Authors/Ockham/Summa Logicae/Book II/Chapter 16

Latin	English
[2.16 DE PROPOSITIONIBUS REDUPLICATIVIS IN QUIBUS PONITUR HAEC DICTIO ‘IN QUANTUM’]	16: On Reduplicative Propositions
Circa propositiones reduplcativas est primo sciendum quod illa propositio vocatur reduplicativa in qua ponitur haec dictio ‘in quantum’, vel aequivalens, et tenetur reduplicative; quia secundum aliquos potest aliquando teneri reduplicative, et tunc facit propositionem reduplicativam, et potest aliquando teneri specificative, et tunc non facit propositionem reduplicativam.	With respect to reduplicative propositions it should first be known that a proposition is called reduplicative in which occurs the expression ‘insofar as’ or some equivalent, grasped reduplicatively. For according to some, this expression can sometimes be grasped reduplicatively, and then it makes the proposition reduplicative; and it can sometimes be understood specificatively, and then does not make the proposition reduplicative.
Secundo sciendum quod in propositione reduplicativa ipsa reduplicatio, scilicet haec dictio ‘in quantum’, vel aequivalens, aliquando est affirmata, quia scilicet negatio non praecedit eam, et aliqando est negata, quia scilicet negatio praecedit eam, sicut hic ‘Sortes non currit in quantum est homo’. Si autem reduplicatio non sit negata, vel hoc est in propositione affirmativa, sicut hic ‘Sortes in quantum homo est risibilis’, vel in propositione negativa, sicut hic ‘Sortes in quantum homo non currit’.	Second, it should be known that in a reduplicative proposition the reduplication itself, namely, the expression ‘insofar as’ or equivalent, sometimes is affirmed, namely because a negation does not precede it, and sometimes is denied, because a negation does precede it – as in “Socrates does not run, insofar as he is a man”. Now if the reduplication is not denied, either this is in an affirmative proposition such as “Socrates, insofar as he is a man, is capable of laughter”, or this is in a negative proposition such as “Socrates, insofar as he is a man, does not run”.
Primo igitur videndum est quid requiritur ad veritatem propositionis affirmativae reduplicativae; secundo quid ad veritatem propositionis negativae, in qua tamen reduplicatio non est negata; tertio quid requiritur ad veritatem propositionis in qua reduplicatio est negata.	Therefore, first we must consider what is required for the truth of an affirmative reduplicative proposition. Second, what is required for the truth of a negative proposition in which, nevertheless, the reduplication is not negated Third, what is required for the truth of a proposition in which the reduplication is negated.
Circa primum sciendum est quod talis propositio potest distingui, eo quod potest esse reduplicatio gratia concomitantiae vel gratia causae.	As far as the first point, it should be known that such a proposition can be distinguished, in that the reduplication can happen from either concomitance or a cause.
Si fiat reduplicatio gratia concomitantiae, tunc ad veritatem ipsius requiruntur quatuor propositiones tamquam exponentes eam: una, in qua praedicatum principale vere praedicetur de subiecto principali; alia, in qua illud super quod cadit reduplicatio praedicetur de subiecto principali; tertia, in qua praedicatum principale praedicetur de illo super quod cadit reduplicatio universaliter; quarta erit una condicionalis vera, ab illo super quod cadit reduplicatio ad praedicatum principale, illo modo quo ab inferiori ad superius dicitur esse bona consequentia et quo modo dicitur quod ex uno convertibilium sequitur reliquum.	If the reduplication happens from concomitance, then for the truth of it four propositions are required, as though expounding it. One, in which the principal predicate is truly predicated of the principal subject. Another, in which what the reduplication subsumes is predicated of the principal subject. The third, in which the principal predicate is predicated of what the reduplication subsumes, taken universally. The fourth will be a true conditional from what the reduplication subsumes to the principal predicate, in the way by which there is said to be a valid consequence from an inferior to a superior, and in the way in which it is said that one of two convertible propositions follows from the other.
