From The Logic Museum
According to the Kneales, the Perihermeneias (text) is one of Aristotle's earlier logical works. The Greek name means 'On Exposition'. It was called by that name by most medieval writers (using various spellings such as Pery Hermaneias &c), but has been known by the Latin De Interpretatione since the Renaissance.
Boethius (472-524) was a fifth century Christian who wrote extensively on logic, philosophy and mathematics. He is seen as important mainly as a medium by which the culture of antiquiry was transmitted to the middle ages. In particular, his Latin versions of Aristotle's Categories and the De Interpretatione (below) were probably the only texts available to philosophers of the early medieval period.Before the rise of the universities, Aristotle's works were mostly known, if at all, through the translations and commentaries of Boethius. Boethius' commentary probably owes its survival to its inclusion in Alcuin's program for the revival of classical scholarship in the court schools of Charlemagne.
He is also important because his writings and translations are in Latin, which in the Middles Ages became the language in which all philosophical, theological and logical discourse was carried on. As is well known, many of the technical terms in those disciplines, which are now carried on English, French, German &c, were imported wholesale from the Latin. Thus, even where Boethius' Latin does not accurately reflect Aristotle's Greek, it accurately reflects much of the thinking and terminology that was used afterwards, because his translation became the basis of the future development of the discipline. The basis of medieval semantics and truth theory lies in Boethius' Latin, rather than Aristotle's Greek
The Perihermeneias contains the main account of Aristotle's theory of meaning and truth, and was a starting point for medieval 'terminist' semantics. Some of the ideas are as follows:
1. A noun and a verb are the minimum requirements for making a sentence (which Boethius calls oratio). Not every sentence is a proposition (oratio enuntiativa), since prayers are sentences, but not propositions. A proposition is only what has in it either truth or falsity (enuntiativa vero non omnis sed in qua verum vel falsum inest). Note that only once does Boethius use the word 'propositio' for what Edghill translates as 'the admission of a premiss'. However, later writers such is Ockham preferred 'proposition', which is the ancestor of our modern 'proposition'.
2. Spoken words are signs of mental modifications (Boethius: notae passionum anima - literally passions or modifications of the soul). While the signs are not necessarily the same (i.e. if the written or spoken languages are different) these modifications are the same in all people (eaedem omnibus passiones animae sunt). This later developed into the idea, defended by Ockham and Buridan and others, that spoken propositions, i.e. sentences, represent mental propositions of which they are the outward signs.
3. Universal signs are 'of a nature' to be predicated of many. The Latin formula was universale quod in pluribus natum est praedicari, repeated by writers of logic textbooks such as Peter of Spain and a hundred others since.
4. An affirmation is a assertion of something about something (affirmatio vero est enuntiatio alicuius de aliquo), a denial is an assertion of something "from" something (negatio vero enuntiatio alicuius ab aliquo). The Latin formulation neatly reflects the Greek, where the difference between a 'positive' affirmation, and 'negative' denial is expressed simply by prepositions. Affirmation (kataphasis) is apophansis tinos kata tinos, (something of something) and denial (apophasis) is apophansis tinos apo tinos. 'Nego' in Latin means to deny.
5. Every affirmation has an opposite denial, and similarly every denial an opposite affirmation (omni affirmationi est negatio opposita et omni negationi affirmatio). This was the basis of the well-known 'square of opposition'.
6. The distinction between singular and general propositions.
7. The idea of 'wide scope' or 'sentence' negation. Aristotle says that a denial must deny exactly whatthe affirmation affirms, (idem oportet negare negationem quod affirmavit affirmatio) .
8. In the case of that which is or which has taken place, either the affirmation or the denial is true or false. (In his ergo quae sunt et facta sunt necesse est affirmationem vel negationem veram vel falsam esse). This leads to the famous puzzle that nothing nothing exists or happens by accident. Of whatever happens tomorrow, it is true today to say that it happens tomorrow. But if it is true, for example, that a sea battle (navale bellum) will happen tomorrow, this suggests it is unavoidably true, and that what will happen in the future will happen by necessity.
