Authors/Ockham/Summa Logicae/Book I/Chapter 53

Latin	English
[CAP. 53. DE PROPRIETATIBUS RELATIVORUM]
Viso quid Aristoteles sensit de relativis videndum est de proprietatibus quas attribuit eis. Et est prima proprietas quod aliquibus relativis inest contrarietas, non tamen omnibus. Quod aliquibus insit contrarietas patet, nam virtus et vitium sunt relativa et tamen sunt contraria. Sciendum quod 'contraria relativa' vocantur hic illa quae non possunt simul eidem competere per praedicationem, sed cuicumque competit unum, eidem potest successive competere aliud. Et isto modo ‘pater’ et ‘filius' non sunt contraria, quia idem potest simul esse pater et filius, quamvis non respectu eiusdem. Sic etiam nihil contrariatur triplo, quia cuicumque competit triplum, eidem vel potest simul alia relatio competere vel numquam.	Seeing what Aristotle intends about relatives, we shall now discuss the properties that he attributes to them. The first property is that there is an inherent contradiction between some relatives, but not all. That some are inherently contradictory is obvious, for virtue and vice are relative, and they are opposed. It is clear that those are called "contrary relatives" that cannot be predicated at the same time to the same thing, but to whatever one can be applied, to the same thing the other can subsequently be applied. So also, nothing is contrary to a triple, for whatever comprises a triple, that same thing can simultaneously participate in other relations, or in none.
Secunda proprietas relativorum est quod suscipiunt magis et minus, quamvis non omnia, nam aliqua sumpta cum istis adverbiis 'magis' et 'minus' possunt de aliquo praedicari successive, sicut aliquid est primo magis simile alicui et postea minus simile vel e converso. Sed hoc non est possibile de triplo nec de duplo nec de aequali, et sic de multis aliis.	A second property of relatives is that they are receptive of being more or less, although not all are, for some which are taken with the adverbs ‘more’ and ‘less’ can be predicated successively of something, just as something is first more similar to something, and afterwards less similar or conversely. But this is not possible of ‘triple’, nor of ‘double’, nor ‘equal’, and so for many others.
Tertia proprietas est quod omnia relativa dicuntur ad convertentiam, hoc est cuicumque relativo potest addi casus obliquus sui correlativi, nisi contingat quod nomina nobis deficiant, et tunc licitum est fingere nomen, et tunc recto illius potest convenienter addi obliquus alterius; et obliquus illius potest convenienter addi recto alterius. Sicut si iste sit dominus, oportet quod sit servi dominus; et si sit similis, oportet quod sit simili similis. Similiter si 'ala' sit relativum, ita quod non sit possibile quod aliquid sit ala nisi sit alicuius ala, tunc licitum est fingere nomen sibi correspondens ad quod dicatur secundum convertentiam ut dicatur quod est ala alati, et e converso quod alatum est ala alatum. Et sic de omnibus aliis.	A third property is that all relatives are predicated reciprocally. That is, to any relative there can be added to a noun in the oblique case of its correlative (unless it happens that such names are lacking to us, and then it is OK to make up a name), and then to the nominative case of the one there can be appropriately added the oblique case of the other, and to the oblique case of the one there can be appropriately added the nominative case of the other. For example, if that person is a master, he has to be the master of a servant, and if he is similar, he has to be similar to someone. Similarly, if ‘wing’ is a relative, so that it is not possible that something is a wing unless it is a wing of something, then it is OK to to make up a name corresponding to it ad quod it is predicated reciprocally, so that it is said that it is a wing of the winged-thing, and conversely that a winged thing is winged with a wing. And the same for all the others.
Sciendum est tamen quod aliquando idem nomen ponitur in recto et in obliquo. Et ista vocantur relativa similium nominum sive relationes aequiparantiae, sicut 'omne simile est simili simile' et 'omne aequale est aequali aequale' et sic de multis, ubi idem nomen ponitur in recto et in obliquo. Quandoque autem aliud nomen ponitur in recto et in obliquo, sicut si sit pater, est filii pater, et non oportet quod sit patris pater; et si est servus, est domini servus, et non oportet quod sit servi servus. Et ista vocantur relativa dissimilium nominum sive relativa disquiparantiae. Hoc tamen generale est quod semper licitum est addere obliquum recto illius relativi, secundum Damascenum Logica sua, cap.29.	It is clear, however, that sometimes the same word is used both directly and obliquely. And these are called relatives with the same names or equivalent [i.e., reciprocal] relations, 'every similar is similar to a similar' and 'every equal is equal to an equal', and so of many [relations], where the same word is used directly and obliquely. And when a different word is used directly and obliquely, such as if someone is a father, it is the father of a son, and must not be the father of a father; and if he is a servant, he is the servant of a master, not the servant of a servant. And these are called relatives with different names or non-equivalent relations. However, it generally applies that it is always permissible to add a word in oblique case directly to its relation, according to his Damascene Logic, Chapter 29.
Quarta proprietas relativorum est quod relativa sunt simul natura. Quae est sic intelligenda quod esse exsistere non potest verificari de uno nisi verificetur de reliquo, si propositio formetur. Sicut si haec sit vera 'duplum est', haec erit vera 'dimidium est'; et si haec sit vera 'pater est', haec erit vera 'filius est' et e converso. Et eodem modo intelligendum est quando dicitur quod 'relativa perempta se perimunt', hoc est si negativa sit vera in qua esse negatur ab uno illorum, alia negativa erit vera in qua negatur esse a reliquo. Sicut si haec sit vera 'pater non est', haec erit vera 'filius non est', et e converso.	A fourth property of relatives is that they are reciprocal by their nature. By which it should be understood that if a proposition is formed, its existence cannot be verified for one without being verified for the other. So if for the one it is true that "it is double", for the other it is true that "it is half"; and if for one it is true that "he is a father", for the other it is true that "he is a son", and vice-versa. And in the same way, it should be understood that when it is said, "terminated relationships terminate each other", it means that if a negative is true in which one of the relations is negated, there is another negative that is true by which the other [reciprocal relation] is negated. Such as if for the one person it is true that "he is not a father", for another it is true that "he is not a son", and vice-versa.
Et est sciendum quod istae regulae non sunt generales, secundum Philosophum in Praedicamentis, nam probat ibidem ex intentione quod ista proprietas non convenit omnibus relativis, sicut probat de scientia et scibili et sensu et sensibili. Et quamvis non probet de aliis, nec de aliis exemplificet, tamen in multis aliis capit instantiam sicut in illis. Nam 'calefactivum' et 'calefactibile' sunt correlativa, et tamen non sequitur 'calefactivum est, igitur calefactibile est', nec e converso. Similiter non sequitur 'dealbabile non est, ergo dealbativum non est'. Et ita in multis capit instantiam.	It should be noted that these rules are not general; according to the Philosopher in the Categories, for there he tests it from the view that these properties do not apply to all relatives, as he tests science and knowledge and sense and sensation. And although he does not test it of the others nor provides examples of the others, nevertheless in many others he finds examples as in these. For "able to heat" and "heatable" are correlative, and yet it does not follow that "it is able to heat, therefore it is heatable", nor the converse. Similarly it does not follow that "it is not whitenable, therefore it does not whiten". And so it applies in many cases.