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Pre-Aristotelian essay on definitions

Eftichis Papadopetrakis, Petros Skaltsas

University of Patras

ABSTRACT:   The first indications regarding definition use are found, according to the saved documents, in the Pre-Socratics.  However, the first theoretical problem-thoughts must have been Sophists’work, in the name of their teaching about the names correctness.  The first systematic work that has been thoroughly saved attributes to Plato.  In his dialectic, aiming at the essential prominence of each being through successive dissections, the possibility of a definition is provided referring to the object under consideration.

Key words: Pre-Socratics, sophists, Plato, dialectic, definition.  

1. The etymology of the related terminology

The modern Greek word ορισμός (definition) is the ancient Greek word ÐrismÒj, which appears for the first time in texts by Aristotle, judging, of course, from preserved texts. It is derived from the verb Ðr…zw, which comes from the noun oâron (το) or oâroj (ο), which constitute older forms of Óroj.

The word Óroj, means a local boundary, border: [Thucydides, book 4, 92, 4, 9]

The verbs oÙr…zw, Ðr…zw, (define) are derivatives of oâroj and Óroj, respectively. They mean the action of setting limits: to delimit, to separate, to constitute the limit, τo divide or separate from, as a boundary, and appear in texts from the 5^th century on. With the meaning of delimit, to separate, be a boundary between, it appears in Herodotus and Sophocles [Herodotus, Euterpe, 16, 9]. But particularly in Sophocles (496-406 B.C.), that is, in the Attic dialect, it also appears as Ðr…zw to define: [Sophocles, Trachiniae, line 754]

The term ÐrismÒj (definition): (i) marking out by boundaries, limitation, (ii) the definition of a word, it does not appear in texts before Aristotle.

              2.  Definitions in Pre-Socratean times

The idea of definition, as a necessity for the semantic delimiting of a word, must have been, in its first form, the accomplishment of the Greek thought of the 5^th century B.C. Aristotle (384-323 B.C.) attributes those first endeavours to the Pythagoreans, and we have no reason to doubt him:

«The Pythagoreans… and regarding the question of essence they began to make statements and definitions, but treated the matter too simply. For they both defined superficially and thought that the first subject of which a given definition was predicable was the substance of the thing defined, as if one supposed that 'double' and '2' were the same, because 2 is the first thing of which 'double' is predicable. But surely to be double and to be 2 are not the same; if they are, one thing will be many-a consequence which they actually drew».

[Aristote, Metaph , 987a, 12-20]

At another point in Metaphysics Aristotle mentions that, apart from the Pythagoreans, Democritus also dealt with definitions:

«Now Socrates devoted his attention to the moral virtues, and was the first to seek a general definition of these (for of the Physicists Democritus gained only a superficial grasp of the subject³ and defined, after a fashion, "the hot" and "the cold"; while the Pythagoreans  at an earlier date had arrived at definitions of some few things--whose formulae they connected with numbers--e.g., what "opportunity" is, or "justice" or "marriage"); and he naturally inquired into the essence of things; for he was trying to reason logically, and the starting-point of all logical reasoning is the essence. At that time there was as yet no such proficiency in Dialectic that men could study contraries independently of the essence, and consider whether both contraries come under the same science. There are two innovations which, may fairly be ascribed to Socrates: inductive reasoning and general definition. Both of these are associated with the starting-point of scientific knowledge. But whereas Socrates regarded neither universals nor definitions as existing in separation»

[Aristotle, Metaph, 1078b.17 10 to 78b.30]

      However, at the time of Aristotle definitions constitute a part of the premises or principles, in other words, of the agreements that were laid down as preconditions in order for a dialectic discussion to start, and, by extension, the expounding of a science such as geometry or arithmetic.

«If we wish to construct one, in the first place, we must realize that few if any of those who hold discussions reason out a definition, but all take as their starting-point some such assumption as those take who deal with geometry and numbers and all other studies».

[Aristotle, Top, 153α, 7-12]

Therefore, the habit of mathematicians of setting out definitions together with other the principles (the postulates and the common concepts) explains the fact that quite a few definitions have been preserved written in the imperative, like the postulates.

«Let magnitudes which have the same ratio be called proportional».

               [Euclid, book 5, HOR.6]

«Of quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right-angled but not equilateral; a rhombus that which is equilateral but not right-angled; and a rhomboid that which has its opposite sides and angles equal to one another but is neither equilateral nor right-angled. And let quadrilaterals other than these be called trapezia». [Euclid, book 1, HOR.22]

      It is very likely that this habit, that is, of considering definitions to be part of the principles, has its roots in the technique of dialectic, as the technique of συζητείν (to discuss).

3.     The Sophists and definition

In the context of intellectual life in the 5^th century B.C. the movement of the Sophists came to the fore. They were the contemporaries of the Natural philosophers, and the two groups influenced each other.