Verbi gratia ad veritatem istius ‘Sortes in quantum homo est coloratus’ requiritur veritas istius ‘Sortes est coloratus’ et istius ‘Sortes est homo’ et istius ‘omnis homo est coloratus’ et istius ‘si homo est, coloratus est’ vel istius ‘si a est homo, a est coloratum’. Et quia talis condicionalis est falsa, ideo talis reduplicativa ‘Sortes in quantum homo est coloratus’ est similiter falsa, quia scilicet habet unam exponentem falsam.	For example, for the truth of “Socrates, insofar as he is a man, has a colour” the truth of these propositions is required: “Socrates has a colour”, “Socrates is a man”, “Every man has a colour”, and “If a man exists, then something which has a colour exists”, or “If a is a man, then a is coloured”. And because such a conditional is false, it follows that the reduplicative proposition “Socrates, insofar as he is a man, has a colour” is likewise false, namely because it has a false exponent.
Si autem reduplicatio fiat gratia causae, tunc ad veritatem talis reduplicativae, praeter quatuor praedictas exponentes, requiritur quod illud super quod cadit reduplicatio exprimat causam importati per praedicatum, vel quod sit illud cui primo inest praedicatum principale, vel quod illi prius insit praedicatum principale quam pronomini demonstranti illud pro quo subiectum principale supponit.	But if the reduplication happens from a cause, then for the truth of such a reduplicative, besides the four exponents just mentioned, it is required what the reduplication subsumes is due to the cause of what is conveyed by the predicate, or that it is that in which the principal predicate inheres primarily, or that the principal predicate inheres in it prior to its inhering in a pronoun referring to what the principal subject supposits for.
Sicut per istam ‘isosceles in quantum triangulus habet tres’ etc. denotatur quod isosceles habet tres etc., et quod isosceles est triangulus, et quod omnis triangulus habet tres etc., et quod si aliquid est triangulus, habet tres etc., et simul cum hoc quod hoc praedicatum ‘habere tres’ prius verificetur de triangulo quam de isoscele, illo modo quo logicus utitur ‘priori’ et ‘posteriori’, quae sunt condiciones propositionum. Similiter per istam ‘ignis in quantum calidus est calefactivus’ denotantur praedicta, et ideo est vera.	For example, by “An isosceles, insofar as it is a triangle, has three angles” it is denoted that an isosceles has three [angles], and that an isosceles is a triangle, and that every triangle has three angles, etc., and that if something is a triangle, then it has three angles etc. And together with this, it is denoted that the predicate ‘has three [angles]’ is verified of ‘triangle’ prior to its being verified of ‘isosceles’, in the way that a logician uses ‘prior’ and ‘posterior’, namely, for relations among propositions. Likewise, by means of “Fire, insofar as it is hot, is warmth-producing” the aforesaid are denoted, and therefore [the proposition] is true.
Similiter ista est vera ‘homo in quantum habens animam intellectivam est susceptibilis disciplinae’, quia -- praeter quatuor exponentes -- anima intellectiva est causa disciplinae, et hoc extendendo nomen causae ad subiectum alicuius; quod sufficit ad veritatem talis reduplicativae.	Likewise, “A man, insofar as he has an intellective soul, is susceptible of learning” is true, because, apart from the four exponents, an intellective soul is the cause of learning – by extending the name ‘cause’ to the subject of some [quality]. Which suffices for the truth of such a reduplicative.
Sed ista ‘homo in quantum risibilis est susceptibilis disciplinae’ est falsa, quamvis sit vera si fiat reduplicatio gratia concomitantiae; et hoc quia praedictae quatuor exponentes sunt verae.	But “A man, insofar as he is capable of laughter, is susceptible of learning” is false, although it is true if the reduplication happens from concomitance, and this is because the aforesaid four exponents are true.
Ex praedictis potest colligi regula talis quod a propositione reduplicativa ad suam praeiacentem est semper consequentia formalis, et hoc quia semper sua praeiacens est una exponens reduplicativae, et ideo sequitur formaliter ‘homo in quantum animal est sensibilis, igitur homo est sensibilis’; similiter ‘ignis in quantum calidus est calefactivus, igitur ignis est calefactivus’.	From the aforesaid can be gathered the rule that there is always a formal consequence from a reduplicative proposition to its original. This is because its original is always one exponent of a reduplicative, and so “A man, insofar as he is an animal, is sentient; therefore a man is sentient” follows formally. Likewise, this follows: “Fire, insofar as it is hot, warms; therefore fire warms”.
