on account of a limit that proposes the meaningfulness of definition: horos. Horos refuses the definitive presence of any archē, any original, full presence since it gives definition only to the boundary as taking place as the split, between ousia and logos, that is however based upon the substance (hypostasis, that is in this case also very much stone), the matter that supports meaning, that must already be there in the raising of the question of definition.
In the Pseudo-Platonic work titled Definitions (Ὅροι) the horos, the definition, is thus defined:
Ὅρος λόγος ἐκ διαφορᾶς καὶ γένους συγκείμενος.
Horos is a logos comprised of difference and genus.21
It is both composed of difference and the matter itself that signifies how words differ from one another. The meaning of the word horos, then, is the question of definition as such. It questions its own signification, thus throwing into question its very identification with itself. And, of course, this was the problem from the very beginning, when we realised that we cannot tell the difference between a stone and a horos unless we have already identified it as such, and then the difference exists in us first and foremost, in our division between organic and inorganic nature. And it was also the problem raised by the untranslatability of the horos, not because it does not mean ‘boundary, limit, letters, stone, landmark, term, definition’ and so forth, but because it means the contiguity, and existential contingence, of the different and similar. Its meaning, or signifying (something else, itself) remains on the boundary as what is common to all these terms, and they are definable in reference to what they are not, as much as to what they are. As definition it is the very difference that they have in common, binding them and making them distinct. The point is that it does not cease to be one while it is the other. As Hegel states, ‘What is true of substances is also true of differences; for as synonyms they have both name and definition in common.’22
Aristotle’s Topics raises the problem of the definition of particulars, while in the Metaphysics it is a question of essence (ousia) in logos, it is also a problem of substance; as anyone would realise should an example of the horos come hurtling through the air to land with a thud upon his head.
According to the Aristotelian definition, horos is a word whose meaning can be explicated by using a combination of other words, thus providing a similar meaning through difference. All words, when it comes to defining them, require us to indicate or point towards other words, and it is important to note that in this respect horos is just like any other word. It is just that what becomes apparent in the definition of horos is how the structure of language itself is determined by and dependent on this idea of horos as always indicating separation as well as contiguity, as if there is something alien within itself, as if it houses the collusion between the same and the different within its own definition. Is this because horos signifies the origin of writing, whether it is the stone that is read as the boundary-stone or the inscription or the definition that provides us with the essence of a thing? ‘The sign,’ states Hegel, ‘is some immediate intuition, representing a totally different import from what naturally belongs to it; it is the pyramid into which a foreign soul has been conveyed, and where it is conserved.’23 The sign, and this is its traditional position, comes in between the logos and the word, between the word and its definition. And yet, in the case of the horos the other words are only other words, that is, they can be defined as such because they must always be preceded by the split inherent to horos, hence the regressive definition of definition.
The horos as sign (inscription or raw stone) is the indication of the divisive force, the material intervention between horos and its definition, i.e. horos. It is not what horos signifies that is different or other; what it signifies is horos. Horos signifies what is other than horos, or to put it otherwise, a determined sign, a determinate or definite meaning is other than horos. Horos, ‘definition,’ is identical to itself only by signifying what it is not, that is the indefinite and the indeterminate which always falls to either side, of which it, horos, is the boundary.
The definition never seems to go anywhere without regress, without doubling back on our words. The horos interminably raises questions about meaning and essence, word and substance, by placing itself in an identical/non-identical relation with meaning, the sign, the letter and inscription, the stone as such. It is the materialisation of the problem, marking the aporia at the heart of the structure of language, or the passage without passage to anywhere, only to continue through and on towards further problems. Horos, as Aristotle states, is a matter of substitution, of giving a word in place of a name (logos ant’ onomatos), or another word (or phrase) in place of a word (logos anti logon). That is, definition is necessarily a matter of substitution, as if nothing less than matter itself can step in to mediate the relation between words and their latent substitutability. Horos is peculiar as a name for the operation of replacing or substituting the name or word with something that has the potential of being both same and different. As such, it is the title that puts the authority of logos, the authenticity of the name into question every time and in this case the problem is that of all those indeterminate ‘places’ of logic (ta topika).
The horos demands that whatever is on either side of the sign, meets and joins in a relation of both same and other with the other side. Here the sign could be conceived as something like the Sausurrian bar, separating and joining at once and bringing into distinction what is meant and what is said, like a primeval curse that condemned our thoughts and our speech to be forever out of joint and our words always replacable. This juncture may seem accidental to language, as if the potential exists of actually saying what we meant if only we could find the right words, while in the meantime thought overflows into a mere trickle of language. Consequently we have a sense of alienation from our speech and what we mean or want to say, as if there is a disjuncture between language and meaning, writing and reading. This (dis)juncture is horos, bringing into definition the matter with and of language. Needless to say, language contained the seed of its discontent long before any more arboreal structures were attributed it. Horos was there from the beginning, a stone that was read by us, whether or not it was written, the line of definition between the human and the ‘natural,’ as such its meaning was already assured. But where did this faculty for meaning already invested in the stone come from? In terms of any significant meaning attributed to the stone, the distinction rests with us.
The Parenthetical Horos
To what degree does the horos in Aristotle’s work retain the substantial meaning of being ‘stone’ even while it performs the function of meaning ‘definition’ or ‘determination’? Finley believed that the context of the stone, the actual archaeological finding, changed the word’s meaning so that every use of the horos became locally semantically specific. For example, the horos as boundary of temple lands was distinct from the horos that showed fiscal encumbrance, despite both being stones inscribed with the same word and with potentially no other noticeable differences.