The Square of Opposition
The idea that there are certain logical relationships between the four kinds of Aristotelian proposition, when they have the same subject and predicate, is developed in chapters six and seven. It became the basis of a diagram originating with Boethius and used by medieval logicians to classify these possible logical relations. The four propositions - the universal affirmative ('every man is just'), the universal negative ('no man is just'), the particular affirmative ('some man is just') and the particular negative ('some man is not just') - are placed in the four corners of a square, and the relations represented as lines drawn between them.
Pairs of propositions are called contradictories (contradictoriae) when they cannot at the same time both be true or both be false, contraries (contrariae) when both cannot at the same time be true, subcontraries (subcontrariae) when both cannot at the same time be false, and subalternates (subalternae) when the truth of the one proposition implies the truth of the other, but not conversely. The corresponding relations are known as contradiction (contradictio), contrariety (contrarietas), subcontrariety (subcontrarietas) and subalternation (subalternatio). Thus
- Universal statements are contraries: 'every man is just' and 'no man is just' cannot be true together, although one may be true and the other false, and also both may be false (if one at least man is not just, and at least one man is not just).
- Particular statements are subcontraries. 'Some man is just' and 'some man is not just' cannot be false together
- The universal affirmative and the particular affirmative are subalternates, because in Aristotelian semantics 'every A is B' implies 'some A is B'. This fact has caused endless controversy since the middle of the nineteenth century, following the development of modern semantics where there is no such implication. Similarly the universal negative and the particular negative are subalternates since, again, 'no A is B' was thought to imply 'some A is not B'.
- The universal affirmative and the particular negative are contradictories. Clearly if some A is not B, not every A is B. Conversely, though this is not intuitive for modern semantics, it was thought that if every A is not B, some A is not B. This interpretation has also caused much controversy. Note that Aristotle's Greek does not represent the particular negative as 'some A is not B', but as 'not every A is B', and Boethius' Latin faithfully follows him. However, in Boethius commentary on the Perihermeneias, he renders the particular negative as 'quidam A non est B', literally 'a certain A is not a B', which under any ordinary reading of the Latin (see Lewis and Short, e.g.) is existential, implying the existence of a particular A which is not a B. Terence Parsons has suggested (here) that the Latin 'quidam A non est B' does not have existential import, but this seems implausible, given that it means that a certain, or a particular A, is not B.
Logic Museum online text
- Boethius translation (including Greek and English in parallel)
- II 1-2 De interpretatione vel Periermenias. Translatio Boethii, ed. L. Minio-Paluello; Translatio Guillelmi de Moerbeka, ed. G. Verbeke, rev. L. Minio-Paluello, Desclée De Brouwer, Bruges-Paris 1965. Contains the vulgate text of the Perihermeneias, which goes back to Boethius, and the version composed with the lemmas of the Aristotelian text in William of Moerbeke's translation of Ammonius' commentary.
- Kneale, W. & M., The Development of Logic, Oxford, 1971
- ↑ Minio-Paluello, 'Note sull Aristotele latino medievale', Rivista di filosofia neo-scolastico, xliv (1952) 398-401, 'Les traductions et les commentaires Aristoteliciens de Boece', Studia Patristica, ii (1957) 358-65
- ↑ Cicero invented some of the Latin equivalents for Greek terms, such as propositio, meaning the leading premiss of an argument, which contrasts with assumptio meaning the additional premiss. Kneale (p. 178) claims that 'propositio' was used by Quintilian in the more general sense of 'statement' or 'indicative sentence', in which it was used throughout the middle ages.
- ↑ Leading to a difficulty in English of translating related words such as those for negation, negativity, signs of negation and so on. For if we use 'denial' or 'deny', which is the most accurate in some cases, we have to translate the corresponding abstract terms such as 'negatio' by the English abstract term 'negation', leading to the impression that there are a different family of words, where in Latin there is just one family.