Authors/Ockham/Summa Logicae/Book II/Chapter 24

Latin	English
[2.24. DE CONVERSIONE PROPOSITIONUM MODALIUM. ET PRIMO DE CONVERSIONE PROPOSITIONUM DE NECESSARIO]	Chapter 24. On the Conversion of Modal Propositions. And First on the conversion of Propositions of Necessity.
Viso quomodo propositiones de inesse convertuntur, videndum est quomodo propositiones modales convertuntur. Et primo de conversione propositionum de necessario.	Having seen how propositions of inherence are converted, we must see how modal propositions are converted. And first about the conversion of propositions of necessity.
Est autem primo sciendum quod, sicut dictum est prius, quando modus ponitur cum dicto, illa propositio est distinguenda secundum compositionem et divisionem. Et ideo primo videndum est de conversione talium propositionum in sensu compositionis et aequivalentium eis, secundo de conversione talium propositionum in sensu divisionis et aequivalentium eis.	But it must first be known that, as was said before, when a mode is placed with what is said, that proposition must be distinguished according to composition and division. And therefore, we must first consider the conversion of such propositions in the sense of composition and their equivalents, and secondly the conversion of such propositions in the sense of division and their equivalents.
Circa primum sciendum est breviter quod tales propositiones convertuntur sicut suae de inesse, quia in conversione talium arguitur semper per istam regulam 'si unum convertibilium est necessarium, reliquum est necessarium'; vel per istam 'si antecedens est necessarium, consequens est necessarium'. Unde in conversione simplici, large sumpta, arguitur per primam regulam, in conversione per accidens arguitur per secundam regulam. Verbi gratia sic arguendo 'nullum hominem esse asinum est necessarium, igitur nullum asinum esse hominem est necessarium', arguitur per istam regulam. Cum ista convertantur, sicut dictum est prius, 'nullus homo est asinus' et 'nullus asinus est homo', si haec sit necessaria 'nullus homo est asinus' oportet quod haec sit necessaria 'nullus asinus est homo'. Et sicut dictum est de istis, ita dicendum est de aliis. Et hoc est universaliter verum de omnibus, sive sint reduplicativae sive exclusivae sive exceptivae sive quaecumque aliae propositiones categoricae.	Regarding the first, it should be noted briefly that such propositions are converted like the propositions of inherence, because in the conversion of such propositions, it is always argued by this rule 'if one of the convertibles is necessary, the remaining is necessary'; or by this 'if the antecedent is necessary, the consequent is necessary'. Hence in a simple conversion, broadly taken, it is argued by the first rule, in an accidental conversion it is argued by the second rule. For example, by arguing thus 'it is necessary that no man be a donkey, therefore it is necessary that no donkey be a man', it is argued by this rule. Since these are converted, as was said before, 'no man is a donkey' and 'no donkey is a man', if the latter is necessary 'no man is a donkey', it must be necessary that the former is necessary 'no donkey is a man'. And as was said of these, so must be said of the others. And this is universally true of all, whether they are reduplicative or exclusive or exceptive or any other categorical propositions.