Whenever a Greek referred to a stone of either type, he said simply horos, without any qualifying adjective (or he used the related word horizō), because there could be no confusion between the two in context, just as there was no confusion between the horos as “boundary” and horos as “boundary stone.”24
The horos might have had different meanings, but these were not homonyms. All the different meanings coalesce within the same semantic field, or perhaps more appropriately, on the boundary of the same semantic field. Its reticence to be pinned down or determined by a single meaning derives from the ‘essence,’ the ti esti, of the word itself. This could be why its matter is important, why the materiality of the horos always remains with it: the stone has to be there, keeping things, and us, grounded during the attempts at definition and determination of words and things. If horos is the convergence of sign, signifier and signified, word and meaning of ‘term’ or ‘definition’ as well as the letters inscribed, and without excepting the stone (whether inscribed or not), it cannot help but keep referring to itself as both identification and difference between word and thing, and between definition and essence. When we try to define it, we keep coming upon the same problem: we cannot help but put the term to use before we actually resolve upon its meaning or meanings.
Finley bewails the reduction of the diverse functions of the horos in translation, though acknowledging the difficulty of finding adequate substitutes. He assumes that lurking somewhere behind the horos there is a multiplicity of meanings that not only can but must be separated out in order to be both understood and used. And yet, this failure to adequately distinguish in translation the differences of meaning and use that adhere to the horos does of course reinforce the fact that in Greek these are different non-divisible aspects of the one term. That it remains one word means that if it engenders any effect upon us, it should certainly be that of pure perplexity, arriving as we do at the limit of meaningful definition or determination. And what does the horos signify if not the problem of arriving at the limit of determination or definition?
Perhaps the very difference that is underscored by its Latinate translations (definition, determination) is inherent to the horos—not yet arrived at philosophy’s finale, nor quite deified, as if it represents the tendency to abstract (de-) from ontology to find its resolution in the question of either being or logos, but struggles to bring them together. The Romans resolved the problem by deifying the boundary (between being and language) as the god Terminus. Not only has Terminus lost his divinity in our eyes, but he has been reformed into the central station of our comings and goings, the electric opening to the possibility to further circuits, or the end point, pure and simple.
Assuming, then, that there’s more than mere difference of spelling between these Latinate variations of the horos, could these undertakings lead us somewhere other than back to the horos? To somewhere else, an alibi of sorts, where the intention would presumably be to breach the horos or to define it, to understand the limit or to transcend it? The work of horos is definition. But why ‘work’? Is the desire to define words what motivates philosophy, its determinative ontological impetus? Or is it, more accurately, its ontological impotence? As Hegel states in his preface,
to judge a thing that has substance and solid worth is quite easy, to comprehend it is much harder, and to blend judgement and comprehension in a definitive description is the hardest thing of all.25
How does whosoever it is go about defining this hardest thing? Is the ‘hardest thing,’ das schwerste, the matter with philosophy, the probably phallic preoccupation, and the idée fixe of determining philosophy itself? According to Hegel it is to be found only in philosophy’s actualisation as science. The definition of the ‘hardest thing of all’ (already achieved by Hegel in his preface) is brought to fulfilment and actualised when the philia of philosophy is revoked by philosophy as a science. That is, when the coming night requires that we light the hard lamps of reason and no longer do it for the love of it, but because we know what it is. Is this a problem of desire or volition, as Hegel implies, ‘freed from the material’?26 Does philosophy find satisfaction in wisdom in the absence of love, and its praxis and poiēsis? And yet the determination to follow these desires or the desire to determine is aroused though never satisfied in philosophy, which takes place in the hours of leisure, in the space between production and reproduction. But must that mean that this space is infertile, insubstantial, and the work it engenders is abstract and lacks materiality? What is the difference between, on the one hand, occupation and love, and on the other their products, object and subject? What difference, in effect, is there between substance and logos other than their determinations, that is to say, definition itself?
Here in the earlier pages of Hegel’s preface to the Phenomenology of Spirit, and nowhere else in the work, there is a brief encounter with the horos. Placed in the original text in the Roman alphabet, it is even capitalised in good Germanic form, as if Hegel could not help but retain the letter’s material trace in the inscribed stone even when engaging with the most abstract or conceptual determination. The horos, shielded by parentheses from any reference to its lithic counterpart, is introduced as the object upon which the Romantics concentrate their contemptuous gaze.
Dieses prophetische Reden meint gerade so recht im Mittelpunkt und der Tiefe zu bleiben, blickt verächtlich auf die Bestimmtheit (den Horos) und hält sich absichtlich von dem Begriffe und der Notwendigkeit entfernt, als von der Reflexion, die nur in der Endlichkeit hause.
Still less must this complacency which abjures Science claim that such rapturous haziness is superior to Science. This prophetic talk supposes that it is staying right in the centre and in the depths, looks disdainfully at determinateness (Horos), and deliberately holds aloof from Notion and Necessity as products of that reflection which is at home only in the finite.27
Ironically, if the romantics had gazed upon the horos, lying on its side, overgrown with chicory and chamomile in the shadow of the ravaged Parthenon I am sure they would have been thrilled. A textual confusion in regards to what remains of this ruin infiltrating the text of Hegel is worth noting. In the German text, the horos is parenthetical (den Horos). In the translation by Miller, the Greek word occurs capitalised in Latin script (Horos), while in the translation by Baille it is, oddly enough, transcribed back into the Greek (ὅρος).28 In the German text of the Felix Meiner Verlag edition, it is given in Latin script with the German article. It would appear that the horos is already influencing the translation not of meaning but of the letters themselves, with the ambiguity of transliteration. What is the original: those Greek letters read by Hegel in the text of Aristotle and adopted by Baille but which leave out the capitalised ‘H’ that was read upon the stone? Or is it the term reinscribed in the Hegelian German having passed through a Roman heritage, inadvertently reinventing the archaic ‘H’? Obviously the horos itself problematises this notion of an authentic writing. If this small extract is supposed to direct us toward finitude through determination, the translation once again obscures the clarity of such a path. Taken all together, the texts themselves betray the claim to a determined science through language, providing us with the textual proof of the problem of ‘naming’ (and after all is this said in the name of ‘Spirit’ or ‘Mind,’ nous or anima, or is Geist something else entirely?).
