Jean-François Monteil, ancien maître de conférences de linguistique générale à l’Université Michel de Montaigne de Bordeaux
Adresse électronique :
Jean-francois.monteil@neuf.fr
Les deux sites associés :
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ENG Knol-C 011 Organon, Peri Hermeneias, Chapter 7
Professor Paul Gohlke is the only translator to fully respect Aristotle’s own conception of indeterminates. He was the first to perceive the linguistic problem raised by the indeterminate negative. All the other translators of De interpretatione mistakenly render Aristotle’s indeterminates, which are particulars, as universals. The origin of this mistake lies in one of the two Arab translations.
ENG Knol 102 On the Aristotelian Organon. Importance of the chapter 7 of De Interpretatione (or Peri Hermeneias), second book of the Organon. In the light of the works of Isidor Pollak and Paul Gohlke the text of De Interpretatione, chapter 7, is at last established.
Scholars should take into account the following work: Pollak (I.), Die Hermeneutik des Aristoteles in der arabischen Übersetzung des Ishak ibn Honain (Abhandlungen für die Kunde des Morgenlandes, XIII, Band, Number 1), Leipzig, 1913, p. 11, Notes 189 and 190. Esti leukos anthropos and Ouk esti leukos anthropos are to be interpreted as particulars. They mean something like Es gibt einen weissen Menschen There are white men and Es gibt einen nicht weissen Menschen There are not-white men respectively. The nearly universal translation Der Mensch ist weiss Man is white, Der Mensch ist nicht weiss Man is not white-nearly universal translation due to one of the two Arab translations mentioned by Pollak- is awful, since it renders propositions which have the sense of particulars by propositions which have the sense of universals.The replacement of Der Mensch is weiss by Ein Mensch is weiss A man is white is no improvement, indeed, for Ein Mensch ist sterblich A man is white is a universal as well as Der Mensch ist sterblich. Ackrill, no doubt, considers his own translation A man is white as a pis aller. Does he not write himself “It is a pity that Aristotle introduces indeterminate statements at all”? The problem raised by the poisoning indeterminate propositions of On Interpretation, chapter 7, is not a trifle to be despised by scholars. A good interpretation of the Aristotelian unquantified propositions brings about a chain reaction whose final stage is the substitution of Blanché’s hexagon for the logical square. The logical hexagon creates the conditions for a better understanding of the relation between natural language and logic.Der Stein, den die Bauleute verworfen haben, der ist zum Eckstein geworden !devient ENG Knol-C 011 et le présent KNOLmnc 1Useful link: De Interpretatione ” Dossier” 19 of Tract Eight-8 de Jean-François Monteil de Cestas
Contents
A Jacques Brunschwig
– site non personnel de l’Université 3 de Bordeaux: http://erssab.u-bordeaux3.fr
– site personnel : http://www.grammar-and-logic.com
-mindnewcontinent
Professor Paul Gohlke is the only translator to fully respect Aristotle’s own conception of indeterminates. He was the first to perceive the linguistic problem raised by the indeterminate negative. All the other translators of De interpretatione mistakenly render Aristotle’s indeterminates, which are particulars, as universals. The origin of this mistake lies in one of the two Arab translations.
In Peri Hermeneias, chapter 7, Aristotle mainly studies the four marked natural propositions, which are at the origin of the logical square:
–A Pas anthropos leukos Everyman (is) white
–E Oudeis anthropos leukos No man (is) white
– I Esti tis anthropos leukos Some man (is) white
–O Ou pas anthropos leukos Not everyman (is) white.
He also studies two propositions said to be indeterminate in so far as they are devoid of quantifying morphemes like Tis-Some or Pas-Every : Esti anthropos leukos, Ouk esti anthropos leukos. Since Aristotle explicitly says that they are both true, he implicitly says that they are particular propositions. Therefore, the affirmative one Esti anthropos leukos means There are white men, the negative one Ouk esti anthropos leukos means There are non-white men. Semantically, the indeterminate propositions of On interpretation, chapter 7, are equivalent to the marked particulars Some men are white and Not everyman is white (or Some men are not white).