Ex istis sequitur quod multae propositiones, quae a multis conceduntur tam in philosophia quam in theologia, sunt simpliciter falsae de virtute sermonis. Cuiusmodi sunt tales ‘creatura in quantum est in Deo est realiter divina essentia’, ‘Pater et Filius spirant in quantum sunt unum’, ‘homo in quantum creatura non est ens’, ‘obiectum in quantum intelligibile habet esse diminutum’ et huiusmodi, quia omnes tales habent aliquam exponentem falsam. Et eodem modo, proportionaliter, dicendum est de consimilibus.	From these [remarks], it follows that many propositions which are conceded by many both in philosophy and theology are absolutely false, strictly speaking. Of which sort are: “A creature, insofar as it is in God, is really the divine essence”, “The Father and the Son generate [the Spirit) insofar as they are one”, “A man, insofar as he is a creature, is not a being”, “An object, insofar as it is intelligible, has diminished being”, and so on, because all such propositions have some false exponent. And the same thing, in proportion, should be said about similar propositions.
Et si aliquae tales propositiones vel consimiles inveniantur in auctoribus, sive Sanctis sive philosophis, exponendae sunt, quia auctores frequenter loquuntur non de virtute sermonis, sicut patet intuenti libros eorum.	And if some such propositions or similar are found in the authorities – whether Saints or philosophers –they should be expounded, because authorities frequently do not speak literally, as is clear to anyone who examines their books carefully.
Per praedicta possunt solvi talia sophismata ‘aliqua in quantum conveniunt differunt’, ‘aliqua in quantum differunt conveniunt’.	From the aforesaid can be resolved such sophisms as “Some things, insofar as they agree, differ” and “Some things, insofar as they differ, agree”.
Nam accipiendo ‘convenire’ secundum quod verificatur de omnibus exsistentibus in rerum natura et ‘differre’ pro omnibus quae quocumque modo differunt, hoc est sunt et non sunt idem, sic omnes tales et consimiles verae sunt si fiat reduplicatio gratia concomitantiae, quia sicut manifeste patet, quatuor praedictae exponentes talium sunt verae.	For by taking ‘to agree’ in the sense in which it is verified of all things which exist in reality, and taking ‘to differ’ for all things which differ in any way whatsoever, i.e. are and are not the same, then all such propositions and ones just like them are true, if the reduplication happens from concomitance. Because, as is manifestly clear, the four previously mentioned exponents of such propositions are true.
Si autem fiat reduplicatio gratia causae, sic sunt falsae, nam ‘convenire’ non prius convenit nec dicitur de differentibus quam de convenientibus, nec etiam importat causam talem, ideo falsae sunt, sic accipiendo eas.	But if the reduplication happens from a cause, thus they are false, for ‘to agree’ neither agrees with nor is said of differing things prior to its being said of things which agree, nor even does it designate the cause of their differing. Therefore, the propositions are false if taken in this sense.
Sed secus est de istis ‘aliqua in quantum sunt similia, sunt dissimilia’, ‘aliqua in quantum sunt dissimilia, sunt similia’, nam ista consequentia non valet ‘ista sunt similia, ergo sunt dissimilia’, nec e converso. Nec etiam sequitur ‘conveniunt in hoc praedicabili ‘dissimile’, igitur sunt similia’, quia ad hoc quod sint similia requiritur quod habeant qualitates eiusdem speciei specialissimae.	But it is otherwise for “Some things, insofar as they are similar, are dissimilar”, “Some things, insofar as they are dissimilar, are similar”, for “These are similar; therefore they are dissimilar” is not valid, nor conversely. Nor either is “They agree in the predicable ‘dissimilar’, therefore they are similar”, because for them to be similar it is required that they have qualities of the same most specific species.
