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New page: <body lang=EN-GB style='font-family:Garamond'> <hr> BOETHIUS' TRANSLATION OF THE PERIHERMANEIAS <hr> <a href = "#intro">Introduction</a> <a href =...

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<hr> BOETHIUS' TRANSLATION OF THE PERIHERMANEIAS <hr>


<a href = "#intro">Introduction</a> 
<a href = "#c1">Chapter 1</a>. The spoken word is a symbol of thought. 
<a href = "#c2">Chapter 2</a>. Definition of noun 
<a href = "#c3">Chapter 3</a>. Definition of verb 
<a href = "#c4">Chapter 4</a>. Definition of sentence 
<a href = "#c5">Chapter 5</a>. Simple and compound propositions 
<a href = "#c6">Chapter 6</a>. Contradictory propositions 
<a href = "#c7">Chapter 7</a>. Universal, indefinite and particular propositions. Contrary propositions 
<a href = "#c8">Chapter 8</a>. Definition of single propositions. 
<a href = "#c9">Chapter 9</a>. Propositions which refer to present, past and future 
<a href = "#c10">Chapter 10</a>. Pairs of affirmations and denials 
<a href = "#c11">Chapter 11</a>. Apparently simple propositions which are really compound 
<a href = "#c12">Chapter 12</a>. Propositions concerning necessity and posssibility. 
<a href = "#c13">Chapter 13</a>. Relation between such propositions. 
<a href = "#c14">Chapter 14</a>. Contrary affirmations and denials 

 <a name = "intro">Introduction

The following is not a parallel translation, but rather two translations, one English, one Latin,
of the Greek text of Aristotle's Perihermaneias
(commonly known by its Latin name De Interpretatione).
The Latin is Boethius's translation, made in the late fifth or early sixth century A.D.
The English is the translation by E.M. Edghill of Bekker's 1831 text, published in 1928 by Oxford University Press.

While the differences between the between Edghill's English and Boethius' Latin) are not large<a href = "#note1">[1]</a>,
it is obviously not intended as an English translation of Boethius.
The purpose of this page is to to provide a background to Latin logical language using a classic text that most English readers will be familiar with.
(You may also find
<a href = "http://www.orbilat.com/Languages/Latin/Grammar/Latin-Pronouns_Indefinite.html">this</a>
guide to Latin quantifiers useful).

History

According to the Kneales, The Perihermaneias is one Aristotle's earlier logical works.
The Greek name means 'On Exposition'. It was called by that name by most medieval writers (using various spellings such as Pery Hermaneias &c),
but has been known by the Latin De Interpretatione since the Renaissance.

Boethius (472-524) was a fifth century Christian who wrote extensively on logic, philosophy and mathematics.
He is seen as important mainly as a medium by which the culture of antiquiry was transmitted to the middle ages.
In particular, his Latin versions of Aristotle's Categories
(also in the Logic Museum <a href = "boethiuscategories.htm">here</a>) and the De Interpretatione (below)
were probably the only texts available to philosophers of the early medieval period (Minio-Paluello,
'Note sull Aristotele latino medievale', Rivista di filosofia neo-scolastico, xliv (1952) 398-401,
'Les traductions et les commentaires Aristoteliciens de Boece', Studia Patristica, ii (1957) 358-65.Before the rise of the universities, Aristotle’s works were mostly known,
if at all, through the translations and commentaries of Boethius.
Boethius’ commentary probably owes its survival to its inclusion in Alcuin’s program for the revival of classical
scholarship in the court schools of Charlemagne.


He is also important because his writings and translations are in Latin,
which in the Middles Ages became the language in which all philosophical, theological and logical discourse was carried on.
As is well known, many of the technical terms in those disciplines, which are now carried on English, French, German &c,
were imported wholesale from the Latin. Thus, even where Boethius' Latin does not accurately reflect Aristotle's Greek,
it accurately reflects much of the thinking and terminology that was used afterwards, because his translation became the
basis of the future development of the discipline.
The basis of medieval semantics and truth theory lies in Boethius' Latin, rather than Aristotle's Greek

 The Perihermaneias 

The Perihermaneias contains the main account of Aristotle's theory of meaning and truth, and was
a starting point for medieval 'terminist' semantics. Some of the ideas are as follows:


1. A noun and a verb are the minimum requirements for making a sentence (which Boethius calls oratio).
Not every sentence is a proposition (oratio enuntiativa), since prayers are sentences, but not propositions.
A proposition is only what has in it either truth or falsity
(enuntiativa vero non omnis sed in qua verum vel falsum inest).

Note that only once does Boethius use the word 'propositio'
for what Edghill translates as 'the admission of a premiss'<a href = "#note2">[2]</a>.
However, later writers such is Ockham preferred 'proposition', which is the ancestor of our modern 'proposition'.

2. Spoken words are signs of mental modifications (Boethius: notae passionum anima - literally passions or modifications of the soul).
While the signs are not necessarily the same (i.e. if the written or spoken languages are different)
these modifications are the same in all people (eaedem omnibus passiones animae sunt).
This later developed into the idea, defended by Ockham and Buridan and others, that spoken propositions,
i.e. sentences, represent mental propositions of which they are the outward signs.

3. Universal signs are 'of a nature' to be predicated of many.
The Latin formula was universale quod in pluribus natum est praedicari, repeated by writers of logic textbooks
such as Peter of Spain and a hundred others since.


4. An affirmation is a assertion of something about something (affirmatio vero est enuntiatio alicuius de aliquo),
a denial is an assertion of something "from" something (negatio vero enuntiatio alicuius ab aliquo).
The Latin formulation neatly reflects the Greek, where the difference between a 'positive' affirmation,
and 'negative' denial is expressed simply by prepositions –
affirmation (kataphasis) is apophansis tinos kata tinos, (something of something)
and denial (apophasis) is apophansis tinos apo tinos. 'Nego' in Latin means
to deny<a href = "#note3">[3]</a>.

5. Every affirmation has an opposite denial, and similarly every denial an opposite affirmation
(omni affirmationi est negatio opposita et omni negationi affirmatio). This was the basis of the well-known
'square of opposition' - see below.

6. The distinction between singular and general propositions.

7. The idea of 'wide scope' or 'sentence' negation. Aristotle says that a denial must deny exactly whatthe affirmation affirms,
(idem oportet negare negationem quod affirmavit affirmatio)


8. In the case of that which is or which has taken place, either the affirmation or the denial is true or false.
(In his ergo quae sunt et facta sunt necesse est affirmationem vel negationem veram vel falsam esse).
This leads to the famous puzzle that nothing nothing exists or happens by accident.
Of whatever happens tomorrow, it is true today to say that it happens tomorrow. But if it is true,
for example, that a sea battle (navale bellum) will happen tomorrow, this suggests it is
unavoidably true, and that what will happen in the future will happen by necessity.


The Square of Opposition


The idea that there are certain logical relationships between the four kinds of Aristotelian proposition,
when they have the same subject and predicate, is developed in chapters
<a href = "#c6">six</a> and <a href = "#c7">seven</a>.
It became the basis of a diagram originating with Boethius and used by medieval logicians to classify
these possible logical relations. The four propositions - the universal affirmative ('every man is just'),
the universal negative ('no man is just'),
the particular affirmative ('some man is just') and the particular negative ('some man is not just') -
are placed in the four corners of a square, and the relations represented as lines drawn between them.

Pairs of propositions are called contradictories (contradictoriae) when they cannot at the same time both be true or both be false,
contraries (contrariae) when both cannot at the same time be true, subcontraries (subcontrariae) when both cannot at the same time be false,
and subalternates (subalternae) when the truth of the one proposition implies the truth of the other, but not conversely.
The corresponding relations are known as contradiction (contradictio), contrariety (contrarietas), subcontrariety (subcontrarietas) and subalternation (subalternatio).

Thus

* Universal statements are contraries: 'every man is just' and 'no man is just' cannot be true together, although one may be true and the other false,
and also both may be false (if one at least man is not just, and at least one man is not just).

* Particular statements are subcontraries. 'Some man is just' and 'some man is not just' cannot be false together

* The universal affirmative and the particular affirmative are subalternates, because in Aristotelian semantics
'every A is B' implies 'some A is B'. This fact has caused endless controversy since the middle of the nineteenth century,
following the development of modern semantics where there is no such implication. Similarly the universal negative
and the particular negative are subalternates since, again, 'no A is B' was thought to imply 'some A is not B'.

* The universal affirmative and the particular negative are contradictories. Clearly if some A is not B,
not every A is B. Conversely, though this is not intuitive for modern semantics, it was thought that if every A is not B,
some A is not B. This interpretation has also caused much controversy. Note that Aristotle's Greek does not
represent the particular negative as 'some A is not B', but as 'not every A is B', and Boethius' Latin faithfully
follows him. However, in Boethius commentary on the Perihermaneias,
he renders the particular negative as 'quidam A non est B', literally 'a certain A is not a B',
which under any ordinary reading of the Latin (see Lewis and Short, e.g.) is existential, implying the existence of
a particular A which is not a B. Terence Parsons has suggested (<a href = "http://plato.stanford.edu/entries/square">here</a>)
that the Latin 'quidam A non est B' does not have existential import, but this seems implausible,
given that it means that a certain, or a particular A, is not B.


<blockquote>
<table border="0" cellpadding="0" cellspacing="0" summary="">
<tr>
<td align="center"><img src="../latin/pictures/A.jpg" width="120" height="14"></td>
<td>----------- contraries -----------</td>
<td align="center"><img src="../latin/pictures/E.jpg" width="120" height="16"></td>
</tr>
<tr> <td align="center">every man runs</td> <td></td> <td align="center">no man runs</td> </tr>
<tr> <td align="center">|</td> <td> </td> <td align="center">|</td> </tr>
<tr> <td align="center">|</td> <td> </td> <td align="center">|</td> </tr>
<tr> <td align="center">|</td> <td>     \                                /     </td> <td align="center">|</td> </tr>
<tr> <td align="center">|</td> <td> </td> <td align="center">|</td> </tr>

<tr> <td align="center">subalternates</td> <td align="center">contradictories</td> <td align="center">subalternates</td> </tr>

<tr> <td align="center">|</td> <td> </td> <td align="center">|</td> </tr>
<tr> <td align="center">|</td> <td>     /                                \     </td> <td align="center">|</td> </tr>
<tr> <td align="center">|</td> <td> </td> <td align="center">|</td> </tr>
<tr> <td align="center">|</td> <td> </td> <td align="center">|</td> </tr>
<tr>
<td align="center"><img src="../latin/pictures/I.jpg" width="120" height="16"></td>
<td>-------- subcontraries -----------</td>
<td align="center"><img src="../latin/pictures/O.jpg" width="140" height="18"></td>
</tr>
<tr> <td align="center">a certain man runs</td> <td></td> <td align="center">a certain man does not run</td> </tr>
</table>
</blockquote>
 

Hyperlinks


Another advantage of using Boethius' Latin is that medieval commentators on Aristotle refer to this translation, or very similar translations, in making references.
Thus I have placed bookmarks in the main positions which other medieval writers refer to.
For example, if Aquinas writes 'ibi:
<a href = "#inhisergo">in his ergo quae sunt et quae facta sunt et cetera</a>',
which is his way of identifying the particular passage in Aristotle's text which begins with those words,
we have the much easier way of using the hyperlink to take us there. No heavy books, no leafing through pages of indecipherable contractions. Progress indeed.

I am developing a set of pages in the Logic Museum consisting of medieval commentaries
(such as by Aquinas, Abelard and Boethius himself) on the Perihermaneias.

<hr>References 
Kneale, W. & M., The Development of Logic, Oxford, 1971


<hr>
Aristotle's Perhermaneias. Latin translatin by Boethius, English translation by Edghill.
<table rules = groups>
<table border cellpadding = 10 span = 2>
<COL width=45%>
<COL width=55%>
<thead>
<tr> <th>Latin</th><th>English</th>
</tr> </thead> <tbody>
<tr> <td> ARISTOTELES: DE INTERPRETATIONE
</td> <td>
</td> </tr>
<tr> <td> <a name = "c1">[01] Primum oportet constituere quid sit nomen et quid verbum, postea quid est negatio et affirmatio et enuntiatio et oratio.
</td> <td> First we must define the terms 'noun' and 'verb', then the terms 'denial' and 'affirmation', then 'proposition' and 'sentence.'