But an attentive Hellenist cannot but recognize that the form of the negative indeterminate Ouk esti anthropos leukos with the negative adverb ouk bearing on an esti signifying there is conveys the meaning of a negative universal proposition There is not any white man, that is, No man is white. Aristotle himself confesses it. For the indeterminate negative to be interpreted as a particular negative, one must mentally replace Ouk esti anthropos leukos by Esti ou leukos anthropos There is a non-white man with the negation ou bearing on leukos and not on the verb esti there is.
Gohlke’s attitude is exemplary. On the one hand, he renders the indeterminates by particulars as Aristotle wants. On the other, he courageously says that we have to do with a “fait du Prince” since Aristotle enjoins us to interpret a sentence which obviously has the meaning of a universal negative as if it were a particular negative. All translators, save Gohlke, render the indeterminate propositions of chapter 7, which, according to Aristotle, are particular propositions, that are true by universal propositions, that are false. The unmarked natural universal Man is white L’homme est blanc is used to translate a sentence There are white men Il y a des hommes blancs that means Some men are white Certains hommes sont blancs. In the same way, the universal Man is not white, L’homme n’est pas blanc, which is the unmarked universal negative and has therefore the same referent as the marked universal negative No man is white Aucun homme n’est blanc, is used to render a particular negative signifying that only some men are not white.
Our papers explain this aberration. There exists a system of three pairs of natural contradictories:
pair a Men are white versus Men are not white
pair b All men are white versus Some men are not white
pair c Some men are white versus No man is white.
First act of the drama: Aristotle removes Pair a where two natural unmarked universals oppose one another contradictorily: Men are white (or Man is white Ho anthropos esti leukos) versus Men are not white (or Man is not white Ho anthropos ouk esti leukos).
Second act: to render the indeterminates, one of the two translators mentioned by I. Pollak, much embarrassed by the indeterminate negative, thinks it judicious to make use of the two unmarked universals removed by Aristotle and for this reason available.
The mutilation has disastrous consequences for linguistics and logic. Aristotle’s indeterminates are useless. However the problematic indeterminate negative may be interpreted, they add nothing to the four marked propositions of chapter 7. Therefore, an erroneous translation of them is of little importance in itself. But the drawback is that the incredible rendering hides the fact that Aristotle mutilates the system of natural language. How could people be aware that he eliminates Ho anthropos esti leukos Man is white and Ho anthropos ouk esti leukos Man is not white, when they see these sentences used to translate Aristotle’s indeterminates?
So, in Chapter 7 of On Interpretation, Aristotle alters a system of three pairs of natural mutually contradictory propositions, in that he eliminates the pair where two natural universals Men are white ( Man is white) and Men are not white (Man is not white) oppose each other contradictorily (see the first diagram below). This alteration has serious consequences. These are the two natural pairs that Aristotle considers exclusively:
– All men are white ( Everyman is white) versus Some men are not white (Not all men are white Not everyman is white)
– Some men are white versus No man is white
They are illegitimately identified with the two pairs of logical contradictories constituting the logical square: A versus O and I versus E :
– I (Ex)f(x) & g(x). At least one member of mankind is white versus E (x)f(x) →~g(x) Whatever x may be, if x is man, then x is non-white
Thus, the level of natural language and that of logic are confused.
– A is the logical universal affirmative Whatever x may be, if x is man, then x is white, Whichever the member of mankind, he is white (x) f(x) → g(x). This logical universal affirmative is mistakenly confused with what I call the natural marked universal affirmative All men are white Everyman is white. In fact, A represents the referent not only of All men are white Everyman is white but also of what I call the natural unmarked universal affirmative Men are white Man is white.
–E is the logical universal negative Whatever x may be, if x is man, then x is non-white, Whichever the member of mankind, he is non-white (x) f(x) → ~g(x). This logical universal negative is mistakenly confused with what I call the natural marked universal negative No man is white. In fact, E represents the referent not only of No man is white but also of what I call the natural unmarked universal negative Men are not white Man is not white.
