Authors/Ockham/Summa Logicae/Book II/Chapter 21

Latin	English
[2.21 DE CONVERSIONE PROPOSITIONUM DE INESSE ET DE PRAESENTI]	Chapter 21 On the Conversion of Present-Tense Propositions of inherence.
Postquam dictum est quid requiritur ad veritatem propositionum categoricarum, nunc restat dicere de conversionibus. Et primo dicendum est de conversione prpositionum de inesse, secundo de conversione propositionum modalium.	Having said what is required for the truth of categorical propositions, it now remains to speak about conversions. And first we must speak about the conversion of propositions of inherence, secondly about the conversion of modal propositions.
Circa primum dicendum est primo de conversione propositionum de inesse et de praesenti, secundo de conversione propositionum de inesse de praeterito et de futuro.	Regarding the first, we must speak first about the conversion of propositions of inherence and in the present, second about the conversion of propositions of inherence and in the past and the future.
Est autem primo sciendum quod conversio est quando de subiecto fit praedicatum et e converso. Aliquando autem fit talis transpositio nulla alia mutatione facta ex parte vocis, aliquando autem fit mutatio ex parte vocis praeter transpositionem terminorum.	But it must first be known that conversion occurs when the subject becomes the predicate and vice versa. Sometimes, however, such a transposition occurs without any other change being made on the part of the words, but sometimes a change is made on the part of the words apart from the transposition of the terms.
Secundo sciendum quod propositio de inesse de praesenti aliquando est propositio in recto, aliquando in abliquo.	Secondly, it should be known that a proposition of inherence in the present is sometimes a proposition in the nominative case, sometimes in an oblique case.
Tertio sciendum quod conversio est triplex, scilicet simplex, per accidens et per contrapositionem. Conversio simplex est quando manet eadem [qualitas et] quantitas utriusque propositionis. Potest tamen magis large accipi conversio simplex, ut dicatur conversio simplex quando est mutua conversio, ita quod sicut ratione camplexorum ex convertente sequitur conversa, ita sequitur e Converso. Et ita frequenter accidit, quamvis sit diversa quantitas antecedentis et consequentis, sicut quando singularis convertitur in particularem et e converso.	Thirdly, it should be known that conversion is threefold, namely simple, accidental and contra-positional. Simple conversion is when the same [quality and] quantity of both propositions remains. However, simple conversion can be taken more broadly, so that it is called simple conversion when there is a mutual conversion, so that just as by reason of complex things the converted follows from the converting, so it follows from the converse. And this frequently happens, although the quantity of the antecedent and the consequent is different, as when the singular is converted into the particular and vice versa.
Conversio per accidens dicitur illa quando non manet eadem quantitas antecedentis et consequentis. Potest tamen aliter vocari conversio per accidens, quando non est canuersio mutua. Sicut bene sequitur 'omnis homo est albus, igitur aliquod album est homo'; sed e converso non sequitur.	Accidental conversion is called that when the quantity of the antecedent and the consequent does not remain the same. However, it can be called accidental conversion in another way when there is no mutual reversal. Just as it follows well that 'every man is white, therefore some white thing is a man'; but the converse does not follow.
Conversio per Cantrapositionem dicitur, quando termini finiti mutantur in terminos infinitos.	Conversion by contraposition is called when finite terms are changed into infinite terms.
Quarto sciendum quod universalis negativa de recto convertitur simpliciter, large accipiendo conversionem simplicem; et hoc nulla mutatione facta ex parte vocis praeter transpositionem terminorum, nisi forte vox mutetur secundum genus grammaticale. Sed stricte accipiendo conversionem simplicem, non semper sic convertitur; sicut non sequitur 'nullus asinus est Sortes, igitur nullus Sortes est asinus', sed sequitur 'igitur Sortes non est asinus'.	Fourthly, it should be known that the universal negative is converted in the nominative simply, taking simple conversion broadly; and this with no change made on the part of the words other than the transposition of the terms, unless perhaps a word is changed according to grammatical gender. But taking simple conversion strictly, it is not always converted in this way; just as it does not follow that 'no donkey is Socrates, therefore no Socrates is a donkey', but it follows that 'therefore Socrates is not a donkey'.