</td> </tr>
<tr> <td> Sunt ergo ea quae sunt in voce earum quae sunt in anima passionum notae, et ea quae scribuntur eorum quae sunt in voce. Et quemadmodum nec litterae omnibus eaedem, sic nec eaedem voces; quorum autem hae primorum notae, eaedem omnibus passiones animae sunt, et quorum hae similitudines, res etiam eaedem.
</td> <td> Spoken words are the symbols of mental experience and written words are the symbols of spoken words. Just as all men have not the same writing, so all men have not the same speech sounds, but the mental experiences, which these directly symbolize, are the same for all, as also are those things of which our experiences are the images.
</td> </tr>
<tr> <td> De his quidem dictum est in his quae sunt dicta de anima -- alterius est enim negotii -- ; est autem, quemadmodum in anima aliquotiens quidem intellectus sine vero vel falso, aliquotiens autem cum iam necesse est horum alterum inesse, sic etiam in voce; circa compositionem enim et divisionem est falsitas veritasque.
</td> <td> This matter has, however, been discussed in my treatise about the soul, for it belongs to an investigation distinct from that which lies before us. As there are in the mind thoughts which do not involve truth or falsity, and also those which must be either true or false, so it is in speech. For truth and falsity imply combination and separation.

</td> </tr>
<tr> <td> Nomina igitur ipsa et verba consimilia sunt sine compositione vel divisione intellectui, ut 'homo' vel 'album', quando non additur aliquid; neque enim adhuc verum aut falsum est. Huius autem signum: 'hircocervus' enim significat aliquid sed nondum verum vel falsum, si non vel 'esse' vel 'non esse' addatur vel simpliciter vel secundum tempus.
</td> <td> Nouns and verbs, provided nothing is added, are like thoughts without combination or separation; 'man' and 'white', as isolated terms, are not yet either true or false. In proof of this, consider the word 'goat-stag.' It has significance, but there is no truth or falsity about it, unless 'is' or 'is not' is added, either in the present or in some other tense.

</td> </tr>
<tr> <td> <a name = "c2">[02] DE NOMINE Nomen ergo est vox significativa secundum placitum sine tempore, cuius nulla pars est significativa separata; in 'equiferus' enim 'ferus' nihil per se significat, quemadmodum in oratione quae est 'equus ferus'. At vero non quemadmodum in simplicibus nominibus, sic se habet et in compositis; in illis enim nullo modo pars significativa est, in his autem vult quidem sed nullius separati, ut in 'equiferus' <'ferus'>.
</td> <td> By a noun we mean a sound significant by convention, which has no reference to time, and of which no part is significant apart from the rest. In the noun 'Fairsteed,' the part 'steed' has no significance in and by itself, as in the phrase 'fair steed.' Yet there is a difference between simple and composite nouns; for in the former the part is in no way significant, in the latter it contributes to the meaning of the whole, although it has not an independent meaning. Thus in the word 'pirate-boat' the word 'boat' has no meaning except as part of the whole word.

</td> </tr>
<tr> <td> "Secundum placitum" vero, quoniam naturaliter nominum nihil est sed quando fit nota; nam designant et inlitterati soni, ut ferarum, quorum nihil est nomen.
</td> <td> The limitation 'by convention' was introduced because nothing is by nature a noun or name-it is only so when it becomes a symbol; inarticulate sounds, such as those which brutes produce, are significant, yet none of these constitutes a noun.
</td> </tr>
<tr> <td> 'Non homo' vero non est nomen; at vero nec positum est nomen quod illud oporteat appellari -- neque enim oratio aut negatio est -- sed sit nomen infinitum.
</td> <td> The expression 'not-man' is not a noun. There is indeed no recognized term by which we may denote such an expression, for it is not a sentence or a denial. Let it then be called an indefinite noun.
</td> </tr>
<tr> <td> 'Catonis' autem vel 'Catoni' et quaecumque talia sunt non sunt nomina sed casus nominis. Ratio autem eius est in aliis quidem eadem sed differt quoniam, cum 'est' vel 'fuit' vel 'erit' adiunctum, neque verum neque falsum est, nomen vero semper; ut 'Catonis est' vel 'non est' -- nondum enim aliquid neque rerum dicit neque mentitur.
</td> <td> The expressions 'of Philo', 'to Philo', and so on, constitute not nouns, but cases of a noun. The definition of these cases of a noun is in other respects the same as that of the noun proper, but, when coupled with 'is', 'was', or will be', they do not, as they are, form a proposition either true or false, and this the noun proper always does, under these conditions. Take the words 'of Philo is' or 'of or 'of Philo is not'; these words do not, as they stand, form either a true or a false proposition.
</td> </tr>
<tr> <td> <a name = "c3">[03] DE VERBO Verbum autem est quod consignificat tempus, cuius pars nihil extra significat; et est semper eorum quae de altero praedicantur nota.
</td> <td> A verb is that which, in addition to its proper meaning, carries with it the notion of time. No part of it has any independent meaning, and it is a sign of something said of something else.
</td> </tr>
<tr> <td> Dico autem quoniam consignificat tempus, ut 'cursus' quidem nomen est, 'currit' vero verbum -- consignificat enim nunc esse -- ; et semper eorum quae de altero dicuntur nota est, ut eorum quae de subiecto vel in subiecto.
</td> <td> I will explain what I mean by saying that it carries with it the notion of time. 'Health' is a noun, but 'is healthy' is a verb; for besides its proper meaning it indicates the present existence of the state in question. Moreover, a verb is always a sign of something said of something else, i.e. of something either predicable of or present in some other thing.
</td> </tr>
<tr> <td> 'Non currit' vero et 'non laborat' non verbum dico; consignificat quidem tempus et semper de aliquo est, differentiae autem huic nomen non est positum; sed sit infinitum verbum, quoniam similiter in quolibet est vel quod est vel quod non est.
</td> <td> Such expressions as 'is not-healthy', 'is not, ill', I do not describe as verbs; for though they carry the additional note of time, and always form a predicate, there is no specified name for this variety; but let them be called indefinite verbs, since they apply equally well to that which exists and to that which does not.
</td> </tr>
<tr> <td> Similiter autem vel 'curret' vel 'currebat' non verbum est sed casus verbi; differt autem a verbo quoniam hoc quidem praesens significat tempus, illa vero quod complectitur.
</td> <td> Similarly 'he was healthy', 'he will be healthy', are not verbs, but tenses of a verb; the difference lies in the fact that the verb indicates present time, while the tenses of the verb indicate those times which lie outside the present.
</td> </tr>
<tr> <td> Ipsa quidem secundum se dicta verba nomina sunt et significant aliquid -- constituit enim qui dicit intellectum, et qui audit quiescit -- sed si est vel non est nondum significat. Neque enim 'esse' signum est rei vel 'non esse', nec si hoc ipsum 'est' purum dixeris: ipsum quidem nihil est, consignificat autem quandam compositionem quam sine compositis non est intellegere.
</td> <td> Verbs in and by themselves are substantival and have significance, for he who uses such expressions arrests the hearer's mind, and fixes his attention; but they do not, as they stand, express any judgement, either positive or negative. For neither are 'to be' and 'not to be' the participle 'being' significant of any fact, unless something is added; for they do not themselves indicate anything, but imply a copulation, of which we cannot form a conception apart from the things coupled.
</td> </tr>
<tr> <td> <a name = "c4">[04] DE ORATIONE Oratio autem est vox significativa, cuius partium aliquid significativum est separatum (ut dictio, non ut affirmatio); dico autem ut 'homo' significat aliquid (sed non quoniam est aut non est; sed erit affirmatio vel negatio, si quid addatur) sed non una 'hominis' syllaba; nec in hoc quod est 'sorex' 'rex' significat sed vox est nunc sola.

</td> <td> A sentence is a significant portion of speech, some parts of which have an independent meaning, that is to say, as an utterance, though not as the expression of any positive judgement. Let me explain. The word 'human' has meaning, but does not constitute a proposition, either positive or negative. It is only when other words are added that the whole will form an affirmation or denial. But if we separate one syllable of the word 'human' from the other, it has no meaning; similarly in the word 'mouse', the part 'ouse' has no meaning in itself, but is merely a sound.
</td> </tr>
<tr> <td> In duplicibus vero significat quidem sed non secundum se, quemadmodum dictum est.
</td> <td> In composite words, indeed, the parts contribute to the meaning of the whole; yet, as has been pointed out, they have not an independent meaning.
</td> </tr>
<tr> <td> Est autem oratio omnis quidem significativa non sicut instrumentum sed (quemadmodum dictum est) secundum placitum; enuntiativa vero non omnis sed in qua verum vel falsum inest; non autem in omnibus, ut deprecatio oratio quidem est sed neque vera neque falsa.
</td> <td> Every sentence has meaning, not as being the natural means by which a physical faculty is realized, but, as we have said, by convention. Yet every sentence is not a proposition; only such are propositions as have in them either truth or falsity. Thus a prayer is a sentence, but is neither true nor false.
</td> </tr>
<tr> <td> Et caeterae quidem relinquantur (rhetoricae enim vel poeticae convenientior consideratio est; enuntiativa vero praesentis considerationis est).
</td> <td> Let us therefore dismiss all other types of sentence but the proposition, for this last concerns our present inquiry, whereas the investigation of the others belongs rather to the study of rhetoric or of poetry.
</td> </tr>
<tr> <td> <a name = "c5">[05] Est autem una prima oratio enuntiativa affirmatio, deinde negatio; aliae vero coniunctione unae.
</td> <td> The first class of simple propositions is the simple affirmation, the next, the simple denial; all others are only one by conjunction.
</td> </tr>
<tr> <td> Necesse est autem omnem orationem enuntiativam ex verbo esse vel casu; et enim, hominis rationi si non aut 'est' aut 'erit' aut 'fuit' aut aliquid huiusmodi addatur, nondum est oratio enuntiativa. Quare autem unum quiddam est et non multa 'animal gressibile bipes' -- neque enim eo quod propinque dicuntur unum erit -- est alterius hoc tractare negotii.
</td> <td> Every proposition must contain a verb or the tense of a verb. The phrase which defines the species 'man', if no verb in present, past, or future time be added, is not a proposition. It may be asked how the expression 'a footed animal with two feet' can be called single; for it is not the circumstance that the words follow in unbroken succession that effects the unity. This inquiry, however, finds its place in an investigation foreign to that before us.
</td> </tr>
<tr> <td> <a name = "estautemuna">
Est autem una oratio enuntiativa quae unum significat vel coniunctione una, plures autem quae plura et non unum vel inconiunctae.
</td> <td> We call those propositions single which indicate a single fact, or the conjunction of the parts of which results in unity: those propositions, on the other hand, are separate and many in number, which indicate many facts, or whose parts have no conjunction.
</td> </tr>
<tr> <td> Nomen ergo et verbum dictio sit sola, quoniam non est dicere sic aliquid significantem voce enuntiare, vel aliquo interrogante vel non sed ipsum proferentem.
</td> <td> Let us, moreover, consent to call a noun or a verb an expression only, and not a proposition, since it is not possible for a man to speak in this way when he is expressing something, in such a way as to make a statement, whether his utterance is an answer to a question or an act of his own initiation.
</td> </tr>
<tr> <td> Harum autem haec quidem simplex est enuntiatio, ut aliquid de aliquo vel aliquid ab aliquo, haec autem ex his coniuncta, velut oratio quaedam iam composita. Est autem simplex enuntiatio vox significativa de eo quod est aliquid vel non est, quemadmodum tempora divisa sunt.
</td> <td> To return: of propositions one kind is simple, i.e. that which asserts or denies something of something, the other composite, i.e. that which is compounded of simple propositions. A simple proposition is a statement, with meaning, as to the presence of something in a subject or its absence, in the present, past, or future, according to the divisions of time.
</td> </tr>
<tr> <td> <a name = "c6">[06] Affirmatio vero est enuntiatio alicuius de aliquo, negatio vero enuntiatio alicuius ab aliquo.
</td> <td> An affirmation is a positive assertion of something about something, a denial a negative assertion.
</td> </tr>
<tr> <td> <a name = "quoniamautemest">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.
</td> <td> Now it is possible both to affirm and to deny the presence of something which is present or of something which is not, and since these same affirmations and denials are possible with reference to those times which lie outside the present, it would be possible to contradict any affirmation or denial. Thus it is plain that every affirmation has an opposite denial, and similarly every denial an opposite affirmation.
</td> </tr>
<tr> <td> <a name = "etsichoc">
Et sit hoc contradictio, affirmatio et negatio oppositae; <a name = "dicoautem">dico autem opponi eiusdem de eodem, <a name = "nonautem">non autem aequivoce <a name = "etquaecumque">
et quaecumque caetera talium determinamus contra sophisticas importunitates.
</td> <td> We will call such a pair of propositions a pair of contradictories. Those positive and negative propositions are said to be contradictory which have the same subject and predicate. The identity of subject and of predicate must not be 'equivocal'. Indeed there are definitive qualifications besides this, which we make to meet the casuistries of sophists.
</td> </tr>
<tr> <td> <a name = "c7">[07] <a name = "quoniamautemsunt">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, <a name = "platovero">'Plato' vero eorum quae sunt singularia), <a name = "necesseest">necesse est autem enuntiare quoniam inest aliquid aut non, aliquotiens quidem eorum alicui quae sunt universalia, aliquotiens vero eorum quae sunt singularia.
</td> <td> Some things are universal, others individual. By the term 'universal' I mean that which is of such a nature as to be predicated of many subjects, by 'individual' that which is not thus predicated. Thus 'man' is a universal, 'Callias' an individual. Our propositions necessarily sometimes concern a universal subject, sometimes an individual.
</td> </tr>
<tr> <td> <a name = "siergouniversaliter">Si ergo universaliter enuntiet in universali quoniam est aut non,
erunt contrariae enuntiationes (<a name = "dicoautemin">dico autem in universali enuntiationem universalem ut 'omnis homo albus est', 'nullus homo albus est'); <a name = "quandoautem">quando autem in universalibus non universaliter,
non sunt contrariae, <a name = "quaeautem">quae autem significantur est esse contraria
(<a name = "dicoautemnon">dico autem non universaliter enuntiare in his quae sunt universalia, ut 'est albus homo', 'non est albus homo'; <a name = "cumenim">cum enim universale sit homo, non universaliter utitur enuntiatione;
'omnis' namque non 'universale' sed 'quoniam universaliter' consignificat).
In eo vero quod praedicatur universaliter universale praedicare universaliter non est verum; nulla
enim affirmatio erit, in qua de universaliter praedicato universale praedicetur, ut 'omnis homo omne animal'.
</td> <td> If, then, a man states a positive and a negative proposition of universal character with regard to a universal, these two propositions are 'contrary'. By the expression 'a proposition of universal character with regard to a universal', such propositions as 'every man is white', 'no man is white' are meant. When, on the other hand, the positive and negative propositions, though they have regard to a universal, are yet not of universal character, they will not be contrary, albeit the meaning intended is sometimes contrary. As instances of propositions made with regard to a universal, but not of universal character, we may take the 'propositions 'man is white', 'man is not white'. 'Man' is a universal, but the proposition is not made as of universal character; for the word 'every' does not make the subject a universal, but rather gives the proposition a universal character.
</td> </tr>
<tr> <td> <a name = "opponiautem">Opponi autem affirmationem negationi dico contradictorie quae universale significat eidem quoniam non universaliter,
ut 'omnis homo albus est', '<a name = "nonomnishomo">non omnis homo albus est', 'nullus homo albus est', 'quidam homo albus est';
<a name = "contrarievero">contrarie vero universalem affirmationem et universalem negationem, <a name = "utomnis">ut 'omnis homo iustus est', 'nullus homo iustus est'; <a name = "quocircahas">quocirca has quidem impossibile est simul veras esse, <a name = "hisvero">
his vero oppositas contingit in eodem, 'non omnis homo albus est', et 'est quidam homo albus'.
</td> <td> An affirmation is opposed to a denial in the sense which I denote by the term 'contradictory', when, while the subject remains the same, the affirmation is of universal character and the denial is not. The affirmation 'every man is white' is the contradictory of the denial 'not every man is white', or again, the proposition 'no man is white' is the contradictory of the proposition 'some men are white'. But propositions are opposed as contraries when both the affirmation and the denial are universal, as in the sentences 'every man is white', 'no man is white', 'every man is just', 'no man is just'. We see that in a pair of this sort both propositions cannot be true, but the contradictories of a pair of contraries can sometimes both be true with reference to the same subject; for instance 'not every man is white' and some men are white' are both true.