But it does seem like an odd place to reference the horos, especially given its significance within Aristotelian logic. For Hegel, parenthetical ‘determinateness’ (Horos) intervenes in the German text, has an end and aim, and is consistent with philosophy as a science tracing its history from Aristotle. It is the task of logic to provide determinations with their concept, to translate them into concepts, one might almost say, to relocate or remove (abstract) them to the middle point. The horos comes into the text this once and then never resurfaces, and yet what Hegel calls a mittelpunkt remains as something like a place-saver for the horos. As Hegel states in his Science of Logic,
since the real difference belongs to the extremes, this middle term is only the abstract neutrality, the real possibility of those extremes; it is as it were, the theoretical element of the concrete existence of chemical objects, of their process and its result. In the material world water fulfils the function of this medium; in the spiritual world, so far as the analogue of such a relation has a place there, the sign in general, and more precisely language is to be regarded as fulfilling that function. [my emphasis] 29
For Hegel ‘only what is completely determined is at once exoteric, comprehensible, and capable of being learned and appropriated by all.’30 Determination is really what is at issue in the Logic, even though the horos does not appear as such. Determination is in fact the ‘real issue,’ the search for that middle position that remains ever the same that would provide both method and content for the work of logic (or a philosophy that has exhausted the love of wisdom).
[T]he real issue [die Sache selbst] is not exhausted by stating it as an aim, but by carrying it out, nor is the result the actual whole, but rather the result together with the process through which it came about.31
Once we’ve achieved a state of satisfaction, we want to remember how we got there. The question that Hegel entertains and that the Romantics spurn is then how one can arrive at what is definite (horos) from the same place, beginning here at home in the finite? Or must we concede the logic of the Irish joke, that if it is there that we want to be going to, we ought not to be starting from here? Such determinations must, according to Hegel, be freed for use. The bonds that hold them might be a not purely conceptual presence in material life.
In real life, it is then a matter of making use of the thought determinations. From the honor of being contemplated for their own sake, such determinations are debased to the position of serving in the creation and exchange of ideas required for the hustle and bustle of social life. They are in part used as abbreviations, because of their universality. Indeed, what an infinite host of particulars relating to external existence and to action are summed up in a representation, for instance, of battle, war, nation, or of sea and animal, etc.!32
If we return to Aristotle (who is both here at home with us and somewhere else entirely), we see that for him the real issue is the question of defining being, or substance; it is the problem of definition itself. It ‘led those who questioned along the way and compelled them to the search’ (αὐτὸ τὸ πρᾶγμα ὡδοποίησεν αὐτοῖς καὶ συνηνάγκασε ζητεῖν). For Aristotle as for Hegel this is neither ‘real’ nor an ‘issue.’33 If it must be considered in translation, that is as a matter of translation, the only ‘thing’ that Sache has in common with pragma is the ‘same.’ The thing itself (die Sache selbst/αὐτὸ τὸ πρᾶγμα) raises the same problem (aporia) or the problem of the same—τὴν ἐν ὕλης εἴδει λεγομένην, that is what the matter is. Kind of.
Giving one of his favourite examples, of the concave shaped versus the snub nose, Aristotle states that the ‘essence’ (whatever that is), the τί ἐστι of things must be sought and defined (ζητεῖν καὶ ὁρίζεσθαι) in relation to matter, not without matter (μὴ ἄνευ τῆς ὕλης).34 Or, to return to Hegel, it is the limit or difference between the lifeless thing, bare matter or a ‘corpse,’ and the perfect living form. Aristotle and Hegel, then, have something in common. They have a common term, and the same thing propels the hunt and remains as the hunter’s companion. This ‘thing,’ then, must be the same as its definition—it is given and what is given is what continues to need determination (horizesthai). Although this thing seems to come out of nowhere, and then ‘walk alongside’ (sym-bainō), Aristotle (and here he is at one with Hegel) would argue that this is no accident (symbebēkos). The organic unity ‘in which truth exists can only be the scientific system of such truth,’ which for Hegel is determined by the word Gestalt, for Aristotle the symbiosis between morphē and physis.35 Once the determination is formulated and the term emptied of meaning, the search propels the philosopher onto further determinations.
And yet there is still something missing that would provide the substance for this work of bringing to definition, a tool of sorts, but a tool that must do a double duty, just as the arrow is provident of nutrition and harbinger of death, as in Herakleitos’s aphorism ‘the name of the bow is life, its work is death’ (τῶι οὖν τόξωι ὄνομα βίος, ἔργον δὲ θάνατος).36 That is, something whose name concurs with its work or activity. We are looking for something that is properly aphoristic, something that defines itself and is divided off from everything else (apo-horizō) but is not therefore discrete (diōrismenon). We might say the search is for ‘perfect definition.’ Is this why Nietzsche turned to the aphorism as the short, sweet answer to the question of form and method in philosophy?
The task of philosophy is to work upon each term so closely in order to find a definition that corresponds exactly with its substance that in the end the word itself is worn away, leaving nothing but what is left over, an abstraction that necessarily must also be subjected in turn. This is what Derrida calls the general economy of the philosophical text, the re-examination over and again of the same terms that are thereby simultaneously worn away and, in the history of philosophy, acquire too much interest.37 Definitions abound and tend to circle about in the same place. Already we can feel the pull of the agora where certain stones are turned to profit and provide the outlines for denominative evaluations. Given that the Categories is the principal work of determination, we should have a glimpse of the intrinsic part played by the horos in the name itself which is situated quite unexpectedly in the agora (κατηγορίαι, kata- agora) as the theoretical task of drawing up accounts (au logisamenos) of speaking and intercourse (agoreuō).38 In Adorno’s words, ‘nothing escapes the market-place,’ and this holds emphatically in the philosophical work of definition.39
Ὅρος δὲ τοῦ μὲν ἀπὸ διανοίας ἐντελεχείᾳ γιγνομένου ἐκ τοῦ δυνάμει ὄντος, ὅταν βουληθέντος γίγνηται μηθενὸς κωλύοντος τῶν ἐκτός,40
The horos of that which comes to be in actuality by intention out of being in potentiality, comes to be if, when the thing is willed, nothing outside of it prevents this.
