Mediaeval and Renaissance Logic (eBook)

Dov M. Gabbay, John Woods (Herausgeber)

eBook Download: EPUB

2008 | 1. Auflage
728 Seiten
Elsevier Science (Verlag)
978-0-08-056085-4 (ISBN)

Infos

Medieval and Renaissance Logic is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science and AI, linguistics, cognitive science, argumentation theory, philosophy, and the history of ideas.

- Provides detailed and comprehensive chapters covering the entire range of modal logic
- Contains the latest scholarly discoveries and interpretative insights that answer many questions in the field of logic

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Starting at the very beginning with Aristotle's founding contributions, logic has been graced by several periods in which the subject has flourished, attaining standards of rigour and conceptual sophistication underpinning a large and deserved reputation as a leading expression of human intellectual effort. It is widely recognized that the period from the mid-19th century until the three-quarter mark of the century just past marked one of these golden ages, a period of explosive creativity and transforming insights. It has been said that ignorance of our history is a kind of amnesia, concerning which it is wise to note that amnesia is an illness. It would be a matter for regret, if we lost contact with another of logic's golden ages, one that greatly exceeds in reach that enjoyed by mathematical symbolic logic. This is the period between the 11th and 16th centuries, loosely conceived of as the Middle Ages. The logic of this period does not have the expressive virtues afforded by the symbolic resources of uninterpreted calculi, but mediaeval logic rivals in range, originality and intellectual robustness a good deal of the modern record. The range of logic in this period is striking, extending from investigation of quantifiers and logic consequence to inquiries into logical truth; from theories of reference to accounts of identity; from work on the modalities to the stirrings of the logic of relations, from theories of meaning to analyses of the paradoxes, and more. While the scope of mediaeval logic is impressive, of greater importance is that nearly all of it can be read by the modern logician with at least some prospect of profit. The last thing that mediaeval logic is, is a museum piece.Mediaeval and Renaissance Logic is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science and AI, linguistics, cognitive science, argumentation theory, philosophy, and the history of ideas.- Provides detailed and comprehensive chapters covering the entire range of modal logic - Contains the latest scholarly discoveries and interpretative insights that answer many questions in the field of logic

Inhalt

Front Cover 1
Handbook of the History of Logic: Mediaeval and Renaissance Logic 4
Copyright Page 5
Contents 6
Preface 8
List of Contributors 10
Chapter 1. Logic before 1100: The Latin Tradition 12
Chapter 2. Logic at the Turn of the Twelfth Century 76
Chapter 3. Peter Abelard and his Contemporaries 94
Chapter 4. The Development of Supposition Theory in the Later 12th through 14th Centuries 168
Chapter 5. The Assimilation of Aristotelian and Arabic Logic up to the Later Thirteenth Century 292
Chapter 6. Logic and Theories of Meaning in the Late 13th and Early 14th Century including the Modistae 358
Chapter 7. The Nominalist Semantics of Ockham and Buridan: A 'Rational Reconstruction' 400
Chapter 8. Logic in the 14th Century after Ockham 444
Chapter 9. Medieval Modal Theories and Modal Logic 516
Chapter 10. Treatments of the Paradoxes of Self-reference 590
Chapter 11. Developments in the Fifteenth and Sixteenth Centuries 620
Chapter 12. Relational Logic of Juan Caramuel 656
Chapter 13. Port Royal: The Stirrings of Modernity 678
Index 712

Textauszug

Logic at the Turn of the Twelfth Century

John Marenbon

This chapter is not, like the others in the book, a survey of the logical doctrines of a period, because I at least (and perhaps other scholars too) am not yet in a position to write such a survey. It is simply a guide to the material, to the technical problems it presents and some of the theories historians have elaborated about it, along with an indication of a few of the philosophical themes which are waiting to be explored. 'The turn of the twelfth century' is a deliberately vague title, designed to indicate the hole between where the previous chapter finished and Abelard's work, the subject of the following chapter. But plugging this gap — even as here, with a sponge and a nailbrush — is not a straightforwardly chronological matter. Abelard's Dialectica, the main subject of the next chapter, may have been being written as early as 1110: a good deal of what is discussed here was probably written no earlier, and some of the texts may in fact date from the 1120s or 1130s. But the writings and writers discussed here have at least traditionally been seen as providing the prelude to Abelard's work. They form a separate group in their methods and concerns from the writings of Abelard's contemporaries and the later twelfth-century schools considered in the final section of the next chapter.1

1 THE CURRICULUM

The study of logic in this period was based around the Boethian curriculum that had come into general use about a century before. Writing around the year 1110, Abelard summarizes the situation neatly [Peter Abelard, 1970, 146]:

The Latin treatment of this art is furnished by seven books, the work of three authors. For so far in the Latin world there are just two of them by Aristotle, the Categories and On Interpretation, and one by Porphyry ... We generally use four by Boethius: On Division, the Topics and his Categorical and Hypothetical Syllogisms.

By the Topics (Liber topicorum), On Topical differentiae is meant. The commentary on Cicero's Topics became much less popular once this text was actively studied and commented on, from c. 1100 onwards. Note the absence of On Definition, known but not a regular feature of the logical curriculum. Note too that Abelard is here just listing the texts studied; Boethius's commentaries on Aristotle and Porphyry continued to be indispensable aids.