</td> </tr>
<tr> <td> <a name = "quaecumqueigitur">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';
<a name = "quaecumqautem">quaecumque autem in universalibus non universaliter, non semper haec vera est,
illa vero falsa (<a name = "simulenimverum">simul enim verum est dicere quoniam est homo albus et non est homo albus, et est homo probus et non est homo probus;
<a name = "sienimturpis">si enim turpis, non probus; et si fit aliquid, et non est).
</td> <td> Of such corresponding positive and negative propositions as refer to universals and have a universal character, one must be true and the other false. This is the case also when the reference is to individuals, as in the propositions 'Socrates is white', 'Socrates is not white'.

When, on the other hand, the reference is to universals, but the propositions are not universal, it is not always the case that one is true and the other false, for it is possible to state truly that man is white and that man is not white and that man is beautiful and that man is not beautiful; for if a man is deformed he is the reverse of beautiful, also if he is progressing towards beauty he is not yet beautiful.
</td> </tr>
<tr> <td> <a name = "videbiturautem">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.
</td> <td> This statement might seem at first sight to carry with it a contradiction, owing to the fact that the proposition 'man is not white' appears to be equivalent to the proposition 'no man is white'. This, however, is not the case, nor are they necessarily at the same time true or false.
</td> </tr>
<tr> <td> <a name = "manifestumest"> Manifestum est autem quoniam una negatio unius affirmationis est;
<a name = "hocenim">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; <a name = "dicoautemut">
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'.
</td> <td> It is evident also that the denial corresponding to a single affirmation is itself single; for the denial must deny just that which the affirmation affirms concerning the same subject, and must correspond with the affirmation both in the universal or particular character of the subject and in the distributed or undistributed sense in which it is understood. For instance, the affirmation 'Socrates is white' has its proper denial in the proposition 'Socrates is not white'. If anything else be negatively predicated of the subject or if anything else be the subject though the predicate remain the same, the denial will not be the denial proper to that affirmation, but on that is distinct. The denial proper to the affirmation 'every man is white' is 'not every man is white'; that proper to the affirmation 'some men are white' is 'no man is white', while that proper to the affirmation 'man is white' is 'man is not white'.
</td> </tr>
<tr> <td> <a name = "quoniamergo">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.
</td> <td> We have shown further that a single denial is contradictorily opposite to a single affirmation and we have explained which these are; we have also stated that contrary are distinct from contradictory propositions and which the contrary are; also that with regard to a pair of opposite propositions it is not always the case that one is true and the other false. We have pointed out, moreover, what the reason of this is and under what circumstances the truth of the one involves the falsity of the other.
</td> </tr>
<tr> <td> <a name = "c8">[08] <a name = "unaautem">Una autem est affirmatio et negatio quae unum de uno significat, vel cum sit universale universaliter vel non similiter, ut 'omnis homo albus est', 'non est omnis homo albus', 'est homo albus', 'non est homo albus', 'nullus homo albus est', 'est quidam homo albus', si 'album' unum significat.
</td> <td> An affirmation or denial is single, if it indicates some one fact about some one subject; it matters not whether the subject is universal and whether the statement has a universal character, or whether this is not so. Such single propositions are: 'every man is white', 'not every man is white';'man is white','man is not white'; 'no man is white', 'some men are white'; provided the word 'white' has one meaning.
</td> </tr>
<tr> <td> <a name = "sinvero">Sin vero duobus unum nomen est positum <a name = "exquibus"> ex quibus non est unum, non est una affirmatio; <a name = "utsiquis">ut, si quis ponat nomen 'tunica' homini et equo, 'est tunica alba' haec non est una affirmatio nec negatio una; nihil enim hoc differt dicere quam 'est equus et homo albus', <a name = "hocautem">
hoc autem <a name = "nihidiffert">nihil differt quam dicere 'est equus albus' et 'est homo albus'.
</td> <td> If, on the other hand, one word has two meanings which do not combine to form one, the affirmation is not single. For instance, if a man should establish the symbol 'garment' as significant both of a horse and of a man, the proposition 'garment is white' would not be a single affirmation, nor its opposite a single denial. For it is equivalent to the proposition 'horse and man are white', which, again, is equivalent to the two propositions 'horse is white', 'man is white'.
</td> </tr>
<tr> <td> Si ergo hae multa significant et sunt plures, <a name = "manifestumestquoniam">manifestum est quoniam et prima multa vel nihil significat (neque enim est aliquis homo equus); <a name = "quarenec">quare nec in his necesse est hanc quidem contradictionem veram esse, illam vero falsam.
</td> <td> If, then, these two propositions have more than a single significance, and do not form a single proposition, it is plain that the first proposition either has more than one significance or else has none; for a particular man is not a horse. This, then, is another instance of those propositions of which both the positive and the negative forms may be true or false simultaneously.
</td> </tr>
<tr> <td> <a name = "c9">[09] <a name = "inhisergo"> In his ergo quae sunt et facta sunt necesse est affirmationem vel negationem veram vel falsam esse; in universalibus quidem universaliter semper hanc quidem veram, illam vero falsam, et in his quae sunt singularia, quemadmodum dictum est; in his vero quae in universalibus non universaliter dicuntur, non est necesse (dictum autem est et de his).
</td> <td> In the case of that which is or which has taken place, propositions, whether positive or negative, must be true or false. Again, in the case of a pair of contradictories, either when the subject is universal and the propositions are of a universal character, or when it is individual, as has been said,' one of the two must be true and the other false; whereas when the subject is universal, but the propositions are not of a universal character, there is no such necessity. We have discussed this type also in a previous chapter.
</td> </tr>
<tr> <td> In singularibus vero et futuris non similiter; nam si omnis affirmatio vel negatio vera vel falsa est, et omne necesse est vel esse vel non esse; si hic quidem dicat futurum aliquid, ille vero non dicat hoc idem ipsum, manifestum est quoniam necesse est verum dicere alterum ipsorum si omnis affirmatio vera vel falsa est (utraque enim non erunt simul in talibus).
</td> <td> When the subject, however, is individual, and that which is predicated of it relates to the future, the case is altered. For if all propositions whether positive or negative are either true or false, then any given predicate must either belong to the subject or not, so that if one man affirms that an event of a given character will take place and another denies it, it is plain that the statement of the one will correspond with reality and that of the other will not. For the predicate cannot both belong and not belong to the subject at one and the same time with regard to the future.
</td> </tr>
<tr> <td> Nam si verum est dicere quoniam album vel non album est, necesse est esse album vel non album, et, si est album vel non album, verum est vel affirmare vel negare; et, si non est, mentitur, et si mentitur non est; quare necesse est aut affirmationem aut negationem veram esse.
</td> <td> Thus, if it is true to say that a thing is white, it must necessarily be white; if the reverse proposition is true, it will of necessity not be white. Again, if it is white, the proposition stating that it is white was true; if it is not white, the proposition to the opposite effect was true. And if it is not white, the man who states that it is making a false statement; and if the man who states that it is white is making a false statement, it follows that it is not white. It may therefore be argued that it is necessary that affirmations or denials must be either true or false.
</td> </tr>
<tr> <td> Nihil igitur neque est neque fit nec a casu nec utrumlibet, nec erit nec non erit sed ex necessitate omnia et non utrumlibet (aut enim qui dicit verus est aut qui negat); similiter enim vel fieret vel non fieret; utrumlibet enim nihil magis sic vel non sic se habet aut habebit.
</td> <td> Now if this be so, nothing is or takes place fortuitously, either in the present or in the future, and there are no real alternatives; everything takes place of necessity and is fixed. For either he that affirms that it will take place or he that denies this is in correspondence with fact, whereas if things did not take place of necessity, an event might just as easily not happen as happen; for the meaning of the word 'fortuitous' with regard to present or future events is that reality is so constituted that it may issue in either of two opposite directions.
</td> </tr>
<tr> <td> Amplius, si est album nunc, verum erat dicere primo quoniam erit album, quare semper verum fuit dicere quodlibet illud eorum quae facta sunt quoniam erit; quod si semper verum est dicere quoniam est vel erit, non potest hoc non esse nec non futurum esse.
</td> <td> Again, if a thing is white now, it was true before to say that it would be white, so that of anything that has taken place it was always true to say 'it is' or 'it will be'. But if it was always true to say that a thing is or will be, it is not possible that it should not be or not be about to be,
</td> </tr>
<tr> <td> Quod autem non potest non fieri, impossibile est non fieri; et quod impossibile est non fieri, necesse est fieri; omnia ergo quae futura sunt necesse est fieri. Nihil igitur utrumlibet neque casu erit; nam si a casu, non ex necessitate.
</td> <td> and when a thing cannot not come to be, it is impossible that it should not come to be, and when it is impossible that it should not come to be, it must come to be. All, then, that is about to be must of necessity take place. It results from this that nothing is uncertain or fortuitous, for if it were fortuitous it would not be necessary.
</td> </tr>
<tr> <td> At vero nec quoniam neutrum verum est contingit dicere, ut quoniam neque erit neque non erit.
</td> <td> Again, to say that neither the affirmation nor the denial is true, maintaining, let us say, that an event neither will take place nor will not take place, is to take up a position impossible to defend.
</td> </tr>
<tr> <td> Primum enim, cum sit affirmatio falsa, erit negatio non vera, et cum haec sit falsa, contingit affirmationem esse non veram.
</td> <td> In the first place, though facts should prove the one proposition false, the opposite would still be untrue.
</td> </tr>
<tr> <td> Ad haec, si verum est dicere quoniam album est et magnum, oportet utraque esse, sin vero erit cras, esse cras; si autem neque erit neque non erit cras, non erit utrumlibet, ut navale bellum; oportebit enim neque fieri navale bellum neque non fieri navale bellum.
</td> <td> Secondly, if it was true to say that a thing was both white and large, both these qualities must necessarily belong to it; and if they will belong to it the next day, they must necessarily belong to it the next day. But if an event is neither to take place nor not to take place the next day, the element of chance will be eliminated. For example, it would be necessary that a sea-fight should neither take place nor fail to take place on the next day.
</td> </tr>
<tr> <td> Quae ergo contingunt inconvenientia haec sunt et huiusmodi alia, si omnis affirmationis et negationis vel in his quae in universalibus dicuntur universaliter vel in his quae sunt singularia, necesse est oppositarum hanc esse veram, illam vero falsam, nihil autem utrumlibet esse in his quae fiunt sed omnia esse vel fieri ex necessitate.
</td> <td> These awkward results and others of the same kind follow, if it is an irrefragable law that of every pair of contradictory propositions, whether they have regard to universals and are stated as universally applicable, or whether they have regard to individuals, one must be true and the other false, and that there are no real alternatives, but that all that is or takes place is the outcome of necessity.