– I is the logical particular affirmative There exists at least one x that is man on the one hand and is white on the other There exists at least one member of mankind that is white ($x)f(x)&g(x). This logical particular affirmative is peccaminously confused with what I call the natural particular affirmative Some men are white. There is more information in the natural one than in the logical. The logical particular At least one member of mankind is white merely excludes the content of E, whereas the natural particular Some men are white excludes both the content of E and that of A. For when you say that some men are white, you imply that some are not.
– O is the logical particular negative There exists at least one x that is man on the one hand and is non-white on the other There exists at least one member of mankind that is non-white ($x) f(x)&~g(x). This logical particular negative is peccaminously confused with what I call the natural particular negative Some men are not white. There is more information in the natural one than in the logical. The logical particular At least one member of mankind is non-white merely excludes the content of A, whereas the natural particular Some men are not white excludes both the content of A and that of E. For when you say that some men are not white, you imply that some are.
The reading of the logical propositions is naturally simplified : A becomes Whichever the member of mankind, he is white ; E becomes Whichever the member of mankind, he is non-white ; I becomes At least one member of mankind is white ; O becomes At least one member of mankind is non-white. These readings purposely remain unnatural. Thus, the logical universal affirmative A will not be confused with All men are white Everyman is white, the logical universal negative E will not be confused with with No man is white, the logical particular affirmative I will not be confused with with Some men are white, the logical particular negative O will not be confused with with Some men are not white Not all men are white Not everyman is white.
The exact representation of the four propositions of the logical square
A Whichever the member of mankind, E Whichever the member of mankind,
he is white he is non-white
I- At least one member of mankind O At least one member of mankind is white is non-white
The fallacious representation of the four propositions of the logical square
A All men are white E No man is white
I- Some men are white O Some men are not white
The pair of logical propositions mutually contradictory: A versus O, Whichever the member of mankind, he is white versus At least one member of mankind is non-white must not be confused with the pair of naturalpropositions mutually contradictory All men are white versus Some men are not white.
The pair of logical propositions mutually contradictory: I versus E, At least one member of mankind is white versus Whichever the member of mankind, he is non-white must not be confused with the pair of natural propositions mutually contradictory Some men are whiteversus No man is white.
The unfortunate Aristotelian alteration is concealed by the translation of the propositions mentioned above and known as indeterminate propositions): Esti leukos anthropos, There are white men and Ouk esti leukos anthropos, There are non-white men, (so must be rendered the latter, if we want to conform to Aristotle’s intention). To translate these, which, semantically, are particulars, all scholars, save Paul Gohlke, employ the natural universals excluded by the master Men are white (Man is white) and Men are not white (Man is not white)! The work of Isidor Pollak, published in Leipzig in 1913, probably reveals the origin of this nearly universal translation mistake: the Arab version upon which Al-Farabi unfortunately bases his commentary. The logical hexagon of Robert Blanché adds the meanings Y and U to the four ones of the square. Thanks to these additions, an understanding of the manner in which the logical system and the natural one are linked becomes possible.
