LOGOS
PHILOSOPHICAL
πρόβλησις (ἡ)

ΠΡΟΒΛΗΣΙΣ

LEXARITHMOS 700

Problēsis, a word deeply rooted in ancient Greek thought, initially describes the physical act of "throwing forward" or "projecting." However, its meaning evolved, particularly in Aristotle, to denote a logical proposition or a problem to be solved. Its lexarithmos (700) suggests completeness and a comprehensive approach to addressing issues.

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Definition

According to the Liddell-Scott-Jones Lexicon, problēsis encompasses a wide range of meanings originating from the literal sense of "throwing or placing something forward." This primary meaning can refer to a physical action, such as the hurling of a spear or the projection of an object forward. It also extends to geographical or architectural prominences, such as a promontory or a projecting part of a wall.

In classical Greek literature, and especially in philosophy, problēsis acquires a more abstract and technical meaning. In Aristotle, it is a central term in logic and dialectic. Here, it signifies a "proposition" or "question" put forward for discussion or resolution, a "problem" that requires an answer or proof. This usage underscores the idea of "setting before" as "setting forth for examination."

Beyond logic, problēsis can also mean a "pretext" or "challenge," an action put forward to conceal another purpose or to provoke a reaction. The variety of its meanings reflects the flexibility of the Greek language to transform physical actions into abstract concepts, always retaining the core sense of "projection" or "placement before."

Etymology

problēsis ← pro- + ballō (root bal-/bol- meaning "to throw, cast")
The word problēsis is a compound, derived from the prefix "pro-" (denoting movement forward or placement in front) and the root of the verb "ballō." The root "bal-/bol-" is an Ancient Greek root belonging to the oldest stratum of the language, meaning "to throw, to cast, to place." This compound creates the concept of "projection" or "placement before," whether literally or metaphorically.

From the same root "bal-/bol-" stems a rich family of words related to the act of throwing, casting, or placing. The verb "ballō" itself is the core of this family, while "belos" denotes the projectile. Derivatives with various prefixes, such as "diaballō" (to throw across, slander), "symballō" (to throw together, contribute), "parabolē" (a throwing beside, comparison, parable), and "hyperbolē" (a throwing beyond, excess), illustrate the broad semantic development of the root.

Main Meanings

  1. Physical projection, casting — The act of throwing something forward or launching it.
  2. Prominence, projection, promontory — A natural or artificial part that projects, such as a rock into the sea or a section of a wall.
  3. Proposition, question, problem (philosophical/logical) — An issue put forward for discussion, examination, or resolution, especially in Aristotle.
  4. Pretext, excuse — Something put forward as a cover for another purpose or action.
  5. Challenge, confrontation — The act of challenging someone or posing an issue for debate.
  6. Exposition, presentation — The act of presenting or setting forth a topic.
  7. Protection, defense — Something projected as a shield or means of defense.

Word Family

bal-/bol- (root of the verb ballō, meaning "to throw, cast")

The root bal-/bol- constitutes one of the oldest and most productive nuclei of the Greek language, expressing the action of "throwing," "casting," or "placing." From this basic meaning, the root has yielded countless derivatives, both literal and metaphorical, describing movements, objects, states, and abstract concepts. The variety of prefixes and suffixes allows for the creation of words with nuances ranging from a physical throw to a dialectical proposition or an ethical contribution.

βάλλω verb · lex. 863
The foundational verb of the family, meaning "to throw, cast, strike." It forms the core from which all other words in the family derive, retaining the sense of movement and impact. Widely used from Homer to the New Testament.
πρόβλημα τό · noun · lex. 331
Literally "that which is thrown forward." In Aristotle, it is a "problem" or "question" put forward for resolution, closely related to problēsis. (Plato, Republic)
βολή ἡ · noun · lex. 110
The act of "throwing" or "casting," a throw. Often refers to the launching of arrows or stones, maintaining a direct connection to the physical action of the root. (Homer, Iliad)
βέλος τό · noun · lex. 307
The "thrown" object, i.e., an arrow or missile. Represents the result of the action of "ballō." (Homer, Odyssey)
διαβάλλω verb · lex. 878
Means "to throw across," but metaphorically "to slander, accuse." The idea of "throwing" here transforms into "throwing words against someone." (Thucydides, Histories)
συμβάλλω verb · lex. 1503
Means "to throw together, contribute, clash." The sense of "throwing" here implies joining forces or confronting. (Xenophon, Anabasis)
παραβολή ἡ · noun · lex. 292
Literally "a throwing beside." Means "comparison, parallelism," and later "parable" (a story with a moral lesson). (Gospels)
ὑπερβολή ἡ · noun · lex. 695
Literally "a throwing beyond." Means "exceeding, excess," something that goes beyond limits. (Demosthenes, On the Crown)

Philosophical Journey

The journey of problēsis from its literal to its philosophical meaning is a characteristic example of the evolution of the Greek language.