</td> </tr>
<tr> <td> Quare non oportebit neque consiliari neque negotiari quoniam, si hoc facimus, erit hoc, si vero hoc, non erit.
</td> <td> There would be no need to deliberate or to take trouble, on the supposition that if we should adopt a certain course, a certain result would follow, while, if we did not, the result would not follow.
</td> </tr>
<tr> <td> Nihil enim prohibet in millesimum annum hunc quidem dicere hoc futurum esse, hunc vero non dicere, quare ex necessitate erit quodlibet eorum verum erat dicere tunc.
</td> <td> For a man may predict an event ten thousand years beforehand, and another may predict the reverse; that which was truly predicted at the moment in the past will of necessity take place in the fullness of time.
</td> </tr>
<tr> <td> At vero nec hoc differt si aliqui dixerunt negationem vel non dixerunt; manifestum est enim quod sic se habent res vel si hic quidem affirmaverit, ille vero negaverit; non enim propter negare vel affirmare erit vel non erit, nec in millesimum annum magis quam in quantolibet tempore.
</td> <td> Further, it makes no difference whether people have or have not actually made the contradictory statements. For it is manifest that the circumstances are not influenced by the fact of an affirmation or denial on the part of anyone. For events will not take place or fail to take place because it was stated that they would or would not take place, nor is this any more the case if the prediction dates back ten thousand years or any other space of time.
</td> </tr>
<tr> <td> Quare si in omni tempore sic se habebat ut unum verum diceretur, necesse esset hoc fieri et unumquodque eorum quae fiunt sic se habere ut ex necessitate fieret. Quando enim sere dicit quis quoniam erit, non potest non fieri; et quod factum est, verum erat dicere semper quoniam erit.
</td> <td> Wherefore, if through all time the nature of things was so constituted that a prediction about an event was true, then through all time it was necessary that that should find fulfillment; and with regard to all events, circumstances have always been such that their occurrence is a matter of necessity. For that of which someone has said truly that it will be, cannot fail to take place; and of that which takes place, it was always true to say that it would be.
</td> </tr>
<tr> <td> Quod si haec non sunt possibilia -- videmus enim esse principium futurorum et ab eo quod consiliamur atque agimus aliquid, et quoniam est omnino in his quae non semper actu sunt esse possibile et non, in quibus utrumque contingit et esse et non esse, quare et fieri et non fieri; et multa nobis manifesta sunt sic se habentia, ut quoniam hanc uestem possibile est, incidi et non inciditur sed prius exteritur; similiter autem et non incidi possibile est; non enim esset eam prius exteri nisi esset possibile non incidi; quare et in aliis facturis quaecumque secundum potentiam dicuntur huiusmodi -- manifestum est quoniam non omnia ex necessitate vel sunt vel fiunt sed alia, quidem utrumlibet et non magis vel affirmatio vel negatio, alia vero magis quidem in pluribus alterum sed contingit fieri et alterum, alterum vero minime.
</td> <td> Yet this view leads to an impossible conclusion; for we see that both deliberation and action are causative with regard to the future, and that, to speak more generally, in those things which are not continuously actual there is potentiality in either direction. Such things may either be or not be; events also therefore may either take place or not take place. There are many obvious instances of this. It is possible that this coat may be cut in half, and yet it may not be cut in half, but wear out first. In the same way, it is possible that it should not be cut in half; unless this were so, it would not be possible that it should wear out first. So it is therefore with all other events which possess this kind of potentiality. It is therefore plain that it is not of necessity that everything is or takes place; but in some instances there are real alternatives, in which case the affirmation is no more true and no more false than the denial; while some exhibit a predisposition and general tendency in one direction or the other, and yet can issue in the opposite direction by exception.
</td> </tr>
<tr> <td> Igitur esse quod est quando est, et non esse quod non est quando non est, necesse est; sed non quod est omne necesse est esse, nec quod non est necesse est non esse (non enim idem est omne quod est esse necessario quando est, et simpliciter esse ex necessitate); similiter autem et in eo quod non est. Et in contradictione eadem ratio est; esse quidem vel non esse omne necesse est et futurum esse vel non; non tamen dividentem dicere alterum necessario.
</td> <td> Now that which is must needs be when it is, and that which is not must needs not be when it is not. Yet it cannot be said without qualification that all existence and non-existence is the outcome of necessity. For there is a difference between saying that that which is, when it is, must needs be, and simply saying that all that is must needs be, and similarly in the case of that which is not. In the case, also, of two contradictory propositions this holds good. Everything must either be or not be, whether in the present or in the future, but it is not always possible to distinguish and state determinately which of these alternatives must necessarily come about.
</td> </tr>
<tr> <td> Dico autem, necesse est quidem futurum esse bellum navale cras vel non esse futurum sed non futurum esse cras bellum navale necesse est vel non futurum esse, futurum autem esse vel non esse necesse est.
</td> <td> Let me illustrate. A sea-fight must either take place to-morrow or not, but it is not necessary that it should take place to-morrow, neither is it necessary that it should not take place, yet it is necessary that it either should or should not take place to-morrow.
</td> </tr>
<tr> <td> Quare, quoniam similiter orationes verae sunt quemadmodum et res, manifestum est quoniam quaecumque sic se habent ut utrumlibet sint et contraria ipsorum contingere, necesse est similiter se habere et contradictionem; quod contingit in his quae non semper sunt et non semper non sunt; horum enim necesse est quidem alteram partem contradictionis veram esse vel falsam, non tamen hoc aut illud sed utrumlibet, et magis quidem veram alteram, non tamen iam veram vel falsam.
</td> <td> Since propositions correspond with facts, it is evident that when in future events there is a real alternative, and a potentiality in contrary directions, the corresponding affirmation and denial have the same character. This is the case with regard to that which is not always existent or not always nonexistent. One of the two propositions in such instances must be true and the other false, but we cannot say determinately that this or that is false, but must leave the alternative undecided. One may indeed be more likely to be true than the other, but it cannot be either actually true or actually false.
</td> </tr>
<tr> <td> Quare manifestum est quoniam non est necesse omnes affirmationes vel negationes oppositarum hanc quidem veram, illam autem falsam esse; neque enim quemadmodum in his quae sunt sic se habent etiam in his quae non sunt, possibilium tamen esse aut non esse sed quemadmodum dictum est.
</td> <td> It is therefore plain that it is not necessary that of an affirmation and a denial one should be true and the other false. For in the case of that which exists potentially, but not actually, the rule which applies to that which exists actually does not hold good. The case is rather as we have indicated.
</td> </tr>
<tr> <td> <a name = "c10">[10] <a name = "quoniamautem">Quoniam autem est de aliquo affirmatio significans aliquid, hoc autem est vel nomen vel innominabile, unum autem oportet esse et de uno hoc quod est in affirmatione (nomen autem dictum est et innominabile prius; 'non homo' enim nomen quidem non dico sed infinitum nomen -- unum enim significat infinitum -- quemadmodum et 'non currit' non verbum sed infinitum verbum), erit omnis affirmatio vel ex nomine vel ex verbo.
</td> <td> An affirmation is the statement of a fact with regard to a subject, and this subject is either a noun or that which has no name; the subject and predicate in an affirmation must each denote a single thing. I have already explained' what is meant by a noun and by that which has no name; for I stated that the expression 'not-man' was not a noun, in the proper sense of the word, but an indefinite noun, denoting as it does in a certain sense a single thing. Similarly the expression 'does not enjoy health' is not a verb proper, but an indefinite verb. Every affirmation, then, and every denial, will consist of a noun and a verb, either definite or indefinite.
</td> </tr>
<tr> <td> Praeter verbum autem nulla affirmatio vel negatio; 'est' enim vel 'erit' vel 'fuit' vel 'fit' vel quaecumque alia huiusmodi, verba ex his sunt quae sunt posita (consignificant enim tempus).
</td> <td> There can be no affirmation or denial without a verb; for the expressions 'is', 'will be', 'was', 'is coming to be', and the like are verbs according to our definition, since besides their specific meaning they convey the notion of time.
</td> </tr>
<tr> <td> Quare prima affirmatio et negatio 'est homo -- non est homo', deinde 'est non homo -- non est non homo', 'est omnis homo -- non est omnis homo', 'est omnis non homo -- non est omnis non homo'; et in extrinsecus temporibus eadem ratio est.
</td> <td> Thus the primary affirmation and denial are 'as follows: 'man is', 'man is not'. Next to these, there are the propositions: 'not-man is', 'not-man is not'. Again we have the propositions: 'every man is, 'every man is not', 'all that is not-man is', 'all that is not-man is not'. The same classification holds good with regard to such periods of time as lie outside the present.
</td> </tr>
<tr> <td> Quando autem 'est' tertium adiacens praedicatur, dupliciter dicuntur oppositiones. Dico autem ut 'est iustus homo' 'est' tertium dico adiacere nomen vel verbum in affirmatione.
</td> <td> When the verb 'is' is used as a third element in the sentence, there can be positive and negative propositions of two sorts. Thus in the sentence 'man is just' the verb 'is' is used as a third element, call it verb or noun, which you will.
</td> </tr>
<tr> <td> Quare idcirco quattuor istae erunt, quarum duae quidem ad affirmationem et negationem sese habebunt secundum consequentiam ut priuationes, duae vero minime; dico autem quoniam 'est' aut 'iusto' adiacebit aut 'non iusto'; quare etiam negatio.
</td> <td> Four propositions, therefore, instead of two can be formed with these materials. Two of the four, as regards their affirmation and denial, correspond in their logical sequence with the propositions which deal with a condition of privation; the other two do not correspond with these. I mean that the verb 'is' is added either to the term 'just' or to the term 'not-just', and two negative propositions are formed in the same way.
</td> </tr>
<tr> <td> Quattuor ergo sunt. Intellegimus vero quod dicitur ex his quae subscripta sunt: est iustus homo -- huius negatio: non est iustus homo est non iustus homo -- negatio: non est non iustus homo 'est' enim hoc loco et 'non est' 'iusto' et 'non iusto' adiacet.
</td> <td> Thus we have the four propositions. Reference to the subjoined table will make matters clear: A. Affirmation B. Denial Man is just Man is not just \ / X / \ D. Denial C. Affirmation Man is not not-just Man is not-just Here 'is' and 'is not' are added either to 'just' or to 'not-just'.
</td> </tr>
<tr> <td> Haec igitur, quemadmodum in Resolutoriis dictum est, sic sunt disposita. Similiter autem se habet et si universalis nominis sit affirmatio, ut 'omnis est homo iustus', 'omnis est homo non iustus'.
</td> <td> This then is the proper scheme for these propositions, as has been said in the Analytics. The same rule holds good, if the subject is distributed. Thus we have the table: A'. Affirmation B'. Denial Every man is just Not every man is just \ / X D'. Denial / \ C'. Affirmation
Not every man is not-just Every man is not-just
</td> </tr>
<tr> <td> Sed non similiter angulares contingit veras esse, contingit autem aliquando.