Similiter, singularis affirmativa convertitur simpliciter in particularem et indefinitam vel singularem, sicut sequitur 'Sortes est homo, igitur homo est Sortes' et 'aliquis homo est Sortes' et e converso. Similiter sequitur 'Sortes est Plato, igitur Plato est Sortes' et e converso.	Similarly, the affirmative singular is simply converted into the particular and indefinite or singular, as follows: 'Socrates is a man, therefore a man is Socrates' and 'some man is Socrates' and vice versa. Similarly, 'Socrates is Plato, therefore Plato is Socrates' and vice versa.
Singularis negativa convertitur simpliciter in universalem negativam vel singularem negativam, sicut sequitur 'Sortes non est albus, igitur nullum album est Sortes' et e converso. Similiter sequitur 'Sortes non est Plato, igitur Plato non est Sortes' et e Converso. Et ita singularis, secundum quod praedicatum est terminus cammunis vel singularis, in diversam propositionem convertitur conversione simplici.	A singular negative is simply converted into a universal negative or a singular negative, as follows: 'Socrates is not white, therefore no white thing is Socrates' and vice versa. Similarly, 'Socrates is not Plato, therefore Plato is not Socrates' and vice versa. And thus a singular, accordingly as the predicate is a common term or singular, is converted into a different proposition by simple conversion.
Similiter, tam indefinita quam particularis affirmativa convertitur tam in propositionem particularem quam indefinitam vel singularem, secundum quod habet pro praedicato terminum communem vel singularem. Sicut sequitur 'homo est albus, igitur aliquod album est homo' et 'album est homo'; et sequitur 'aliquis homo est albus, igitur aliquod album est homo' et 'album est homo'. Similiter sequitur 'homo est Sortes, igitur aliquis homo est Sortes, igitur Sortes est homo' et e converso.	Similarly, both indefinite and particular affirmatives are converted into particular or indefinite or singular propositions, according as they have a common or singular term for the predicate. As it follows: 'a man is white, therefore some white man is a man' and 'a white thing is a man'; and it follows that 'some man is white, therefore some white man is a man' and 'a white thing is a man'. Similarly it follows that 'a man is Socrates, therefore some man is Socrates, therefore Socrates is a man' and vice versa.
Similiter, universalis affirmativa tantum convertitur per accidens, quia non est ibi canuersio mutua; et hoc quando terminus praedicatus est terminus cammunis. Et tunc canuertitur per accidens tam in particularem quam indefinitam. Sicut sequitur 'omnis homo est albus, igitur aliquod album est homo' et 'album est homo', et non e converso. Quando autem habet praedicatum terminum singularem, tunc etiam convertitur per accidens in propositionem singularem; bene enim sequitur 'omnis homo est Sortes, igitur Sortes est homo' et non e converso.	Similarly, the universal affirmative is only accidentally converted, because there is no mutual conversion there; and this is when the predicate term is a common term. And then it is accidentally converted both into a particular and an indefinite. As follows 'every man is white, therefore some white thing is a man' and 'a white thing is a man', and not vice versa. But when it has a singular predicate term, then it is also accidentally converted into a singular proposition; for it follows well that 'every man is Socrates, therefore Socrates is a man' and not vice versa.
Particularis negativa non Convertitur, nec simpliciter nec per accidens. Non enim sequitur 'aliquod animal non est homo, igitur aliquis homo non est animal', nec sequitur 'ergo nullus homo est animal'. Eodem modo indefinita negativa non convertitur, quia semper particularis et indefinita convertuntur. Et hoc saltem est verum quando subiectum utriusque suppanit personaliter.	The particular negative is not converted, neither simply nor accidentally. For it does not follow that 'some animal is not a man, therefore some man is not an animal', nor does it follow that 'therefore no man is an animal'. In the same way, the indefinite negative is not converted, because the particular and the indefinite are always converted. And this is at least true when the subject of both supposits personally.
Aliquas de praedictis conversionibus probat Philosophus I Priorum quia tamen planae sunt et non indigent magna probatione, idea duxi pertranseundum.	The Philosopher proves some of the aforementioned conversions in Prior Analytics I, but because they are simple and do not require great proof, I decided to pass over them.
