SELECTED BIBLIOGRAPHY ON ANCIENT GREEK LOGIC (in progress...)
Ancient logic and its modern interpretations. Edited by Corcoran
John. Dordrecht: Reidel 1974.
Proceedings of the Buffalo Symposium on modernist interpretations of ancient
logic, 21 and 22 April, 1972.
Contents: Preface IX; Part One: Ancient semantics; Norman Kretzmann: Aristotle
on spoken sound significant by convention 3; Ronald Zirin: Inarticulate noises
23; Newton Garver: Notes for a linguistic reading of the Categories 27;
Part Two: Modern research in ancient logic; Ian Mueller: Greek mathematics and
Greek logic 35; John Mulhern: Modern notations and ancient logic 71; Part Three:
Aristotle's logic; John Corcoran: Aristotle's natural deduction system 85; Mary
Mulhern: Corcoran on Aristotle's logical theory 133; Part Four: Stoic logic;
Josiah Gould: Deduction in Stoic logic 151; John Corcoran: Remarks on Stoic
deduction 169; Part Five: Final session of the Symposium; John Corcoran: Future
research on ancient theories of communication and reasoning 185; A panel
discussion on future research in ancient logical theory 189; Index of names
209-211.
The Cambridge history of Hellenistic philosophy. Edited by Algra
Keimpe et al. Cambridge: Cambridge University Press 1999.
Part II. Logic and language. Chapter 4: Introduction by Jonathan Barnes
65; Chapter 5: Logic by Jonathan Barnes, Susanne Bobzien and Mario Mignucci 77;
Chapter 6: Language by Dirk M. Schenkeveld 177-225
Théories de la phrase et de la proposition de Platon à Averroés.
Edited by Büttgen Philippe, Dieble Stéphane, and Rashed Marwan. Paris: Éditions
Rue d'Ulm 1999.
Sommaire: Philippe Büttgen, Stéphane Diebler et Marwan Rashed: Avant-propos
VII-IX; I. Aux origines ontologiques du langage rationnel; Claude Imbert: Le
dialogue platonicien en quête de son identité 3; Denis O'Brien: Théories de la
proposition dans le Sophiste de Platon 21; Francis Wolff: Proposition,
être et vérité: Aristote ou Antisthène? 43; II. Entre logique et sémantique:
l'autonomie problématique de la théorie aristotélicienne; Barbara Gernez: La
théorie de la lexis chez Aristote 67; Jacques Brunschwig: Homonymie et
contradiction dans la dialectique aristotélicienne 81; Pierre Chiron: La période
chez Aristote 103; III. La théorie stoïcienne et ses enjeux; Jean-Baptiste
Gourinat: La définition et les propriétés de la proposition dans
le stoïcisme ancien 133; Frédérique Ildefonse: La théorie stoïcienne de la
phrase (énoncé, proposition) et son influence chez les grammairiens 151; Marc
Baratin: La conception de l'énoncé dans les textes grammaticaux latins 171; IV -
D'Aristote à l'aristotélisme; Henri Hugonnard-Roche: La théorie de la
proposition selon Proba, un témoin syriaque de la tradition grecque (VIe siècle)
191; Philippe Hoffmann: Les analyses de l'énoncé: catégories et parties du
discours selon les commentateurs néoplatoniciens 209; Abdelali Elamrani-Jamal:
La proposition assertorique (de inesse) selon Averroès 249; Ali
Benmakhlouf: Averroès et les propositions indéfinies 269; Maroun Aouad: Les
prémisses rhétoriques selon les Isarat d'Avicenne 281; Épilogue; Jean
Jolivet: Sens des propositions et ontologie chez Pierre Abélard et Grégoire de
Rimini 307; Index des auteurs anciens 325; Index des auteurs modernes 333-336
Greek, Indian and Arabic Logic. Edited by Gabbay Dov and Woods John.
Amsterdam: Elsevier 2004.
Handbook of the History of Logic: vol. 1.
Contents: Preface by Dov Gabbay and John Woods VII; List of contributors IX;
Logic before Aristotle: development or birth? by Julius Moravcsik 1; Aristotle'
early logic by John Woods and Andrew Irvine 27; Aristotle's underlying logic by
George Boger 101; Aristotle's modal syllogism by Fred Johnson 247; Indian logic
by Jonardon Ganeri 309; The Megarians and the Stoics by Robert R. O'Toole and
Raymond E. Jennings 397; Arabic logic by Tony Street 523; The translation of
Arabic works on logic into Latin in the Middle Ages and Renaissance by Charles
Burnett 597; Index 607-628
La logica nel pensiero antico. Edited by Alessandrelli M. and Nasti
de Vincentis Mauro. Napoli: Bibliopolis 2009.
(Not yet published)
Atti del colloquio, Roma, 28-29 novembre 2000
Allen James. Inference form signs. Ancient debates about the nature of
evidence. New York: Oxford University Press 2001.
Asmis Elizabeth. Epicurean semiotics. In Knowledge through signs. Ancient
semiotic theories and practices. Edited by Manetti Govanni. Turnhout:
Brepols 1996. pp. 155-185
Barnes Jonathan. Proof and the syllogism. In Aristotle on Science. The
"Posterior analytics". Edited by Berti Enrico. Padova: Editrice Antenore
1981. pp. 17-59
Proceedings of the Eight Symposium Aristotelicum held in Padua from September 7
to 15, 1978
Barnes Jonathan, "Peripatetic negations," Oxford Studies in Ancient
Philosophy 4: 201-214 (1986).
Barnes Jonathan, "Epicureans signs," Oxford Studies in Ancient
Philosophy.Supplementary volume 6: 91-134 (1988).
Barnes Jonathan. Logical form and logical matter. In Logica, mente e
persona. Studi sulla filosofia antica. Edited by Alberti Antonina. Firenze:
Leo S. Olschki Editore 1990. pp. 7-119
Barnes Jonathan. Logic in Academica I and the Lucullus. In
Assent and argument. Studies in Cicero's "Academic books". Proceedings of the
7th Symposium Hellenisticum (Utrecht, August 21-25, 1995). Edited by Inwood
Brad and Mansfeld Jaap. Leiden: Brill 1997. pp. 140-160
"I consider first the conception of logic which Cicero manifests in his Academic
works; and then I look at the attack on logic which he delivers at Lucullus
91-8. 1 use the English word 'logic' as a rough translation of the Latin
dialectica and the Greek dialektiké. I am interested in the views
which Cicero expresses: I do not discuss the sources of these views or the
extent to which they are original to Cicero; nor do I offer any opinion as to
whether Cicero himself accepted all or any of the views which he expressed." p.