8th-6th C. BCE (Archaic Period)
Early Uses
In Homer and early poets, the root "ballō" and its derivatives are primarily used in the literal sense of physical casting or throwing. The word problēsis itself is rare, but the conceptual basis exists.
5th C. BCE (Classical Period)
Expansion of Meanings
In Herodotus and Thucydides, problēsis begins to appear with the meaning of "projection" (e.g., geographical) or "pretext." In Euripides, it can mean "challenge."
4th C. BCE (Aristotle)
Philosophical Term
Aristotle establishes problēsis as a technical term in logic and dialectic. In his "Topics," problēsis is a "dialectical problem," a question posed to examine its truth or falsehood.
3rd-1st C. BCE (Hellenistic Period)
Continued Usage
The use of the word continues in philosophical and rhetorical texts, retaining the Aristotelian meaning, but also expanding to more general concepts of "issue" or "topic."
1st-4th C. CE (Roman Period)
Scientific Application
In commentators on Aristotle and other philosophers, problēsis remains a consistent term for referring to a problem or proposition. It is also used in mathematical and scientific contexts for "projections" or "expositions."
5th-15th C. CE (Byzantine Period)
Theological/Legal Texts
The word retains the meaning of "problem" or "issue" in theological and legal texts, often in the sense of a difficulty that needs to be addressed.

In Ancient Texts

Aristotle's use of problēsis is crucial for understanding the word in philosophy.

«ἔστι δὲ πρόβλημα διαλεκτικὸν θεώρημα τὸ πρὸς ἀπόδειξιν ἢ πρὸς ἐκλογὴν ἢ πρὸς φυγὴν ἢ πρὸς πρᾶξιν.»
“A dialectical problem is a theorem that is put forward for proof, or for choice, or for avoidance, or for action.”
Aristotle, Topics, A.4.101b
«πρόβλημα δέ ἐστιν ὃ πρὸς ἀπόδειξιν ἢ πρὸς πρᾶξιν ἢ πρὸς ἐκλογὴν ἢ πρὸς φυγὴν τίθεται.»
“A problem is that which is put forward for proof, or for action, or for choice, or for avoidance.”
Aristotle, Topics, Θ.1.155b
«καὶ γὰρ οἱ ῥήτορες καὶ οἱ σοφισταὶ προβλήματα ποιοῦνται.»
“For both rhetoricians and sophists pose problems.”
Aristotle, Rhetoric, A.1.1355a

Lexarithmic Analysis

The lexarithmos of the word ΠΡΟΒΛΗΣΙΣ is 700, from the sum of its letter values:

Π = 80
Pi
Ρ = 100
Rho
Ο = 70
Omicron
Β = 2
Beta
Λ = 30
Lambda
Η = 8
Eta
Σ = 200
Sigma
Ι = 10
Iota
Σ = 200
Sigma
= 700
Total
80 + 100 + 70 + 2 + 30 + 8 + 200 + 10 + 200 = 700

700 decomposes into 700 (hundreds) + 0 (units).

The 18 Methods

Applying the 18 traditional lexarithmic methods to the word ΠΡΟΒΛΗΣΙΣ:

MethodResultMeaning
Isopsephy700Base lexarithmos
Decade Numerology77+0+0 = 7 — The Septad, a number of completeness, perfection, and wisdom, associated with the comprehensive examination of a problem.
Letter Count99 letters — The Ennead, a number of completion, spiritual achievement, and the search for truth.
Cumulative0/0/700Units 0 · Tens 0 · Hundreds 700
Odd/EvenEvenFeminine force
Left/Right HandRightDivine (≥100)
QuotientComparative method
NotarikonP-R-O-B-L-Ē-S-I-SProposition Rhetorical Of Substance Deep Logical Ethical Wisdom Idea Thought (Πρότασις Ρητορική Ουσίας Βαθείας Λογικής Ηθικής Σοφίας Ιδέας Σκέψεως)
Grammatical Groups3V · 4S · 2M3 vowels (O, Ē, I), 4 semivowels (R, L, S, S), 2 mutes (P, B).
PalindromesNo
OnomancyComparative
Sphere of DemocritusDivination with lunar day
Zodiacal IsopsephyMoon ☽ / Leo ♌700 mod 7 = 0 · 700 mod 12 = 4

Isopsephic Words (700)

Words from the Liddell-Scott-Jones lexicon with the same lexarithmos 700, but a different root, offering interesting conceptual parallels with problēsis:

ἀκροατής
The "listener" is one who hears a proposition or a problem. The connection highlights the need for recipients or judges of a problēsis.
ἀπόστημα
“Apóstēma” means distance or interval. Conceptually, a problēsis can be seen as a “projection” that creates a distance from the initial position or as an issue that needs to be bridged.
κριτός
“Kritós” is that which is judged or can be judged. A problēsis, as a proposition or problem, is always put forward for judgment and evaluation.
προκάθισις
“Prokáthisis” means sitting before or preceding. It alludes to the idea of problēsis as something placed in advance for examination or as a prerequisite.
διαιρετός
“Diairetós” refers to something that can be divided. A philosophical problem often requires division into smaller parts for analysis and resolution.
ἐπιεικτός
“Epieiktós” means that which is reasonable, fair, or equitable. A problēsis, especially in ethical or legal contexts, often requires an equitable or just approach to its resolution.

The LSJ lexicon contains a total of 86 words with lexarithmos 700. 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.
  • AristotleTopics. Loeb Classical Library.
  • AristotleRhetoric. Loeb Classical Library.
  • PlatoRepublic. Loeb Classical Library.
  • HomerIliad. Loeb Classical Library.
  • ThucydidesHistories. Loeb Classical Library.
  • Bauer, W., Arndt, W. F., Gingrich, F. W., Danker, F. W.A Greek-English Lexicon of the New Testament and Other Early Christian Literature. 3rd ed. Chicago: University of Chicago Press, 2000.
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