Alia regula est quod arguendo ab inferiori ad superius sine distributione a parte subiecti principalis, est bona consequentia. Unde ista consequentia est bona ‘Sortes in quantum homo est risibilis, igitur animal in quantum homo est risibile’, quia impossibile est exponentes antecedentis esse veras sine exponentibus consequentis; et hoc sive fiat reduplicatio gratia concomitantiae sive gratia causae.	Another rule is that arguing from an inferior to a superior, without distribution, on the part of the principal subject, is a good consequence. Hence, this is a good consequence: “Socrates, insofar as he is a man, is capable of laughter; therefore an animal, insofar as he is a man, is capable of laughter”, because it is impossible for the exponents of the antecedent to be true unless the exponents of the consequent are true. And this holds whether the reduplication happens from concomitance or to a cause.
Similiter, arguendo a parte praedicati principalis est bona consequentia. Sed arguendo ab illo super quod cadit reduplicatio ad suum superius, est fallacia consequentis, sicut hic ‘Sortes in quantum homo est risibilis, igitur Sortes in quantum animal est risibilis’.	Likewise, when one argues in the same way with respect to the principal predicate, it is a good consequence. But when one argues from that which the reduplication subsumes to its superior, there is a fallacy of consequent, as in “Socrates, insofar as he is a man, is capable of laughter; therefore Socrates, insofar as he is an animal, is capable of laughter”.
Nam si ista consequentia esset bona, sequeretur quod ista consequentia esset bona ‘omnis homo est risibilis, igitur omne animal est risibile’, per istam regulam: quando reduplicativa infert reduplicativam, exponentes antecedentis inferunt exponentes consequentis.	For if that consequence were good, then it would follow that the consequence “Every man is capable of laughter; therefore every animal is capable of laughter” would be valid, by the rule “When a reduplicative implies a reduplicative, the exponents of the antecedent imply the exponents of the consequent”.
Verumtamen sciendum est quod aliter posset aliquis uti talibus propositionibus, non de virtute sermonis; et tunc possent negari tales consequentiae. Et sic respondendum esset ad auctoritates si invenirentur dicere oppositum alicuius istorum.	Nevertheless, it should be known that someone could use these propositions in some other way and not literally, and then such consequences could be denied. And so it would have to be replied to authorities if they were found to say the opposite of some what was said here.
Secundo videndum est principaliter de reduplicativa negativa, in qua tamen reduplicatio non est negata, cuiusmodi est talis propositio ‘homo in quantum rationalis non est asinus’.	The second thing to consider is principally to discuss a negative reduplicative, in which, nevertheless, the reduplication is not denied, of which sort is “A man, insofar as he is rational, is not a donkey”.
Et est sciendum quod talis propositio reduplicativa, si fiat reduplicatio gratia concomitantiae, habet quatuor exponentes: duas negativas et unam affirmativam et unam condicionalem. Affirmativa exponens est illa in qua illud super quod cadit reduplicatio vere affirmatur de subiecto principali.	And it should be known that such a reduplicative proposition, if the reduplication happens from concomitance, has four exponents: two negative, one affirmative, and one conditional. The affirmative exponent is that in which what the reduplication subsumes is truly affirmed of the principal subject.
Negativarum exponentium una est praeiacens illius propositionis reduplicativae, in qua scilicet praedicatum principale negatur a subiecto principali; alia negativa exponens est illa in qua praedicatum principale negatur ab illo super quod cadit reduplicatio universaliter sumpto.	One of the negative exponents is the original of the reduplicative proposition in question, namely, in which the principal predicate is denied of the principal subject. The other negative exponent is a proposition in which the principal predicate is denied of what the reduplication, taken universally, subsumes.
Condicionalis est illa in qua a positione illius super quod cadit reduplicatio sequitur negatio praedicati principalis. Sicut ista ‘homo in quantum risibilis non est asinus’ habet istas exponentes ‘homo est risibilis’, ‘homo non est asinus’, ‘nullum risibile est asinus’, ‘si aliquid est risibile, ipsum non est asinus’.	The conditional is a proposition in which the negation of the principal prediate follows from the positing of what the reduplication subsumes. For example, “A man, insofar as he is capable of laughter, is not a donkey” has these exponents: “A man is capable of laughter”, “A man is not a donkey”, “Nothing capable of laughter is a donkey”, “If something is capable of laughter, then it is not a donkey”.