For Aristotle, definition in conjunction with the stone, a by-product of a willed becoming, is not actually found in nature. Why? Aside from the fact that the Greeks had no concept of nature, as we do today, it was because matter (hylē) is aoristē, like suffering it rejects such terms of definition. Aristotle says that both matter and suffering (pathē) are indeterminate (aorista).41 Αnd yet do we not give form to matter (form does not reproduce itself: ‘men produce men, bedsteads do not produce bedsteads’)?42 We give expression to suffering because we are all bound up in determination so that our determination to draw up boundaries comes to be read (by us) in the world around us, as our point of resistance against a world where all is in flux.
τὸ δ᾽ ἄπειρον ἢ τὸ ἀδύνατον διελθεῖν τῷ μὴ πεφυκέναι διιέναι, καθάπερ ἡ φωνὴ ἀόρατος, ἢ τὸ διέξοδον ἔχον ἀτελεύτητον, ἢ ὃ μόλις, ἢ ὃ πεφυκὸς ἔχειν μὴ ἔχει διέξοδον ἢ πέρας: ἔτι προσθέσει ἢ ἀφαιρέσει ἢ ἄμφω.43
The infinite [apeiron] is either that which cannot be traversed (just as sound is by nature invisible); or that which admits endless traverse; or scarcely admits of traverse; or, though it would naturally admit of traverse [diexodon] or limit [peras], does not do so. Whether in addition, subtraction or both.
So the horos permits the traversal between what is indeterminable and what is determined by drawing up the boundaries of definition (in us) without establishing an adamant barrier. It marks the place where we get stuck (aporia) and must go on asking (diaporēsai); even infinity comes to its diexodos in a determined refusal to suffer limit and definition and this is where we assume ourselves as subjects of our own experience. As Adorno puts it,
where the thought transcends the bonds it tied in resistance—there is its freedom. Freedom follows the subject’s urge to express itself. The need to lend a voice to suffering is a condition of all truth. For suffering is objectivity that weighs upon the subject; its most subjective experience, its expression, is objectively conveyed.44
The human being experiences movement passively, subjected to its motion, subjected to the necessities of (human) nature, the becoming and corruption of the environment, the rotation of the heavenly bodies and so forth. And yet human beings also experience themselves as separate, beyond this eternal flux but only because we have the potential to draw such distinctions, to infer that the boundaries and limits we experience are natural, already within us as our ‘nature.’ And so, they are written in us as much as they are written in the world around us.
Therefore, that distinction, which is found in the horismos between same and other, suddenly takes place on an entirely different site and scale. It is no longer the assimilation of the other into the same that Levinas diagnosed as the violence of ontology, the autarchy of the I and the betrayal of the ethical relation.45 Definition is, rather, the obligation or the responsibility of recognising a still greater limit before a greater other, an absolute other that is ontologically irreducible to the same, what could be said to be the real limit or horos.46 We could say, then, that here the chief definition of the horos is inescapable, it is the limit that human life is confronted by in the face of the desire for the divinity of the other.
On the Horizon of Temporality
The horizon as a notion and problem for philosophy could have originated in the determinative horos as it appears in Aristotle. Before modern philosophy, horos was already structuring the experience both of language and the actual world for the Ancient Greeks, especially in the setting of the Athenian market and Athenian imperialist expansion, where the problem of boundaries (or their transgression) became at once politically and philosophically charged. It is at the very least interesting to consider that for ancient philosophy it was the horos, boundary and stone, that was in some sense the determining element for the linguistic experience of the world, while in modern philosophy a derivative of the same word, expanded to the edge of our vision, plays ‘the all-determining role’ in the theory of horizon-intentionality.47 To put it simply, you cannot take the on (the essence or ‘being’) out of the horizon, even when defining it (horos).
In Hegel’s History of Philosophy, ‘determinations’ abound and are clearly associated with the principal task of defining everything from Aristotle’s Organon to his Metaphysics.
The Categories (κατηγορίαι), of which the first work treats, are the universal determinations, that which is predicated of existent things (κατηγορεῖται): as well that which we call conceptions of the understanding, as the simple realities of things. This may be called an ontology, as pertaining to metaphysics; hence these determinations also appear in Aristotle’s Metaphysics.48
But which ‘determination’ proliferates into ontology? Do the horos and the horismos perform differently in the dénouement from categorical determination to the ontological undertaking? And what does it signify that we cannot translate the horos or the horismos in their pure Latinate form (fines, terminus), but always as definite, determined? That is, without the de- of the absolute or the divinity (deus), that awe prefixed to the terror (δέος) that resounds in destruction? Certainly, these translations keep us at a distance from the boundary, but they also seem to push us off (de-) the path of pure ontology, as if the Roman god Terminus had taken upon himself the responsibility for maintaining a certain awed distance before the horos, binding our definitions and determinations with an interminable slip toward a deontological stance, especially when it comes to approaching linguistic boundaries. And yet there is something evocative about the horismos. Like an echo of a call to action (socialism, communism, nationalism, fascism) the horismos prompts movement, a kind of impetus found in saying regardless of form and content. Heidegger picks up on the project of definition.
The question asks about being. What does being mean? Formally, the answer is: Being means this and that. The question seeks an answer which determines something which is somehow already given in the very questioning. The question is what is called a question of definition.49
According to Heidegger the ‘being-in-the-world of the human being is determined in its ground through its speaking.’50 In his seminar on the Basic Concepts of Aristotelian Philosophy, Heidegger cannot resist the temptation to define this ground as his terminologically inherited square metre of Greek soil.