140
Barnes Jonathan et al. Part II. Logic and language. In The Cambridge
history of Hellenistic philosophy. Edited by Algra Keimpe et al. Cambridge:
Cambridge University Press 1999. pp. 65-225
Chapter 4: Introduction by J. Barnes; Chapter 5: Logic by J. Barnesi S. Bobzien,
M. Mignucci; Chapter 6: Language by D. Schenkeveld, J. Barnes
Barnes Jonathan. Peripatetic logic: 100 BC - AD 200. In Greek and Roman
philosophy 100 BC - 200 AD. Vol. II. Edited by Sharples Robert W. and
Sorabji Richard. London: Institute of Classical Studies 2007. pp. 531-546
Barnes Jonathan. Truth, etc. Six lectures on ancient logic. Oxford:
Clarendon Press 2007.
Barnouw Jeffrey. Propositional perception. Phantasia, predication, and
sign in Plato, Aristotle, and the Stoics. Lanham: University Press of
America 2002.
Bobzien Susanne, "Wholly hypothetical syllogisms," Phronesis.A Journal
for Ancient Philosophy: 87-137 (2000).
"In antiquity we encounter a distinction of two types of hypothetical
syllogisms. One type are the 'mixed hypothetical syllogisms'. The other type is
the one to which the present paper is devoted. These arguments went by the name
of 'wholly hypothetical syllogisms'. They were thought to make up a
self-contained system of valid arguments. Their paradigm case consists of two
conditionals as premisses, and a third as conclusion. Their presentation, either
schematically or by example, varies in different authors. For instance, we find
'If (it is) A, (it is) B; if (it is) B, (it is) C; therefore, if (it is) A, (it
is) C'. The main contentious point about these arguments is what the ancients
thought their logical form was. Are A, B, C schematic letters for terms or
propositions? Is 'is', where it occurs, predicative, existential, or veridical?
That is, should 'A esti' be translated as 'it is an A', 'A exists', 'As
exist' or 'It is true/the case that A'? If A, B, C are term letters, and 'is' is
predicative, are the conditionals quanti ed propositions or do they contain
designators? If one cannot answer these questions, one can hardly claim to know
what sort of arguments the wholly hypothetical syllogisms were. In fact, all the
above-mentioned possibilities have been taken to describe them correctly. In
this paper I argue that it would be mistaken to assume that in antiquity there
was one prevalent understanding of the logical form of these arguments even if
the ancients thought they were all talking about the same kind of argument.
Rather, there was a complex development in their understanding, starting from a
term-logical conception and leading to a propositional-logical one. I trace this
development from Aristotle to Philoponus and set out the deductive system on
which the logic of the wholly hypothetical syllogisms was grounded."
Bobzien Susanne, "The development of Modus Ponens in Antiquity: from
Aristotle to the 2nd Century AD," Phronesis.A Journal for Ancient Philosophy
47: 359-394 (2002).
"Aristotelian logic, as it was taught from late antiquity until the 20th
century, commonly included a short presentation of the argument forms modus
(ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens,
and modus tollendo ponens. In late antiquity, arguments of these forms
were generally classified as 'hypothetical syllogisms'. However, Aristotle did
not discuss such arguments, nor did he call any arguments 'hypothetical
syllogisms'. The Stoic indemonstrables resemble the modus ponens/tollens
arguments. But the Stoics never called them 'hypothetical syllogisms'; nor did
they describe them as ponendo ponens, etc. The tradition of the four
argument forms and the classification of the arguments as hypothetical
syllogisms hence need some explaining. In this paper, I offer some explanations
by tracing the development of certain elements of Aristotle's logic via the
early Peripatetics to the logic of later antiquity. I consider the questions:
How did the four argument forms arise? Why were there four of them? Why were
arguments of these forms called 'hypothetical syllogisms'? On what grounds were
they considered valid? I argue that such arguments were neither part of
Aristotle's dialectic, nor simply the result of an adoption of elements of Stoic
logic, but the outcome of a long, gradual development that begins with
Aristotle's logic as preserved in his Topics and Prior Analytics;
and that, as a result, we have a Peripatetic logic of hypothetical inferences
which is a far cry both from Stoic logic and from classical propositional logic,
but which sports a number of interesting characteristics, some of which bear a
cunning resemblance to some 20th century theories."
Bochenski Joseph, "Notes historiques sur les propositions modales," Revue
de Sciences Philosophiques et Théologiques 26: 673-692 (1937).
Bochenski Joseph. Ancient formal logic. Amsterdam: North-Holland
1951.
Contents: I. Prolegomena 1; II. The Forerunners 14; III. Aristotle 19; IV. The
Old Peripateticians 72; V. The Stoic-Megaric School 77; VI. The last period 103;
Bibliography 110; Index of Greek terms 118; Index of names 121.
"The present book is intended to supply mathematical logicians with a synthetic
outline of the main aspects of ancient formal logic which are known in the
present state of research. In order to avoid misunderstandings, each of the
above terms has to be explained.
The reader is supposed to be a mathematical logician, i.e., to know both
the symbolisms and the (English) language of contemporary mathematical logic;
those who are not acquainted with it must be warned that several terms used in
that language have a particular meaning, different from the meaning attributed
to the terms of the same form in other contexts.
The subject of the book is formal Logic; by this we understand a science
such as was developed by Aristotle in his Prior Analytics, i.e.,
essentially the theory of syllogisms as defined in An. Pr. A 1, 24b
18-20. Along with the syllogisms proper, the structure of the sentences and
semiotics will be studied; contrariwise, not only all ontological, psychological
and epistemological problems, but even methodological topics will be omitted in
so far as possible. This is perhaps regrettable; but there are several good
books on those subjects while there is none on ancient formal logic as a
whole - and the limitation of space forced us to omit everything which was not
strictly formal.
By ancient formal logic, Greek logic from the beginning of Greek Philosophy
until the end of Antiquity is meant. We have, it is true, some Latin textbooks
of formal logic - but they all seem based on, or even copied from, Greek
sources. It is perhaps worthwhile mentioning that there is also an ancient
Indian Logic; this lies, however, outside our present scope.
What is offered here is an outline, moreover a very fragmentary one. A
complete account of ancient formal logic cannot be written at the present date
because of the lack of scientific monographs on individual logicians and topics.
The initial aim of the author was to limit himself to a reassumption of
monographs already published; in the course of the work he was compelled,
however, to use some of his own unpublished researches on Aristotle and had the
exceptional fortune of reading the manuscript of Dr Benson Mates' book on Stoic
logic. He also collected some new data on other topics. In spite of this,
considerable parts of ancient logic have hardly been touched upon - e.g. the
logic of the Commentators - while others, Aristotle included, have been treated
in a way which is far from being complete. On the whole, what the book contains
may be considered as a kind of starting point for future research. Yet, it is
hoped that even this will supply logicians with some information difficult to be
found elsewhere and give a general idea of what the ancient logic was and how it
developed." pp. 1-2
Burnyeat Myles. The origins of non-deductive inference. In Science and
speculation. Studies in Hellenistic theory and practice. Edited by Barnes
Jonathan et al. Cambridge: Cambridge University Press 2005. pp. 193-238
Calogero Guido. Storia della logica antica. Bari : Laterza 1967.