The theories related to the natural laws of life and society constituted   characteristics of Ionian thought by Anaximander (610-547 B.C.) and later constituted one of the strongest influences on the Sophists, as far as the shift in emphasis towards man and humanism is concerned.

The job of creating good speakers, in other words, training in the art of συζητείν (to discuss) (the work of the teaching of rhetoric), was taken on by the Sophists. «To be a good speaker as well as a man of action was, as Lesky underlines, an ambition of the Greeks at the time of Homer». [Guthrie, 1991:447]

Rhetoric as a specialised skill and useful art is said to have been introduced in Syracuse by two Sicilians, Korax and Teisias, around the beginning of the 5^th century B.C. [Guthrie, 1991: 225]

Aristotle pointed out significantly that the birth of rhetoric in Syracuse coincided with the expulsion of the tyrants and the establishment of democracy. «Rhetoric is a pre-eminently democratic art which cannot, whether in its political or its legal form, prosper under tyranny». [Guthrie, 1991:225]

Guthrie observed that the Sophists may not have been those who discovered rhetoric, but they were naturally prepared to intervene and to meet the demand for rhetoric, which accompanied the development of personal freedom throughout Greece.

On a philosophical level the question of the relationship between language and its content is raised.

Guthrie identifies two schools that developed in that period, the first in Sicily with Korax and Teisias, which was continued by Empedocles, Gorgias and Polos, and whose main aim was proper, that is, elegant speech. The second school was that of the Sophists who had gathered in Athens, of Pythagoras from Abdera, Prodicus from Kea and Hippias from Elis (fl. 425 B.C.). The aim of the latter, apart from education in the wider sense of the word, was the correct use of language (ορθοέπεια, ορθότης ονομάτων). Thus appeared the systematic study of grammar, etymology and synonyms.

Prodicus (470-460 B.C.) dealt with the synonymy of words. Socrates attended Prodicus’s lectures on the importance of the accurate use of words. [Guthrie, 1991: 336]

The correct use of language (ορθοέπεια, ορθότης ονομάτων) the semantic delimiting of the word, that is, the idea of definition. [Guthrie, 1991:225] mentions that the method of dichotomous division, which will be referred to below, was not invented by Plato, but was widespread in the 5^th century B.C.

Antisthenes, one of the Sophists, «did not recognise the possibility of forming a definition by predictive proposition» [Georgoulis, 1994: 158]. For that reason he said that the semantic content, which names contain as indicative aspects of things, should suffice. That can also be seen from his maxim «The beginning of all education is an encounter with words» [Arrian, Epict. diss. 1, 17, 10] In other words, the beginning/principle of education is the study of the meanings of words. Consequently, the starting point of all epistemological investigation must consist of the study of the meanings of words.

After Plato others were also against the possibility of ορίζειν (to define), such as:

«Speusippus, Plato’s successor, ascertained that one argument against the possibility of ορίζειν (the knowledge of the features of essence presupposes the knowledge of an infinite number of facts), an argument which was later repeated and developed by the Sceptics». [History of the Greek Nation, 1974: 282, Vol. 5]

4.     Plato’s advice

The practice of definition may have appeared in its first form in Pre-Socratean times, but systematic study with the subject appeared with Plato in the context of his dialectic – it constituted a favourite occupation of the members of the academy – to be completed in a relatively self-contained theory by Aristotle.

The 5^th century B.C. was, amongst many other things, the century of the peak of Sophistic dialectic, as the technique of συζητείν; as an art that, with its clever ploys, whether by taking advantage of polysemy or with notional or lexical games tricks the opponent into being inconsistent. 

Following his teacher Socrates, Plato continues to compete with the Sophists. Therefore, he countered the Sophist dialectic, which had at that time reaches its peak, with his ontological dialectic, of which the primary aim is the discovery of the essence of being and the nomination of a phrase (λόγος) which stands for that essence, in other words, of a definition.

«…with the sophist, and must search out and make plain by argument what he is. For as yet you and I have nothing in common about him but the name; » [Plato, Soph,, 218c, 1-2]

Therefore, Plato does not set out to formulate a theory and a methodology of definition. His aim is to determine the essence of the subject of the discussion and to bring to the fore the λόγος, that is, the phrase that, with its description, stands for that essence, so that the interlocutors have not only the name but also the content in common. Thus, the possibility for a definition to be determined is a consequence of the methodology that is followed for the determination of the essence of the being, which is none other than the method of dichotomous division that is to be found at the practical core of Platonic dialectic.