Two informative papers to be be read on the site http://www.grammar-and-logic.com or on the site http://erssab.u-bordeaux3.fr:
-paper 1 Paul Gohlke-Two. “A German exception: the translation of On Interpretation by Professor Gohlke. His tenth note on indeterminate propositions.(published in la Revue des Etudes anciennes 2001-Numéro 3-4)”
-paper 2 “From the logical square to the logical hexagon.The logical square of Aristotle or square of Apuleius.The logical hexagon of Robert Blanché in Structures intellectuelles. The triangle of Indian logic mentioned by J.M Bochenski
The crucial document: Gohlke’s tenth note
The complete text of the tenth footnote:
10 Hier kommt der Übersetwer in die grösste Verlegenheit, Aristoteles sagt ouk esti leukos anthropos, und der Zusammenhang verlangt ganz eindeutig, dies als eingeschränketes Urteil aufzufassen. Dies wäre nicht erreicht, wenn man sagte, ‘es kommt vor…’, ‘es kommt nicht vor…’, man muss die Verneinung zum Argumentsatz setzen ‘es kommt vor, dass nicht’. Und man darf ja auch nicht übersetzen ‘Mensch ist nicht weiss’, weil dies für uns keine eingeschränkte Aussage bedeuten würde. Sie kann dies freilich auch im griechischen Wortlaut nicht, denn Aristoteles sagt 17b 35 ja selber, man müsse den Satz im ersten Augenblick für gleichbedeutend halten mit ‘Kein Mensch ist weiss’. Wir stellen also fest, dass auf dieser Stufe lediglich das Fehlen von pas das Zeichen für die Einschränkung des Urteils ist, und wir erinnern an Erl.7 und an die Gruppe (4) im Kapitel, wo diesselbe Formel offenbar wiederum einen eingeschrankten Satz ausdrücken soll.
The translation with comments:
1 Hier kommt der Übersetwer in die grösste Verlegenheit, Aristoteles sagt ouk esti leukos anthropos, und der Zusammenhang verlangt ganz eindeutig, dies als eingeschränketes Urteil aufzufassen.
The translator is very confused here. Aristotle says Ouk esti leukos anthropos and the context clearly demands that this sentence be interpreted as a particular judgment Certains hommes ne sont pas blancs Some men are not white.
Comments
The sequence Ouk esti leukos anthropos conveys the meaning There does not exist white man, that is, the sense of a universal negative judgment No man is white. Hence, the confusion of the translator.
2 Dies wäre nicht erreicht, wenn man sagte, ‘es kommt vor…’, ‘es kommt nicht vor…’, man muss die Verneinung zum Argumentsatz setzen ‘es kommt vor, dass nicht’.
The right interpretation would be impossible, if after rendering the indeterminate affirmative Esti leukos anthropos by Es kommt vor, dass Mensch weiss ist It happens that man is white Sometimes man is white, one translated Ouk esti leukos anthropos by Es kommt nicht vor, dass Mensch weiss ist It does not happen that man is white At no time is man white.
The negation must be placed in a subordinate proposition, functioning as subject of the principal proposition in the affirmative form Es kommt vor, dass… It happens that.. sometimes. It is necessary, therefore, to render Ouk esti leukos anthropos by Es kommt vor, dass Mensch nicht weiss ist It happens that man is not white Sometimes man is not white.
Comments
Let us sum up: Ouk esti leukos anthropos must not be translated as Il n’arrive pas qu’ hommesoit blanc, At no time is man whitebut rather by Il arrive qu’homme ne soit pasblanc, Sometimes man is not white. Let us recall that to render Ouk esti leukos anthropos and give such a sentence the meaning of a particular proposition, Gohlke uses three different expressions.
1 – Es kommt vor, dass Mensch nicht weiss ist.
Il arrive qu’homme ne soit pas blanc.
It happens that man is not white.
2 – Bisweilen ist Mensch nicht weiss.
Quelquefois homme n’est pas blanc.
Sometimes man is not white.
3 – Es gibt einen nicht weissen Menschen.
Il y a un homme non-blanc.
There are non-white men.
To better understand what Gohlke does, let us use the expression es gibt, il y a, there is (are). The indeterminate assertion will be rendered by Es gibt einen weissen Menschen Il y a un homme blanc there are white men – a sentence which has the value of a particular proposition. The indeterminate affirmative therefore does not pose a problem. This is not the case for the indeterminate negative. If because of its place, the adverb of negation ouk bears on the verb esti, il existe, there is (are), then it is necessary to translate Es gibt nicht einen weissen Menschen, that is, in good German Es gibt keinen weissen Menschen Il n’y a pas d’homme blanc There is no white man. But then, the indeterminate negative has the value of a universal negative whereas Aristotle wants it to have the meaning of a particular negative. To conform to the intentions of the Master, one must therefore translate as if the adverb of negation ouk bore on the word leukos, as if one had Esti ou leukos anthropos. Therefore, one must render Es gibt einen nicht weissen Menschen, il y a un homme non blanc, There are non-white men.