Sciendum est etiam quod Philosophus, I Priorum, tantum probat illas de necessario converti in sensu compositionis vel eis aequivalentes et non alias, quia neutra probatio sua procedit de aliis, sicut ibi patet. Unde ista propositio 'si unum convertibilium est possibile, reliquum est passibile' non valet nisi quantum ad propositiones de possibili sumptas in sensu compositionis. Nec etiam ista 'cuicumque actui repugnat necessitas, potentiae eiusdem actus repugnat necessitas eadem', hoc est cuicumque propositioni de inesse repugnat aliqua propositio de necessario, propositioni de possibili correspondenti illi de inesse repugnat eadem propositio de necessario. Unde si istae duae repugnant 'aliquis homo currit' et 'necesse est nullum animal currere', istae duae repugnabunt 'possibile est aliquem hominem currere' et 'necesse est nullum animal currere'. Et hoc est verum generaliter quando utraque de modo accipitur in sensu compositionis vel aequivalens sibi. Si enim una acciperetur in sensu divisionis, regula non valeret, nam instantiae sunt multae. Sicut istae duae repugnant 'aliquod verum est impossibile' et 'necesse est nullum verum esse impossibile', et tamen istae duae stant simul 'aliquod verum potest esse impossibile' et 'necesse est nullum verum esse impossibile', illa de necessario sumpta in sensu compositionis, quia utraque istarum est vera. Et ita Philosophus in libro Priorum non loquitur de conversione propositionum de necessario nisi quando sumuntur in sensu compositionis vel aequivalenter.	It should also be noted that the Philosopher, in Book I of the Prior Analytics, only proves that those are necessarily convertible in the sense of composition or equivalent to them and not others, because neither of his proofs proceeds from the others, as is clear there. Hence this proposition 'if one of the convertibles is possible, the rest is passible' is valid only as regards propositions of possibility taken in the sense of composition. Nor also this 'to whatever act necessity is incompatible, the same necessity is incompatible to the power of the same act', that is, to whatever proposition of inherence some proposition of necessity is incompatible, to the proposition of possibility corresponding to that of inherence the same proposition of necessity is incompatible. Hence if these two are incompatible 'some man runs' and 'it is necessary for no animal to run', these two will be incompatible 'it is possible for some man to run' and 'it is necessary for no animal to run'. And this is true generally when both are taken modally in the sense of composition or equivalent to each other. For if one were taken in the sense of division, the rule would not hold, for there are many instances. Just as these two are incompatible, 'something true is impossible' and 'it is of necessity that nothing true be impossible', and yet these two stand together, 'something true can be impossible' and 'it is of necessity that nothing true be impossible', the one taken of necessity in the sense of composition, because both of these are true. And so the Philosopher in the book of the Prior Analytics does not speak of the conversion of propositions of necessity except when they are taken in the sense of composition or equivalently.
Circa conversionem propositionum de necessario, sumptarum in sensu divisionis et aequivalentium, est sciendum quod non sunt convertibiles nulla facta mutatione seu variatione ex parte vocis praeter transpositionem terminorum. Non enim sequitur per naturam conversionis 'nullus homo de necessitate est asinus, igitur nullus asinus de necessitate est homo', quia non sequitur in sensu divisionis acceptis aliis propositionibus. Unde non sequitur 'nullum impossibile esse verum est necessarium, igitur nullum verum esse impossibile est necessarium', quia antecedens est verum et consequens falsum. Nullum enim impossibile potest esse verum, et tamen aliquod verum potest esse impossibile. Haec enim modo est vera 'ego non fui Romae', et tamen potest esse impossibilis: si enim uadam Romam, postea erit impossibilis.	Regarding the conversion of propositions of necessity, taken in the sense of division and equivalents, it should be known that they are not convertible by any change or variation made on the part of the word other than the transposition of the terms. For it does not follow by the nature of the conversion that 'no man is of necessity a donkey, therefore no donkey is of necessity a man', because it does not follow in the sense of division taken from the other propositions. Hence it does not follow that 'nothing impossible to be true is necessary, therefore for nothing true to be impossible is necessary', because the antecedent is true and the consequent false. For nothing impossible can be true, and yet something true can be impossible. For this is true now, 'I was not in Rome', and yet it can be impossible: for if I go to Rome, it will be impossible afterwards.
Similiter non sequitur 'creans de necessitate est Deus, igitur Deus de necessitate est creans', quia antecedens est verum et consequens falsum. Similiter non sequitur 'homo de necessitate intelligitur a Deo, igitur aliquod intellectum a Deo de necessitate est homo', quia antecedens est verum et consequens falsum. Similiter non sequitur 'homo albus de necessitate est homo, igitur homo de necessitate est homo albus'.	Similarly, it does not follow that 'the creator is of necessity God, therefore God is of necessity the creator', because the antecedent is true and the consequent false. Similarly, it does not follow that 'man is of necessity understood by God, therefore something understood by God is of necessity man', because the antecedent is true and the consequent false. Similarly, it does not follow that 'a white man is of necessity a man, therefore a man is of necessity a white man'.