Cavini Walter. La negazione di frase nella logica greca. In Studi su
papiri greci di logic e medicina. Edited by Cavini Walter et al. Firenze:
Olschki 1985. pp. 7-126
Celluprica Vincenza. La logica antica. Torino: Loescher 1978.
Antologia di testi con ampia introduzione
Chiaradonna Riccardo. La constitution de la logique tardo-antique et
l'élaboration d'une logique "matérielle" en syriaque. In Aristotele e I suoi
esegeti neoplatonici. Logica e ontologia nelle interpretazioni greche e arabe.
Atti del Convegno internazionale Roma 19-20 ottobre 2001. Edited by
Celluprica Vincenza and D'Ancona Costa Cristina. Napoli: Bibliopolis 2004. pp.
55-83
Chiesa Curzio. Sémiosis - signes - symboles. Introduction aux théories du
signe linguistique de Platon et d'Aristote. Bern: Peter Lang 1991.
Conso Daniele, "Remarques sur la terminologie du "Liber Peri Hermeneias" et
de la tradition logique de langue latine antérieure à Boèce," Latomus.Revue
d'Études Latines 60: 944-961 (2001).
"Après avoir rappelé les principales concordances et divergences entre la
terminologie logique latine avant et après Boèce, on examine deux choix propres
soit à l'auteur du Peri hermeneias (PH) transmis sous le nom d'Apulée,
soit à la première tradition logique de langue latine: celui de "pars"
("particula") et celui de "formula" ("forma" chez Martianus Capella), choix
auquels Boèce substituera "terminus" et "figura", pour rendre le notion de
"terme" (horos chez Aristote) et celle de "figure (du syllogisme)" (skhema
chez Aristote). Dans chaque cas, on passe en revue la distribution des emplois
dans le PH et chez Martianus, en signalant les attestations antérieures ou
postérieures à ces traités. On s'interroge enfin sur les raisons possibles du
choix effectué par l'auteur du PH et maintenu ou modifié par Martianus Capella.
Corcoran John, "Conceptual structure of Classical logic," Philosophy and
Phenomenological Research 33: 25-47 (1972).
Corcoran John, "Schemata: the concept of Schema in the history of logic,"
Bulletin of Symbolic Logic 12: 219-240 (2006).
"Schemata have played important roles in logic since Aristotle's Prior
Analytics. The syllogistic figures and moods can be taken to be argument
schemata as can the rules of the Stoic propositional logic. Sentence schemata
have been used in axiomatizations of logic only since the landmark 1927 von
Neumann paper [31]. Modern philosophers know the role of schemata in
explications of the semantic conception of truth through Tarski's 1933
Convention T [42]. Mathematical logicians recognize the role of schemata in
first-order number theory where Peano's second-order Induction Axiom is
approximated by Herbrand's Induction-Axiom Schema [23]. Similarly, in
first-order set theory, Zermelo's second-order Separation Axiom is approximated
by Fraenkel's first-order Separation Schema [17]. In some of several closely
related senses, a schema is a complex system having multiple components one of
which is a template-text or scheme-template, a syntactic string
composed of one or more "blanks" and also possibly significant words and/or
symbols. In accordance with a side condition the template-text of a
schema is used as a "template" to specify a multitude, often infinite, of
linguistic expressions such as phrases, sentences, or argument-texts, called
instances of the schema. The side condition is a second component. The
collection of instances may but need not be regarded as a third component. The
instances are almost always considered to come from a previously identified
language (whether formal or natural), which is often considered to be another
component. This article reviews the often-conflicting uses of the expressions
'schema' and 'scheme' in the literature of logic. It discusses the different
definitions presupposed by those uses. And it examines the ontological and
epistemic presuppositions circumvented or mooted by the use of schemata, as well
as the ontological and epistemic presuppositions engendered by their use. In
short, this paper is an introduction to the history and philosophy of schemata."
[17] Abraham Fraenkel - Part I. Historical introduction - to Paul Bernays
- Axiomatic set theory (1958) - Reprint Dover 1991 pp. 3-35.
[23] Jacques Herbrand, Logical Writings, (W. Goldfarb, Tr. Goldfarb, and
van J. Heijenoort, editors), Harvard University Press, Cambridge, MA, 1971
[31] Johann von Neumann, Zur Hilbertschen Beweistheorie, Mathematische
Zeitschrift, vol. 26 (1927), pp. 1-46.
[42] Adam Tarski, The concept of truth in the languages of the deductive
sciences, Prace Towarzystwa Naukowego Warszawskiego, Wydzial III Nauk
Matematyczno-Fizycznych, vol. 34 (1933), reprinted in [50], pp. 13-172;
expanded English translation in [48], pp. 152-278.
[48] Adam Tarski, Logic, Semantics, Metamathematics, papers from 1923 to 1938,
2nd ed., Hackett, Indianapolis, 1983, edited with introduction and analytic
index by J. Corcoran (first editiion 1956)
[50] Jan Zygmunt (editor), Alfred Tarski, Pisma Logiczno-Filozoficzne, 1
Prawda, Wydawnictwo Naukowe PWN, Warsaw, 1995
de Rijk Lambertus Marie, "On ancient and mediaeval semantics and
metaphysics. Part I," Vivarium 15: 81-120 (1977).
"1. Introduction. The aim of this study is, rather than to give a contribution
to the history of semantics as such, to show (i) the interdependence of Ancient
(and Mediaeval) semantic views and metaphysical doctrines, and (2) how some
Mediaeval semantic points of view may be clarified when traced back to the
corresponding Ancient views. As far as Antiquity is concerned, Plato, Aristotle
and the Stoics as well as Neoplatonism and Peripatetics are discussed. However,
it should be noticed at the outset that in many cases it is practically
impossible to discern exactly what precisely in the different views found in
Late Antiquity came from what School, let alone to attribute the various views
to specific authors. To my mind, in his inspiring paper on the logical doctrines
in the Neoplatonic and the Peripatetic schools (*) A. C. Lloyd made the correct
approach to the subject matter. When discussing the question how much of the
Neoplatonic views is borrowed from Stoic logicians his answer is that
substantially it is nothing but the fact that the forms of Neoplatonism are
sometimes conditioned by Stoic logical doctrine and terminology; what still
remained under those adventitious shapes is the intrinsic impetus and natural
direction of Neoplatonism itself (Lloyd, 158)." p. 81.
