Aristotle's De Interpretione Chapters 6 and 7

ARISTOTLE'S DE INTERPRETATIONE CHAPTERS 6 AND 7

Below is a translation of chapters 6 and 7 of Aristotle's Perihermaneias or De Interpretatione ('On Exposition'). It does not translate Aristotle's Greek, but Boethius' Latin translation of Aristotle's Greek. While this may seem eccentric (why not go back to Aristotle's Greek?) there are a number of reasons for this.

Medieval logicians and philosophers mostly did not understand Greek. In order to understand what they thought Aristotle was talking about, we need to understand the meaning of the Latin translations that they used – particularly where they are inaccurate or misleading. To understand the various commentaries written on these chapters, the English translation must reflect any ambiguities in the Latin (since the commentators sometimes offer different versions of what Aristotle meant), and must as far as possible reflect the word order of the Latin (since the commentators deal with the text in short passages taken in the order of the Latin text). This translation will form the basis for translations of the medieval commentaries on the Perihermaneias.

Another reason for translating the Latin, not the Greek, is to have a consistent way of translating the 'incipits' which the medieval commentators used in lieu of page or line numbers to locate a passage. I have marked these in bold. For example, when Aquinas writes 'Deinde cum dicit: et sit hoc contradictio etc, he is locating the following passage in the Latin text:

Et sit hoc contradictio, affirmatio et negatio oppositae; dico autem opponi eiusdem de eodem, non autem aequivoce et quaecumque caetera talium determinamus contra sophisticas importunitates.

The Perihermaneias

I have another page here here which has background information on the whole book, and which includes Edghill's translation (from the Greek). This translation is of chapters six and seven only. In these chapters, Aristotle defines and discusses the logical relationships between the different types of proposition, as follows.

Chapter 6 begins with the definition of affirmation as the assertion 'something about something' (alicuius de aliquo), and denial as the assertion of 'something from something' (alicuius ab aliquo), the definition of true and false affirmation and falsity, and the definition of contradiction, as the opposition of affirmation and negation.

There can only be true opposition when the opposed proposition denies exactly the same thing as the affirmation affirmed. Thus Aristotle stipulates that the same proper name must not be 'equivocal'. E.g. 'Alexander seized Helen' is true of Alexander of Troy, and 'Alexander did not seize Helen' is true of Alexander of Macedonia. This example was much discussed by medieval logicians, particular in the context of negation. A denial must be of whatever was affirmed. Negation is thus the removal of what was affirmed, and no more, i.e. it is sentence negation. (However, as will be shown, sentence negation and predicate negation can be represented in terms of the other. To deny that every man is white, is to deny whiteness of some particular man. To say that it is not the case that some man is white, is to deny whiteness of every man).

Chapter 7 begins with the distinction between singular and universal propositions, and the definition of universal terms as those which are naturally predicated of many. (Thus distinguishing between terms like 'sun' and 'moon', which are naturally predicated of more than one thing, but in fact predicated of only one, and singular terms like 'Plato' which are naturally predicated of only one thing.

Aristotle defines so-called contrary assertions such as 'every A is B' and 'no A is B', and distinguishes between propositions that assert universally, i.e., which use signs of quantity like 'every', 'no' and 'some', and 'indefinite' propositions that do not use signs of quantity. Contraries cannot be true at the same time

He defines 'contradictory' as the relation of universal and particular propositions, and says that of contradictories, one must be true, the other false. Thus the contradictory opposites of contraries (i.e. what the medievals called subcontraries) can be true at the same time although they cannot be false. The contradictories of indefinite propositions, however ('an A is B' and 'an A is not B') can be true at the same time.

At this point some of the commentaries (such as Boethius and Apuleius) include the figure known as the the 'square of opposition'. The four propositions (universal affirmative and negative on top, the particular affirmative and negative below) are arranged in a square. The relation of contrariety connects the two propositions at the top, subcontrariety the two below. The diagonals connect the contradictory opposites.