Et ideo tales praedicto modo converti non possunt; sed subiecto consequentis, quod fuit praedicatum antecedentis, addendus est modus necessitatis cum hoc 'aliquid quod est', ut ista 'omne impossibile de necessitate non est verum' convertatur sic 'igitur aliquid, quod de necessitate non est verum, est impossibile'. Similiter ista 'creans de necessitate est Deus' convertitur in istam 'igitur aliquid, quod de necessitate est Deus, est creans'. Et ista 'homo de necessitate intelligitur a Deo' convertitur sic 'igitur aliquid, quod de necessitate intelligitur a Deo, est homo'. Et ita de aliis.	And therefore, such cannot be converted in the aforesaid way; but to the subject of the consequent, which was the predicate of the antecedent, the mode of necessity must be added with this 'something that is', so that the statement 'everything impossible is not necessarily true' is converted thus 'therefore something that is not necessarily true is impossible'. Similarly, the statement 'a creator is of necessity God' is converted into the statement 'therefore something that is of necessity God is a creator'. And the statement 'man is of necessity understood by God' is converted thus 'therefore something that is of necessity understood by God is man'. And so with the others.
Ex quibus patet quod stricte accipiendo propositionem de modo et propositionem de inesse, propositio de necessario, sumpta in sensu divisionis vel aequivalens ei, non convertitur in propositionem de necessario sed in propositionem de inesse.	From which it is clear that by strictly taking the modal proposition and the proposition of inherence, the proposition of necessity, taken in the sense of division or equivalent to it, is not converted into a proposition of necessity but into a proposition of inherence.
Patet etiam ex praedictis quod talis consequentia non valet 'tantum necessarium de necessitate est verum, igitur omne verum de necessitate est necessarium', quia ista universalis non est convertibilis cum praedicta exclusiva sed ista 'omne, quod de necessitate est verum, est necessarium', quia semper propasitiones habentes exponentes diversimode convertuntur, secundum quod exponentes earum diversimode convertuntur. Unde secundum quod exponentes unius exclusivae aliter canuertuntur quam exponentes alterius exclusivae, secundum hoc una exclusiva aliter convertitur quam alia. Similiter non sequitur 'tantum creans de necessitate est Deus, igitur omne quod est Deus, de necessitate est creans' sed sic 'igitur omne quod de necessitate est Deus, est creans'.	It is also clear from the above that such a consequence does not hold: 'Only what is necessary is necessarily true, therefore everything true is necessarily necessary', because this universal is not convertible with the aforementioned exclusive, but rather 'everything that is necessarily true is necessary', because the exponents that always have propositions are converted in different ways, according as their exponents are converted in different ways. Hence, according as the exponents of one exclusive are converted differently than the exponents of another exclusive, according to this one exclusive is converted differently than another. Similarly, it does not follow that 'only God is necessarily the creator, therefore everything that is God is necessarily the creator', but rather that 'therefore everything that is necessarily God is the creator'.
Causa autem quare in praedictis Consequentiis est antecedens verum et cansequens falsum, dicta est prius, ubi dictum est quamodo aliter appellat praedicatum suam formam quam subiectum. Et ideo illud ibi dictum summe est imprimendum memoriae ad sciendum quid requiritur ad veritatem propositionum de praeterito et de futuro et de modo et aequivalentium eis.	But the reason why in the aforementioned consequences the antecedent is true and the consequent false was stated earlier, where it was stated how the predicate calls its form differently from the subject. And therefore, what was said there must be impressed upon the memory in order to know what is required for the truth of propositions about the past and the future and about manner and their equivalents.