ΠΕΡΙΤΤΟΣ
Perittos, a word of dual philosophical and mathematical significance in ancient Greece. From the Pythagorean distinction of numbers into 'even' and 'odd', where the odd was associated with the masculine and the perfect, to the Aristotelian concept of 'superfluous' or 'excessive' that deviates from the mean. Its lexarithmos (1065) reflects the complexity of the notion of transcendence and distinctiveness.
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According to the Liddell-Scott-Jones Lexicon, περιττός (adjective) primarily means 'that which is over, superfluous, redundant', and by extension 'excessive, useless, futile'. The word carries an interesting dual meaning: it can refer to something that is merely 'additional' or 'excessive', but also to something that is 'extraordinary', 'distinguished', or 'superior'.
In mathematics, particularly in Pythagorean philosophy, an odd number (ἀριθμὸς περιττός) is a number not exactly divisible by two, in contrast to an even number (ἄρτιος). The Pythagoreans attributed special properties to odd numbers, associating them with the masculine, the finite, the perfect, and the good, while even numbers were linked to the feminine, the infinite, and the bad. This distinction had profound cosmological and ethical implications.
Beyond its numerical usage, περιττός is used to describe anything that exceeds measure or necessity. In Aristotelian ethics, the 'peritton' (excess) is often contrasted with the 'meson' (mean) and the 'elleipon' (deficiency), signifying the extreme that leads to vice or error. However, it can also denote something 'unusual' or 'remarkable', highlighting the complexity of its semantic journey.
Etymology
From the same root derive words denoting surplus, such as the verb «περισσεύω» ('to exceed, to abound') and the noun «περίσσεια» ('abundance, superfluity'). The meaning of 'odd' number is linked to the idea of 'additional' or 'that which remains' after division into pairs. The connection to «τέλειος» and «ἄρρεν» highlights the Pythagorean cosmology where numbers and their properties held deeper philosophical implications, while «ἄζυγος» underscores the concept of 'unpaired'.
Main Meanings
- Odd number — In Pythagorean and ancient Greek mathematical thought, a number not exactly divisible by two, in contrast to an even number. Associated with the masculine, the finite, and the perfect.
- That which is over, additional — Something that exists beyond necessity or expectation. E.g., «περιττὰ χρήματα» (superfluous money).
- Excessive, useless, futile — Something that is beyond measure, without utility or purpose. In Aristotelian ethics, the excess that leads to error or vice.
- Extraordinary, superior, distinguished — Something that surpasses the ordinary in a positive way, indicating excellence or uniqueness. E.g., «περιττὸς ἀνήρ» (an exceptional man).
- Strange, peculiar — Something unusual or outside the norm, causing surprise or wonder.
- Pleonasm (rhetorical term) — In rhetoric, the use of additional words or expressions not strictly necessary for meaning, but adding emphasis or style.
Word Family
περί- (preposition) + -ττ- (Ancient Greek root)
The root of «περιττός» is composed of the preposition περί-, meaning 'around, beyond, over', and an Ancient Greek root -ττ- signifying exceeding or superfluity. This compound creates a family of words that explore the concepts of 'additional', 'excessive', and 'extraordinary'. This root, though not as prolific as others, has yielded key terms for understanding ancient Greek conceptions of numbers, measure, and ethics.
Philosophical Journey
The semantic journey of «περιττός» is closely linked to the evolution of philosophical and mathematical thought in ancient Greece.
In Ancient Texts
Three characteristic passages highlight the main uses of «περιττός»:
Lexarithmic Analysis
The lexarithmos of the word ΠΕΡΙΤΤΟΣ is 1065, from the sum of its letter values:
1065 decomposes into 1000 (hundreds) + 60 (tens) + 5 (units).
The 18 Methods
Applying the 18 traditional lexarithmic methods to the word ΠΕΡΙΤΤΟΣ:
| Method | Result | Meaning |
|---|---|---|
| Isopsephy | 1065 | Base lexarithmos |
| Decade Numerology | 3 | 1+0+6+5 = 12 → 1+2 = 3 — Triad, the first odd number after unity, a symbol of completeness and harmony, but also of the beginning of differentiation. |
| Letter Count | 8 | 8 letters — Octad, a number of balance and justice, but also of the excess that can disrupt this balance. |
| Cumulative | 5/60/1000 | Units 5 · Tens 60 · Hundreds 1000 |
| Odd/Even | Odd | Masculine force |
| Left/Right Hand | Right | Divine (≥100) |
| Quotient | — | Comparative method |
| Notarikon | Π-Ε-Ρ-Ι-Τ-Τ-Ο-Σ | Panta En Roē Ischys Tēs Taxeōs Ousias Sophias (Always in Flux, the Power of Order, Essence, Wisdom). |
| Grammatical Groups | 3V · 5C | 3 vowels (E, I, O) and 5 consonants (P, R, T, T, S). |
| Palindromes | No | |
| Onomancy | — | Comparative |
| Sphere of Democritus | — | Divination with lunar day |
| Zodiacal Isopsephy | Mercury ☿ / Capricorn ♑ | 1065 mod 7 = 1 · 1065 mod 12 = 9 |
Isopsephic Words (1065)
Words from the Liddell-Scott-Jones lexicon with the same lexarithmos (1065) but different roots:
The LSJ lexicon contains a total of 91 words with lexarithmos 1065. 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, 9th ed. with revised supplement. Oxford: Clarendon Press, 1996.
- Plato — Theaetetus, edited by John Burnet, Oxford University Press, 1903.
- Aristotle — Nicomachean Ethics, edited by I. Bywater, Oxford University Press, 1894.
- Nestle, E., Aland, K. — Novum Testamentum Graece, 28th ed. Stuttgart: Deutsche Bibelgesellschaft, 2012.
- Kirk, G. S., Raven, J. E., Schofield, M. — The Presocratic Philosophers: A Critical History with a Selection of Texts, 2nd ed. Cambridge University Press, 1983 (for the Pythagoreans).
- Long, A. A., Sedley, D. N. — The Hellenistic Philosophers, Vol. 1: Translations of the Principal Sources with Philosophical Commentary. Cambridge University Press, 1987.