Aristotle then digresses at length on a puzzle about whether 'a man is not white' is universal or particular. Finally, he summarises. 'It is manifest' that there is one negation of one affirmation. For the negation must deny what the affirmation has affirmed, and of the same thing, either of something singular, or of something universal, or universally or not universally.

Sources

Petrus Abaelardus Glossae Magistri Petri Abaelardi super Librum Perihermeneias, eds. Jacobi & Strub.
------------ Dialectica Praedicameenta de Praedicamentis Aristotelis Liber Primus De Substantia , Assen: Van Gorcum 1970. Liber Secundus De Specierum Differentiis Categoricarum.
S. Thomas de Aquino, Expositio libri Peryermeneias, Textum Leoninum Taurini 1955 edition, downloaded from the web site of Roberto Busa SJ
Boethius, De interpretatione vel Periermenias, in Aristoteles Latinus II 1-2, Translatio Boethii, ed. L. Minio-Paluello, Desclée De Brouwer, Bruges-Paris 1965.
------------ Commentarium in Librumm Aristotelis Perihermeneias, (minor commentary) primae editionis, liber primus (ed. Meiser, Teubner 1887).
------------ In Librum Aristotelis de Interpretatione, (minor commentary), ninth century manuscript held in the Schoenberg collection. Manuscript Number: ljs101. Details here.
------------ Commentarium in Librumm Aristotelis Perihermeneias, (major commentary), Secundae editionis, liber primus (ed. Meiser, Teubner 1887).

Latin English

Latin English

[06] Affirmatio vero est enuntiatio alicuius de aliquo, negatio vero enuntiatio alicuius ab aliquo. Now an affirmation is an assertion of something 'about' something, but a negation an assertion of something 'from' something.

Quoniam autem est enuntiare et quod est non esse et quod non est esse et quod est esse et quod non est non esse, et circa ea extrinsecus praesentis temporis similiter omne contingit quod quis affirmaverit negare et quod quis negaverit affirmare; quare manifestum est quoniam omni affirmationi est negatio opposita et omni negationi affirmatio. Now since it is [possible] to assert both that what is the case is not so,and what is not the case is so, and what is the case is so, and what is not the case is not so, and [since] concerning those things which are outside the present time it is similarly possible to deny anything someone has affirmed, or affirm anything which someone has denied, from this it is manifest that to every affirmation there is a negation opposed, and to every negation an affirmation.

Et sit hoc contradictio, affirmatio et negatio oppositae; dico autem opponi eiusdem de eodem, non autem aequivoce et quaecumque caetera talium determinamus contra sophisticas importunitates. Also, let a 'contradiction' be affirmation and negation opposed. And I say that the same is opposed to the same: but not equivocally, and any other such qualifications we make against sophistical quibblings.

[07] Quoniam autem sunt haec quidem rerum universalia, illa vero singillatim (dico autem universale quod in pluribus natum est praedicari, singulare vero quod non, ut 'homo' quidem universale, 'Plato' vero eorum quae sunt singularia), necesse est autem enuntiare quoniam inest aliquid aut non, aliquotiens quidem eorum alicui quae sunt universalia, aliquotiens vero eorum quae sunt singularia. But since some things are universal, others singular (now I call 'universal' that which is naturally predicated of many, but 'singular' that which is not – 'man' e.g. is universal, but 'Plato' belongs to those which are singular), it is necessary to assert that something is in something or not, sometimes for example in one of the things which are universal, but sometimes in one of the things which are singular.

Si ergo universaliter enuntiet in universali quoniam est aut non, erunt contrariae enuntiationes (dico autem in universali enuntiationem universalem ut 'omnis homo albus est', 'nullus homo albus est'); quando autem in universalibus non universaliter, non sunt contrariae, quae autem significantur est esse contraria. If therefore one universally asserts in a universal that it is something or not, the assertions will be contrary (I call a proposition in something universal such as 'every man is white' or 'no man is white' a universal assertion). When they are in universals but not universally, they are not contraries, but it is [possible] that what are signified are contraries.