Et propter hoc tales falsae sunt de virtute sermonis ‘logicus in quantum logicus diffet a grammatico’, quia ista exponens est falsa ‘omnis logicus differt a grammatico’; ‘album in quantum album differt a dulci’ et consimiles.	Because of this, propositions such as the following are literally false: “A logician, insofar as he is a logician, differs from a grammarian”, because the exponent “Every logician differs from a grammarian” is false. “A white thing, insofar as it is white, differs from a sweet thing”; and suchlike.
Similiter tales sunt falsae ‘intellectus in quantum intellectus non vult’, ‘anima in quantum intellectus non vult’, ‘anima in quantum activa non patitur’, ‘anima in quantum passiva non agit’, ‘ignis in quantum calidus non est siccus’, ‘corpus in quantum alteratur non movetur localiter’, et sic de multis aliis, quia omnes tales habent aliquam exponentem falsam.	Likewise, such propositions are false: “An intellect, insofar as it is an intellect, does not will”, “A soul, insofar as it is an intellect, does not will”, “A soul, insofar as it is active, is not passive”, “A soul, insofar as it is passive, is not active”, “Fire, insofar as it is hot, is not dry”, “A body, insofar as it is altered, does not have local motion”, and so on for many others. For all such propositions have some false exponent.
Si autem fiat reduplicatio gratia causae, sic requiritur quod praedicatum principale primo vel prius negetur ab illo super quod cadit reduplicatio quam a pronomine demonstrante illud pro quo subiectum principale supponit; et hoc semper supponendo quod habeat quatuor praedictas exponentes.	But if the reduplication happens from a cause, it is required that the principal predicate be denied of what the reduplication subsumes, primarily or prior to its being denied of a pronoun referring to what the principal subject supposits for, always assuming that the proposition has the four aforesaid exponents.
Et propter hoc, sic reduplicando, haec est falsa ‘homo in quantum risibilis non est asinus’.	And for this reason, if the reduplication is done this way, then “A man, insofar as he is capable of laughter, is not a donkey” is false.
Similiter est intelligendum, sicut prius, quod semper a propositione reduplicativa ad suam praeiacentem est consequentia formalis. Et ideo ista consequentia est formalis ‘logicus in quantum logicus differt a grammatico, igitur logicus differt a grammatico’, ex qua sequitur quod logicus non est grammaticus.	Likewise, it should be understood, just as before, that there is always a formal consequence from a reduplicative proposition to its original. And so this consequence is formal: “A logician, insofar as he is a logician, differs from a grammarian; therefore a logician differs from a grammarian”, from which it follows that a logician is not a grammarian.
Tertio videndum est de propositione ubi reduplicatio est negata. Et est sciendum quod talis propositio est contradictoria alicuius propositionis reduplicativae in qua reduplicatio est affirmata.	Third, we must consider a proposition where the reduplication is negated. And it should be known that such a proposition is the contradictory of a reduplicative proposition in which the reduplication is affirmed.
Et ideo ad eius veritatem sufficit opposita cuiuscumque exponentis reduplicativae, cui contradicit; quia regula generalis est quod quando aliqua propositio contradicit alicui habenti plures exponentes, ad veritatem illius sufficit veritas cuiuscumque oppositae exponentis.	And so the opposite of any exponent of its contradictory reduplicative is sufficient for the truth of such a proposition, because it is a general rule that when some proposition contradicts some proposition having several exponents, the truth of the opposite of any exponent is sufficient for the truth of that proposition.
Unde ad veritatem istius ‘Sortes non est homo in quantum albus’ sufficit veritas istius ‘Sortes non est hamo’ et istius ‘Sortes non est albus’ et istius ‘aliquod album non est homo’ et istius ‘non, si est album, est homo’.	Hence, for the truth of “It is not the case that Socrates is a man insofar as he is white” it suffices that any of the following are true: “Socrates is not a man”, “Socrates is not white”, “Some white thing is not a man”, “It is not the case that if it is white, then it is a man”.
Notandum est etiam quod istae dictiones ‘secundum quod’, ‘ut’, ‘sub ratione’ et huiusmodi sunt aequivalentes isti dictioni ‘in quantum’, et ideo faciunt propositiones reduplicativas. Et idem est dicendum de talibus propositionibus quod iam dictum est de talibus ubi ponitur haec dictio ‘in quantum’.	It should also be noted that the expressions ‘according as . . .’, ‘as’, ‘under the aspect of . . .’, etc., are equivalent to the expression ‘insofar as’, and so they make propositions reduplicative. And the same must be said, as has already been said of propositions in which the expression ‘insofar as’ occurs.