(*) Neoplatonic Logic and Aristotelian Logic in: Phronesis, A Journal for
Ancient Philosophy (1) 1956, 58-72 and 146-160, henceforth quoted as Lloyd. This
study should be corrected in many points, however.
"2. Participation and the multiplication of the Form in Plato; 2.1. A
particular's partaking of several Forms; 2.2. The Forms' capacity for mutual
communion; 2.3 The Forms and their being known; 2.4. The Forms' epistemologic
function and their ontological status. The basic question of what is the extent
of the World of Forms appears with Plato in two distinct shapes: (a) which are
the several classes of things belonging to the Ideal World? and (b) where Forms
are found? As a matter of fact the two questions are clearly related.
The former is concerned whenever is asked about the transcendent nature of
organic and even anorganic (both honorable and undignified) things as well as
mathematical and moral entities (**). In last analysis this form of the question
has much to do with the hierarchic order of the transcendent world. However, it
is first the second question that should come under review now; it is concerned
with the status of the Forms. Next, the former question as confined to the
Hierarchy of Being will be discussed in the second part of this section." pp.
96-97.
(**) The classical passages are found in the Phaedo, Republic, Parmenides,
Timeus, and the Seventh letter, 342 A.D.
2.4.1. The different status of the Platonic Form; 2.4.2. The hierarchic
arrangement of the Forms; 2.5. The threefold status of the Forms as found with
Plato; 2.5.1 The Form taken in its transcendent status; 2.5.2. The Form taken in
its immanent status; 2.5.3. The Form taken in its mental status.
de Rijk Lambertus Marie, "On ancient and mediaeval semantics and
metaphysics. Part II. The multiplication of Being in Aristotle's Categories,"
Vivarium 16: 81-117 (1978).
"On ancient and mediaeval semantics and metaphysics. Part II. The multiplication
of Being in Aristotle's Categories," Vivarium 16: 81-117 (1978).
"3. The multiplication of being in Aristotle's Categories.
3.1. Introduction. One of the results of the preceding section may be that Lloyd
(1956, p. 59) seems to be wrong in asserting that in Plato's view the role of
the universal is played by the Idea exclusively, and that only by the time of
the Middle Academy, that is, for the Platonists of the first two centuries A.D.,
the performers of this role have been multiplied. As a matter of fact the
distinction between Plato and his followers of the Middle Academy on this score
would seem to be a different one. The ontological problems of participation were
felt as early as in the Platonic dialogues (see our section 2), as well as the
logical ones concerning predication (which will be discussed in a later
section). Well, the Platonists of the first two centuries A.D., introduced
explicitly a threefold distinction I of the Platonic Form or rather of its
status which was (only) implied with Plato. I think, Lloyd is hardly more
fortunate in ascribing (ibid.) this introduction chiefly to the influence of
Aristotelian logic on Platonic interpretation. It is true, in stating the basic
distinction between en hypokeimenoi and kath' hypokeimenou
Aristotle tried to face the same cluster of fundamental problems which induced
later Platonists to the distinction of the Forms as taken before or after the
methexis (cf. Simplicius, In Arist. Categ., 79, 12ff.). However, Plato's
disciple, Aristotle (the most unfaithful one, in a sense, as must be
acknowledged) was as deeply engaged on the same problems as were his
condisciples and the Master himself in his most mature period. It is certainly
not Aristotle who played the role of a catalyst and was the first to provoke the
multiplication of the Platonic Form in order to solve problems which were not
recognized before in the Platonic circle. On the contrary, Plato himself had
saddled his pupils with a basic and most intricate problem, that of the nature
of participation and logical predication. It was certainly not left quite
unsolved in the later dialogues, but did still not have a perspicuous solution
which could be accepted in the School as a scholastic one. So any of his serious
followers, (who were teachers in the School, at the same time) was bound to
contrive, at least, a scholastic device to answer the intricate question. To my
view, Aristotle's solution should be discussed in this framework. For that
matter, Aristotle stands wholly on ground prepared by his master to the extent
that his works on physic and cosmology, too, are essentially discussions held
within the Academy (Cp. Werner Jaeger, Aristotle. Fundamentals of the history
of his development, Oxford 1949, 308)." pp. 81-82
3.2. Aristotle's classification of being as given in the Categories;
3.2.1. The common view: categories = predicates; 3.2.2. The things said 'aneu
symplokés'; 3.2.3. The doctrine of substance given in the Categories;
3.2.4. The ontological character of the classification; 3.2.5. Some obscurities
of the classification; 3.2.6. The different status of the 'things' meant;
3.2.6.1 The first item of the classification; 3.2.6.2. The second item of the
classification; 3.2.6.3. The third item of the classification; 3.2.6.4. The
ontological status of the 'things' meant in the items (2) and (3); 3.2.6.5. The
fourth item of classification; 3.2.7. The relation between the different
'things'; 3.3. Categories and predicables; 3.3.1. The opposition of category and
predicable; 3.3.2. The impact of the opposition; 3.3.3. The obscure position of
the differentia; 3.3.4. Conclusion.
de Rijk Lambertus Marie, "On ancient and mediaeval semantics and
metaphysics. Part III. The categories as classes of names," Vivarium 18:
1-62 (1980).
"4. The Categories as class of names; 4.1. Status quaestionis. The
previous sections contain several hints to the close interrelation between three
major issues in Plato's doctrine, viz. the question about the true nature of the
Forms and those about participation and predication. Indeed, for the founder of
the theory of the Forms, predication was bound to become a problem. Forms are
immutable and indivisible; yet other Ideas have to participate in them; they are
unique, by themselves and subsistent; yet, when saying 'John is man' (or
white), 'Peter is man' (or white), should there be one
perfect, eternal, immutable etc. Form of MAN (or WHITE) in the one and
another in the other? Or, as I have put it above [1977: 85]: if John, Peter, and
William are wise, does this mere fact mean that there must be something which
they are all related to in exactly the same manner, namely WISDOM itself?
