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PHILOSOPHICAL
ὁρισμός (ὁ)

ΟΡΙΣΜΟΣ

LEXARITHMOS 690

The horismos (definition), a pivotal concept in Greek philosophy, is not merely a description but the demarcation of a thing's essence. Evolving from the physical 'boundaries' (ὅροι) of land, the word came to signify the intellectual delimitation of concepts, the precise 'rendering' of what something is. Its lexarithmos (690) suggests a balance and completeness in understanding.

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Definition

According to the Liddell-Scott-Jones Lexicon, ὁρισμός (from the verb ὁρίζω) originally means 'a marking out of boundaries, a definition of limits,' primarily in a geographical or legal context. This primary sense of 'limit' or 'restriction' is fundamental to understanding its philosophical evolution. The word denotes the act of setting an end, a boundary, separating something from its surroundings.

In philosophy, particularly from the time of Socrates and Plato, ὁρισμός acquired the technical meaning of 'the rendering of the essence of a thing,' a 'definitive description' or 'explanation.' The search for definitions was central to the Socratic method, aiming to comprehend universal concepts and avoid the confusion and relativism of the Sophists. Plato, in his dialogues, often strives to arrive at the definition of concepts such as justice, virtue, or knowledge.

Aristotle further systematized the concept of ὁρισμός, making it a cornerstone of logic and scientific knowledge. For Aristotle, a definition is a statement that declares the essence of a thing, composed of its genus and specific difference (genus et differentia specifica). It is the revelation of 'what it is' (τὸ τί ἐστι) of a thing, indispensable for demonstration and scientific understanding. Thus, ὁρισμός transformed from a simple demarcation into a tool for achieving true knowledge.

Etymology

horismos ← horizō ← horos (from the Indo-European root *ser- meaning 'row, line')
The word 'horismos' derives from the verb 'horizō,' which in turn comes from the noun 'horos.' The original root *ser- denotes the concept of a row, line, or boundary. This etymological journey highlights the transition from the material sense of a physical boundary (e.g., a landmark, border) to the abstract sense of a conceptual boundary, i.e., the determination and description of a thing's essence. This evolution is characteristic of how the Greek language developed philosophical concepts from everyday words.

The cognate words of 'horismos' reveal the variety of meanings the root 'hor-' can take. The verb 'horizō' is the direct source and means 'to set boundaries, to define, to decide.' The noun 'horos' is the original root, meaning 'boundary, border, landmark,' but also 'definition' in its philosophical use. The adjective 'horistikos' describes something that is definitive or related to definition, while 'aoristos' denotes the lack of boundary or definition, the indefinite. Other words like 'aphorizō' (to set off by boundaries, separate) and 'diorizō' (to distinguish, define precisely) extend the semantic field of the root to acts of separation and precise determination.

Main Meanings

  1. Demarcation, setting of boundaries — The original and literal meaning, referring to the act of establishing physical or legal limits, e.g., for a field or a region.
  2. Boundary, landmark — The limit itself or the marker indicating it, often used interchangeably with 'horos'.
  3. Philosophical definition, definitive description — The technical meaning in classical philosophy, the rendering of a thing's essence, its 'ti esti' (what it is). A central concept in Plato and Aristotle.
  4. Decision, determination, ordinance — The act of deciding or determining something, often in the sense of an official resolution or decree.
  5. Distinction, separation — The action of distinguishing or separating one thing from another, by setting clear limits between them.
  6. Limitation, restrictive condition — Something that restricts or places limits on a situation or an action.

Word Family

hor- (root of horos, meaning 'boundary, limit')

The root 'hor-' is fundamental to understanding the concept of boundary, demarcation, and, by extension, definition. Starting from the simple idea of a physical landmark or border (horos), this root evolved to describe the act of determining, distinguishing, and conceptually circumscribing. Each member of the word family highlights a different aspect of this basic meaning: from the action of delimiting to the quality of being defined or undefined, and from the boundary itself to the agent of definition. Its semantic evolution mirrors the development of Greek thought from the concrete to the abstract.

