ΚΥΚΛΟΣ ΛΟΓΙΚΟΣ
The κύκλος λογικός, or "circular argument," is a fundamental logical fallacy described by ancient Greek philosophers, most notably Aristotle. It refers to an argument where the truth of the proposition to be proven is already assumed as true in the premises. Its lexarithmos (1143) suggests a complex structure associated with the completion of a cycle, yet also with being trapped within it.
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In ancient Greek philosophy, the "κύκλος λογικός" (Latin: *circulus in probando* or *petitio principii*) denotes a logical fallacy consisting in the assumption of the conclusion as a premise. This implies that the argument relies on the very proposition it seeks to prove, thereby creating a vicious circle of reasoning. This fallacy renders the argument invalid, as it fails to provide independent support for the truth of its conclusion.
Aristotle, in his *Prior Analytics* and *Topics*, was the first to systematically analyze this fallacy. He described the "circle" as a situation where "the same thing is defined by means of the same thing," rendering the demonstration redundant or non-existent. The recognition of the *κύκλος λογικός* was crucial for the development of the scientific method, which requires premises to be more known or more credible than the conclusion.
The concept is not limited to formal logic but extends to broader philosophical discussions, such as in epistemology, where it may refer to systems of knowledge based on arbitrary principles or arguments that cannot find external foundation. The *κύκλος λογικός* underscores the necessity for non-circular, linear, or hierarchical grounding of knowledge.
Etymology
The composition of the two roots, "κυκλ-" and "λογ-", is purely Greek and describes the inherent structure of the fallacy. From the root "κυκλ-" derive words denoting circular motion or form, while from the root "λογ-" stem terms related to logic and the process of reasoning. The confluence of these concepts in "κύκλος λογικός" highlights the Greek capacity to forge precise philosophical terms through compounding.
Main Meanings
- Circular Proof / Circular Reasoning — The primary meaning in logic, where the conclusion of an argument is used as a premise for its own demonstration.
- Logical Fallacy — Refers to the category of fallacies that invalidate an argument due to its self-referential nature.
- Vicious Circle — A broader concept describing a situation where a series of events or arguments leads back to the beginning, without genuine progress or resolution.
- Petitio Principii (Latin Translation) — The Latin term frequently employed in Western philosophy to describe the same logical fallacy, literally "begging the question."
- Self-Referentiality — The property of a system or argument to refer to itself, lacking external foundation.
- Lack of External Justification — The inability of an argument to rely on independent, accepted truths.
Word Family
κυκλ- (root of κύκλος, meaning 'circle, circuit')
The root κυκλ- is Ancient Greek and belongs to the oldest stratum of the language, denoting the concept of a circle, rotation, and repetition. From this root stems a rich family of words describing circular forms, movements, or processes. In the case of "κύκλος λογικός," this root combines with the root λογ- (from λόγος, reason) to describe a specific circular structure in reasoning, highlighting its self-referential and often fallacious nature. Each member of the family develops an aspect of the circular idea, from the physical shape to the abstract concept of repetition.
Philosophical Journey
The concept of *κύκλος λογικός* has its roots in the development of ancient Greek logic and rhetoric, with Aristotle being the primary founder of its systematic analysis.
In Ancient Texts
Aristotle, as the first to systematically analyze the fallacy of *κύκλος λογικός*, provides the clearest and most foundational descriptions of it:
Lexarithmic Analysis
The lexarithmos of the word ΚΥΚΛΟΣ ΛΟΓΙΚΟΣ is 1143, from the sum of its letter values:
1143 decomposes into 1100 (hundreds) + 40 (tens) + 3 (units).
The 18 Methods
Applying the 18 traditional lexarithmic methods to the word ΚΥΚΛΟΣ ΛΟΓΙΚΟΣ:
| Method | Result | Meaning |
|---|---|---|
| Isopsephy | 1143 | Base lexarithmos |
| Decade Numerology | 9 | 1+1+4+3 = 9. The Ennead, a number of completion and return to the beginning, symbolizes the perfection of a cycle, but also being trapped within it, without escape. |
| Letter Count | 14 | 12 letters (ΚΥΚΛΟΣ ΛΟΓΙΚΟΣ). The Dodecad, a number of fullness and cosmic order, may suggest the apparent completeness of a circular argument, which nevertheless lacks true progress. |
| Cumulative | 3/40/1100 | Units 3 · Tens 40 · Hundreds 1100 |
| Odd/Even | Odd | Masculine force |
| Left/Right Hand | Right | Divine (≥100) |
| Quotient | — | Comparative method |
| Notarikon | K-Y-K-L-O-S L-O-G-I-K-O-S | Knowledge Yields Knavish Logic, Obscuring Sophistic Logic's Obvious Guile, Implying Knowledge's Obscure Sophistry. |
| Grammatical Groups | 5V · 8C | 5 vowels and 8 consonants. This ratio suggests a balance between the fluidity of sound and the stability of structure, reflecting the apparent coherence of circular reasoning. |
| Palindromes | No | |
| Onomancy | — | Comparative |
| Sphere of Democritus | — | Divination with lunar day |
| Zodiacal Isopsephy | Venus ♀ / Cancer ♋ | 1143 mod 7 = 2 · 1143 mod 12 = 3 |
Isopsephic Words (1143)
Words from the Liddell-Scott-Jones lexicon with the same lexarithmos (1143) as *κύκλος λογικός*, but from different roots, offering an interesting numerological correspondence:
The LSJ lexicon contains a total of 78 words with lexarithmos 1143. 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 — Prior Analytics. Translated with commentary.
- Aristotle — Topics. Translated with commentary.
- Barnes, Jonathan — Aristotle: Posterior Analytics. Clarendon Press, 1994.
- Ross, W. D. — Aristotle's Prior and Posterior Analytics. Oxford: Clarendon Press, 1949.
- Long, A. A., Sedley, D. N. — The Hellenistic Philosophers. Cambridge University Press, 1987.