Hae igitur duae oppositae sunt, aliae autem ad 'non homo' ut subiectum aliquod addito, ut est iustus non homo -- non est iustus non homo est non iustus non homo -- non est non iustus non homo Magis plures autem his non erunt oppositiones;

hae autem extra illas ipsae secundum se erunt, ut nomine utentes 'non homo'.
</td> <td> Yet here it is not possible, in the same way as in the former case, that the propositions joined in the table by a diagonal line should both be true; though under certain circumstances this is the case.

We have thus set out two pairs of opposite propositions; there are moreover two other pairs, if a term be conjoined with 'not-man', the latter forming a kind of subject. Thus:

A." B." Not-man is just Not-man is not just \ / - X

D." / \ C." Not-man is not not-just Not-man is not-just

This is an exhaustive enumeration of all the pairs of opposite propositions that can possibly be framed. This last group should remain distinct from those which preceded it, since it employs as its subject the expression 'not-man'.
</td> </tr>
<tr> <td> In his vero in quibus 'est' non convenit, ut in eo quod est 'currere' vel 'ambulare', idem faciunt sic posita ac si 'est' adderetur, ut est currit omnis homo -- non currit omnis homo currit omnis non homo -- non currit omnis non homo non enim dicendum est 'non omnis homo' sed 'non' negationem ad id quod est 'homo' addendum est; 'omnis' enim non universale significat sed quoniam universaliter; manifestum est autem ex eo quod est 'currit homo -- non currit homo; currit non homo -- non currit non homo'; haec enim ab illis differunt eo quod non universaliter sunt; quare 'omnis' vel 'nullus' nihil aliud consignificat nisi quoniam universaliter de nomine vel affirmat vel negat; ergo et caetera eadem oportet apponi.
</td> <td> When the verb 'is' does not fit the structure of the sentence (for instance, when the verbs 'walks', 'enjoys health' are used), that scheme applies, which applied when the word 'is' was added. Thus we have the propositions: 'every man enjoys health', 'every man does-not-enjoy-health', 'all that is not-man enjoys health', 'all that is not-man does-not-enjoy-health'. We must not in these propositions use the expression 'not every man'. The negative must be attached to the word 'man', for the word 'every' does not give to the subject a universal significance, but implies that, as a subject, it is distributed. This is plain from the following pairs: 'man enjoys health', 'man does not enjoy health'; 'not-man enjoys health', 'not man does not enjoy health'. These propositions differ from the former in being indefinite and not universal in character. Thus the adjectives 'every' and no additional significance except that the subject, whether in a positive or in a negative sentence, is distributed. The rest of the sentence, therefore, will in each case be the same.
</td> </tr>
<tr> <td> Quoniam vero contraria est negatio ei quae est 'omne est animal iustum' illa quae significat quoniam 'nullum est animal iustum', hae quidem manifestum est quoniam numquam erunt neque verae simul neque in eodem ipso, his vero oppositae erunt aliquando: 'non omne animal iustum' -- <'est aliquod animal iustum'>.
</td> <td> Since the contrary of the proposition 'every animal is just' is 'no animal is just', it is plain that these two propositions will never both be true at the same time or with reference to the same subject. Sometimes, however, the contradictories of these contraries will both be true, as in the instance before us: the propositions 'not every animal is just' and 'some animals are just' are both true.
</td> </tr>
<tr> <td> Sequuntur vero eam quidem quae est 'nullus est homo iustus' illa quae est 'omnis est homo non iustus', illam vero quae est 'est aliqui iustus homo' opposita quoniam 'non omnis homo est non iustus'; necesse est enim esse aliquem.
</td> <td> Further, the proposition 'no man is just' follows from the proposition 'every man is not just' and the proposition 'not every man is not just', which is the opposite of 'every man is not-just', follows from the proposition 'some men are just'; for if this be true, there must be some just men.
</td> </tr>
<tr> <td> Manifestum est autem quoniam etiam in singularibus, si est verum interrogatum negare, quoniam et affirmare verum est, ut 'putasne Socrates sapiens est?', 'non est', quoniam 'Socrates igitur non sapiens est'.
</td> <td> It is evident, also, that when the subject is individual, if a question is asked and the negative answer is the true one, a certain positive proposition is also true. Thus, if the question were asked Socrates wise?' and the negative answer were the true one, the positive inference 'Then Socrates is unwise' is correct.
</td> </tr>
<tr> <td> In universalibus vero non est vera quae similiter dicitur, vera autem negatio, ut 'putasne omnis homo sapiens?', 'non', 'omnis igitur homo non sapiens'; hoc enim falsum est sed 'non igitur omnis homo sapiens' vera est; haec autem est opposita, illa vero contraria.
</td> <td> But no such inference is correct in the case of universals, but rather a negative proposition. For instance, if to the question 'Is every man wise?' the answer is 'no', the inference 'Then every man is unwise' is false. But under these circumstances the inference 'Not every man is wise' is correct. This last is the contradictory, the former the contrary.
</td> </tr>
<tr> <td> Illae vero secundum infinita contraiacentes nomina vel verba, ut in eo quod est 'non homo' vel 'non iustus', quasi negationes sine nomine vel verbo esse videbuntur sed non sunt; semper enim vel veram esse vel falsam necesse est negationem, qui vero dixit 'non homo' nihil magis de homine sed etiam minus verus fuit vel falsus, si non aliquid addatur.
</td> <td> Negative expressions, which consist of an indefinite noun or predicate, such as 'not-man' or 'not-just', may seem to be denials containing neither noun nor verb in the proper sense of the words. But they are not. For a denial must always be either true or false, and he that uses the expression 'not man', if nothing more be added, is not nearer but rather further from making a true or a false statement than he who uses the expression 'man'.
</td> </tr>
<tr> <td> Significat autem 'est omnis non homo iustus' nulli illarum idem, nec huic opposita ea quae est 'non est omnis non homo iustus'; illa vero quae est 'omnis non iustus non homo' illi quae est 'nullus iustus non homo' idem significat.
</td> <td> The propositions 'everything that is not man is just', and the contradictory of this, are not equivalent to any of the other propositions; on the other hand, the proposition 'everything that is not man is not just' is equivalent to the proposition 'nothing that is not man is just'.
</td> </tr>
<tr> <td> Transposita vero nomina vel verba idem significant, ut 'est homo albus -- est albus homo'; nam si hoc non est, eiusdem multae erunt negationes sed ostensum est quoniam una unius est.
</td> <td> The conversion of the position of subject and predicate in a sentence involves no difference in its meaning. Thus we say 'man is white' and 'white is man'. If these were not equivalent, there would be more than one contradictory to the same proposition, whereas it has been demonstrated' that each proposition has one proper contradictory and one only.
</td> </tr>
<tr> <td> Eius enim quae est 'est albus homo' negatio est 'non est albus homo'; eius vero quae est 'est homo albus', si non eadem est [quae etiam] ei quae est 'est albus homo', erit negatio vel ea quae est 'non est non homo albus' vel ea quae est 'non est homo albus'.
</td> <td> For of the proposition 'man is white' the appropriate contradictory is 'man is not white', and of the proposition 'white is man', if its meaning be different, the contradictory will either be 'white is not not-man' or 'white is not man'. Now the former of these is the contradictory of the proposition 'white is not-man',
</td> </tr>
<tr> <td> Sed altera quidem est negatio eius quae est 'est non homo albus', alia vero eius quae est 'est albus homo', quare erunt duae unius.
</td> <td> and the latter of these is the contradictory of the proposition 'man is white'; thus there will be two contradictories to one proposition.
</td> </tr>
<tr> <td> Quoniam igitur transposito nomine vel verbo eadem fit affirmatio vel negatio manifestum est.
</td> <td> It is evident, therefore, that the inversion of the relative position of subject and predicate does not affect the sense of affirmations and denials.
</td> </tr>
<tr> <td> <a name = "c11">[11] At vero unum de pluribus vel plura de uno affirmare vel negare, si non est unum ex pluribus, non est affirmatio una neque negatio.
</td> <td> There is no unity about an affirmation or denial which, either positively or negatively, predicates one thing of many subjects, or many things of the same subject, unless that which is indicated by the many is really some one thing.
</td> </tr>
<tr> <td> Dico autem "unum" non, si unum nomen sit positum, non sit autem unum ex illis, ut homo est fortasse et animal et bipes et mansuetum sed ex his unum fit; ex albo autem et homine et ambulare non unum.
</td> <td> do not apply this word 'one' to those things which, though they have a single recognized name, yet do not combine to form a unity. Thus, man may be an animal, and biped, and domesticated, but these three predicates combine to form a unity. On the other hand, the predicates 'white', 'man', and 'walking' do not thus combine.
</td> </tr>
<tr> <td> Quare nec si unum aliquid de his affirmet aliquis, erit una affirmatio sed vox quidem una, affirmationes vero multae, nec si de uno ista sed similiter plures.
</td> <td> Neither, therefore, if these three form the subject of an affirmation, nor if they form its predicate, is there any unity about that affirmation. In both cases the unity is linguistic, but not real.
</td> </tr>
<tr> <td> Si ergo dialectica interrogatio responsionis est petitio, vel propositionis vel alterius partis contradictionis, propositio vero unius contradictionis est, non erit una responsio ad haec; nec una interrogatio, nec si sit vera.
</td> <td> If therefore the dialectical question is a request for an answer, i.e. either for the admission of a premiss or for the admission of one of two contradictories-and the premiss is itself always one of two contradictories-the answer to such a question as contains the above predicates cannot be a single proposition.
</td> </tr>
<tr> <td> Dictum autem de his est in Topicis. Similiter autem manifestum est quoniam nec hoc ipsum 'quid est?' dialectica est interrogatio; oportet enim datum esse ex interrogatione eligere utram velit contradictionis partem enuntiare, quia oportet interrogantem determinare utrum hoc sit homo an non hoc.
</td> <td> For as I have explained in the Topics, question is not a single one, even if the answer asked for is true. At the same time it is plain that a question of the form 'what is it?' is not a dialectical question, for a dialectical questioner must by the form of his question give his opponent the chance of announcing one of two alternatives, whichever he wishes. He must therefore put the question into a more definite form, and inquire, e.g.. whether man has such and such a characteristic or not.
</td> </tr>
<tr> <td> Quoniam vero haec quidem praedicantur composita, ut unum sit omne praedicamentum eorum quae extra praedicantur, alia vero non, quae differentia est? De homine enim verum est dicere et extra animal et extra bipes et ut unum, et hominem et album et haec ut unum; sed non, si citharoedus et bonus.
</td> <td> Some combinations of predicates are such that the separate predicates unite to form a single predicate. Let us consider under what conditions this is and is not possible. We may either state in two separate propositions that man is an animal and that man is a biped, or we may combine the two, and state that man is an animal with two feet. Similarly we may use 'man' and 'white' as separate predicates, or unite them into one. Yet if a man is a shoemaker and is also good, we cannot construct a composite proposition and say that he is a good shoemaker.
</td> </tr>
<tr> <td> Si enim, quoniam alterutrum dicitur, et utrumque dicitur, multa et inconvenientia erunt.
</td> <td> For if, whenever two separate predicates truly belong to a subject, it follows that the predicate resulting from their combination also truly belongs to the subject, many absurd results ensue.
</td> </tr>
<tr> <td> De homine enim et 'hominem' verum est dicere et 'album', quare et omne; rursus, si album, et omne, quare erit homo albus hoc in infinitum; et rursus musicus albus ambulans, et haec eadem frequenter implicita.
</td> <td> For instance, a man is man and white. Therefore, if predicates may always be combined, he is a white man. Again, if the predicate 'white' belongs to him, then the combination of that predicate with the former composite predicate will be permissible. Thus it will be right to say that he is a white man so on indefinitely.
</td> </tr>
<tr> <td> Amplius si Socrates Socrates et homo, et bipes, et homo bipes.
</td> <td> Or, again, we may combine the predicates 'musical', 'white', and 'walking', and these may be combined many times. Similarly we may say that Socrates is Socrates and a man, and that therefore he is the man Socrates, or that Socrates is a man and a biped, and that therefore he is a two-footed man.