Dico autem non universaliter enuntiare in his quae sunt universalia, ut 'est albus homo', 'non est albus homo'; cum enim universale sit homo, non universaliter utitur enuntiatione. 'Omnis' namque non universale [est] sed quoniam universaliter [homine] consignificat. In eo vero quod universale praedicatur, id quod est [universale] universaliter praedicare non est verum. Nulla enim affirmatio erit, in qua de universali praedicato universale praedicetur, ut 'omnis homo omne animal'. Now I say that propositions such as 'a man is white' [or] 'a man is not white' do not universally assert in what are universal. For while 'man' is universal, the assertion is not employed universally. For 'every' is not universal, but rather signifies universally with ['man']. But in respect of that which, being universal, is predicated, it is not true to to predicate that which is universal universally. For it will be no affirmation, in which it is predicated universally [reading universaliter] of a universal predicate, such as 'every man is every animal'.

Opponi autem affirmationem negationi dico contradictorie quae universal[iter] significat eidem quoniam non universaliter, ut 'omnis homo albus est', 'non omnis homo albus est', 'nullus homo albus est', 'quidam homo albus est'; contrarie vero universalem affirmationem et universalem negationem, ut 'omnis homo iustus est', 'nullus homo iustus est'; quocirca has quidem impossibile est simul veras esse, his vero oppositas contingit in eodem, 'non omnis homo albus est', et 'est quidam homo albus'. Now I say an affirmation is opposed to a negation 'as a contradictory', which universally signifies the same as what the other signifies, but not universally, such as 'every man is white', 'not every man is white', 'no man is white', 'a certain man is white', but 'as a contrary' a universal affirmation and a universal negation, such as 'every man is just', 'no man is just'. For which reason, of course, it is impossible for them to be true together, but their opposites, 'not every man is white', and 'a certain man is white', may be true at the same time [in eodem].

Quaecumque igitur contradictiones universalium sunt universaliter, necesse est alteram esse veram vel falsam, et quaecumque in singularibus sunt, ut 'est Socrates albus', 'non est Socrates albus'; quaecumque autem in universalibus non universaliter, non semper haec vera est, illa vero falsa (simul enim verum est dicere quoniam est homo albus et non est homo albus, et est homo probus et non est homo probus; si enim turpis, non probus; et si fit aliquid, et non est). Accordingly, whatever are contradictions of universals universally, it is necessary that one is true, the other false, also whatever are of singulars, as 'Socrates is white', 'Socrates is not white'. But whatever are [contradictions] in universals not universally, it is will not always be the case that one is true, the other false (for it is true to say at the same time that a man is white, and a man is not white, and a man is honest, and a man is not honest. E.g. if he is dishonourable, and not honourable, and if he becomes something, and is not it).

Videbitur autem subito inconveniens esse, idcirco quoniam videtur significare 'non est homo albus' simul etiam quoniam nemo homo albus est; hoc autem neque idem significat neque simul necessario. It will seem at first sight inconsistent, because 'a man is not white' seems to signify at the same time also that no one [is] a white man. However it does not signify the same thing, nor necessarily at the same time.

Manifestum est autem quoniam una negatio unius affirmationis est; hoc enim idem oportet negare negationem quod affirmavit affirmatio, et de eodem, vel de aliquo singularium vel de aliquo universalium, vel universaliter vel non universaliter; dico autem ut 'est Socrates albus', 'non est Socrates albus' (si autem aliud aliquid vel de alio idem, non opposita sed erit ab ea diversa), huic vero quae est 'omnis homo albus est' illa quae est 'non omnis homo albus est', illi vero quae est 'aliquis homo albus est' illa quae est 'nullus homo albus est', illi autem quae est 'homo albus est' illa quae est 'non est homo albus'. Now it is manifest that there is one negation of one affirmation. For the negation must deny what the affirmation has affirmed, and of the same thing, either of something singular, or of something universal, or universally or not universally. Now I mean, [dico] for example, 'Socrates is white', 'Socrates is not white'. But if another thing [is predicated] of something, or the same thing of another thing, it will not be opposed, but different from it, but to 'every man is white', [there is opposed]'not every man is white', and to 'some man is white', 'no man is white', and to 'a man is white', 'a man is not white'.

