Authors/Ockham/Summa Logicae/Book III-1/Chapter 65

Latin	English
Cap. 65. De syllogismo facto ex propositionibus habentibus plures exponentes	Chapter 65. On syllogisms made from propositions having several exponents.
Postquam visum est quomodo syllogismus fit ex propositionibus tam de inesse quam de modo quae exponentes places non habent, videndum est quomodo syllogismus fit ex propositionibus plures exponentes habentibus, cuiusmodi sunt exclusivae, exceptivae, reduplicativae et huiusmodi, de quibus dictum est prius.	After it has been seen how a syllogism is formed from assertoric propositions and of a mode that do not have exponents, we must see how a syllogism is formed from propositions that have several exponents, such as exclusive, exceptive, reduplicative, and the like, which were discussed earlier.
Pro quibus utendum est ista regula generali, quod quandocumque quaelibet exponens conclusionis vel ipsa conclusio sequitur ex aliquibus exponentibus praemissarum vel ex aliqua exponente unius praemissae et alia praemissa, semper est syllogismus bonus, et aliter non. Et ideo ad videndum an talis discursus sit bonus vel non, oportet diligenter videre quae sunt exponentes talium praemissarum et conclusionis et quomodo se habent secundum consequentiam ad invicem. Sicut ad videndum an iste discursus sit bonus ‘omnis homo, in quantum homo, est risibilis; animal est homo; igitur animal, in quantum homo, est risibile', oportet videre exponentes maioris et conclusionis. Unde exponentes maioris sunt istae 'omnis homo est homo', 'omnis homo est risibilis', 'si aliquid est homo, ipsum est risibile’. Exponentes conclusionis sunt istae 'animal est homo', 'animal est risibile', 'omnis homo est risibilis', 'si aliquid est homo, ipsum est risibile’. Nunc autem sequitur 'omnis homo est homo, igitur animal est homo’. Similiter sequitur 'omnis homo est risibilis, ƿ igitur animal est risibile'. Aliae duae exponentes conclusions sunt exponentes maioris. Ex quo patet quod omnes exponentes conclusionis sequuntur ex antecedente, et ita discursus est bonus. Et ideo quilibet talis discursus est bonus 'quilibet logicus, in quantum logicus, differt a grammatico; grammaticus est logicus; igitur grammaticus, in quantum logicus, differt a grammatico’; sed maior est falsa.	For which we must use this general rule, that whenever any exponent of the conclusion or the conclusion itself follows from some exponents of the premises or from some exponent of one premise and another premise, it is always a good syllogism, and otherwise not. And therefore, to see whether such a discourse is good or not, it is necessary to carefully see what the exponents of such premises and conclusion are and how they relate to each other in terms of consequence. Just as to see whether this discourse is good ‘every man, insofar as he is a man, is able to laugh; an animal is a man; therefore, an animal, insofar as it is a man, is able to laugh’, it is necessary to see the exponents of the major and the conclusion. Hence the exponents of the major are these 'every man is a man', 'every man is able to laugh', 'if something is a man, it is able to laugh'. The exponents of the conclusion are these 'animal is a man', 'animal is able to laugh', 'every man is able to laugh', 'if something is a man, it is able to laugh'. Now, however, it follows 'every man is a man, therefore an animal is a man'. Similarly, it follows 'every man is able to laugh, therefore an animal is able to laugh'. The other two exponents of the conclusions are exponents of the major. From which it is clear that all the exponents of the conclusion follow from the antecedent, and thus the discourse is good. And therefore, any such discourse is good: 'every logician, insofar as he is logical, differs from a grammarian; a grammarian is logical; therefore, a grammarian, insofar as he is logical, differs from a grammarian'; but the major is false.
Ex isto patet quod semper in prima figura ex maiore reduplicativa et minore reduplicativa vel non reduplicativa sequitur conclusio reduplicativa. Sicut sequitur 'omnis homo, in quantum rationalis, est susceptibilis disciplinae; animal est homo; igitur animal, in quantum rationale, est susceptibile disciplinae'; 'omne agens, in quantum agens, differt a passo; aliquod passum est agens; igitur aliquod passum, in quantum agens, differt a passo'. Et non solum sequitur conclusio reduplicativa, sed etiam sequitur conclusio sine reduplicatione, quae est praeiacens illius reduplicativae. Quod autem omnes tales syllogismi sunt boni, patet, quia, sicut inductive patet, quaelibet exponens consequentis sequitur ex aliqua exponente antecedentis vel ex aliqua exponente et minore, vel est eadem cum aliqua exponente maioris.	From this it is clear that in the first figure a reduplicative conclusion always follows from a reduplicative major and a reduplicative or non-reduplicative minor. As it follows: 'every man, insofar as he is rational, is susceptible to discipline; an animal is a man; therefore an animal, insofar as he is rational, is susceptible to discipline'; 'every agent, insofar as he is an agent, differs from the subject; some subject is an agent; therefore some subject, insofar as he is agent, differs from the subject'. And not only does a reduplicative conclusion follow, but also a conclusion without reduplication follows, which is prior to that reduplicative. But that all such syllogisms are good is clear, because as is clear inductively, any exponent of the consequent follows from some exponent of the antecedent or from some exponent and a minor or is the same as some exponent of the major.