Let us sum up as we have done at the beginning of this commentary but using now the expression es gibt, il y a, there is (are): the sequence Ouk esti leukos anthropos must not be rendered as Il n’y a pas d’homme blanc There is no man who is white but as Il y a un homme non-blanc, There are non-white men.
3 Und man darf ja auch nicht übersetzen ‘Mensch ist nicht weiss’, weil dies für uns keine eingeschränkte Aussage bedeuten würde.
It is not allowed either to translate Ouk esti leukos anthropos by Mensch ist nicht weiss Homme n’est pas blanc Man is not white. For a German, the sentence Mensch ist nicht weiss cannot have the meaning of a particular negative Einige Menschen sind nicht weiss, Certains hommes ne sont pas blancs, Some men are not white.
Comments
According to Germanists, the sequences Mensch ist weiss, Mensch ist nicht weiss are ungrammatical : the noun Mensch used without an article cannot have a syntactic function of subject. Nevertheless, Gohlke conjures up the sentence Mensch ist nicht weiss. In spite of its ungrammatical character, the ungrammatical Mensch ist nicht weiss induces a meaning one must consider. The sequence of these four words corresponds to the four words used in the original Greek sentence Ouk esti leukos anthropos. But in Ouk esti leukos anthropos and Mensch ist nicht weiss, the same four components are produced in a different order. The sequence Mensch ist nicht weiss represents the four words of the Greek sentence arranged in a order capable of producing an ungrammatical but understandable German sentence Mensch ist nicht weiss. If, despite its ungrammatical character, the sequence Mensch ist nicht weiss is produced, a German will interpret it par défaut. He will interpret it, as if it was Der Mensch ist nicht weiss with the content of a negative universal proposition Kein Mensch ist weiss. He would interpret it as a Der Mensch ist nicht weiss in which a non-native speaker, somebody speaking German“ wie ein Franzose” might have dropped the article Der. Anyhow, it is certain that according to Gohlke, a German would never give it the meaning of a negative particular proposition Einige Menschen sind nicht weiss, Certains hommes ne sont pas blancs, Some men are not white. If Gohlke rejects Mensch ist nicht weiss, it is certain that he rejects as well Der Mensch ist nicht weiss, that is to say, the L’homme n’est pas blanc of Tricot, the Man is not white of Cooke, the Al insan laysa huwa abyadof Ishak ibn Honain.
4 Sie kann dies freilich auch im griechischen Wortlaut nicht,
To tell the truth, the indeterminate negative from the original Greek text Ouk esti leukos anthropos cannot have the meaning of a particular negative proposition Einige Menschen sind nicht weiss, Certains hommes ne sont pas blancs, Some men are not white.
Comments
Placed as it is, the adverb of negation ouk bears on the verb esti. If esti signifies Il existe, there is (are), then ouk esti leukos anthropos signifies Es gibt keinen weissen Mensch, Il n’existe pas d’homme blanc, there are not white men. As a consequence,Ouk esti leukos anthropos signifies Kein Mensch ist weiss, Aucun homme n’est blanc, No man is white.
5 denn Aristoteles sagt 17b 35 ja selber, man müsse den Satz im ersten Augenblick für gleichbedeutend halten mit ‘Kein Mensch ist weiss’.
For, as Aristotle says himself in 17b 35, one must at first sight consider the sentence Ouk esti leukos anthropos as synonymous with Oudeis anthropos leukos, Kein Mensch is weiss, Aucun homme n’est blanc, No man is white.