ὅρος ὁ · noun · lex. 440
The original word of the root, meaning 'boundary, border, landmark.' In classical philosophy, it also acquires the meaning of 'definition,' as the intellectual limit that determines the essence of a thing. (Plato, Phaedo 96a).
ὁρίζω verb · lex. 987
The verb from which 'horismos' is derived. It means 'to set boundaries, to define, to determine, to decide.' It is the action of delimitation, whether physical or conceptual. (Thucydides, Histories 1.13.4).
ὁριστής ὁ · noun · lex. 888
One who defines, who sets boundaries, or who provides definitions. A 'horistēs' is one who has the authority or ability to set limits or formulate precise definitions. (Plato, Republic 534b).
ὁριστικός adjective · lex. 980
That which pertains to definition, which is definitive, conclusive, or capable of defining. Often used in logical and grammatical contexts to denote precision and conclusiveness. (Aristotle, On Interpretation 17a).
ἀόριστος adjective · lex. 951
That which has no limits, which is undefined, vague, indeterminate. It is the negation of 'horismos,' indicating a lack of clarity or determination. (Plato, Philebus 24e).
ἀφορίζω verb · lex. 1488
Means 'to set off by boundaries, to separate, to isolate, to define clearly.' It emphasizes the act of setting limits to distinguish something from something else. (Luke 6:22, in the NT for excommunication).
διορίζω verb · lex. 1001
Means 'to distinguish, to define precisely, to determine clearly.' It reinforces the concept of accurate delimitation and distinction, often in a detailed or official manner. (Plato, Laws 768c).

Philosophical Journey

The concept of definition evolved from a practical need for demarcation into a fundamental tool of philosophical thought.

PRE-CLASSICAL ERA
Homer, Hesiod
The root 'horos' appears primarily with the meaning of a physical boundary, a landmark separating properties or regions. The abstract concept of a philosophical definition is not yet present.
5TH CENTURY BCE
Sophists, Socrates
With the rise of the Sophists and the questioning of objective knowledge, Socrates begins the search for stable definitions of ethical concepts (virtue, justice), laying the groundwork for the philosophical use of the term.
4TH CENTURY BCE
Plato
Plato develops the Socratic method, using dialogue to arrive at precise definitions of the Forms. Definition is the means to access true knowledge and the essence of things, as seen in dialogues like the 'Sophist' and 'Statesman'.
4TH CENTURY BCE
Aristotle
Aristotle systematizes definition as a logical tool. In his 'Analytics' and 'Topics,' he defines definition as a statement declaring the essence of a thing, composed of genus and specific difference, making it essential for scientific demonstration.
HELLENISTIC PERIOD
Stoics, Epicureans
The philosophical schools of the Hellenistic period continue to use definition as a core element of their logic and ethics. The Stoics, in particular, emphasize the precision of their concepts and definitions.
KOINE GREEK / NEW TESTAMENT
Biblical Usage
In the New Testament, the term 'horismos' is rare, but the verb 'horizō' is used with the meaning of 'to determine, decide, appoint,' especially in a theological context, e.g., for the determination of Christ as the Son of God (Rom. 1:4).

In Ancient Texts

Three characteristic passages highlighting the significance of definition in ancient Greek thought:

«ἀλλ’ ἴσως οὐδὲν ἄλλο ἢ ὁρισμὸς ἦν τὸ ζητούμενον.»
But perhaps nothing else than definition was what was sought.
Plato, Sophist 251a
«ὁρισμὸς γὰρ οὐσίας ἐστὶν ὁ δηλῶν τὸ τί ἦν εἶναι.»
For definition is a statement of essence that reveals what it was to be.
Aristotle, Topics Z 141a26
«τοῦ ὁρισμοῦ δ’ ἔργον ἐστὶ τὸ τὴν οὐσίαν δηλοῦν.»
The function of definition is to make clear the essence.
Aristotle, Metaphysics Z 1031a12

Lexarithmic Analysis

The lexarithmos of the word ΟΡΙΣΜΟΣ is 690, from the sum of its letter values:

Ο = 70
Omicron
Ρ = 100
Rho
Ι = 10
Iota
Σ = 200
Sigma
Μ = 40
Mu
Ο = 70
Omicron
Σ = 200
Sigma
= 690
Total
70 + 100 + 10 + 200 + 40 + 70 + 200 = 690

690 decomposes into 600 (hundreds) + 90 (tens) + 0 (units).