«Plato’s dialectic», comments Gottfried Martin «is among his greatest achievements, though it simultaneously constitutes that part of his philosophy that presents the greatest difficulty in terms of comprehension. The fact that dialectics essentially begins with Plato is something about which I can refer to Hegel, in whose judgement one can have complete confidence, since he gave dialectics the form that proved to be effective in our time. Hegel states: «As far as Plato’s dialectics are concerned now, what began with him is the most interesting and yet the most difficult of his works, so that usually nobody goes near it, when they study Platonic texts» [Gottfried Martin???].

However, Platonic dialectics constitute a continuation and at the same time a rejection of the dialectics of the Sophists and Eleatics, whereas it constitutes a more direct continuation of the Socratic version, that is, of the maieutic method. The fact that in the Sophist, the basic work in which Plato sets out his method of dichotomous division, it is not at all without importance that he chose as one of his interlocutors an anonymous Eleatic, a supporter of Parmenides and Zeno and thus an expert in the Eleatic dialectic, and two mathematicians: Theodorus of Cyrene  (425 B.C.), a famous mathematician and astronomer of his time and his student Theaetetus (415-369 B.C.), known for his proof of irrational ratios up to root 17, two of the most experienced intellectuals of the time to form and to use good definitions in the context of their science.

Therefore, within that orchestrated discussion, Plato presents for the first time his method the basic work in which Plato sets out his method of dichotomous division, the continuous dichotomous division of a more general concept. That process consists of a contrastive analysis from the whole and general to the partial and specific and vice-versa. The result of this process, on the ontological level, is the determination of the essence of an object by means of the identification of its basic components and, simultaneously, on the linguistic level, the formation of its definition, by means of the comparison of the words that stand for the basic components, which have come to light through the method of dichotomous division. «The one logical action» writes D. Glinos characteristically “is the concise conception of the parts in a concept, in an ‘idea’. The other logical action is the division into ‘species’. In the Republic that is the main feature that distinguishes a quarrel from a dialectic. [D.Glinos, Sophist, 132]. As Plato himself also characterises his method immediately after its successful application in the Sophist:

«Stranger: Shall we not say that the division of things by classes and the avoidance of the belief that the same class is another, or another the same, belongs to the science of dialectic?

Theaetetus: Yes, we shall».  [Plato, Soph., 253d, 1]

Plato did not set out in any work the rules of his method in their entirety.   However, a careful examination of the dialogues Phaedrus, Sophist and Statesman can extract those rules:

a) With the exception of the first step, when before us we have only one class, that which every time is divided into two is always the class that is found on the right-hand part.

«Stranger: let us divide in two the class we have taken up for discussion, and proceed always by way of the right-hand part of the thing divided». [Plato, Soph., 264d, 10]

b) The right of the two parts, the products of the dichotomy, must always form a species and not a simple part of the concept that is being divided. The species is naturally always part of the concept that has been divided, but each part does not always constitute a species. Plato mentions the following about kinds in the dialogue Statesman:

«Stranger: That class and part are separate from one another.

Younger Socrates: But what did you say?

Stranger: That when there is a class of anything, it must necessarily be a part of the thing of which it is said to be a class; but there is no necessity that a part be also a class. Please always give this, rather than the other, as my doctrine». [Plato, Polit., 263b, 5 26, 3b, 9]

The method does not pay particular attention to the left-hand part, since the subject is in the other part. However, it can be seen from the development of the example of the angling, it may not cover all the species that remain after the separation of the right-hand part.

c) The division must follow the natural structure of things and not break up concepts:

«Phaedrus: And what is the other principle, Socrates?

Socrates: That of dividing things again by classes, where the natural joints are, and not trying to break any part, after the manner of a bad carver. As our two discourses just now assumed one common principle, unreason, and then, just as the body, which is one, is naturally divisible into two, right and left, with parts called by the same names, so our two discourses conceived of madness as naturally one principle within us, and one discourse, cutting off the left-hand part, continued to divide this until it found among its parts a sort of left-handed love, which it very justly reviled, but the other discourse, leading us to the right-hand part of madness, found a love having the same name as the first,  but divine, which it held up to view and praised as the author of our greatest blessings.

Phaedrus: Very true». [Plato, Phaedr. 265 d/e]

d) It is essential to exhaust systematically all the length and breadth of the concept that is continually divided into two, step by step, like enumeration.

«that unless a man take account of the characters of his hearers  and is able to divide things by classes and to comprehend particulars under a general idea, he will never attain the highest human perfection in the art of speech. But this ability he will not gain without much diligent toil». [Plato, Phaedr., 273 d/e]

e) The process of dichotomous division finishes when it arrives at an indivisible species, which does not contain other species:

«Phaedrus: Yes, I thought so, too; but please recall to my mind what was said.

