Theory and History of Ontology
by Raul Corazzon - e-mail: raul.corazzon[at]formalontology.it
For an overview see the Index of the Pages, the SITE MAP or the Alphabetical Index of the Philosophers: A-F - G-O - P-Z; You can also download this page as 
Table of Contemporary Ontologists 
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Index of the Section: "Ontology and History of Logic"
Ontology and History of Logic in Western Thought. An Introduction
Aristotle's Earlier Dialectic: the Topics and Sophistical Refutations
Theory of Predication and Ontological Analysis in Aristotle's Categories
Aristotle's De Interpretatione: Semantics and Philosophy of Language
Aristotle's Modal Syllogistic in the Prior Analytics
Peripatetic Logic: Eudemus of Rhodes and Theophrastus of Eresus
The Development of Ancient Logic after Aristotle to the Hellenistic Period
The Dialectical School, Stoic Logic and the Doctrine of Lekta (Sayables)
Stoic Logicians: Diodorus Cronus, Philo of Megara, Chrysippus
The Contribution of Boethius to the Development of Medieval Logic
History of Medieval Logic after Boethius to Late Scholasticism
Medieval Theories of Supposition (Reference) and Mental Language
The Development of Renaissance and Modern Logic from 1400 to Boole
Leibniz on Logic and Semiotics: the Project of a Universal Language
A Selection of Great Logicians from Aristotle to Gödel (1931)
INTRODUCTION: THE REDISCOVERY OF STOIC LOGIC
"The first reactions to the negative appraisal of Stoic philosophy have come not from historians or philosophers specializing in antiquity, but from logicians being interested in the development of ancient logic.
(...)
Now in addition to what has been said in connection with the nineteenth-century misinterpretations and misconceptions, let me quote another view about the specific reasons for the disappreciation as well as for the rehabilitation of Stoic logic; it is found in I. M. Bochenski's Ancient Formal Logic (Amsterdam, 1951), and it clearly portrays the difference in attitude of the logicians of the twentieth century towards the Stoic logical system:
Modern history of Logic had been started during the XIXth century, but its state was very bad at that time -- indeed until 1930 approximately -- because of two phenomena. On one hand, most of the historians of logic took for granted what Kant said on it; namely that 'formal logic was not able to advance a single step (since Aristotle) and is thus to all appearance a closed and complete body of doctrine'; consequently, there was, according to them, no history of logic at all, or at the most, a history of the decay of Aristotelian doctrines. On the other hand, authors writing during that period were not formal logicians and by 'logic' they mostly understood methodology, epistemology and ontology. . . . We may place the beginning of recent research in our domain in 1896 when Peirce made the discovery that the Megarians had the truth-value definition of implication. (pp. 4-5)
Now whether it is Peirce to whom we owe the revival of interest in Stoic logic or not, what certainly is the case is that, from the early decades of the twentieth century on, given the important developments in the field of symbolic logic, it has finally become obvious that Stoic logic differed essentially from Aristotelian logic and should be studied on its own merits. The articles and books on Stoic logic which since then have been published, have examined in detail the Stoic contribution to the development of a logical calculus:
J. Łukasiewicz, 'Zur Geschichte der Aussagenlogik', Erkenntnis, 5 (1935).
B. Mates, Stoic Logic (Berkeley, 1953).
O. Becker, Zwei Untersuchungen zur antiken Logik (Wiesbaden, 1957).
W. and M. Kneale, The Development of Logic (Oxford, 1962).
M. Mignucci, Il significato della logica stoica (Bologna, 19672).
I. Mueller, 'Stoic and Peripatetic Logic', Archiv fur Geschichte der Philosophie, 51 (1969), 173-87.
M. Frede, Die stoische Logik (Gottingen, 1974).
M. Frede, 'Stoic vs. Aristotelian syllogistic', Archiv fur Geschichte der Philosophie, 56 (1974), 1-32."
From: Katerina Ierodoakonou - Introduction. The study of Stoicism: its decline and its revival - in: K. Ierodiakonou (ed.), - Topics in Stoic philosophy - Oxford, Clarendon Press, 1999 pp. 15-17
"Modern mathematical logic has taught us to distinguish within formal logic two basic disciplines, no less different from one another than arithmetic and geometry. These are, the logic of propositions and the logic of terms. The difference between the two consists in the fact that in the logic of propositions there appear, besides logical constants, only propositional variables, while in the logic of terms term variables occur.
