ΛΗΜΜΑ
The term lemma, deeply rooted in ancient Greek logic and mathematics, refers to a proposition that is accepted or taken for granted as a stepping stone to prove another theorem. Evolving from its initial meaning of 'gain' or 'that which is received,' it became a fundamental concept in philosophy and science. Its lexarithmos (119) suggests the complexity and synthetic nature of thought required to construct arguments.
Definition
According to the Liddell-Scott-Jones Lexicon, λῆμμα (to) originally means 'that which is taken or received; gain, profit, revenue.' This primary sense, found in texts from the Classical period, emphasizes the idea of acquiring or obtaining something, whether material or immaterial.
In philosophy and logic, particularly from the time of Aristotle, λῆμμα acquired a more specialized meaning: it refers to a 'premise,' an 'assumption,' or a 'proposition' that is accepted as true without further proof, in order to serve as the basis for an argument or a syllogism. It is the starting point, the postulate upon which further thought is constructed.
In mathematics, the concept of a lemma became established as an 'auxiliary theorem' or 'subsidiary proposition.' This is a smaller, intermediate theorem that is proven first, not for its own sake, but because its proof is essential for the demonstration of a larger and more significant theorem. Its use is central to the construction of complex mathematical proofs.
Furthermore, the term is also used in rhetoric to denote a point conceded by the audience or opponent, and in everyday language to describe 'gain' or 'revenue,' sometimes with the negative connotation of illicit gain or a bribe. In modern lexicography, 'lemma' is the headword of an entry in a dictionary.
Etymology
Related words include the verb λαμβάνω, as well as derivatives such as λῆψις (lēpsis, the act of taking), λήπτης (lēptēs, one who takes), ἀνάληψις (analēpsis, taking up, assumption), κατάληψις (katalēpsis, grasping, comprehension), πρόληψις (prolēpsis, pre-conception, anticipation), and ἐπίληψις (epilēpsis, seizure, epilepsy). All these words retain the basic idea of 'taking' or 'grasping' with various nuances.
Main Meanings
- That which is taken or received; gain, profit, revenue — The original and general meaning, referring to anything acquired or collected, often as financial benefit.
- Premise, assumption, proposition (Logic) — A proposition accepted as true or given in an argument, without requiring further proof within the context of that argument.
- Auxiliary theorem (Mathematics) — An intermediate theorem proven as a preparatory step for the demonstration of a more significant theorem.
- Starting point, basis of an argument — The fundamental principle or initial postulate upon which a discussion or proof is constructed.
- Bribe, illicit gain — A negative connotation of gain, implying an unfair acquisition of money or benefits.
- Headword, entry word in a lexicon — The main word or entry in a dictionary, which is the subject of the definition.
Philosophical Journey
The semantic evolution of λῆμμα reflects the development of Greek thought, from practical concepts of gain to the abstract structures of logic and mathematics.
In Ancient Texts
Three characteristic passages illustrating the different uses of λῆμμα in ancient Greek literature:
Lexarithmic Analysis
The lexarithmos of the word ΛΗΜΜΑ is 119, from the sum of its letter values:
119 decomposes into 100 (hundreds) + 10 (tens) + 9 (units).
The 18 Methods
Applying the 18 traditional lexarithmic methods to the word ΛΗΜΜΑ:
| Method | Result | Meaning |
|---|---|---|
| Isopsephy | 119 | Base lexarithmos |
| Decade Numerology | 2 | 1+1+9 = 11 → 1+1 = 2 — Duality, opposition, pairing. This reflects the relationship between premise and conclusion, or the idea of taking and giving. |
| Letter Count | 5 | 5 letters — Pentad, the number of balance, synthesis, and human reason. |
| Cumulative | 9/10/100 | Units 9 · Tens 10 · Hundreds 100 |
| Odd/Even | Odd | Masculine force |
| Left/Right Hand | Right | Divine (≥100) |
| Quotient | — | Comparative method |
| Notarikon | L-E-M-M-A | Logic, Epistemology, Method, Mathematics, Argument — An interpretive connection to the core principles of philosophical and scientific thought. |
| Grammatical Groups | 2V · 0S · 3C | 2 vowels (ē, a), 0 semivowels, 3 consonants (l, m, m). The structure suggests a balanced and stable foundation, just as a lemma provides stability to an argument. |
| Palindromes | No | |
| Onomancy | — | Comparative |
| Sphere of Democritus | — | Divination with lunar day |
| Zodiacal Isopsephy | Moon ☽ / Pisces ♓ | 119 mod 7 = 0 · 119 mod 12 = 11 |
Isopsephic Words (119)
Words from the Liddell-Scott-Jones lexicon with the same lexarithmos (119), revealing interesting conceptual connections:
The LSJ lexicon contains a total of 24 words with lexarithmos 119. 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. Oxford: Clarendon Press, 1940.
- Aristotle — Topics. Loeb Classical Library, Harvard University Press.
- Plato — Laws. Loeb Classical Library, Harvard University Press.
- Proclus — Commentary on Euclid's Elements. Teubner, Leipzig.
- Heath, T. L. — A History of Greek Mathematics. Oxford: Clarendon Press, 1921.
- Barnes, J. — Aristotle: A Very Short Introduction. Oxford University Press, 2000.