Quoniam ergo uni negationi una affirmatio opposita est contradictorie, et quae sint hae, dictum est, et quoniam aliae sunt contrariae et quae sint hae, et quoniam non omnis vera vel falsa contradictio, et quare, et quando vera vel falsa. It has been said therefore that to one negation there is one affirmation opposed as a contradictory, and what they are, and that some are contrary and what they are, and that not every contradiction is true or false, and when true or false.

Latin	English
Latin	English
[06] Affirmatio vero est enuntiatio alicuius de aliquo, negatio vero enuntiatio alicuius ab aliquo.	Now an affirmation is an assertion of something 'about' something, but a negation an assertion of something 'from' something.
Quoniam autem est enuntiare et quod est non esse et quod non est esse et quod est esse et quod non est non esse, et circa ea extrinsecus praesentis temporis similiter omne contingit quod quis affirmaverit negare et quod quis negaverit affirmare; quare manifestum est quoniam omni affirmationi est negatio opposita et omni negationi affirmatio.	Now since it is [possible] to assert both that what is the case is not so,and what is not the case is so, and what is the case is so, and what is not the case is not so, and [since] concerning those things which are outside the present time it is similarly possible to deny anything someone has affirmed, or affirm anything which someone has denied, from this it is manifest that to every affirmation there is a negation opposed, and to every negation an affirmation.
Et sit hoc contradictio, affirmatio et negatio oppositae; dico autem opponi eiusdem de eodem, non autem aequivoce et quaecumque caetera talium determinamus contra sophisticas importunitates.	Also, let a 'contradiction' be affirmation and negation opposed. And I say that the same is opposed to the same: but not equivocally, and any other such qualifications we make against sophistical quibblings.
[07] Quoniam autem sunt haec quidem rerum universalia, illa vero singillatim (dico autem universale quod in pluribus natum est praedicari, singulare vero quod non, ut 'homo' quidem universale, 'Plato' vero eorum quae sunt singularia), necesse est autem enuntiare quoniam inest aliquid aut non, aliquotiens quidem eorum alicui quae sunt universalia, aliquotiens vero eorum quae sunt singularia.	But since some things are universal, others singular (now I call 'universal' that which is naturally predicated of many, but 'singular' that which is not – 'man' e.g. is universal, but 'Plato' belongs to those which are singular), it is necessary to assert that something is in something or not, sometimes for example in one of the things which are universal, but sometimes in one of the things which are singular.
Si ergo universaliter enuntiet in universali quoniam est aut non, erunt contrariae enuntiationes (dico autem in universali enuntiationem universalem ut 'omnis homo albus est', 'nullus homo albus est'); quando autem in universalibus non universaliter, non sunt contrariae, quae autem significantur est esse contraria.	If therefore one universally asserts in a universal that it is something or not, the assertions will be contrary (I call a proposition in something universal such as 'every man is white' or 'no man is white' a universal assertion). When they are in universals but not universally, they are not contraries, but it is [possible] that what are signified are contraries.
Dico autem non universaliter enuntiare in his quae sunt universalia, ut 'est albus homo', 'non est albus homo'; cum enim universale sit homo, non universaliter utitur enuntiatione. 'Omnis' namque non universale [est] sed quoniam universaliter [homine] consignificat. In eo vero quod universale praedicatur, id quod est [universale] universaliter praedicare non est verum. Nulla enim affirmatio erit, in qua de universali praedicato universale praedicetur, ut 'omnis homo omne animal'.	Now I say that propositions such as 'a man is white' [or] 'a man is not white' do not universally assert in what are universal. For while 'man' is universal, the assertion is not employed universally. For 'every' is not universal, but rather signifies universally with ['man']. But in respect of that which, being universal, is predicated, it is not true to to predicate that which is universal universally. For it will be no affirmation, in which it is predicated universally [reading universaliter] of a universal predicate, such as 'every man is every animal'.