The simplest way of making this difference clear is to examine the Stoic and the Peripatetic versions of the law of identity. To avoid misunderstanding let me at once say that, so far as our sources indicate, the two laws of identity were only incidentally formulated by the ancients, and in no way belong to the basic principles of either logic. The Stoic law of identity reads "if the first, then the first", and is to be found as a premiss in one of the inference-schemata cited by Sextus Empiricus. (1) The Peripatetic law of identity is "a belongs to all a", and is not mentioned by Aristotle, but can be inferred from a passage in Alexander's commentary on the Prior Analytics. (2) Using variable letters we can write the Stoic law of identity in the form "if p then p"; the Peripatetic law can be recast in the form "all a is a". In the first law the expression "if ... then" is a logical constant, and "p" a propositional variable; only propositions such as "it is day" can be meaningfully substituted for "p". This substitution yields a special case of the Stoic law of identity: "if it is day, it is day". In the second law the expression "all ... is" is a logical constant, and "a" a term variable; "a" can be meaningfully replaced only by a term, and, in accordance with a tacit assumption of Aristotelian logic, only by a general term at that, such as "man" Upon substitution we get a special case of the Peripatetic law of identity: "all man is man". The Stoic law of identity is a thesis of the logic of propositions, whereas the Peripatetic law is a thesis of the logic of terms.
This fundamental difference between the logic of propositions and the logic of terms was unknown to any of the older historians of logic. It explains why there has been, up to the present day, no history of the logic of propositions, and, consequently, no correct picture of the history of formal logic as a whole. Indispensable as Prantl's 3) work is, even today, as a collection of sources and material, it has scarcely any value as an historical presentation of logical problems and theories. The history of logic must be written anew, and by an historian who has fully mastered mathematical logic. I shall in this short paper touch upon only three main points in the history of propositional logic. Firstly I wish to show that the Stoic dialectic, in contrast to the Aristotelian syllogistic, is the ancient form of propositional logic; and, accordingly, that the hitherto wholly misunderstood and wrongly judged accomplishments of the Stoics should be restored their due honour. Secondly I shall try to show, by means of several examples, that the Stoic propositional logic lived on and was further developed in medieval times, particularly in the theory of "consequences". Thirdly I think it important to establish something that does not seem to be commonly known even in Germany, namely that the founder of modern propositional logic is Gottlob Frege.
(...)
The fundamental difference between Stoic and Aristotelian logic does not lie in the fact that hypothetical and disjunctive propositions occur in Stoic dialectic, while in Aristotelian syllogistic only categorical propositions appear. Strictly speaking, hypothetical propositions can be found in Aristotle's syllogistic also, for each proper Aristotelian syllogism is an implication, and hence a hypothetical proposition. For example, "If a belongs to all b and c belongs to all a, then c belongs to all b". (7) The main difference between the two ancient systems of logic lies rather in the fact that in the Stoic syllogisms the variables are propositional variables, while in Aristotle's they are term variables. This crucial difference is completely obliterated, however, if we translate the above-mentioned Stoic syllogism as Prantl does (I, p. 473):
If the first is, the second is
But the first is
Therefore the second is.
By adding to each variable the little word "is", which occurs nowhere in the ancient texts, Prantl, without knowing or wishing it, falsely converts Stoic propositional logic into a logic of terms. For in Prantl's schema only terms, not propositions, can be meaningfully substituted for "the first" and "the second". As far as we can judge from the fragmentary state of the Stoic dialectic that has come down to us, all Stoic inference-schemata contain, besides logical constants, only propositional variables. Stoic logic is therefore a logic of propositions. (8)" pp. 197-200
(1) Sextus, Adv. Math. VIII 292 (missing in Arnim): ei to poton, to poton. Good as H. von Arnim's collection is (Stoicorum veterum fragmenta [SVF], vol. II, Leipzig 1903), it does not begin to serve as source material for Stoic dialectic.
(2) Alexander, In anal. pr. comm., ed. Wallies, p. 34, 1. 19.
(7) Aristotle, An. pr. II. 11. 61b34
(8) I have defended this interpretation of the Stoic dialectic since 1923; see J. Łukasiewicz, "Philosophische Bemerkungen zu mehrwertigen Systemen des Aussagen-kalkuls", Comptes rendus des séances de la Société des Sciences et des Lettres de Varsovie 23 (1930), cl. III, pp. 51-77. ["Philosophical Remarks on Many-Valued Systems of Propositional. Logic", pp. 153-178 of this volume.] I rejoice in having found in H. Scholz, Geschichte der Logik (Berlin, 1931), p. 31, a supporter of this point of view.