And if 'John is wise', 'Peter is wise', and 'William is wise' are
all true statements, what exactly is the meaning of the predicate name
'wise'? The former question is concerned with participation, the latter with
predication. Well, that the crux of the latter problem is not the separate
existence of the Forms (chôrismos) clearly appears from the fact that
also the author of the Categories, who had entirely
abandoned all kind of chôrismos, could apparently not get rid of a
similar problem: if the categories really are classes of 'things there are' (1 a
20) (i.e. 'real' substances, 'real' natures, and 'real' properties), rather than
concepts (i.e. logical attributes), what kind of 'thing' is meant by a
term qua 'category'? So for Aristotle the semantic problem still
remained. His distinction between en hypokeimenôi and kath'
hypokeimenou could only hide the original problem. It is often said that
these phrases refer to different domains, the metaphysical and the logical one,
respectively. We have already found some good reasons to qualify this opposition
(see [1978], 84; 88). It seems to be useful now to collect all kind of
information from Aristotle's writings, not only the Categories, about the
proper meaning of the categories. This will be the aim of our sections 4.2-4.7."
pp. 1-2
4.2. On some modern interpretations of 'kata symplokên'; 4.3. Aristotle's use
of the categories; "For this section see also my Utrecht dissertation,
The place of the Categories of Being in Aristotle's philosophy, Assen 1952
pp. 76-88. I have to correct or to adjust my former views on several points.";
4.31. The categories as a classification of reality; 4. 32. The categories as a
classification of sentence predicates; 4.33. The categories as a classification
of 'copulative being'; 4.4. How did Aristotle arrive at his list of categories?;
4.5. Are the categories the 'highest predicates'?; 4.6. The categories taken as
names in Metaph. Z 1-6 and Anal. Post. I 4; 4.7. An attempt at a
reinterpretation of Categories, chs. 1-5; 4.8. Aristotle's view on
relatives; 4.9. Conclusion.
de Rijk Lambertus Marie, "On ancient and mediaeval semantics and
metaphysics. Part IV. Plato's semantics in his critical period (First part),"
Vivarium 19: 1-46 (1981).
"5. Plato's semantics in his critical period; 5.1. Introduction. In
concluding the previous section I argued (1980: nr. 4.9, p. 62) that Aristotle's
Categories may be viewed as dealing with the several ways in which an
individual man can be named without destroying his concrete unity. A well-known
passage of Plato's Sophist (251 A 8ff.) was referred to in which Plato
deals with the puzzle of one man with many names. It is true, Plato labels the
puzzle as just 'a magnificent entertainment for the young and the late-learners'
(251 B), and is more interested in the related question of how 'things'
like Rest and Change (presently called Kinds) can also have several
attributes (attributive names) and the general problem of attribution as
implying the 'Communion' of Kinds'. But it is obvious at the same time that in
this shape too the puzzle is mainly concerned with the notions of naming,
asserting and predication. So Plato's Sophist unavoidably has to be part
of our discussion.
A further argument for taking the Sophist into consideration may be found
in Ammonios' commentary to Aristotle's De interpretatione. He remarks (ad
17 a 26ff.: Comm. in Aristot. graeca IV 5, p. 83, 8-13, ed. Busse)
that the analysis of the apophantikos logos as given by Aristotle is to
be found scattered all over Plato's Sophist (261 Cff.) right after that
master's excellent expositions about Non-being mixed with Being (peri tou
synkekramenou tôi onti me ontos). For that matter, on more than one
item of Aristotle's Categories and De interpretatione the Ancient
commentators refer to related questions and discussions in Plato's later
dialogues, especially the Sophist. I hope to show in sections (5) and (6)
that the views found in the Categories and De interpretatione are
most profitably compared with what Plato argues in the related discussions of
the Sophist." p. 1. 5.2. On the main theme of Plato's Sophist; 5.3. Plato's preliminary attempt
to search 'the Sophist' (216A-231E); 5.4. The semantic character of the
procedure; 5.5. On current views about 'what is' and 'what is not'; 5.5.1.
Introductory: on the genus of image-making; 5.5.2. What should be understood by
the phrase 'what is not'? (237B-242B); 5.5.2.1. On the notion of 'what
absolutely is not'; 5.5.2.2. On the association of 'what is not' with likeness
and falsehood; 5.5.3. Pluralists and Monists about 'what is'; 5.5.3.2. On 'what
is' as taken by the Monists; 5.5.4. Materialists and Idealists about 'what is';
5.5.4.1. The Materialists (245E-247E); 5.5.4.2 The Idealists (248A-249D);
5.5.4.3. Does 'what is in change' include Forms?; 5.6. The general problem of
name-giving (249D-256D); 5.6.1. 'Being' as a (formally) separate and
(materially) all-embracing Form.
de Rijk Lambertus Marie, "On ancient and mediaeval semantics and
metaphysics. Part V. Plato's semantics in his critical period (Second part),"
Vivarium 19: 81-125 (1981).
"5. Plato's semantics in his critical period (Continuation); 5.6.2. The
problem of giving several names and the Communion of Kinds; 5.6.2.1. On the
'trivial' question of 'one individual -- many names'; 5.6.2.2. Giving several
names and the Communion of Kinds; 5.6.3. Dialectic and the Communion of Forms. In order to clarify the Communion of Kinds an analogy is drawn between the
vowels which 'form a sort of bond running through the whole system (253 A 4-5)
and certain Forms that are 'running through all' (253 C 1). Just as without the
help of vowels it is impossible for one of the other letters to fit in with any
other (A 5-6), similarly it is the special Forms that make possible Communion
and are responsible for Division (C 2-3). It seems to be useful to have a look
at the impact of this analogy." p. 95 5.6.3.1. The precise impact of the wovel-analogy; 5.6.3.2. The proper task of
Dialectic; 5.6.3.3. The description of the dialectician's practice; 5.6.4. On
the Communion of Forms as occurring in particulars; 5.6.5. The question of 'what
is not' reduced into a problem of name-giving; 5.6.6. Four antinomies concerning
the Five Kinds raised and solved (254D-255E); 5.6.6.1. The first round: on the
relations of Being, Rest and Change; 5..6.6.2. The second round: on the
relations of Change, Rest, Same and Other; 5.6.6.3. The third round: 'What is'
and 'the Same' disentangled; 5.6.6.4. The fourth round: 'What is' and 'the
Other' disentangled; 5.6.6.5. On the different uses of kath' hauto; 5.6.6.6.
'What is' and 'the Other' disentangled. Continuation; 5.6.6.6. 'What is' and
'Other' disentangled. Continuation."
de Rijk Lambertus Marie, "On ancient and mediaeval semantics and
metaphysics. Part VI. Plato's semantics in his critical period (Third part),"
Vivarium 20: 97-127 (1982). 5.6.7. How the diverse Kinds have communion with one another; 5.7. The
reinstatement of 'What is not' (256d-259D); 5.7.1. Forms being and Forms not
being: 5.7.2. The not-being of 'What is'; 5.7.3. The being of what is not';
5.7.4. Are there Forms corresponding to negative expressions?; 5.7.5. The
Parmenidean dogma refuted. Summary.
"5. 8 Conclusion. From our analysis of Soph., 216 A-259 D it may be
concluded that Plato did certainly not abandon his theory of Forms. We may try
to answer, now, the main questions scholarship is so sharply divided about (see
Guthrie [A History of Greek Philosophy] V, 143ff.). They are, in
Guthrie's formulation: (1) does Plato mean to attribute Change to the Forms
themselves, or simply to enlarge the realm of Being to include life and
intelligence which are not Forms?, and (2) is he going even further in dissent
from the friends of Forms and admitting what they called Becoming --changing and
perishable objects of the physical world -- as part of the realm of True Being?