We want to understand what definition means by questioning back to what it meant for the Greeks, for Aristotle. Ὁρισμός: “circumscription,” “delimitation.” Ὁρισμός: λόγος οὐσίας. What is meant by λόγος, by οὐσία, by λόγος οὐσίας?51
Are these questions bound to birth some kind of substantial resolution? The solution that is found in Heidegger is the return to the Greek, the return to the Aristotelian problem of determination: ‘what is this λόγος? It is the fundamental determination of the being of the human being as such.’52 Thus Heidegger also comes to the conclusion that each word relates interminably to the other. For Heidegger it is the word logos that bears the brunt of human determinism, rather than the horos or the horismos. And yet, he can project a limit, his project of determination. The horismos is then different from the logos insofar as it is also ‘the title for Aristotelian fundamental research—or, more precisely, for Greek fundamental research as such—the basic concept per se, the term.’53
So here we are back at the beginning, to what should be a clear determination of the horos, both title and work. As it was for Aristotle, so for Heidegger, the (re)search presents itself as a knot or bond that we must follow; ‘What is pre-given is a bond that is indeterminate as to content but determinate as to the way of actualization.’54 And yet, this term is not as it appears. Heidegger is not talking about the horos; he is talking about the project of definition giving ground to philosophy itself: ‘If it is genuine, a concretely determined problematic of philosophical research will run in its own directedness to the end, an end philosophy as such must have made fast for itself.’55 The way is, of course, the diaporêsai made concrete in the posing of the question of definition (as the question of being). ‘Ὁρισμός is a λόγος, a “speaking” about something, an addressing of the matter “itself in that which it is,” καθ᾽ αὐτό.’56 For Heidegger, this project of definition becomes the basic horizon of metaphysics. Belittling its nominative ancestor, horos, the horizon takes shape from the present participle of the verb horizo (ὁρίζω) and henceforth takes prominence as that which provides the outline of our world, our horizon. And with the horizon, the Greek horismos ceases to feature for Heidegger.
Heidegger never wrote a chapter on the horizon as such, almost as if he took it and its connection to the Aristotelian notion of ‘determining’ (horismos) for granted (it might be the original ‘gift’ -es gibt- upon which all determinations were thereafter based). It is important to remember that the Greeks needed to clarify the horizon by articulating the circle in addition to the determining participle, ὁ τοῦ ὁρίζοντος κύκλος, ὁ ὁρίζων κύκλος.57 In a way the addition of the circle serves to expand the horos exponentially, but also to limit it, insofar as it forecloses its claim to the substantial, the lithic horos. Unlike so many of his concepts, Heidegger’s horizon is not an immediate adoption of the Greek term; in using the word he is making explicit reference to a more widely used notion of the horizon.
Mediaeval European thought used the idea of the horizon as indicative of the boundary between the spiritual and human spheres, and although the horizon was a notion used in modern interpretations as an epistemological boundary opening onto human knowledge, as an idea it nonetheless remained largely a metaphor.58 It is significant that Husserl, while retaining the idea of the horizon in its broadest sense as ‘what consciousness co-intends in such a way that what is co-intended determines the sense of appearing objectivities,’ ceased to use it as a metaphor for human experience.59 For Husserl, the horizon is a perceptual notion of an object’s twofold horizon, inner and outer. The inner horizon is constituted of the potential perception of an object from all angles; an object’s outer horizon is extendible indefinitely through the object’s relation to other objects, and these others’ relation to others and so on. Here the indefinite extendability of the horizon is glimpsed in the object itself—as phenomenon—hence the horizon is defined as the outer extreme of our relation with the phenomenal world and simultaneously defines our co-existence with objects; ‘horizon is a structure of determination that predelineates the purview within which each and every phenomenon appears.’60 The horizon is ‘intuitive emptiness’ given and inseparable from intuitive fullness; it structures and is the structure of our experience in the world.
Where the horizon is normally experienced as a line, demarcated according to the objects which are within it—that within the perceptual field from here to there, or more generally still, an extendable limit, something to transcend— for the later Heidegger the horizon remains a limit, but a limit whose significance lies on the other side. The ‘horizon, the sphere of the constant that surrounds man, is not a wall shutting man off; the horizon is transparent; it points beyond to what is not made fast, to what becomes and can become, to the possible.’61 Upon the appearance of objects, and according to representational, calculative thinking, the being of the horizon is experienced only as a plane, this side that faces us of the surrounding ‘openness.’ Gegnet, a term awkwardly but perhaps necessarily translated as ‘that-which-regions,’ is ‘an abiding expanse which, gathering all, opens itself, so that in it openness is halted and held, letting everything merge in its own resting.’62 Heidegger seeks to shift this experience of the horizon into a relation, a suspension of ‘calculative thinking,’ through ‘meditative thinking’ (less thinking more thanking). This suspension is also a matter of space, or temporality, because meditative thinking maintains the ‘openness’ that lets the horizon be ‘releasement to that-which-regions’ (Gelassenheit zur Gegnet).63 By having recourse to Heidegger’s earlier texts, a different concept of the horizon can be found—one that is not subordinated, as it is in the Conversation, to the more fundamental concept of Gegnet.
Horizons proliferate in Being and Time. On the first page, we are presented with the schema of the horizon as the possibility of ontological interpretation, in the form of a simile. ‘Our provisional aim is the Interpretation of Time as the possible horizon for any understanding whatsoever of Being.’64 In the final sentence on the last page we are again presented with the question of the horizon as something like a metaphor for time, ‘Does time manifest itself as the horizon of Being?’ What links temporality with the horizon, ‘has something like a horizon’?65 The answer can be addressed by his deference to the Greek ‘determination’ witnessed in his peculiar attempts to translate early Greek philosophy in its most material aspect, which is not to say a ‘literal translation.’ Heidegger’s project of determination was undertaken under the aegis of an attempt to get to the ‘root’ of matters, the question of determination as such.
Hence, the similitude between temporality and horizon is represented in the grammatical form, so appropriately named, of the infinitive ὁρίζειν, ‘that radical “determining” that occurs at the interface between language and being.’66 The possibility, or more precisely, the potentiality, of determining provides the whereupon (woraufhin), out of where (von wo aus), the whence, dependent upon which the question of being is to be posed.67 ‘The prefiguration of horizons is but an alternative way of describing a foreshadowed structure of the hermeneutic situation.’68 This location is the horizon; a horizonal-schema delineated in Heidegger’s ecstatic translation of German into three basic Latinate tenses, a final task which remained incomplete. Hence the whence of temporality, the vor von, originates not only in the horizon as limit but in the determination (horismos) as such, where logos is the first horizon of being.