</td> </tr>
<tr> <td> Quoniam ergo, si quidam simpliciter ponat complexiones fieri, plurima inconvenientia contingit dicere, manifestum est; quemadmodum autem ponendum est, nunc dicemus.
</td> <td> Thus it is manifest that if man states unconditionally that predicates can always be combined, many absurd consequences ensue. We will now explain what ought to be laid down.
</td> </tr>
<tr> <td> Eorum igitur quae praedicantur et de quibus praedicantur, quaecumque secundum accidens dicuntur vel de eodem vel alterum de altero, haec non erunt unum; ut homo albus est et musicus sed non est idem musicus et albus; accidentia enim sunt utraque eidem.
</td> <td> Those predicates, and terms forming the subject of predication, which are accidental either to the same subject or to one another, do not combine to form a unity. Take the proposition 'man is white of complexion and musical'. Whiteness and being musical do not coalesce to form a unity, for they belong only accidentally to the same subject.
</td> </tr>
<tr> <td> Nec si album musicum verum est dicere, tamen non erit album musicum unum aliquid; secundum accidens enim musicum album, quare non erit album musicum.
</td> <td> Nor yet, if it were true to say that that which is white is musical, would the terms 'musical' and 'white' form a unity, for it is only incidentally that that which is musical is white; the combination of the two will, therefore, not form a unity.
</td> </tr>
<tr> <td> Quocirca nec citharoedus bonus simpliciter sed animal bipes; non enim secundum accidens.
</td> <td> Thus, again, whereas, if a man is both good and a shoemaker, we cannot combine the two propositions and say simply that he is a good shoemaker, we are, at the same time, able to combine the predicates 'animal' and 'biped' and say that a man is an animal with two feet, for these predicates are not accidental.
</td> </tr>
<tr> <td> Amplius nec quaecumque insunt in alio; quare neque album frequenter neque homo homo animal vel bipes; insunt enim in homine animal et bipes.
</td> <td> Those predicates, again, cannot form a unity, of which the one is implicit in the other: thus we cannot combine the predicate 'white' again and again with that which already contains the notion 'white', nor is it right to call a man an animal-man or a two-footed man; for the notions 'animal' and 'biped' are implicit in the word 'man'.
</td> </tr>
<tr> <td> Verum est autem dicere de aliquo et simpliciter, ut quendam hominem hominem aut quendam album hominem album; non semper autem sed quando in adiecto quidem aliquid oppositorum inest quae consequitur contradictio, non verum sed falsum est (ut mortuum hominem 'hominem' dicere), quando autem non inest, verum.
</td> <td> On the other hand, it is possible to predicate a term simply of any one instance, and to say that some one particular man is a man or that some one white man is a white man. Yet this is not always possible: indeed, when in the adjunct there is some opposite which involves a contradiction, the predication of the simple term is impossible. Thus it is not right to call a dead man a man. When, however, this is not the case, it is not impossible.
</td> </tr>
<tr> <td> Vel etiam quando inest quidem semper non verum, quando vero non inest, non semper verum est; ut 'Homerus est aliquid' ut 'poeta'; ergo etiam 'est' aut non? Secundum accidens enim praedicatur 'esse' de Homero; quoniam enim poeta est sed non secundum se, praedicatur de Homero quoniam est.
</td> <td> Yet the facts of the case might rather be stated thus: when some such opposite elements are present, resolution is never possible, but when they are not present, resolution is nevertheless not always possible. Take the proposition 'Homer is so-and-so', say 'a poet'; does it follow that Homer is, or does it not? The verb 'is' is here used of Homer only incidentally, the proposition being that Homer is a poet, not that he is, in the independent sense of the word.
</td> </tr>
<tr> <td> Quare in quantiscumque praedicamentis neque contrarietas inest, si definitiones pro nominibus praedicantur, et secundum se praedicantur et non secundum accidens, in his et simpliciter verum erit dicere.
</td> <td> Thus, in the case of those predications which have within them no contradiction when the nouns are expanded into definitions, and wherein the predicates belong to the subject in their own proper sense and not in any indirect way, the individual may be the subject of the simple propositions as well as of the composite.
</td> </tr>
<tr> <td> Quod autem non est quoniam opinabile est, non est verum dicere esse aliquid; opinatio enim eius non est quoniam est sed quoniam non est.
</td> <td> But in the case of that which is not, it is not true to say that because it is the object of opinion, it is; for the opinion held about it is that it is not, not that it is.
</td> </tr>
<tr> <td> <a name = "c12">[12] His vero determinatis perspiciendum est quemadmodum sese habent negationes et affirmationes ad se invicem, hae scilicet quae sunt de 'possibile esse' et 'non possibile' et 'contingere' et 'non contingere' et 'impossibile' et de necessario; habet enim aliquas dubitationes.
</td> <td> As these distinctions have been made, we must consider the mutual relation of those affirmations and denials which assert or deny possibility or contingency, impossibility or necessity: for the subject is not without difficulty.
</td> </tr>
<tr> <td> Nam si eorum quae complectuntur illae sibi invicem oppositae sunt contradictiones, quaecumque secundum 'esse' vel 'non esse' disponuntur, ut eius quae est 'esse hominem' negatio 'non esse hominem', non autem ea quae est 'esse non hominem', et eius quae est 'esse album hominem' ea quae est 'non esse album hominem' sed non ea quae est 'esse non album hominem' (si enim de omnibus aut dictio aut negatio lignum erit verum dicere esse non album hominem; quod si, hoc modo, et quantiscumque 'esse' non additur, idem faciet quod pro 'esse' dicitur, ut eius quae est 'ambulat homo' non vel quae est 'ambulat non homo' negatio est sed ea quae est 'non ambulat homo'; nihil enim differt dicere 'hominem ambulare' vel 'hominem ambulantem esse').
</td> <td> We admit that of composite expressions those are contradictory each to each which have the verb 'to be' its positive and negative form respectively. Thus the contradictory of the proposition 'man is' is 'man is not', not 'not-man is', and the contradictory of 'man is white' is 'man is not white', not 'man is not-white'. For otherwise, since either the positive or the negative proposition is true of any subject, it will turn out true to say that a piece of wood is a man that is not white. Now if this is the case, in those propositions which do not contain the verb 'to be' the verb which takes its place will exercise the same function. Thus the contradictory of 'man walks' is 'man does not walk', not 'not-man walks'; for to say 'man walks' merely equivalent to saying 'man is walking'.
</td> </tr>
<tr> <td> Quare si hoc modo in omnibus, et eius quae est 'possibile esse' negatio est 'possibile non esse', non ea quae est 'non possibile esse'.
</td> <td> If then this rule is universal, the contradictory of 'it may be' is may not be', not 'it cannot be'.
</td> </tr>
<tr> <td> Videtur autem idem posse et esse et non esse; omne enim quod est possibile dividi vel ambulare et non ambulare et non dividi possibile est; ratio autem est quoniam omne quod sic possibile est non semper in actu est, quare inerit ei etiam negatio; potest igitur et non ambulare quod est ambulabile et non videri quod est visibile.
</td> <td> Now it appears that the same thing both may and may not be; for instance, everything that may be cut or may walk may also escape cutting and refrain from walking; and the reason is that those things that have potentiality in this sense are not always actual. In such cases, both the positive and the negative propositions will be true; for that which is capable of walking or of being seen has also a potentiality in the opposite direction.
</td> </tr>
<tr> <td> At vero impossibile est de eodem oppositas veras esse dictiones; non igitur est ista negatio; contingit enim ex his aut idem ipsum dicere et negare simul de eodem, aut non secundum 'esse' vel 'non esse' quae apponuntur fieri affirmationes vel negationes.
</td> <td> But since it is impossible that contradictory propositions should both be true of the same subject, it follows that' it may not be' is not the contradictory of 'it may be'. For it is a logical consequence of what we have said, either that the same predicate can be both applicable and inapplicable to one and the same subject at the same time, or that it is not by the addition of the verbs 'be' and 'not be', respectively, that positive and negative propositions are formed.
</td> </tr>
<tr> <td> Si ergo illud impossibilius est, hoc erit magis eligendum. Est igitur negatio eius quae est 'possibile esse' ea quae est 'non possibile esse'.
</td> <td> If the former of these alternatives must be rejected, we must choose the latter. The contradictory, then, of 'it may be' is 'it cannot be'.
</td> </tr>
<tr> <td> Eadem quoque ratio est et in eo quod est 'contingens esse'; et enim eius negatio 'non contingere esse'. Et in aliis quoque simili modo ut 'necessario' et 'impossibili'.
</td> <td> The same rule applies to the proposition 'it is contingent that it should be'; the contradictory of this is 'it is not contingent that it should be'. The similar propositions, such as 'it is necessary' and 'it is impossible', may be dealt with in the same manner.
</td> </tr>
<tr> <td> Fiunt enim quemadmodum in illis 'esse' et 'non esse' appositiones, subiectae vero res hoc quidem album illud vero homo, eodem quoque modo hoc loco 'esse' quidem subiectum fit, 'posse' vero et 'contingere' appositiones determinantes, quemadmodum in illis 'esse' et 'non esse' veritatem, similiter autem hae etiam in 'esse possibile' et 'esse non possibile'.
</td> <td> For it comes about that just as in the former instances the verbs 'is' and 'is not' were added to the subject-matter of the sentence 'white' and 'man', so here 'that it should be' and 'that it should not be' are the subject-matter and 'is possible', 'is contingent', are added. These indicate that a certain thing is or is not possible, just as in the former instances 'is' and 'is not' indicated that certain things were or were not the case.
</td> </tr>
<tr> <td> Eius vero quae est 'possibile est non esse' negatio est 'non possibile est non esse'. Quare et sequi sese invicem videbuntur; idem enim possibile est esse et non esse; non enim contradictiones sibi invicem sunt huiusmodi 'possibile est esse' et 'possibile est non esse'.
</td> <td> The contradictory, then, of 'it may not be' is not 'it cannot be', but 'it cannot not be', and the contradictory of 'it may be' is not 'it may not be', but cannot be'. Thus the propositions 'it may be' and 'it may not be' appear each to imply the other: for, since these two propositions are not contradictory, the same thing both may and may not be.
</td> </tr>
<tr> <td> Sed 'possibile esse' et 'non possibile esse' numquam simul sunt; opponuntur enim. Ut vero 'possibile non esse' et 'non possibile non esse' numquam simul sunt.
</td> <td> But the propositions 'it may be' and 'it cannot be' can never be true of the same subject at the same time, for they are contradictory. Nor can the propositions 'it may not be' and 'it cannot not be' be at once true of the same subject.
</td> </tr>
<tr> <td> Similiter autem et eius quae est 'necessarium esse' non ea quae est, 'necessarium non esse' sed 'non necessarium esse'; eius vero quae est 'necessarium non esse' ea quae est 'non necessarium non esse'.
</td> <td> The propositions which have to do with necessity are governed by the same principle. The contradictory of 'it is necessary that it should be', is not 'it is necessary that it should not be,' but 'it is not necessary that it should be', and the contradictory of 'it is necessary that it should not be' is 'it is not necessary that it should not be'.
</td> </tr>
<tr> <td> Et eius quae est 'impossibile esse' non 'impossibile non esse' sed 'non impossibile esse'; eius vero quae est 'impossibile non esse' ea quae est 'non impossibile non esse'.
</td> <td> Again, the contradictory of 'it is impossible that it should be' is not 'it is impossible that it should not be' but 'it is not impossible that it should be', and the contradictory of 'it is impossible that it should not be' is 'it is not impossible that it should not be'.
</td> </tr>
<tr> <td> Et universaliter vero, quemadmodum dictum est, 'esse' quidem et 'non esse' oportet ponere quemadmodum subiecta, negationem vero et affirmationem haec facientem ad unum apponere.
</td> <td> To generalize, we must, as has been stated, define the clauses 'that it should be' and 'that it should not be' as the subject-matter of the propositions, and in making these terms into affirmations and denials we must combine them with 'that it should be' and 'that it should not be' respectively.
</td> </tr>
<tr> <td> Et has putare oportet esse oppositas dictiones et negationes,
<blockquote>
'possibile -- non possibile', 
'contingens -- non contingens', 
'impossibile -- non impossibile', 
'necessarium -- non necessarium', 
'uerum -- non verum'.
</blockquote>