The first question should be answered in the negative. Indeed, Plato is
defending a certain Communion of Forms, but this regards their immanent
status and, accordingly, the physical world primarily, rather than the 'Forms
themselves' (or: 'in their exalted status' as Guthrie has it, p. 159). As to the
second question, to Guthrie's mind Plato's language makes it almost if not quite
insoluble. I think that if one pays Plato's expositions the patient attention he
asks for 'at 259 C-D and follows his analysis stage by stage, the exact
sense and the precise respect in which he makes his statements (cf. 259 D 1-2:
ekeinêi kai kat' ekeino ho physi) about Being and Not-being, Sameness and
Otherness, and so on will appear. It will be easily seen, then, that there is no
recantation at all in Plato's development. He still maintains, as he will
maintain in his later works (e.g. Philebus, 14 D ff.) the Transcendent
Forms as what in the last analysis are the only True Being. But Plato succeeds
in giving a fuller sense to the old notions of 'sharing' and 'presence in'
without detracting the 'paradigm' function of the Forms in any respect. Matter,
Change and Becoming is given a better position in the Theory of Forms in that
their immanent status has been brought into the focus of Plato's interest. From
his Parmenides onwards Plato has been searching for the solution of his
metaphysical problems and has actually found it in the Sophist in a new
view of participation. Forms in their exalted status are just a too eminent
cause for the existence of the world of Becoming. But their being shared in,
i.e. their immanent status, make them so to speak 'operable' and yet preserve
their dignity of being paradeigmatic standards. What makes something to be a
horse is, no doubt, the Transcendent Form, HORSENESS, but it only can partake
of that Form and possess it as an immanent form. So the Highness of the Form
and the unworthy matter can come together as matter 'informed', that is,
affected by an immanent form.
Plato never was unfaithful to his original view about Forms as the only True
Being. In our dialogue, too, he brings the eminence of True Being (taken, of
course, as a Transcendent Form) into relief by saying (254 A) that the
true philosopher, through his devotion to the Form, 'What is' ('Being'), dwells
in the brightness of the divine, and the task of Dialectic, accordingly, is
described from that very perspective (see Part (5), 96ff.). Focussing on the
immanence of the Forms does not detract anything from their 'exalted status',
since immanent forms are nothing else but the Transcendent Forms as partaken of
by particulars.(...)
In his critical period Plato never ceased to believe in the Transcendent World.
The important development occurring there consists in his taking more seriously
than before their presence in matter and their activities as immanent
forms. In the Sophist he uses all his ingenuity to show that a correct
understanding of the Forms may safeguard us from all extremist views on being
and not-being and zealous exaggerations of the Friends of Forms as well." pp.
125-127.
Di Cesare Donatella. La semantica nella filosofia greca. Roma:
Bulzoni 1980.
Dumont Jean-Paul. Confirmation et disconfirmation. In Science and
speculation. Studies in Hellenistic theory and practice. Edited by Barnes
Jonathan et al. Cambridge: Cambridge University Press 2005. pp. 273-303
Ebbesen Sten. Theories of language in the Hellenistic age and in the twelfth
and thirteenth centuries. In Language and learning. Philosophy of language in
the Hellenistic age. Proceedings of the Ninth Symposium Hellenisticum.
Edited by Frede Dorothea and Inwood Brad. Cambridge: Cambridge University Press
2005. pp. 299-319
"It is a generally accepted view that 'philosophy of language' as well as
'grammar' as a philosophical discipline were invented in antiquity by the Stoics
or by grammarians inspired by them. It is also the accepted view that these
achievements were passed on to the Latin West in the Middle Ages through authors
like Priscian and Boethius, to be augmented and refined by the schoolmen from
the beginning of the twelfth century on. But though the general route of the
tradition that indirectly relates to the beginning of linguistic philosophy in
Hellenistic times is uncontested, there is little knowledge about any direct
influence of the Hellenistic philosophers on that period. Sten Ebbesen takes his
readers into the relatively uncharted waters of the influence of Hellenistic
philosophy on the Middle Ages by tracing Stoic influence on certain issues.
Ebbesen focuses on three points. First he points out how the question of
'imposition', i.e. the assignment of phonemes to natural things was taken up by
the members of the Porretan school in order to show how moral and rational
vocabulary arose through a transformation of the natural vocabulary, so as to
allow discussion of non-natural phenomena in the sphere of culture, reason, and
even theology. Second he shows that Boethius of Dacia and other members of the
'modist school' in the late thirteenth century developed a theory of formal
grammar and logic, a theory that showed how the 'modes' of signifying,
supplemented by a theory of representing logical relationships, is based on
modes of understanding and ultimately related to the modes of being. Though
among the modists the conviction prevailed that language is based on convention
they did not hold that expressions are introduced at random; hence etymology, as
first adumbrated in Plato's Cratylus, has its role to play in linguistic
theory. Finally Ebbesen shows that the static conception of the modists that
assumed invariable rules of language was changed into a dynamic theory of
language by Roger Bacon, whose theory allowed for changing rules of language
without loss of intelligibility.
Thus we find in the Middle Ages ghost-like replicas of the controversies among
the ancient philosophers of language, whether it concerns the 'imposition of
words' inspired by Plato's Cratylus, the quest to account for the
relation between language and the objects in the world that was a main
concern of the Stoics, and the controversy between analogist and anomalist
accounts of language. Ebbesen does not claim that those medieval discussions
were based on any direct knowledge of the Hellenistic philosophers or on that of
Plato's Cratylus. He holds, however, that these medieval positions could
not have been developed had there not been the rich tradition of the Hellenistic
age, passed on to them in the reflections of Boethius and Priscian." From the
Introduction by Dorothea Frede and Brad Inwood, pp. 12-13
Gourinat Jean-Baptiste. Comment peut-on faire l'histoire de la logique de
l'Antiquité? In Comment écrire l'histoire de la philosophie? Edited by
Zarka Yves Charles. Paris: Presses Universitaires de France 2001. pp. 253-257
Graeser Andreas, "On language, thought, and reality in Ancient Greek
philosophy," Dialectica 31: 359-388 (1977).
Reprinted in: A. Graeser - Issues in the philosophy of language past and
present - Bern, Peter Lang, 1999, pp. 9-41
Henle Paul, "On the fourth figure of the syllogism," Philosophy of
Science 16: 94-104 (1949).
Hoffmann Ernst. Die Sprache und die archaische Logik. Tübingen: Mohr
(Siebeck) 1925.
Translated in Italian by Luca Guidetti as: Il linguaggio e la logica arcaica
- Preface by Enzo Melandri - Ferrara, Spazio Libri Editori, 1991
Huby Pamela M., "Elementary logic in the ancient world," Bulletin of the
Institute of Classical Studies 47: 119-128 (2004).