Et si dicatur contra aliqua praedictarum quod secundum Porphyrium et Philosophum species non praedicatur de genere, nec inferius de superiori, et singulare sive individuum non praedicatur nisi de uno solo, ergo tales conversiones non valent 'omnis homo est animal, ergo aliquod animal est homo' et huiusmadi:	And if it is said against some of the above that according to Porphyry and the Philosopher, species is not predicated of genus, nor inferior of superior, and singular or individual is not predicated except of one alone, then such conversions are not valid as 'every man is an animal, therefore some animal is a man' and the like:
Dicendum quad Porphyrius et Philosophus intendunt quad inferius non praedicatur de superiari cammuniari ad plura actualiter quam sit inferius, ipsa superiori universaliter sumpto, et hoc praedicatione vera. Unde non intendunt nisi quad nulla talls sit vera 'omne animal est homo', 'omnis homo est Sortes' et sic de aliis; quin tamen particulares et indefinitae sint verae non negant.	It must be said that Porphyry and the Philosopher intend that the inferior is not predicated of the superior to be actually more than the inferior is, taken universally, and this is a true predication. Hence they intend only that none of the statements is true: 'every animal is a man', 'every man is Socrates' and so on; yet they do not deny that particular and indefinite statements are true.
Praedicta dicta sunt de propositionibus in recto. Sed de prapositionibus in obliquo non est omnino eodem modo dicendum, sed in illis frequenter oportet aliquam mutationem facere ex parte vocis praeter solam transpositionem terminorum. Et hoc addendo frequenter ad praedicatum participium verbi, quod est copula, sicut sic arguendo 'nullus homo est in domo, igitur nullus exsistens in domo est homo'. Similiter sic arguendo 'nullus homo videt asinum, igitur nullus videns asinum est homo'. Et hoc est verum quando obliquitas cadit a parte praedicati; quia si cadat a parte subiecti, non oportet. Unde ista 'omnem hominem videt asinus' debet sic converti 'ergo asinus videt hominem'; similiter 'Filium generat Pater, igitur Pater generat Filium'.	The above has been said about propositions in the nominative case. But about prepositions in an oblique case, it is not entirely the same to say, but in them it is frequently necessary to make some change on the part of the wording besides the mere transposition of the terms. And this is frequently added to the predicate participle of the verb, which is a copula, as in the argument 'no man is in the house, therefore no one existing in the house is a man'. Similarly in the argument 'no man sees a donkey, therefore no one seeing a donkey is a man'. And this is true when the obliqueness falls on the part of the predicate; because if it falls on the part of the subject, it is not necessary. Hence the statement 'every man sees a donkey' should be converted to 'therefore a donkey sees a man'; similarly 'the Father generates the Son, therefore the Father generates the Son' (the word order is reversed in Latin).
Circa praedicta est sciendum quad quanda in tali propositione ponitur adverbialis determinatio vel aliqua determinatio aequivalens adverbiali determinationi, illa determinatio in conversa non debet esse determinatia verbi, sed debet esse determinatio participii eiusdem verbi. Et tunc in tali casu, sive propositio convertibilis sit in recto sive in obliquo oportet resoluere verbum in suum participium et in hoc verbum 'est'; et ita oportet aliquam variationem vocis facere praeter transpositianem terminorum. Et idea ista 'alteratum currit velaciter' non debet sic converti 'ergo currens est velaciter alteratum', nam ponatur quad idem tarde alteretur et velociter currat, tunc est antecedens verum et consequens falsum; sed debet sic converti 'igitur velociter currens est alteratum', ita quad li velociter sit determinatia huius participii 'currens' et non huius verbi 'est'. Similiter ista 'creans semper est Deus' non debet sic converti 'igitur Deus est semper creans', sed sic 'igitur aliquid quod semper est Deus, est creans'.	Regarding the above, it should be known that when in such a proposition an adverbial determination or some determination equivalent to an adverbial determination is placed, that determination in the inverse should not be the determination of the verb, but should be the determination of the participle of the same verb. And then in such a case, whether the convertible proposition is in the nominative or an oblique case, it is necessary to resolve the verb into its participle and into this verb 'is'; and thus it is necessary to make some variation of the word besides the transposition of the terms. And the idea 'an altered thing runs rapidly' should not be converted thus 'therefore a rapidly altered thing is running', for if it is assumed that the same thing alters slowly and runs quickly, then the antecedent is true and the consequent false; but it should be converted thus 'therefore rapidly running is the altered thing', so that rapidly is the determination of the participle 'running' and not of the verb 'is'. Similarly, 'a creating thing is always God' should not be converted thus 'therefore God is always creating', but thus 'therefore something that is always God, is creating'.