The 18 Methods

Applying the 18 traditional lexarithmic methods to the word ΟΡΙΣΜΟΣ:

MethodResultMeaning
Isopsephy690Base lexarithmos
Decade Numerology66+9+0 = 15 → 1+5 = 6 — Hexad, the number of harmony, balance, and completeness, reflecting the pursuit of precise knowledge through definition.
Letter Count77 letters — Heptad, the number of perfection, wisdom, and completion, symbolizing the full understanding offered by a good definition.
Cumulative0/90/600Units 0 · Tens 90 · Hundreds 600
Odd/EvenEvenFeminine force
Left/Right HandRightDivine (≥100)
QuotientComparative method
NotarikonΟ-Ρ-Ι-Σ-Μ-Ο-ΣOrthos Rhetorikos Ischyros Saphes Monadikos Ousiastikos Skopos (interpretive: Right, Rhetorical, Strong, Clear, Unique, Essential, Purpose)
Grammatical Groups3V · 4C · 0S3 vowels (o, i, o), 4 consonants (r, s, m, s), 0 semivowels.
PalindromesNo
OnomancyComparative
Sphere of DemocritusDivination with lunar day
Zodiacal IsopsephyMars ♂ / Libra ♎690 mod 7 = 4 · 690 mod 12 = 6

Isopsephic Words (690)

Words from the Liddell-Scott-Jones Lexicon with the same lexarithmos (690), but different roots, highlighting the numerical complexity of the Greek language:

ἀστραπή
The 'astrapē' (lightning, flash) represents an instantaneous, fleeting brilliance, in contrast to 'horismos' which seeks stable and lasting understanding. Their numerical identity might suggest the speed with which an idea can 'illuminate' understanding, like a definition.
κατάλληλος
The adjective 'katallēlos' (suitable, appropriate) denotes the quality of fitting something, just as a definition must perfectly fit its object. Their isopsephy may emphasize the necessity of precision and appropriateness in definition.
μυθοποιία
The 'mythopoiia' (myth-making) stands in contrast to the precision of definition. While definition seeks truth and essence, myth-making crafts narratives. Their numerical connection might underscore the distance between imagination and logical exactitude.
σκόπιμος
The term 'skopimos' (done with purpose, expedient) is linked to intention and goal. A definition is always purposeful, aiming to clarify and determine. Their isopsephy may highlight the teleological nature of the search for definition.
τόνος
The 'tonos' (tension, emphasis, musical note) can refer to the precision and emphasis required by a definition. Just as a tone defines timbre, so too does a definition define essence. Their numerical relationship may suggest the need for clarity and accuracy in expression.
ἀποδείκνυμι
The verb 'apodeiknymi' (to show forth, demonstrate) is closely related to the function of definition. Definition is often the first step in proving or revealing the truth of a thing. Their isopsephy underscores the demonstrative character and cognitive value of definition.

The LSJ lexicon contains a total of 70 words with lexarithmos 690. For the full catalog and AI semantic filtering, see the interactive tool.

Sources & Bibliography

  • Liddell, H. G., Scott, R., Jones, H. S.A Greek-English Lexicon, with a revised supplement. Oxford: Clarendon Press, 1996.
  • PlatoSophist, Republic, Philebus. Loeb Classical Library editions.
  • AristotleTopics, Posterior Analytics, Metaphysics. Loeb Classical Library editions.
  • Jaeger, WernerPaideia: The Ideals of Greek Culture. Oxford University Press, 1945.
  • Barnes, JonathanAristotle: A Very Short Introduction. Oxford University Press, 2000.
  • Guthrie, W. K. C.A History of Greek Philosophy, Vol. 3: The Fifth-Century Enlightenment. Cambridge University Press, 1969.
  • Bauer, Walter, Arndt, William F., Gingrich, F. Wilbur, Danker, Frederick W.A Greek-English Lexicon of the New Testament and Other Early Christian Literature. University of Chicago Press, 2000.
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