Si autem dictio talis non teneatur reduplicative sed specificative, tunc non requiritur quod illud cui additur talis dictio subiciatur universaliter praedicato principali, sed requiritur quod illud super quod cadit reduplicatio importet illud ratione cuius competit praedicatum principale subiecto primo.	But if such an expression is not grasped reduplicatively but rather specificatively, it is not required that what such an expression is added to is the subject with respect to the principal predicate in a universal proposition. Rather, it is required that what the reduplication subsumes designates that in virtue of which the principal predicate belongs to the primary subject.
Verbi gratia si in ista propositione ‘ignis in quantum calidus calefacit’ li in quantum non teneatur reduplicative sed specificative, non oportet quod haec sit vera ‘omne calidum calefacit’, sed requiritur quod hoc nomen ‘calidum’ importet calorem per quem ignis calefacit, immo cui prius et magis per se competit calefacere quam igni, vel saltem quod est principium calefaciendi.	For example, if in the proposition ‘Fire, insofar as it is hot, is warmth-producing’ the expression ‘insofar as’ is not grasped reduplicatively bur rather specificatively, then it does not have to be that ‘Every hot thing is warmth-producing’ is true. But it is required that the name ‘hot’ conveys the heat in virtue of which fire warms. For to warm belongs to heat prior to and more per se than its belonging to fire. Or at least ‘hot’ must convey that heat is a principle of warming.
Et ita ad veritatem talis propositionis requiritur quod praedicatum principale praedicetur de subiecto principali et de illo cui additur dictio talis, et quod illud additum praedicetur de subiecto principali. Sed non requiritur quod praedicatum principale praedicetur universaliter de illo cui additur dictio talis, sed oportet quod importet illud ratione cuius praedicatum principale convenit vere per praedicationem subiecto principali.	And so, for the truth of such a proposition it is required that the principal predicate be predicated of the principal subject and of that which the reduplicative expression is added to, and that the addition be predicated of the principal subject. But it is not required that the principal predicate be predicated universally of that to which the reduplicative expression is added. But it is required that the latter designate that by reason of which the principal predicate truly agrees, through predication, with the principal subject.
Et sic verificantur tale propositiones ‘Sortes in quantum albus disgregat’, ‘Sortes in quantum habet liberum arbitrium peccat’, ‘ens in quantum ens est subiectum metaphysicae’ et huiusmodi. De exemplis tamen non est curandum.	And so are verified such propositions as “Socrates, insofar as he is white, scatters vision”, “Socrates, insofar as he has a free will, sins”, “A being, insofar as it is a being, is the subject of metaphysics”, and so on. But one should not bother with examples.
Oportet etiam scire quod hoc vocabulum ‘in quantum’ et similiter talia ‘secundum quod’, ‘sub ratione’ et huiusmodi aliquando in propositionibus aequivalent alicui adverbio temporis. Sicut unus sensus istius propositionis ‘canis, in quantum significat animal latrabile, facit istam propositionem esse veram: omnis canis est animal’, est iste ‘haec propositio: omnis canis est animal, non est vera nisi quando canis stat pro animali latrabili’. Et similiter dicimus quod haec est vera ‘ista imago est homo, secundum quod homo accipitur improprie’, hoc est, ista est vera quando ‘homo’ accipitur improprie. Sic etiam variis modis et aequivoce accipi potest haec dictio ‘in quantum’.	One should also know that the expression ‘insofar as’ and, likewise, the expressions ‘according as . . .’, ‘under the aspect . . .’, etc., are in some propositions equivalent to an adverb of time. For example, one sense of the proposition “ ‘Dog’, insofar as it signifies an animal which can bark, makes “Every dog is an animal” true” is “The proposition ‘Every dog is an animal’ is true only when ‘dog’ stands for an animal which can bark”. And, likewise, we say that “This image is a man, because ‘man’ is being used in an improper sense”, that is, the proposition is true when ‘man’ is being used improperly. Thus, the expression ‘insofar as’ can also be used in various ways and equivocally.