By means of horismos translated as ‘circumscription,’ ‘delimitation,’ Heidegger determined to seek in Aristotle the ‘indigenous character’ of the concept: ‘We will have to seek out the indigenous character of conceptuality […] We will have to consult the way the Greek conceptuality and its indigenous character look.’69 Determination provides the ground of ontology, appropriating the Aristotelian task of definition as the first step—and the onward march—of the diaporêsai. However, there is a significant slip here toward horismos, which in Aristotle is the pre-determined project of definition. It is here that Heidegger finds his worauf, his scene between the rising and setting (concealment-unconcealment) sun (of being). Within this horiz-on (the defined being) he discovers a land of ontological neutrality, rooting his philosophy to the ground, giving his inquiry a foundation.
The coming to be of terms is expressed in an economic formula and relates to what Heidegger calls the ‘customary meaning’ of ousia, ‘property, possession and goods, household, estate.’70
A determinate concrete context is discovered, seen anew for the first time—the word is missing, the word is coined together with the matter. An expression that was not at hand may immediately become a term, which later dissipates by entering into the general currency and ordinariness of speaking.71
This is the basis of Heidegger’s economy where the ground for other concepts is prefigured in determination as the logos of ousia.
The multifariousness of meaning of οὐσία is therefore not treated here for its own sake, but rather always only in the direction of the proper appropriation of matter, i.e., the understanding of what is addressed in ὁρισμός as λόγος.72
That determination is autochthonous, and that it can be discovered by returning to the place of its ‘conception’ betrays an appropriative desire. That said, the horos does have an intimate relation with the Greek soil, and in itself it is never far away from the economic and the legal bounds of possession. The law of the letter can be said to be exactly this estrangement or alienation written into the experience of time, denoting an elsewhere, an other origin, the fact of natality as the first disconnection with place, that is the prohibition against the ‘return to the ground of definition.’73 But when it comes to horos, the ground is always obfuscated by the stone. We have already seen that whatever was described in the horos was already inscribed in the lost figuration of the letter’s migration, describing the horos just as the rising and setting sun outlines the horizon.
On the one hand, then, with Hegel, we have the preference for the Notion or Concept as determination taking shape; on the other, with Heidegger we have definition as return to the ‘soil’ of determination. In both cases, horismos is appropriated into the work of thinking about being projected (into past and future). Can we overlook the appropriation of determination as the common ground of the human being?
Material Interventions
It is the task of theoretical first philosophy to determine such limits, to find the definition of being as such (ousia). It is a project of differentiation between the immediate identification of being with its name. The conjunction as in the statement of the subject ‘Being as in being,’ ὄντος ᾗ ὄν, or ὂν ᾗ ὄν (absurdly translated into Latin as ‘being qua being’) best describes this project since it is being that is presumed in the question (what is being?), but the method is speculative or theoretical, περὶ χωριστὰ καὶ ἀκίνητα, ‘concerning whatever is separate and immobile.’74 Metaphysics first names ‘being’ and then identifies it with itself through what it is not but resembles, in this case, a letter (eta, ᾗ)—a letter that breaks into identification (between being to either side) and interrupts this otherwise pure reduplication with similarity and difference.
This is none other than the name and work begun in the Categories as the project of definition and completed in the Metaphysics, in the ‘determination’ of substance as ‘separate’ (χωριστόν). Aristotle frequently uses the word onoma where we would expect horos, ‘term’—the name of being and not being.75 If anything can both be and not be—and this is the problem posed by potentiality—what causes them to be the one and not the other? Or, what is the difference, actually, between being and not being, εἶναι καὶ μὴ εἶναι? Aesthetically speaking, one could say it is the μὴ, the ‘not.’ Is it not a peculiarity that negation or deprivation expressed in the logos does not take something away from a positive but on the contrary requires a supplement, α-, μὴ, not, etc.? Privation, being a privation of substance is dependent upon a precedent definition that it can modify (this should put us in mind of the impotentiality inherent in potentiality): ‘privation is negation from a determined (or defined) genus,’ the absence of horos.76 But there is also the conjunction ‘and,’ in which case the question always takes a twofold form, ‘both and not.’ The name for being presents an aporia, while the conjunctions and disjunctions of language move across the plurality of aporiai.
That Aristotle presents metaphysics as the problem of the categories between language and thought is the subject of Derrida’s critical article on Benveniste’s thesis that the categories ‘present different aspects, depending on whether they are categories of thought or language.’77 This is an alleged opposition, which is, of course, the very subject of Aristotle’s metaphysics since the question of being, τὸ τί ἦν εἶναι, is discussed in correspondence with the statement that ‘being is said many ways,’ πολλαχῶς λέγεται τὸ ὄν. But is the chōriston, the ‘separate,’ not a (product of) logos? Is it a name given to substance (ousia) that distinguishes it from everything else? So that οὐθὲν γὰρ τῶν ἄλλων χωριστόν ἐστι παρὰ τὴν οὐσίαν, ‘none of the other [categories] are separate except substance,’ yet everything must be said to have substance to be a subject.78 To find the substance of a thing is supposed to complete the task Derrida calls ‘usury,’ of wearing away and abstracting terms.79 In this case the ‘separate’ (chōriston) is at once the ‘substance of substance’ and the activity of philosophy. Put otherwise, it is natural (κατὰ φύσιν) that things have substance, but it is only the form that is ‘by nature’ (φύσει). Nature is form (μορφὴ), while its kind of form (εἶδος) is not separate from it except in language (οὐ χωριστὸν ὂν ἀλλ᾽ ἢ κατὰ τὸν λόγον).80 Substance as such comprises an aporia (ἔχει δὲ τὸ συμβαῖνον ἀπορίαν) that has to do entirely with ‘definition.’ The taking shape of nature as substance thus brings into definition the aporia of their separation and drives first philosophy as/to its determination. It is therefore the task of philosophy to explain the apparent accident of this aporia.