Sed si minor fuerit reduplicativa et maior non, quamvis sequatur conclusio sine reduplicatione, non tamen sequitur conclusio cum reduplicatione. Unde non sequitur 'omne susceptibile disciplinae est album; omnis homo, in quantum rationalis, est susceptibilis disciplinae; igitur omnis homo, in quantum rationalis, est albus', quia ista exponens consequentis 'si aliquid est rationale, ipsum est album' non sequitur ex aliqua exponente minoris nec etiam cum maiore, sicut inductive patet.	But if the minor is reduplicative and the major is not, although a conclusion follows without reduplication, a conclusion with reduplication does not follow. Hence it does not follow that 'everything susceptible to discipline is white; every man, insofar as he is rational, is susceptible to discipline; therefore every man, insofar as he is rational, is white', because the exponent of the consequent 'if something is rational, it is white' does not follow from any exponent of the minor nor even with the major, as is clear inductively.
Quae dicta sunt, intelligenda sunt quando reduplicatio proprie sumitur et manet non negata. Si enim reduplicatio fuerit negata in maiore et affirmata in conclusione, non valet discursus. Unde quamvis iste discursus sit bonus 'omnis homo, in quantum albus, non est musicus; Sortes est homo; igitur Sortes, in quantum albus, non est musicus', tamen iste discursus non valet 'nullus homo, in quantum albus, est musicus; Sortes est homo; igitur Sortes, in quantum albus, non est musicus'; sed ƿ sequitur ista conclusio 'igitur Sortes non est musicus in quantum est albus’.	What has been said is to be understood when the reduplication is properly taken and remains unnegated. For if the reduplication is negated in the major and affirmed in the conclusion, the discourse is not valid. Hence, although this discourse is good 'every man, insofar as he is white, is not a musician; Socrates is a man; therefore Socrates, insofar as he is white, is not a musician', yet this discourse is not valid 'no man, insofar as he is white, is a musician; Socrates is a man; therefore Socrates, insofar as he is white, is not a musician'; but this conclusion follows 'therefore Socrates is not a musician insofar as he is white'.
In secunda autem figura, quaecumque praemissa sumatur cum reduplicatione et alia sine reduplicatione, non sequitur conclusio reduplicativa. Sicut non sequitur 'omnis homo, in quantum animal, est sensibilis; nullum album est sensibile; igitur omne album, in quantum animal, non est homo’.	But in the second figure, whatever premise is taken with reduplication and another without reduplication, the reduplicative conclusion does not follow. Just as it does not follow that 'every man, as an animal, is sensible; no white thing is sensible; therefore, every white thing, as an animal, is not a man'.
Nec potest syllogismus reduci in primam figuram per conversionem, quia reduplicativa non converitur in reduplicativam. Non enim sequitur ‘omnis homo, in quantum animal, est sensibilis, igitur aliquod sensibile, in quantum animal, est homo’, quia conditionalis exponens consequentis non sequitur ad conditionalem exponentem antecedentis, nec ad aliquam aliarum, sicut manifeste patet.	Nor can a syllogism be reduced to the first figure by conversion, because a reduplicative does not convert into a reduplicative. For it does not follow that ‘every man, insofar as he is an animal, is sensible, therefore something sensible, insofar as it is an animal, is a man’, because the conditional exponent of the consequent does not follow to the conditional exponent of the antecedent, nor to any of the others, as is clearly evident.
Quamvis autem in secunda figura ex talibus piopositionibus non sequatur conclusio reduplicativa, sequitur tamen conclusio in qua negatur reduplicatio, et per consequens non est reduplicativa. Unde bene sequitur 'omnis homo, in quantum animal, est sensibilis; nullum album est sensibile; igitur nullum album, in quantum animal, est homo', quia ex praedictis praemissis sequitur ista conclusio 'nullum album est homo', et sequitur 'nullum album est homo, igitur nullum album, in quantum animal, est homo’.	Although in the second figure a reduplicative conclusion does not follow from such premises, a conclusion nevertheless follows in which reduplication is denied, and consequently it is not reduplicative. Hence it follows well that 'every man, as an animal, is sensible; no white man is sensible; therefore no white man, as an animal, is a man', because from the above premises the conclusion 'no white man is a man' follows, and it follows that 'no white man is a man, therefore no white man, as an animal, is a man'.
Si autem omnes praemissae sunt reduplicativae, ita quod in utraque reduplicatio cadens super idem sit affirmativa, sequitur conclusio reduplicativa.	But if all the premises are reduplicative, so that in each case the reduplicative falling on the same thing is affirmative, a reduplicative conclusion follows.
In tertia autem figura, si maior universalis fuerit reduplicativa et alia non reduplicativa, sequitur conclusio reduplicativa, Sequitur enim 'omnis homo, in quantum animal, est sensibilis; omnis homo est albus; igitur aliquod album, in quantum animal, est sensibile’, quia conversa minore ƿ fit syllogismus regulatus per dici de omni in prima figura, Sed si minor fuerit reduplicativa, non sequitur conclusio reduplicativa. Non enim sequitur 'omnis homo est albus; omnis homo, in quantum animal, est sensibilis; igitur aliquod sensibile, in quantum animal, est album’.	In the third figure, however, if the major universal is reduplicative and the other non-reduplicative, a reduplicative conclusion follows. For it follows 'every man, as an animal, is sensible; every man is white; therefore something white, as an animal, is sensible', because when the minor is converted, it becomes a syllogism governed by 'dici de omni' in the first figure. But if the minor is reduplicative, a reduplicative conclusion does not follow. For it does not follow: 'every man is white; every man, as an animal, is sensible; therefore something sensible, as an animal, is white'.