It has recently been pointed out that there was even in the late eleventh century some knowledge of the text of the Prior Analytics [See Iwakuma, Forthcoming-A, adding to the discussion given by Minio-Paluello in Aristoteles Latinos 111,1-4: ix, 433-6 and in Minio-Paluello, 1954]. But this work had no serious bearing on how logic was studied in the period around 1100, and most of the logicians have a rather inaccurate view of the contents of the Prior Analytics. It was when Abelard came to know the Prior Analytics, at the time he wrote his Logica Ingredientibus, that the text seems to have had some important influence [Martin, Forthcoming]. Similarly, the genuine Aristotelian Topics in Boethius's translation did not start to be used until the time of John of Salisbury, but there is a surprising citation from it in a logical text from the early twelfth century [Rosier-Catach, 1986].

2 THE FORM OF COMMENTARIES

The greater part of the evidence for teaching and thought about logic in the period is in the form of continuous commentaries on the texts of the logical curriculum. (For the sake of convenience in referring to so many anonymous commentaries, alphanumeric designations have been assigned to them. In the case of the Isagoge (I), the Categories(C) and On Interpretation (H), they refer to Marenbon [2000+]. For De topicis differentiis (B), they refer to the catalogue in Green-Pedersen [1984]. Yukio Iwakuma has also assigned numbers to commentaries on On Division (D), On Categorical Syllogisms (SC) and On Hypothetical Syllogisms (SH). They all share the form of being passage by passage treatments of the texts: the first few words of a passage (a lemma) are written out, and there follows a discussion. But they fall into two main types [Marenbon, 2000+, Introduction]. The model for the most widespread type, the 'composite' commentary, was provided by Boethius's commentaries, where each section of the text was discussed discursively, and problems were raised, explained and resolved. (The way in which Boethius acted as a model can be seen from how his commentaries were the main source for the early medieval Isagoge glosses and for P2 and C4.) Boethius, however, did not go in detail through every word of the text (although the elementary first editio on On Interpretation does from time to time gloss individual sentences). The twelfth-century logicians added an element of literal, phrase by phrase commentary, quite often put in the first person, so that the commentator is speaking for Aristotle, Porphyry or Boethius, as if these authors were to have paused to explain their texts more explicitly and ponderously. In the other, slightly less common type, 'literal commentary', this very detailed commentary predominates, and discursive discussion is more limited. Literal commentaries are, then, distant formally from the model of Boethius, and they are usually distant in content too, whereas some composite commentaries contain many passages borrowed from, or closely based on, Boethius. 'Literal' and 'composite' should not, however, be thought of as designating two completely distinct classes: literal commentaries contain some more discursive comments, and composite commentaries can have sections where the exegesis is merely literal. There were also 'problem commentaries' (the best known is Abelard's Logica Nostrorum petitioni sociorum), which concentrated on discussing the difficult issues, with very little or no literal commentary. None of these has been dated to before c. 1120, but they should be born in mind, since it will turn out that the chronology of the commentaries is far less fixable than has been believed.

All these commentaries belong to the activity of teaching and learning logic in the cathedral schools, and especially in the schools of Paris, which were beginning to become important in the early twelfth century. But what exactly is their relation? Were they drawn up to be read out by the master, or are they, rather, lecture-notes taken by students? A few commentaries — notably one on On Interpretation (H5) — contain passages recording questions, discussion and humorous (sometimes obscene) asides that appear to be a very direct record of what went on during a particular set of lectures [Iwakuma, 1999, 94-7]. Other commentaries give the impression of having been more formally written up. Probably there is a range of different relationships between the various texts that survive and the lectures with which they are connected, and it goes beyond a simple choice between teacher's text or lecture notes, since lecture notes might be presented to a teacher for correction or they might form the basis of a student's own lectures, with passages revised ands his own particular take on controversial issues added.

These are conjectures, but one thing at least is clear: the twelfth-century logical commentaries were not usually conceived of or created as literary works, produced by a given, single author. They are, for the most part at least, records of teaching and learning, in which individual masters' views on issues may well play an important role, but which draw often on many sources. The relations between different versions of the same basic commentary show how freely one master would feel he could borrow from and adapt the teaching of another: an example is provided by the 'C8 complex' (see [Marenbon, 2000+] in the revised web-based version of the Categories list). The result is that commentaries have a layered form, with extra material added, perhaps in a number of stages. Where we have manuscripts of different versions, it is easy to see how the later versions are layered, with a stratum that follows the earlier commentary, and one or more strata added. For example, in P3, after a discussion of Porphyry's questions shared by the three manuscripts, one of the manuscripts, now in Paris, adds a passage giving an alternative discussion of the phrase 'only in bare, pure thoughts', in which it is related to non-existents, such as chimaeras. If we had only the Paris manuscript, it would not be so clear that this paragraph was an added layer. We should suspect, therefore, that there are often layers of this sort within commentaries for which only one manuscript survives, or in the earliest version we have of a commentary that went on to be further revised.

A rough modern parallel might make the nature of these twelfth-century manuscripts more vivid. Imagine someone teaching an elementary logic course who has produced a detailed handout, using a standard textbook which she feels free to copy other logicians (she is just using it to teach, as was intended), and free also to change wherever she can improve on the presentation or disagrees on the stance the author has taken on a controversial issue, or where she finds a passage out of date. Suppose, now, a student downloads the handout, but revises it in line with extra...

Produkt-Details

• Erscheint lt. Verlag: 14.3.2008
• Sprache: englisch
• Themenwelt: Sachbuch/Ratgeber
• Themenwelt: Geisteswissenschaften ► Geschichte
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
• Themenwelt: Technik
• ISBN-10: 0-08-056085-7 / 0080560857
• ISBN-13: 978-0-08-056085-4 / 9780080560854