If there is only one ‘definition’ of substance (ousia), substance could not be said to be the determination of anything but itself (ἢ μόνον οὐσίας εἶναι ὅρον ἢ μάλιστα). 81 Hence the definition, horos, marks the twofold task, the ‘problem’ (aporia) of definition and its formulation or expression in logos which leads to further problems (diaporiai): definition as such both can and cannot be, yes and no. The reason for this ambiguity is that substance is said to be of two kinds, the synolon (the composition of word or description and matter) and the logos. But if there is a logos of a substance, it would be separate to the substance, that is, it would be separate only as logos. While if the description, logos, and the form (eidos) were separate from the substance, this would be an idea (the so-called ‘third man’ theory).
διὸ δεῖ, τῶν πρὸς ὅρον ὅταν τις ὁρίζηταί τι τῶν καθ᾽ ἕκαστον, μὴ ἀγνοεῖν ὅτι ἀεὶ ἀναιρεῖν ἔστιν· οὐ γὰρ ἐνδέχεται ὁρίσασθαι. οὐδὲ δὴ ἰδέαν οὐδεμίαν ἔστιν ὁρίσασθαι. τῶν γὰρ καθ᾽ ἕκαστον ἡ ἰδέα, ὡς φασί, καὶ χωριστή· ἀναγκαῖον δὲ ἐξ ὀνομάτων εἶναι τὸν λόγον, ὄνομα δ᾽ οὐ ποιήσει ὁ ὁριζόμενος (ἄγνωστον γὰρ ἔσται, τὰ δὲ κείμενα κοινὰ πᾶσιν· ἀνάγκη ἄρα ὑπάρχειν καὶ ἄλλῳ ταῦτα· οἷον εἴ τις σὲ ὁρίσαιτο, ζῷον ἐρεῖ ἰσχνὸν ἢ λευκὸν ἢ ἕτερόν τι ὃ καὶ ἄλλῳ ὑπάρξει.
Therefore in cases relating to definition [horizētai], when we are trying to define any individual, we must not fail to realise that our definition may always be upset; because it is impossible to define (horizesthai) these things. Nor, indeed, can any Idea be defined; for the Idea is an individual, as they say, and separable; and the formula must consist of words, and the man who is defining must not coin a word, because it would not be comprehensible. But the words which are in use are common to all the things which they denote; and so they must necessarily apply to something else as well. E.g., if a man were to define you, he would say that you are an animal which is lean or white or has some other attribute, which will apply to something else as well.82
The problem with determining any definition is that one is compelled to use other words, and therefore, on the one hand, the definition always crosses over into other definitions as being reliant on these other words, along with all the baggage that comes with them. And on the other hand, the problem of determination simply allows one to continue into other problems of determination (and this is what is expressed by the verb diapōresai). Aristotle, who cannot accept the Platonic Ideas, solves this aporia by referring to incomposite substance as being ‘in potentiality,’ while it is only substance composite with logos that is separate absolutely.
ἔστι δ᾽ οὐσία τὸ ὑποκείμενον, ἄλλως μὲν ἡ ὕλη (ὕλην δὲ λέγω ἣ μὴ τόδε τι οὖσα ἐνεργείᾳ δυνάμει ἐστὶ τόδε τι), ἄλλως δ᾽ ὁ λόγος καὶ ἡ μορφή, ὃ τόδε τι ὂν τῷ λόγῳ χωριστόν ἐστιν: τρίτον δὲ τὸ ἐκ τούτων, οὗ γένεσις μόνου καὶ φθορά ἐστι, καὶ χωριστὸν ἁπλῶς: τῶν γὰρ κατὰ τὸν λόγον οὐσιῶν αἱ μὲν αἱ δ᾽ οὔ. 83
And the substrate is substance; in one sense matter (by matter I mean that which is not in actuality, but is potentially, an individual thing); and in another the word and shape (which is an individual thing and is separate in speech); and thirdly there is the combination of the two, which alone admits of generation and decay, and is separate absolutely—for of substances according to their word some are separate and some are not.
This definition for substance as chōriston, ‘separate,’ can be understood first and foremost in relation to contraries. As he says, substance has no contrary (ὑπάρχει δὲ ταῖς οὐσίαις καὶ τὸ μηδὲν αὐταῖς ἐναντίον εἶναι) that would provide it with something from which to differ.84 But this is not what is particular (ἴδιον τῆς οὐσίας) to substance (quantity also has no contrary). What is particular to substance is that ‘while remaining numerically one and the same, it is capable of admitting contrary qualities,’ (ἡ δὲ γε οὐσία ἓν καὶ ταὐτὸν ἀριθμῷ ὂν δεκτικὸν τῶν ἐναντίων ἐστίν).85 It is its sameness that distinguishes and separates it, such that by changing itself, it can receive contraries, assimilating what is other to the same. But does this similarity, or identification with itself, mean that substance is one and the same (ἓν καὶ ταὐτὸν)?
It cannot be, and this is exactly why Aristotle calls or names substance the chōriston. Because the work of defining it is without substance, ‘always away beyond it’ (chōris, ‘without’ -on, ‘being’). Or is it because substance is indeterminable? By making division (chōrizein) possible, is it the prospect of definition itself? Does the chōriston give substance to the potential conjunction of logos and substance?
According to Levinas, chōriston ‘is the definition of freedom: to maintain oneself against the other, despite every relation with the other to ensure the autarchy of the I.’86 In the name ‘chōriston’ the relation between the contraries is resolved into a singular and separate reduction to the same. Perhaps the chōriston was a terminological ‘solution’ or release (euporia or lysis) to the interminable confrontation between Socratic contraries. That is, it is the essential step that would allow us, not in spite of our dialectic, but by means of it, to arrive at a logical conclusion that could resemble the thing itself (truth). This is the real issue, the reduction of the thing itself not to a common factor, but to the same thing from Aristotle to Hegel. Regardless of how each individual manipulates it, the thing itself remains the same, separate, the immaterial pledge of freedom, a ‘place’ (topos) of definition that prefigures the answer to the question posed in the absolute identification of Cartesian doubt between the question and the questioner. As Levinas states, ‘Western philosophy has most often been an ontology: a reduction of the other to the same by interposition of a middle and neutral term that ensures the comprehension of being.’87 Here philosophy might just succeed as a science but only because the erotic play of two has been replaced by the autonomous hegemony of the one.