Comments
The evocation of what Aristotle himself says about his Ouk esti leukos anthropos is the culminating point of the tenth footnote. We will stop the translation at this point since it is necessary to pause on the image. So, according to Gohlke, the indeterminate negative of Chapter 7 is a universal that Aristotle asks us to interpret as a particular. Professor Sanmartin of Madrid shares this opinion. Other scholars also express their perplexity. Ackrill writes: “It is a pity that Aristotle introduces indefinite statements at all.” Gohlke’s opinion may shock some people but those whom his legitimate perplexities shock must also remember that he is also the only one to translate the indeterminate negative in accordance with the viewpoints of the Master. All of the other translators render the indeterminates in Chapter 7, which have the sense of particular propositions that are true, by universal propositions that are false. The work by Isidor Pollack published at Leipzig in 1913 can perhaps explain this error. An initial Arab translation rendered the indeterminates in accordance with the form they assume in Greek. They were then translated into sentences signifying in Arabic Es gibt weisse Menschen, Il y a des hommes blancs, There are some men who are white and Es gibt keinen weissen Menschen, Il n’y a pas d’homme blanc, There is no man who is white. Then, the translator saw that the sentence Il n’y a pas d’homme blanc cannot have the meaning of a particular negative. He should have noted the difficulty and, as Gohlke did, should have substituted Es gibt nicht-weisse Menschen, Il y a des hommes non blancs, There are non-white men for Es gibt keinen weissen Menschen, Il n’y a pas d’homme blanc, There is no white man. Instead of this, he remodeled Aristotle’s indeterminates by introducing a definite article and by making the verb esti a copula. This did not help anything for the Der Mensch ist nicht weiss, L’homme n’est pas blanc with the generic article is a universal proposition as well as Il n’y a pas d’homme blanc. Even things worsened, since the indeterminate affirmative Esti leukos anthropos, which means Einige Menschen sind weiss, Some men are white became itself a universal that is false Der Mensch is weiss, Man is white. For Der Mensch ist weiss and Alle Menschen sind weiss refer to the same state of things.
These bad translations had bad effects which my paper of Damascus pointed to in 1996. They dissimulate a major fact in Chapter 7: Aristotle’s mutilation of a natural system. The sentences Der Mensch is weiss, L’homme est blanc, (the) Man is white and Der Mensch is nicht weiss, L’homme n’est pas blanc, (the) Man is not white are two great absentees from On interpretation. In Chapter 7, Aristotle did not describe them and yet it was necessary to speak of them. Do they not pertain to the natural system as much as the four marked propositions grouped into two pairs of mutually contradictory propositions : All men are white versus Not all men are white Some men are not white and Some men are white versus No man is white?
These absent sentences play a specific role in information and it is not legitimate to eliminate them. For example, Men are white does not convey the same meaning as All men are white. The proposition All men are white is what I call the marked universal affirmative whereas Men are white is what I call the unmarked universal affirmative. The marked universal contradicts Some men are not white whereas the unmarked universal contradicts Men are notwhite. Both universals affirmative of natural language, indeed, have the same referent in so far as they make known the same fact but they have not the same sense in so far as they do not exclude the same thing. For it is obvious that Some men are not white and Men are not white have not at all the same content. By contrast with the absent sentences, the indeterminates of Chapter 7 do not add anything to the four marked propositions considered by Aristotle. The indeterminate Esti leukos anthropos, Il y a des hommes blancs, There are white men is a sort of variant of the particular affirmative Quelques hommes sont blancs, Some men are white. This is also the case for the indeterminate negative Ouk esti leukos anthropos, however it may be interpreted. If it means There are non-white men, it has the meaning of the marked particular negative Ou pas anthropos leukos Not all men are white Some men are not white. If it means There is no white man, it has the meaning of the marked universal negative Oudeis anthropos leukos, No man is white. The Aristotelian mutilation has regrettable consequences. Because of it, one confuses natural propositions with the logical propositions that resemble them but which are radically different.