"Formal education in elementary logic began in Plato's Academy and can be traced
into the Middle Ages. Evidence from Aristotle, Prior analytics, Apuleius,
De interpretatione, Galen, Institutio logica, and anonymous sources
suggests that many works may have been written to be memorized by students. The
views of the Peripatetics and Stoics, originally different, coalesced, and later
handbooks covered both at an elementary level. The origin of a concept of a
syllogistic mood is obscure; it may have existed for some time before appearing
first in Apuleius."
Hugonnard-Roche Henri. La logique d'Aristote du grec au syriaque.
Paris : Vrin 2004.
Études sur la transmission des textes de l' Organon et leur
interprétation philosophique.
Hurst Martha, "Implication in the Fourth century B.C.," Mind 44:
484-495 (1935).
"Modern analyses of the nature of necessary connection have given rise to more
paradoxes than they have solved. A familiarity with the controversy between
Diodorus and Philo which took place in the Fourth Century B.C. might perhaps
have made unnecessary the anguish which modern logicians have suffered. (1)
The dispute is mentioned in passing by Cicero (2) and is discussed in two places
by Sextus Empiricus (3). The persons concerned in the dispute are named Diodorus
and Philo, and are, I think, to be identified as the Megarians, Diodorus Cronus
and his pupil Philo."
(1) My attention was first called to this dispute by a notice in C. S. Peirce,
Collected Papers 3, 441. In being aware of this dispute Peirce is an
exception among modern logicians. But he failed to grasp its full significance;
so that his knowledge did not save him from the mistakes which they have made.
(2) Academica Priora, II, 143.
(3) Pyrrhoneion Hypotyposeon II, 110, Adversus Mathematicos VIII,
113 ff.
Ildefonse Frédérique. La naissance de la grammaire dans l'Antiquité
grecque. Paris: Vrin 1997.
Kapp Ernst. Greek foundations of traditional logic. New York:
Columbia University Press 1942.
Klein Jacob. Greek mathematics thought and the origin of algebra.
Massachusetts: The M.I.T. Press 1968.
Translated from the original German Die griechische Logistik und die
Entstehung der Algebra (1934-1936) by Eva Brann.
With an appendix containing Vieta's Introduction to the analytical art
translated by J. Winfree Smith.
Kneale William and Kneale Martha. Prosleptic propositions and arguments. In
Islamic philosophy and the classical tradition. Essays presented by his friends
and pupils to Richard Walzer on his seventieth birthday. Edited by Stern
S.M., Hourani Albert, and Brown Vivian. London: Bruno Cassirer 1972. pp. 189-207
Lloyd Antony C., "Neoplatonic logic and Aristotelian logic (First part),"
Phronesis.A Journal for Ancient Philosophy: 58-72 (1956).
Lloyd Antony C., "Neoplatonic logic and Aristotelian logic (Second part),"
Phronesis.A Journal for Ancient Philosophy: 146-160 (1956).
Lloyd Antony C. Neoplatonists's account of predication and mediaeval logic.
In Le néo-platonisme. Actes du Colloque de Royaumont, 9-13 juin 1969.
Paris: Éditions du CNRS 1971. pp. 357-364
Long Anthony A., "Reply to: J. Barnes epicureans signs," Oxford
Studies in Ancient Philosophy.Supplementary volume 6: 135-144 (1988).
Luhtala Anneli. Syntanx and dialectic in Late Antiquity. In Syntax in
antiquity. Edited by Swiggers Pierre and Wouters Alfons. Louvain: Peeters
2003. pp. 205-225
Luhtala Anneli. Grammar and philosophy in Late Antiquity. A study of
Priscian's sources. Philadelphia: John Benjamins 2005.
Łukasiewicz Jan. On the history of the logic of propositions. In Polish
logic 1920-1939. Edited by McCall Storrs. Oxford: Oxford University press
1967. pp. 66-87
Originally published in Polish as Z historii logiki zdan, Przeglad
Filozoficzny, 37, 1934; translated by the author in German as: Zur Geschichte
der Aussagenlogik, Erkenntnis, 5, 1935, pp. 111-131.
Translated in English in: Storrs McCall (ed.) - Polish logic 1920-1939 -
Oxford, Clarendon Press, 1967 pp.66-87 and also in: J. Łukasiewicz - Selected
works - Ludwik Borowski (ed.) - Amsterdam, North-Holland, 1970 pp. 197-217.
Malatesta Michele, "An extension of Gentzen's natural deduction,"
Metalogicon 2: 1-32 (1989).
"Roots of Gentzen's system can be found in the mediaeval logic and in the logic
of the Graeco-Roman age. This logic has the distinguishing characteristic of
using n-adic connectives (n<2) instead of dyadic ones, and this at the object
language level. The texts which exhibit the precious logic are Aulus Gellius'
Noctes Atticae XVI,8, for the logical product or conjunction, and Galen's
Institutio logica for the logical sum or alternation."
Manchester Peter. The syntax of time. The phenomenology of time in Greek
physics and speculative logic from Iamblichus to Anaximander. Leiden: Brill
2005.
Martin John N., "Existence, negation, and abstraction in the Neoplatonic
hierarchy," History and Philosophy of Logic 16: 169-196 (1995).
"The paper is a study of the logic of existence, negation, and order in the
Neoplatonic tradition. The central idea is that Neoplatonists assume a logic in
which the existence predicate is a comparative adjective and in which monadic
predicates function as scalar adjectives that nest the background order. Various
scalar predicate negations are then identifiable with various Neoplatonic
negations. including a privative negation appropriate for the lower orders of
reality and a hyper-negation appropriate for the higher. Reversion to the One
can then be explained as the logical inference of hyper-negations from mundane
knowledge. Part I develops the relevant linguistic and logical theory. and Part
II defends Wolfson and the scalar interpretation against the more traditional
Aristotelian understanding of Whittaker and others of reversion as intensional
abstraction."
Martin John N. Themes in Neoplatonic and Aristotelian logic. Order,
negation and abstraction. Aldershot: Ashgate 2004.
Mignucci Mario, "La teoria della quantificazione del predicato
nell'antichità classica," Anuario Filosófico 16: 11-42 (1983).
Morison Ben. Language. In The Cambridge Companion to Galen. Edited by
Hankinson Robert James. Cambridge: Cambridge University Press 2008. pp. 116-156
Morison Ben. Logic. In The Cambridge Companion to Galen. Edited by
Hankinson Robert James. Cambridge: Cambridge University Press 2008. pp. 66-115
Mueller Ian. Greek mathematics and Greek logic. In Ancient logic and its
modern interpretations. Edited by Corcoran John. Dordrecht: Reidel 1974. pp.