Opponi autem affirmationem negationi dico contradictorie quae universal[iter] significat eidem quoniam non universaliter, ut 'omnis homo albus est', 'non omnis homo albus est', 'nullus homo albus est', 'quidam homo albus est'; contrarie vero universalem affirmationem et universalem negationem, ut 'omnis homo iustus est', 'nullus homo iustus est'; quocirca has quidem impossibile est simul veras esse, his vero oppositas contingit in eodem, 'non omnis homo albus est', et 'est quidam homo albus'.	Now I say an affirmation is opposed to a negation 'as a contradictory', which universally signifies the same as what the other signifies, but not universally, such as 'every man is white', 'not every man is white', 'no man is white', 'a certain man is white', but 'as a contrary' a universal affirmation and a universal negation, such as 'every man is just', 'no man is just'. For which reason, of course, it is impossible for them to be true together, but their opposites, 'not every man is white', and 'a certain man is white', may be true at the same time [in eodem].
Quaecumque igitur contradictiones universalium sunt universaliter, necesse est alteram esse veram vel falsam, et quaecumque in singularibus sunt, ut 'est Socrates albus', 'non est Socrates albus'; quaecumque autem in universalibus non universaliter, non semper haec vera est, illa vero falsa (simul enim verum est dicere quoniam est homo albus et non est homo albus, et est homo probus et non est homo probus; si enim turpis, non probus; et si fit aliquid, et non est).	Accordingly, whatever are contradictions of universals universally, it is necessary that one is true, the other false, also whatever are of singulars, as 'Socrates is white', 'Socrates is not white'. But whatever are [contradictions] in universals not universally, it is will not always be the case that one is true, the other false (for it is true to say at the same time that a man is white, and a man is not white, and a man is honest, and a man is not honest. E.g. if he is dishonourable, and not honourable, and if he becomes something, and is not it).
Videbitur autem subito inconveniens esse, idcirco quoniam videtur significare 'non est homo albus' simul etiam quoniam nemo homo albus est; hoc autem neque idem significat neque simul necessario.	It will seem at first sight inconsistent, because 'a man is not white' seems to signify at the same time also that no one [is] a white man. However it does not signify the same thing, nor necessarily at the same time.
Manifestum est autem quoniam una negatio unius affirmationis est; hoc enim idem oportet negare negationem quod affirmavit affirmatio, et de eodem, vel de aliquo singularium vel de aliquo universalium, vel universaliter vel non universaliter; dico autem ut 'est Socrates albus', 'non est Socrates albus' (si autem aliud aliquid vel de alio idem, non opposita sed erit ab ea diversa), huic vero quae est 'omnis homo albus est' illa quae est 'non omnis homo albus est', illi vero quae est 'aliquis homo albus est' illa quae est 'nullus homo albus est', illi autem quae est 'homo albus est' illa quae est 'non est homo albus'.	Now it is manifest that there is one negation of one affirmation. For the negation must deny what the affirmation has affirmed, and of the same thing, either of something singular, or of something universal, or universally or not universally. Now I mean, [dico] for example, 'Socrates is white', 'Socrates is not white'. But if another thing [is predicated] of something, or the same thing of another thing, it will not be opposed, but different from it, but to 'every man is white', [there is opposed]'not every man is white', and to 'some man is white', 'no man is white', and to 'a man is white', 'a man is not white'.
Quoniam ergo uni negationi una affirmatio opposita est contradictorie, et quae sint hae, dictum est, et quoniam aliae sunt contrariae et quae sint hae, et quoniam non omnis vera vel falsa contradictio, et quare, et quando vera vel falsa.	It has been said therefore that to one negation there is one affirmation opposed as a contradictory, and what they are, and that some are contrary and what they are, and that not every contradiction is true or false, and when true or false.

THE LOGIC MUSEUM Copyright (introduction and translation) (C) E.D.Buckner 2007.