If what is at stake were only a good translation of the indeterminates of Chapter 7, the translating mistake would not be something serious. The indeterminate propositions are useless. To what end would they be employed by the logician ? Aristotle’s indeterminates, we have seen, are semantically equivalent to marked propositions of the logical square. Once more, however the problematic indeterminate negative Ouk esti leukos anthroposmay be interpreted, they add nothing to the four marked propositions of chapter 7. Therefore, an erroneous translation of them is of little importance in itself. But the drawback is that the incredible rendering hides the fact that Aristotle mutilates the system of natural language. How could people be aware that he eliminates Ho anthropos esti leukos Man is white and Ho anthropos ouk esti leukos Man is not white, when they see these sentences used for translating Aristotle’s indeterminates ?
The two sentences Man is white, Man is not white were not studied by Aristotle in On Interpretation, chapter 7. Still, they should have been closely examined like the four propositions, which, marked and explicitly quantified, constitute what is known as the square of Apuleius. Don’t they belong to the natural system as much as Everyman is white, Not everyman is white, Some men are white, No man is white ?
The unmarked sentences Man is white, Man is not white represent what Jean-François Monteil calls the unmarked universals of the natural system.
The system of natural language is both distinct from the underlying logical system and connected with it. Let us consider, for example, the universal affirmative of the underlying logical system A or (x) f(x) → g(x) Whatever x may be, if x has the quality denoted by f, then x has the quality denoted by g. If f represents the quality man and g the quality white, A or (x) f(x) → g(x) becomes Whatever x may be, if x is man, then x is white. It may be reasonably argued, I think, that the logical universal affirmative A or (x) f(x) → g(x) properly represents a referent common to two natural universals affirmative All men arewhite on the one hand and Men are white( or Man is white) on the other. They have the same referent, symbolized by A or (x) f(x) → g(x), in so far as they make known the same reality. Still, they have not the same meaning, we have seen, in so far as they do not exclude the same thing. We say that they have not the same power of contradiction. All men are white apprehends what we call totality T but its specific function is to contradict Some men are not white and exclude the content of it, that is, what we call partial quantity . . Men are white also apprehends totality T but its specific function is to contradict Men are not white and exclude the content of it, that is, what we call zero quantity Z. Logicians and linguists illegitimately confuse the logical universal A or (x) f(x) → g(x) Whatever x may be, if x is man, then x is white and the natural universal All men are white, which is marked. This is illegitimate because the natural universal Men are white, which is unmarked also exists and also contains the referent symbolized by A. Our article: The logical square of Aristotle or square of Apuleius. The logical hexagon of Robert Blanché in Structures intellectuelle The triangle of Indian logic mentioned by J.M Bochenski treats of the topic at large.
A-Extrait d’un courriel de Jacques Brunschwig adressé à un groupe de psychologues intéressés par les problèmes relatifs au carré.
Voici …un essai de bibliographie sélective que j’ai préparée pour ceux d’entre vous qui se sont intéressés au fameux PASTOUT. Je remercie Jean-François Monteil, dont le travail exemplaire m’en a fourni les éléments.
BIBLIOGRAPHIE SÉLECTIVE
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(1957, 1966, 1970) BLANCHÉ (R.), Introduction à la logique
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Jean-François MONTEIL, ISIDOR POLLAK ET LES DEUX TRADUCTIONS ARABES
DIFFÉRENTES DU /DE INTERPRETATIONE D’ARISTOTE, /Revue des Études
Anciennes, 2005. [un “retour” fulgurant, après tant d’années, et
quelles années ? ]
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CONSÉQUENCES CLINIQUES, Paris, EPEL., 2006.
B-Theory and History of Ontology
by Raul Corazzon – e-mail: raul.corazzon[at]formalontology.it
Annotated bibliography on Aristotle’s De Interpretatione (Peri Hermeneias)
SELECTED BIBLIOGRAPHY ON ARISTOTLE’S DE INTERPRETATIONE
Les quatre articles suivants de JFM indiqués dans la selected bibliography
(62) Monteil Jean-François, “De la traduction en arabe et en français d’un texte d’Aristote: le chapitre VII du Peri Hermeneias,” Bulletin d’Etudes Orientales 48: 57-76 (1996).