35-70
Nasti de Vincentis Mauro. Conflict and connectedness: between modern logic
and history of ancient logic. In Logic and philosophy in Italy. Some trends
and perspectives. Edited by Ballo Edoardo and Franchella Miriam. Monza:
Polimetrica 2006. pp. 229-251
Nuchelmans Gabriel. Theories of proposition. Ancient and medieval
conceptions of the bearers of truth and falsity. Amsterdam : North-Holland
1973.
Contents: Preface V; 1. Introduction 1; 2. Plato 13; 3. Aristotle 23; 4. The
Stoic lekton 45; 5. The Stoic axioma 75; 6. Later developments in
Greek antiquity 89; 7. The transition to the Latin West 105; 8. Boethius and the
beginning of the Middle Ages 123; 9. Abelard 139; 10. The doctrine of the
dictum in the century after Abelard 165; 11. Preliminaries to the fourteenth
century debate 177; 12. The complexum theory of Ockham and Holkot 195;
13. Some reist opponents of Ockham and Holkot 209; 14. The theory of the
complexe significabile 227; 15. The oppositions against the theory of the
complexe significabile 243; 16. The significate of a true propositio
273; Selective bibliography 281; Indices 289-309.
"This book is intended as the first part of a history of those problems and
theories in the domain of philosophical semantics which nowadays are commonly
referred to as problems and theories about the nature and the status of
propositions. Although the conceptual apparatus and the terminology by means of
which questions concerning propositions were asked and answered have
considerably varied from period to period, the main types of disputes and
solutions have remained remarkably constant. One of the aims of this study is
precisely to trace the vicissitudes of the vocabulary in which this refractory
topic was treated in the remote past. As is evident from the Bibliography, many
parts of the field have been explored by predecessors. Guided by their results,
I have tried to fill in more details and to design a provisional map of the area
as a whole." (from the Preface)
The two other volumes are: Late-Scholastic and Humanist theories of the
proposition (1980) and Judgment and propostion. From Descartes to Kant
(1983).
Öffenberger Niels. Zur Vorgeschichte der mehrwertigen Logik in der
Antike. Hildesheim: Georg Olms 1990.
Plochmann George Kimball, "Professor Henle on the four figures of
syllogism," Philosophy of Science 19: 333-341 (1952).
Possekel Ute. Evidence of Greek philosophical concepts in the writings of
Ephrem the Syrian. Louvain: Peeters 1999.
See in particular Chapter 7: Incorporeals - pp. 155-195
Prier Raymond Adolph. Archaic logic: symbol and structure in Heraclitus,
Parmenides, and Empedocles. The Hague: Mouton 1976.
Sainati Vittorio. Logica e filosofia. Pisa: ETS 2000.
Salvaneschi Enrica, "Le nozioni di segno linguistico e di struttura nei
filosofi greci," Annali della Scuola Normale Superiore di Pisa 4: 1-55
(1974).
Sedley David. On signs. In Science and speculation. Studies in
Hellenistic theory and practice. Edited by Barnes Jonathan et al. Cambridge:
Cambridge University Press 2005. pp. 239-272
Smiley Timothy, "What is a syllogism?," Journal of Philosophical Logic
2: 136-154 (1973).
Smith Robin, "Completeness of an echtetic syllogistic," Notre Dame
Journal of Formal Logic 24: 224-232 (1983).
Sullivan Mark, "What was true or false in the Old Logic? " Journal
of Philosophy 67 (22): 788-800 (1970).
Thom Paul, "A Lesniewskian reading of ancient ontology: Parmenides to
Democritus," History and Philosophy of Logic 7: 155-166 (1986).
"Parmenides formulated a formal ontology, to which various additions and
alternatives were proposed by Melissus, Gorgias, Leucippus and Democritus. These
systems are here interpreted as modifications of a minimal Lesniewskian
ontology."
Tracy Kevin, "The development of dialectic from Aristotle to Chrysippus",
2006.
Dissertation presented to the University of Pennsylvania (available on ProQuest:
http://gradworks.umi.com/32/25/3225558.html).
"From Aristotle onward, formal logic was an element of ancient Greek dialectic (dialektiké).
Aristotle's Prior Analytics (4th century BCE) is the earliest evidence of
a formal logic in antiquity. The evidence for the formal logic of the Stoic
philosopher Chrysippus (3rd century BCE) is fragmentary; nonetheless it makes
clear that not more than a century or so after Prior Analytics,
Chrysippus revolutionized formal logic. The scholarship on Stoic logic has not
yet presented the history of dialectic from Aristotle to Chrysippus as an
intelligible narrative. Without such a narrative, one cannot explain what, in
general, motivated the innovations of Chrysippus, what made Stoic logic coherent
as a unified project, or what relationship that project had to earlier work in
logic. This dissertation approaches the problem through the presentation and
interpretation of the ancient source material. First it describes the logical
doctrines of Aristotle, Theophrastus, and the 'Megarics' in such a way as to
make clear what questions these predecessors left for Chrysippus. It then
describes how Chrysippus addressed these questions. Finally, it uses the
resulting narrative to give a detailed account of Stoic formal logic. The
dissertation yields five principal conclusions. First, neither the Peripatetics
or the 'Megarics' described logical forms of propositional logic; Chrysippus was
the first to do so. Second, the guiding aim of Chrysippus' logic was to avoid
adopting a semantic stance in describing logical forms and explaining logical
relationships. Third, the Stoics distinguished 'valid' (hugies) from
'true' (aléthes), so that sunartésis is a standard for the
validity rather than the truth of the Stoic conditional (sunhémmenon).
Fourth, the Stoics produced derivations for categorical arguments in their
deduction system. Fifth, the Stoic deduction system is roughly analogous to the
first-order fragment of Frege's system, except on two points: it most likely was
not designed to accommodate the use of polyadic predicates with multiple
quantifiers, although the possibility for doing so inheres in its approach to
the analysis of propositions, and it uses the 'natural' approach rather than the
'axiomatic' approach of Frege."
White Michael J., "Time and determinism in the Hellenistic philosophical
Schools," Archiv für Geschichte der Philosophie 65: 40-62 (1983).
Wolenski Jan, "Scepticism and logic," Logical Analysis and History of
Philosophy 1: 187-194 (1998).
"This paper offers a logical analysis of Scepticism. It is shown that Dogmatism,
Academism and Scepticism as characterized by Sextus Empiricus in Outlines of
Pyrronism form a variety of views which can be ordered by an interpretation
of the classical logical square. In particular, Scepticism appears as a
conjunction of the negations of Dogmatism and Academism. The next problem
concerns the logic proper for Scepticism. Logic based on a dual of the
consequence operation is proposed as satisfying intuitive requirements
associated with doubting. Finally, the attitude of the sceptic toward logic is
discussed. In particular, it is argued that the principle of isosteny
trivializes scepticism if it is applied to logic."
(click on the image to see the PDF file)