</td> <td> We must consider the following pairs as contradictory propositions:

<blockquote>
It may be. It cannot be. 
It is contingent. It is not contingent. 
It is impossible. It is not impossible. 
It is necessary. It is not necessary. 
It is true. It is not true.
</blockquote>
</td> </tr>
<tr> <td> <a name = "c13">[13] Et consequentiae vero secundum ordinem fiunt ita ponentibus: illi enim quae est 'possibile esse' illa quae est 'contingit esse', et hoc illi convertit, et 'non impossibile esse' et 'non necessarium esse'; illi vero quae est 'possibile non esse' et 'contingere non esse' ea quae est 'non necessarium non esse' et 'non impossibile non esse'; illi vero quae est 'non possibile esse' et 'non contingens esse' illa quae est 'necessarium non esse' et 'impossibile esse'; illi vero quae est 'non possibile non esse' et 'non contingens non esse' illa quae est 'necesse esse' et 'impossibile non esse'.
</td> <td> Logical sequences follow in due course when we have arranged the propositions thus. From the proposition 'it may be' it follows that it is contingent, and the relation is reciprocal. It follows also that it is not impossible and not necessary. From the proposition 'it may not be' or 'it is contingent that it should not be' it follows that it is not necessary that it should not be and that it is not impossible that it should not be. From the proposition 'it cannot be' or 'it is not contingent' it follows that it is necessary that it should not be and that it is impossible that it should be. From the proposition 'it cannot not be' or 'it is not contingent that it should not be' it follows that it is necessary that it should be and that it is impossible that it should not be.
</td> </tr>
<tr> <td>
Considerentur autem ex subscriptione quemadmodum dicimus.
</td> <td>

Let us consider these statements by the help of a table:

A. B.
It may be. It cannot be.
It is contingent. It is not contingent.
It is not impossible It is impossible that it

that it should be. should be.
It is not necessary It is necessary that it

that it should be. should not be.

C. D.
It may not be. It cannot not be.
It is contingent that it It is not contingent that

should not be. it should not be.
It is not impossible It is impossible thatit

that it should not be. should not be.
It is not necessary that It is necessary that it

it should not be. should be.
</td> </tr>
<tr> <td> Ergo 'impossibile' et 'non impossibile' illud quod est 'contingens' et 'possibile' et 'non contingens' et 'non possibile' sequitur quidem contradictone sed conversim; illi enim quod est 'possibile esse' negatio 'impossibilis', negationem vero affirmatio; illi enim quod est 'non possibile esse' illud quod est 'impossibile esse'; affirmatio enim est 'impossibile esse', 'non impossibile' vero negatio.
</td> <td> Now the propositions 'it is impossible that it should be' and 'it is not impossible that it should be' are consequent upon the propositions 'it may be', 'it is contingent', and 'it cannot be', 'it is not contingent', the contradictories upon the contradictories. But there is inversion. The negative of the proposition 'it is impossible' is consequent upon the proposition 'it may be' and the corresponding positive in the first case upon the negative in the second. For 'it is impossible' is a positive proposition and 'it is not impossible' is negative.
</td> </tr>
<tr> <td> 'Necessarium' vero quemadmodum, considerandum est. Manifestum est quoniam non eodem modo sed contrariae sequuntur, contradictoriae autem extra.
</td> <td> We must investigate the relation subsisting between these propositions and those which predicate necessity. That there is a distinction is clear. In this case, contrary propositions follow respectively from contradictory propositions, and the contradictory propositions belong to separate sequences.
</td> </tr>
<tr> <td> Non enim est negatio eius quod est 'necesse non esse' 'non necesse esse'; contingit enim veras esse in eodem utrasque; quod enim est necessarium non esse, non est necessarium esse.
</td> <td> For the proposition 'it is not necessary that it should be' is not the negative of 'it is necessary that it should not be', for both these propositions may be true of the same subject; for when it is necessary that a thing should not be, it is not necessary that it should be.
</td> </tr>
<tr> <td> Causa autem est cur non consequatur similiter caeteris, quoniam contrarie 'impossibile' 'necessario' redditur idem ualens; nam si impossibile est esse, necesse est hoc non esse sed non-esse; si vero impossibile non esse, hoc necessarium est esse; quare, si illa similiter possibile et non, haec e contrario, nam idem significat 'necessarium' et 'impossibile' sed, quemadmodum dictum est, contrarie.
</td> <td> The reason why the propositions predicating necessity do not follow in the same kind of sequence as the rest, lies in the fact that the proposition 'it is impossible' is equivalent, when used with a contrary subject, to the proposition 'it is necessary'. For when it is impossible that a thing should be, it is necessary, not that it should be, but that it should not be, and when it is impossible that a thing should not be, it is necessary that it should be. Thus, if the propositions predicating impossibility or non-impossibility follow without change of subject from those predicating possibility or non-possibility, those predicating necessity must follow with the contrary subject; for the propositions 'it is impossible' and 'it is necessary' are not equivalent, but, as has been said, inversely connected.
</td> </tr>
<tr> <td> Aut certe impossibile est sic poni 'necessarii' contradictiones? Nam quod est necessarium esse, possibile est esse; nam, si non, negatio consequetur; necesse enim est aut dicere aut negare; quare si non possibile est esse, impossibile est esse; impossibile igitur est esse quod necesse est esse, quod est inconveniens.
</td> <td> Yet perhaps it is impossible that the contradictory propositions predicating necessity should be thus arranged. For when it is necessary that a thing should be, it is possible that it should be. (For if not, the opposite follows, since one or the other must follow; so, if it is not possible, it is impossible, and it is thus impossible that a thing should be, which must necessarily be; which is absurd.)
</td> </tr>
<tr> <td> At vero illud quod est 'possibile esse' 'non impossibile esse' sequitur, hoc vero illud quod est 'non necessarium esse'; quare contingit quod est necessarium esse non necessarium esse, quod est inconveniens.
</td> <td> Yet from the proposition 'it may be' it follows that it is not impossible, and from that it follows that it is not necessary; it comes about therefore that the thing which must necessarily be need not be; which is absurd.
</td> </tr>
<tr> <td> At vero neque 'necessarium esse' sequitur 'possibile esse' neque 'necessarium non esse'; illi enim utraque contingit accidere, horum autem utrumlibet verum fuerit non erunt illa vera; simul enim possibile esse et non esse; sin vero necesse est esse vel non esse, non erit possibile utrumque.
</td> <td> But again, the proposition 'it is necessary that it should be' does not follow from the proposition 'it may be', nor does the proposition 'it is necessary that it should not be'. For the proposition 'it may be' implies a twofold possibility, while, if either of the two former propositions is true, the twofold possibility vanishes. For if a thing may be, it may also not be, but if it is necessary that it should be or that it should not be, one of the two alternatives will be excluded.
</td> </tr>
<tr> <td> Relinquitur ergo 'non necessarium non esse' sequi 'possibile esse'; hoc enim verum est et de 'necesse non esse'.
</td> <td> It remains, therefore, that the proposition 'it is not necessary that it should not be' follows from the proposition 'it may be'. For this is true also of that which must necessarily be.
</td> </tr>
<tr> <td> Haec enim fit contradictio eius quae sequitur 'non possibile esse'; illud enim sequitur hoc quod est 'possibile esse' et 'necesse esse non esse', cuius negatio 'non necesse esse non esse'. Sequuntur igitur et hae contradictiones secundum praedictum modum, et nihil impossibile contingit sic positis.
</td> <td> Moreover the proposition 'it is not necessary that it should not be' is the contradictory of that which follows from the proposition 'it cannot be'; for 'it cannot be' is followed by 'it is impossible that it should be' and by 'it is necessary that it should not be', and the contradictory of this is the proposition 'it is not necessary that it should not be'. Thus in this case also contradictory propositions follow contradictory in the way indicated, and no logical impossibilities occur when they are thus arranged.
</td> </tr>
<tr> <td> Dubitabit autem aliquis si illud quod est 'necessarium esse' ,'possibile' sequitur. Nam si non consequitur, contradictio sequitur, 'non possibile esse'; et si quis non hanc dicat esse contradictionem, necesse est dicere 'possibile non esse'; sed utraeque falsae sunt de 'necesse esse'.
</td> <td> It may be questioned whether the proposition 'it may be' follows from the proposition 'it is necessary that it should be'. If not, the contradictory must follow, namely that it cannot be, or, if a man should maintain that this is not the contradictory, then the proposition 'it may not be'. Now both of these are false of that which necessarily is.
</td> </tr>
<tr> <td> At vero rursus idem videtur esse possibile incidi et non incidi, et esse et non esse, quare erit necesse esse contingere non esse; hoc autem falsum est.
</td> <td> At the same time, it is thought that if a thing may be cut it may also not be cut, if a thing may be it may also not be, and thus it would follow that a thing which must necessarily be may possibly not be; which is false.
</td> </tr>
<tr> <td> Manifestum est autem quoniam non omne possibile vel esse vel ambulare et opposita ualet sed est in quibus non sit verum; et primum quidem in his quae non secundum rationem possunt, ut ignis calfactibilis et habet uim irrationabilem (ergo secundum rationem potestates ipsae eaedem plurimorum etiam contrariorum sunt; irrationabiles vero non omnes sed, quemadmodum dictum est, ignem non esse possibile calefacere et non, vel quaecumque alia semper agunt; aliqua vero possunt et secundum irrationabiles potestates simul quaedam opposita; sed hoc quidem idcirco dictum est quoniam non omnis potestas; oppositorum est nec quaecumque secundum eandem speciem dicuntur) .
</td> <td> It is evident, then, that it is not always the case that that which may be or may walk possesses also a potentiality in the other direction. There are exceptions. In the first place we must except those things which possess a potentiality not in accordance with a rational principle, as fire possesses the potentiality of giving out heat, that is, an irrational capacity. Those potentialities which involve a rational principle are potentialities of more than one result, that is, of contrary results; those that are irrational are not always thus constituted. As I have said, fire cannot both heat and not heat, neither has anything that is always actual any twofold potentiality. Yet some even of those potentialities which are irrational admit of opposite results. However, thus much has been said to emphasize the truth that it is not every potentiality which admits of opposite results, even where the word is used always in the same sense.
</td> </tr>
<tr> <td> Quaedam vero potestates aequivocae sunt 'possibile' enim non simpliciter dicitur sed hoc quidem quoniam verum est ut in actu, ut 'possibile est ambulare' quoniam ambulat, et omnino possibile est esse quoniam iam est actu quod dicitur 'possibile', illud vero quod forsitan aget, ut 'possibile est ambulare' quoniam ambulabit.
</td> <td> But in some cases the word is used equivocally. For the term 'possible' is ambiguous, being used in the one case with reference to facts, to that which is actualized, as when a man is said to find walking possible because he is actually walking, and generally when a capacity is predicated because it is actually realized; in the other case, with reference to a state in which realization is conditionally practicable, as when a man is said to find walking possible because under certain conditions he would walk.
</td> </tr>
<tr> <td> Et haec quidem in mobilibus solis est potestas, illa vero et in immobilibus; in utrisque vero verum est dicere non impossibile esse ambulare vel esse et quod ambulat iam et agit, et ambulabile. 'Sic' igitur 'possibile' non est verum de 'necessario' simpliciter dicere, alterum autem verum est.
</td> <td> This last sort of potentiality belongs only to that which can be in motion, the former can exist also in the case of that which has not this power. Both of that which is walking and is actual, and of that which has the capacity though not necessarily realized, it is true to say that it is not impossible that it should walk (or, in the other case, that it should be), but while we cannot predicate this latter kind of potentiality of that which is necessary in the unqualified sense of the word, we can predicate the former.
</td> </tr>
<tr> <td> Quare, quoniam partem universale sequitur, illud quod ex necessitate est sequitur 'posse esse' sed non omnino.
</td> <td> Our conclusion, then, is this: that since the universal is consequent upon the particular, that which is necessary is also possible, though not in every sense in which the word may be used.
</td> </tr>
<tr> <td> Et est quidem fortasse principium quod necessarium est et quod non necessarium omnium vel 'esse' vel 'non esse', et alia quemadmodum ista consequentia considerare oportet.
</td> <td> We may perhaps state that necessity and its absence are the initial principles of existence and non-existence, and that all else must be regarded as posterior to these.