“Les propositions indéterminées du chapitre VII de Peri Hermeneias sont des particulières traduites par des universelles fausses. La cause de cette bizarrerie est dans le maître, et non dans les traducteurs. Aristote mutile un système naturel de propositions dont l’intégrité est restaurée par l’hexagone de Robert Blanché. Celui-ci ajoute deux postes au carré: Y (quantité partielle) et U (exclusion de la quantité partielle). Le carré représente A (totalité) et E (quantité zéro), mais pas avec la tierce quantité Y. Or, la quantité partielle (Y) est essentielle: c’est celle des particulières naturelles contenant notoirement plus d’information que les particulières logiques. U (exclusion de la quantité partielle) est le signifié commun aux deux phrases qu’Aristote élimine du système naturel.”
(63) Monteil Jean-François, “Une exception allemande: la traduction du De Interpretatione par le Professeur Gohlke: la note 10 sur les indéterminées d’Aristote,” Revues de Études Anciennes 103: 409-427 (2001).
“Professor Paul Gohlke is the only translator to fully respect Aristotle’s own conception of indeterminates. He was the first to perceive the linguistic problem raised by the indeterminate negative. All the other translators of De Interpretatione mistakenly render Aristotle’s indeterminates, which are particulars, as universals. The origin of this mistake lies in one of the two Arabic translations.”
Kategorien und Hermeneutik, Paderborn, Ferdinand Schöningh, 1951
(64) Monteil Jean-François, “La transmission d’Aristote par les Arabes à la chrétienté occidentale: une trouvaille relative au De Interpretatione,” Revista Española de Filosofia Medieval 11: 181-195 (2004).
“ All men are white versus Some men are not white and Some men are white versus No man is white are the two pairs of natural contradictories illegitimately identified with the two pairs of logical contradictories constituting the logical square: A versus O and I versus E, respectively. Thus, the level of natural language and that of logic are confused. The unfortunate Aristotelian alteration is concealed by the translation of propositions known as indeterminates. To translate these, which, semantically, are particulars, all scholars, save
Paul Gohlke, employ the two natural universals excluded by the Master! The work of Isador Pollak, published in Leipzig in 1913, [Die Hermeneutik des. Aristoteles in der Arabischen übersetzung des Ishiik Ibn Honain] reveals the origin of this nearly universal translation mistake: the Arabic version upon which Al-Farabi unfortunately bases his comment. In adding the vertices Y and U to the four ones of the square, the logical hexagon of Robert Blanché renders possible the understanding of the manner in which the logical system and the natural system are linked.”
Structures Intellectuelles. Essai sur l’organisation systématique des concepts – Paris, Vrin, 1966; Raison et Discours. Défense de la logique réflexive – Paris, Vrin, 1967
(65) Monteil Jean-François, “Isidor Pollak et les deux traductions arabes différentes du De interpretatione d’Aristote,” Revue d’Études Anciennes 107: 29-46 (2005).
“Dans le chapitre VII du De interpretatione, Aristote mutile un système naturel de trois couples de contradictions naturelles. Il évince le couple où deux universelles naturelles Les hommes sont blancs, Les hommes ne sont pas blancs s’opposent contradictoirement. Conséquence grave: les deux couples de contradictoires naturelles, qu’Aristote considère exclusivement, sont identifiés illégitimement aux deux couples de contradictoires logiques constituant le carré logique. Cette mutilation est dissimulée par la traduction des propositions dites “indéterminées”. L’ouvrage d’Isidor Pollak, publié à Leipzig en 1913 (Die Hermeneutik des Aristoteles in der arabischen Übersetzung des Ishak Ibn Honain, Abhandlungen für die Kunde des Morgenlandes, 13,1), révèle l’origine de cette faute de traduction quasi universelle: la version arabe sur laquelle al-Farabi fonde son commentaire.”
To sum up, Aristotle removes the pair of natural contradictories, where two universals oppose one another contradictorily. He unduly identifies the marked natural universals with logical universals. He confuses the level of natural language and that of logic.
Jean-François Monteil de Cestas
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