And the truth of this self-identification is achieved in mathematics, where the indiscretion of auto-philo-sophy (love of one’s own wisdom, or the knowledge of the same) is isolated in situ, freed from the bonds of pre-determined heteronomy. Pure mathematics, says Aristotle, deals with all things alike (ἡ δὲ καθόλου πασῶν κοινή). This might be because mathematics as a field of thought is extracted from the material. According to Aristotle it is because the objects of its study, numbers, have no common term or boundary (horos).
τῶν μὲν γὰρ οῦ ἀριθμοῦ μορίων οὐδείς ἐστι κοινὸς ὅρος, πρὸς ὃν συνάπτει τὰ μόρια αὐτοῦ, οἷον τὰ πέντε εἰ ἔστι τῶν δέκα μόριον, πρὸς οὐδένα κοινὸν ὅρον σύναπτει τὰ πέντε καὶ τὰ πέντε, ἀλλὰ διώρισται.88
In the case of the parts of a number, there is no common boundary [koinos horos] at which they join. For example: two fives make ten, but the two fives have no common boundary, but are separate; the parts three and seven also do not join at any boundary.
It is no coincidence that the proponents of mathematics are modern-day Platonists; something has to be out there as the other but that comes to us, touches us, it might even dawn upon us as a ‘movement’ or e-vent, coming from somewhere else. In mathematics the joint is there, but its community is lacking. Numbers can get it on with one another, break up, get back together, get others involved, but throughout all this, they remain distinct and unchanged. There is a promiscuity here that is, however, not social; numbers are not communal but atavistic. The truth of mathematics then can be ‘defined’ as freedom exactly because it shares no ‘common boundary’ (koinos horos), is without limit and substance, and is not nor has any necessary relation except to itself. There is indeed a violence here, as Levinas was aware, but it is the violence that masquerades as truth flying its banner of freedom for the same as it intervenes in the relations between others.
It is exactly because there is the ‘common term’ (koinos horos) in language that our attempts at definition are always ‘upset’ (anairein).89 The task of definition has the potential of always going beyond its object, hence the verb anairein, which literally means ‘to raise, lift,’ a word that we could translate into the Hegelian aufheben. Every definition consists of something that is also applicable to something else, a certain common boundary or shared term, and can always be used in formulating its opposite; most evidently, we can always define something by what it is not or by giving its contrary.
1 LS: 1255–1256.
2 Ar.Met.1040a6–15.
3 See Christophe Erismann, ‘Aristotele Latinus: The Reception of Aristotle in the Latin World’ in Falcon (2016) 439ff.
4 Owens (1978) 138–152; 180.
5 Ibid. 138.
6 Sachs (1999) xxxvii.
7 Owens (1978) 144.
8 Harman (2018) 257.
9 Ar. Met.1038b10.
10 Ar.Met.1026a1–5.
11 Ar.Top.101b39.
12 Ibid.
13 Ar.Met.1039a20.
14 Ar.Top.101b39.
15 Agamben (1999) 207.
16 Ar.Top.101b39;139a24.
17 Ar.Met.1030a5.
18 Derrida (1982) 80.
19 Ibid.
20 Derrida (1982) 81.
21 Pl.Def.414d10 in Plato (1972).
22 Hegel (1894) 217
23 Hegel (1971) 213. Cf. Derrida (1982) 83.
24 Finley (1952) 5.
25 Hegel (1977) 3. Cf. Hegel (2006) 5.
26 Hegel (1969) 13–14.
27 Hegel (2006) 9; Hegel (1977) 6.
28 Hegel (2003) 6; Hegel (1977) 6.
29 Hegel (1969) 729.
30 Derrida (1982) 80.
31 Hegel (1977) 2.
32 Hegel (1969) 14–15.
33 Ar.Met.984a19.
34 Ar.Met.1026a1–5.
35 Hegel (1977) 5.
36 Herakleitos, fr. 48 (DK 73).
37 ‘White Mythology’ in Derrida (1982) 207ff.
38 Hegel (1894) 212.
39 Adorno (2007) 4.
40 Ar.Met.1049a5.
41 Ar.Met.1049b1
42 Ar.Phys.193a-c.
43 Ar.Met.1066a35.
44 Adorno (2007) 17–18.
45 Levinas (2000) 180f.
46 Bashier (2004) 87.
47 Geniusas (2012) 11.
48 Hegel (1894) 212.
49 Heidegger (1985) 143.
50 Heidegger (2009) 13–15.
51 Ibid. 15.
52 Ibid. 14.
53 Heidegger (2009) 231.
54 Heidegger (2001) 17.
55 Ibid. 12.
56 Heidegger (2009) 14.
57 Ar.Meteor.363a27; Cael.297b34.
58 Geniusas (2012) 3–5.
59 Ibid. 7.
60 Ibid.
61 Inwood (1999) 99–100.
62 Heidegger (1966) 66.
63 Ibid. 74.
64 Heidegger (1962) 364.
65 Ibid. 365.
66 Kisiel (1995) 446.
67 Heidegger (1962) 365, Kisiel (1995) 449–450.
68 Kisiel (1995) 447.
69 Heidegger (2009) 13–15.
70 Ibid. 233.
71 Ibid. 18.
72 Ibid. 232.
73 Ibid. 13.
74 Ar.Met.1026a15; 1026a30.
75 Ar.Met.1006a30, Ar.Met.1050b.
76 Ar.Met.1011a20.
77 ‘The Supplement of Copula: Philosophy before Linguistics’ in Derrida (1982) 175–205.
78 Ar.Phys.185a31; Met.1025b28.
79 Derrida (1982) 209.
80 Ar.Phys.193b5.
81 Ar.Met.1039a14;21.
82 Ar.Met.1040a6–15.
83 Ar.Met.1042a30.
84 Ar.Cat.3b25.
85 Ar.Cat.4a10-b20.
86 Levinas (1969) 47.
87 Ibid. 43.
88 Ar.Cat.4b20.
89 Ar.Met.1040a6.