</td> </tr>
<tr> <td> Manifestum est autem ex his quae dicta sunt quoniam quod ex necessitate est secundum actum est, quare, si priora sunt sempiterna, et quae actu sunt potestate priora sunt. Et haec quidem sine potestate actus sunt, ut primae substantiae, alia vero cum possibilitate, quae natura priora sunt, tempore vero posteriora, alia vero numquam sunt actu sed potestate solum.
</td> <td> It is plain from what has been said that that which is of necessity is actual. Thus, if that which is eternal is prior, actuality also is prior to potentiality. Some things are actualities without potentiality, namely, the primary substances; a second class consists of those things which are actual but also potential, whose actuality is in nature prior to their potentiality, though posterior in time; a third class comprises those things which are never actualized, but are pure potentialities.
</td> </tr>
<tr> <td> <a name = "c14">[14] Utrum autem contraria est affirmatio negationi et oratio orationi quae dicit quoniam 'omnis homo iustus' ei quae est 'nullus homo iustus' aut 'omnis homo iustus' ei quae est 'omnis homo iniustus est', 'Callias iustus est', 'Callias iustus non est', 'Callias iniustus est', quae harum contraria est?
</td> <td> The question arises whether an affirmation finds its contrary in a denial or in another affirmation; whether the proposition 'every man is just' finds its contrary in the proposition 'no man is just', or in the proposition 'every man is unjust'. Take the propositions 'Callias is just', 'Callias is not just', 'Callias is unjust'; we have to discover which of these form contraries.
</td> </tr>
<tr> <td> Nam si ea quae sunt in voce sequuntur ea quae sunt in anima, illic autem contraria est opinio contrarii, ut 'omnis homo iustus' ei quae est 'omnis homo iniustus', etiam in his quae sunt in voce affirmationibus necesse est similiter sese habere.
</td> <td> Now if the spoken word corresponds with the judgement of the mind, and if, in thought, that judgement is the contrary of another, which pronounces a contrary fact, in the way, for instance, in which the judgement 'every man is just' pronounces a contrary to that pronounced by the judgement 'every man is unjust', the same must needs hold good with regard to spoken affirmations.
</td> </tr>
<tr> <td> Quod si neque illic contrarii opinatio contraria est, nec affirmatio affirmationi erit contraria sed ea quae dicta est negatio. Quare considerandum est cui opinatio vera falsae opinioni contraria est, utrum negationi an certe ei quae contrarium esse opinatur.
</td> <td> But if, in thought, it is not the judgement which pronounces a contrary fact that is the contrary of another, then one affirmation will not find its contrary in another, but rather in the corresponding denial. We must therefore consider which true judgement is the contrary of the false, that which forms the denial of the false judgement or that which affirms the contrary fact.
</td> </tr>
<tr> <td> Dico autem hoc modo: est quaedam opinatio vera boni quoniam bonum est, alia vero quoniam non bonum est falsa, alia vero quoniam malum; quae harum contraria est verae? Et si est una, secundum quam contraria? (nam arbitrari contrarias opiniones definiri in eo quod contrariorum sunt, falsum est; boni enim quoniam bonum est et mali quoniam malum eadem fortasse opinio est et vera, sive plures sive una sit; sunt autem ista contraria; sed non eo, quod contrariorum sint, contrariae sed magis eo quod contrarie).
</td> <td> Let me illustrate. There is a true judgement concerning that which is good, that it is good; another, a false judgement, that it is not good; and a third, which is distinct, that it is bad. Which of these two is contrary to the true? And if they are one and the same, which mode of expression forms the contrary? It is an error to suppose that judgements are to be defined as contrary in virtue of the fact that they have contrary subjects; for the judgement concerning a good thing, that it is good, and that concerning a bad thing, that it is bad, may be one and the same, and whether they are so or not, they both represent the truth. Yet the subjects here are contrary. But judgements are not contrary because they have contrary subjects, but because they are to the contrary effect.
</td> </tr>
<tr> <td> Si ergo est boni quoniam est bonum opinatio, est autem quoniam non bonum, est vero quoniam aliquid aliud quod non est neque potest esse (aliarum quidem nulla ponenda est, neque quaecumque esse quod non est opinantur neque quaecumque non esse quod est -- infinitae enim utraeque sunt, et quae esse opinantur quod non est et quae non esse quod est -- sed in quibus est fallacia; hae autem ex his ex quibus sunt generationes; ex oppositis vero generationes, quare etiam fallacia); si ergo quod bonum et bonum et non malum est, et hoc quidem secundum se, illud vero secundum accidens (accidit enim ei malum non esse), magis autem in unoquoque est vera quae secundum sese est, etiam falsa siquidem et vera.
</td> <td> Now if we take the judgement that that which is good is good, and another that it is not good, and if there are at the same time other attributes, which do not and cannot belong to the good, we must nevertheless refuse to treat as the contraries of the true judgement those which opine that some other attribute subsists which does not subsist, as also those that opine that some other attribute does not subsist which does subsist, for both these classes of judgement are of unlimited content.

Those judgements must rather be termed contrary to the true judgements, in which error is present. Now these judgements are those which are concerned with the starting points of generation, and generation is the passing from one extreme to its opposite; therefore error is a like transition.

</td> </tr>
<tr> <td> Ergo ea quae est 'quoniam non est bonum quod bonum est' secundum se consistentis falsa est, illa vero quae est 'quoniam malum' eius quod est secundum accidens, quare magis erit falsa de bono ea quae est negationis opinio quam ea quae est contrarii. Falsus est autem magis circa singula qui habet contrariam opinionem; contrarium enim est eorum quae plurimum circa idem differunt. Quod si harum contraria est altera, magis vero contraria contradictionis, manifestum est quoniam haec erit contraria. Illa vero quae est 'quoniam malum est quod est bonum' implicita est; et enim quoniam non bonum est necesse est idem ipsum opinari.
</td> <td> Now that which is good is both good and not bad. The first quality is part of its essence, the second accidental; for it is by accident that it is not bad. But if that true judgement is most really true, which concerns the subject's intrinsic nature, then that false judgement likewise is most really false, which concerns its intrinsic nature. Now the judgement that that is good is not good is a false judgement concerning its intrinsic nature, the judgement that it is bad is one concerning that which is accidental. Thus the judgement which denies the true judgement is more really false than that which positively asserts the presence of the contrary quality. But it is the man who forms that judgement which is contrary to the true who is most thoroughly deceived, for contraries are among the things which differ most widely within the same class. If then of the two judgements one is contrary to the true judgement, but that which is contradictory is the more truly contrary, then the latter, it seems, is the real contrary. The judgement that that which is good is bad is composite. For presumably the man who forms that judgement must at the same time understand that that which is good is not good.

</td> </tr>
<tr> <td> Amplius, si etiam in aliis similiter oportet se habere, et hic sidetur bene esse dictum; aut enim ubique ea quae est contradictionis aut nusquam; quibus vero non est contraria, de his est quidem falsa ea quae est verae opposita, ut qui hominem non putat hominem falsus est.
</td> <td> Further, the contradictory is either always the contrary or never; therefore, if it must necessarily be so in all other cases, our conclusion in the case just dealt with would seem to be correct. Now where terms have no contrary, that judgement is false, which forms the negative of the true; for instance, he who thinks a man is not a man forms a false judgement.
</td> </tr>
<tr> <td> Si ergo hae contrariae sunt, et aliae contradictionis.
</td> <td> If then in these cases the negative is the contrary, then the principle is universal in its application.
</td> </tr>
<tr> <td> Amplius similiter se habet boni quoniam bonum est et non boni quoniam non bonum est, et super has boni quoniam non bonum est et non boni quoniam bonum est.
</td> <td> Again, the judgement that that which is not good is not good is parallel with the judgement that that which is good is good. Besides these there is the judgement that that which is good is not good, parallel with the judgement that that that is not good is good.
</td> </tr>
<tr> <td> Illi ergo quae est non boni quoniam non bonum verae opinioni quae est contraria?
</td> <td> Let us consider, therefore, what would form the contrary of the true judgement that that which is not good is not good.
</td> </tr>
<tr> <td> Non enim ea quae dicit quoniam malum est; simul enim aliquando erit vera, numquam autem vera verae contraria est; est enim quiddam non bonum malum, quare contingit simul esse veras. At vero nec illa quae est 'non malum'; simul enim et haec erunt.
</td> <td> The judgement that it is bad would, of course, fail to meet the case, since two true judgements are never contrary and this judgement might be true at the same time as that with which it is connected. For since some things which are not good are bad, both judgements may be true. Nor is the judgement that it is not bad the contrary, for this too might be true, since both qualities might be predicated of the same subject.
</td> </tr>
<tr> <td> Relinquitur ergo ei quae est non boni quoniam non bonum contraria quae est non boni quoniam bonum. Quare et ea quae est boni quoniam non bonum ei quae est boni quoniam bonum.
</td> <td> It remains, therefore, that of the judgement concerning that which is not good, that it is not good, the contrary judgement is that it is good; for this is false. In the same way, moreover, the judgement concerning that which is good, that it is not good, is the contrary of the judgement that it is good.
</td> </tr>
<tr> <td> Manifestum ergo est quoniam nihil interest nec si universaliter ponamus affirmationem; huic enim universalis negatio contraria ent, ut opinioni quae opinatur quoniam omne quod est bonum bonum est, vel quoniam nihil eorum quae bona sunt.
</td> <td> It is evident that it will make no difference if we universalize the positive judgement, for the universal negative judgement will form the contrary. For instance, the contrary of the judgement that everything that is good is good is that nothing that is good is good.
</td> </tr>
<tr> <td> Nam eius quae est boni quoniam bonum, si universaliter sit bonum, ea est quae opinatur quicquid bonum est quoniam bonum est. Similiter autem et in non bono.
</td> <td> For the judgement that that which is good is good, if the subject be understood in a universal sense, is equivalent to the judgement that whatever is good is good, and this is identical with the judgement that everything that is good is good. We may deal similarly with judgements concerning that which is not good.
</td> </tr>
<tr> <td> Quare si in opinione se sic habet, sunt autem hae quae sunt affirmationes et negationes notae eorum quae sunt in anima, manifestum est quoniam etiam affirmationi contraria quidem negatio circa idem universalis, ut ei quae est quoniam omne bonum bonum est nel quoniam omnis homo bonus ea quae est vel quoniam nullum vel nullus, contradictorie autem aut non omnis aut non omne.
</td> <td> If therefore this is the rule with judgements, and if spoken affirmations and denials are judgements expressed in words, it is plain that the universal denial is the contrary of the affirmation about the same subject. Thus the propositions 'everything good is good', 'every man is good', have for their contraries the propositions 'nothing good is good', 'no man is good'. The contradictory propositions, on the other hand, are 'not everything good is good', 'not every man is good'.
</td> </tr>
<tr> <td> Manifestum est autem quoniam et veram verae non contingit esse contrariam nec opinionem nec contradictionem; contraria enim sunt quae circa opposita sunt, circa eadem autem contingit verum dicere eundem; simul autem eidem non contingit inesse contraria.
</td> <td> It is evident, also, that neither true judgements nor true propositions can be contrary the one to the other. For whereas, when two propositions are true, a man may state both at the same time without inconsistency, contrary propositions are those which state contrary conditions, and contrary conditions cannot subsist at one and the same time in the same subject.
</td> </tr>
</tbody> </table>

 

<hr>

Footnotes

<a name= "note1">[1The most obvious difference is in the examples, where the Greek proper names are replaced in Latin by quite different ones.
For example, Aristotle talks of 'Philo', Boethius talks of 'Cato'. The famous line 'Thus man is a universal,
Callias an individual' becomes 'ut 'homo' quidem universale, 'Plato' vero eorum quae sunt singularia'].
There are of course more significant differences than that.
<a name= "note2">[2] Cicero invented some of the Latin equivalents for Greek terms,
such as propositio, meaning the leading premiss of an argument, which contrasts with assumptio meaning the additional premiss.
Kneale (p. 178) claims that 'propositio' was used by Quintilian in the more general sense of 'statement' or 'indicative sentence',
in which it was used throughout the middle ages.
<a name= "note3">[3] Leading to a difficulty in English of translating related words such as those for negation,
negativity, signs of negation and so on. For if we use 'denial' or 'deny', which is the most accurate in some cases, we
have to translate the corresponding abstract terms such as 'negatio' by the English abstract term 'negation', leading
to the impression that there are a different family of words, where in Latin there is just one family.

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