Socrates: A man must know the truth about all the particular things of which he speaks or writes, and must be able to define everything separately; then when he has defined them, he must know how to divide them by classes until further division is impossible; and in the same way he must understand the nature of the soul,  must find out the class of speech adapted to each nature, and must arrange and adorn his discourse accordingly, offering to the complex soul elaborate and harmonious discourses, and simple talks to the simple soul. Until he has attained to all this, he will not be able to speak by the method of art, so far as speech can be controlled by method, either for purposes of instruction or of persuasion. This has been taught by our whole preceding discussion». [Plato, Phaedr., 277 b-c]

Therefore, in Plato’s texts the two terms Óroj   and Ðr…zw, changed content (judging, of course, only from the preserved texts of the period). Thus, Óroj, on the one hand, means the agreement between the essence of the being under discussion, that is, its ontological and semantic delimiting, whereas ορίζω means the dialectic procedure (dichotomy) which leads to the formation of that agreement. However, this act of define a term «Óron Ðr…zein» did not refer to the external world, the earth and human relations, but to the intellect and, on a secondary level, to language. Plato refers to the linguistically expressed crystallization of that process as Óroj.

«Theaetetus: What is it? Speak, and we shall soon know.

Stranger: I suggest that everything which possesses any power of any kind, either to produce a change in anything of any nature or to be affected even in the least degree by the slightest cause, though it be only on one occasion, has real existence. For I set up as a definition which defines being, that it is nothing else but power». [Plato, Soph., 247, d/e]

CONCLUSIONS

The word definition is a new word introduced by Aristotle.

The idea of definition, as precondition of semantic limitation of a word, must have started in the 5^th century B.C in the Pre-Socratean times.The sophists worked on the definition on a teaching level.

The systematic work regarding definitions appeared in Plato, in his dialectic, and will be completed by Aristotle with theoretical completion. Plato did not mean to carry out a theory on definitions, but in his dialectic to define the essence of the object in his effort to locate the basic components, and to form the final definition in a lingual level.  

REFERENCES

Aristotle. 1960, «II Posterior Analytics-Topika», Posterior Analytics –Topika,

Translated by E.S.Forster and Hugh Tredennick, Loeb Classical Library.Edition: Harvard University Press, First Edition 1960, Reprinted 1966, 1976, 1989.England, London 1960[Book]

E Bell 1992, «The mathematicians», Crete University Editions, Greece. [Book, translated work]

Ingemar During. 1994, «Aristotle», National Bank Foundation Editions Athens Greece [Book, translated work]

H.  Liddel - Scott, «Lexicon», Edition Greek-Letters Athens - Greece,

[Book, translated work]

«History of the Greek Nation» 1980, Volume E,           Editions: Athens Ekdotiki, [Book]

Chearles Mugler. 1957, «Dictionary Historique de la Terminologie Géométrique Des  Grecs», Edition: Taffin - Lefort, Lille France [Book]

Guthrie W.K.C. 1981, «A history of Greek Philosophy».  Volume VI, Edition: Cambridge University Press London. England [Book, translated work]

Georgoulis K. 1994, «History of the Greek Philosophy», Editions: Dim. Papadimas, Athens. p.158 [Book]

Guthrie W.K.C. 1989, «The sophists».  Editions: «National Bank Educational Foundation», Athens. [Book, translated work] First Edition: Cambridge University Press London 1971. England [Book, translated work]

Plato. «Sophist» Translation by D. Glenos, Zacharopoulos Editions, Athens. [Book]

Taylor. 1967, Article: «Plato and the Mathematicians», Magazine: «Philosophical Quarterly», Volume: 17, Issue 68, (Jul., 1967), pp. 193-203, Editions: Philosophical Quarterly, Corpus Christi College, Oxford England

A.E.Taylor. 1992, «Plato The man and his work», Editions: «National Bank Educational Foundation», Athens. [Book, translated work]

Vitrac Bernard 1998, «Euclide D’Alexandrie, Les Elements»,4 vols, Editions: Presses Universitaires de France Paris [Book]

Thesaurus Linguae Graecae (TLG®) CD ROM. [The Thesaurus Linguae Graecae (TLG®)] is an electronic data bank of University of California, Irvine. Founded in 1972 the TLG has already collected and digitized most literary texts written in Greek from Homer to the fall of Byzantium in AD 1453 with historiographical, lexicographical, and scholiastic texts. https://www.tlg.uci.edu/

Internet sources:

Translation of Euclid Elements:
D.E.Joyce Copyright © 1996, 1997. (June, 1997)
Clark University

Translation of Hippocrates, Aristotle, Herodotus:

http://classics.mit.edu/Browse/browse-Aristotle.html

https://www.chlt.org/sandbox/dh/HippocratesLoeb1/page.225.a.php

http:// herodotus website.co.uk/Text/Book2.htm

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Υπάρχει πρόβλημα στην ημερομηνία  [Guthrie, 1991

Δεν υπάρχει η παραπομπή για [Gottfried Martin???].