From: Jan Łukasiewicz - On the history of the logic of proposition (1934) - Translated in: Selected works - Edited by Ludwik Borkowski - Amsterdam, North-Holland, 1970 pp. 197-217 (Greek omitted)
"I have compiled thus many quotations on purpose, for, although they illuminate one of the most important problems of logic, it nevertheless appears that many of them were either unknown to the historians of logic, or at least not sufficiently appreciated. The reason for this is in my opinion that the history of logic has thus far been treated by philosophers with insufficient training in logic. The older authors cannot be blamed for this, as a scientific logic has existed only for a few decades. The history of logic must be written anew, and by an historian who has a thorough command of modern mathematical logic. Valuable as Prantl's work is as a compilation of sources and materials, from a logical point of view it is practically worthless. To give only one illustration of this, Prantl, as well as all the later authors who have written about the logic of the Stoa, such as Zeller and Brochard, have entirely misunderstood this logic. For anybody familiar with mathematical logic it is self-evident that the Stoic dialectic is the ancient form of modern propositional logic. (26)
Propositional logic, which contains only propositional variables, is as distinct from the Aristotelian syllogistic, which operates only with name variables, as arithmetic is from geometry. The Stoic dialectic is not a development or supplementation of Aristotelian logic, but an achievement of equal rank with that of Aristotle. In view of this it seems only fair to demand of an historian of logic that he know something about logic. Nowadays it does not suffice to be merely a philosopher in order to voice one's opinion on logic.
(26) I have already expressed this idea, in 1923, in a paper read to the first congress of Polish philosophers in Lwow. A short summary of it appeared in Przeglqd Filozoficzny 30 (1927), p. 278. [Łukasiewicz develops his historical analysis of Stoic logic in his article "On the History of the Logic of Propositions" (pp. 197-217 of this book).]" p. 178
From: Jan Łukasiewicz - Philosophical remarks on many-valued systems of propositional calculus (1920) - Translated in: Selected works - Edited by Ludwik Borkowski - Amsterdam, North-Holland, 1970 pp. 153-178
"In the first comprehensive history of western logic Prantl (1) described Stoic logic as "dull," "trivial," and "pedantic." Prantl's dismissal of Stoic logic was accepted by most interpreters of Stoicism for three quarters of a century. However, since the publication of Łukasiewicz's article, "On the History of the Logic of Propositions" in 1934, (2) Prantl's evaluation has been largely abandoned. Bochenski's remark, "The development of formal logic in antiquity reached its peak in the works of the thinkers belonging to the Megaric and Stoic Schools," exemplifies well the radical rehabilitation of the Stoics as logicians. (3) The cause of this rehabilitation is not the discovery of new texts, but rather the twentieth-century revolution in the subject of logic itself. Łukasiewicz and others, working with a full understanding of modern logic, have succeeded in retrieving from the ancient texts a Stoic logical theory of startling originality which rivals the achievement of Aristotle, the founder of logic. The failure of Prantl and his successors to accomplish this retrieval stems not from their obtuseness or stupidity but from the fact that the background scientific knowledge needed to understand the Stoic achievement was not available to them.
A factor contributing to Prantl's low opinion of Stoic logic was the character of the ancient texts themselves. There are no primary sources for Stoic logic analogous to Aristotle's Prior Analytics, and the ancient secondary sources are brief and usually hostile in their treatment of the subject. In many cases Prantl's evaluations simply repeat or develop remarks in the sources themselves. The unsatisfactoriness of the sources (on this see Mates, Stoic Logic 8-10) makes any but a tentative reconstruction of Stoic logic impossible. Unless an indication is given to the contrary, what I describe will be the most certain features of the theory.
One of the uncertain features is chronology. The history of Stoicism proper covers five centuries during which the logical theory, like other doctrines of the school, underwent modification and development. In the case of logic we know of some disagreements within the school and some ideas that can be ascribed to individuals, but most of our sources refer simply to "the Stoics," as if there were a single, unambiguous Stoic logical theory. Commentators have tended to assign the major Stoic achievements in logic to Chrysippus (c. 280 B.C .- c. 206 B.C.), the third leader of the Stoa, of whom it was said, "If there were a dialectic among the gods, it would be none other than the Chrysippean one." (Diogenes Laertius 7.180. At 7.198 Diogenes mentions that Chrysippus wrote 311 books on logical matters.) In general I shall not attempt to assign logical doctrines to specific persons, but simply speak of "Stoic logic." Occasionally, however, it will be necessary to refer to possible disagreements within the school." pp. 1-2
(1) C. Prantl, Geschichte der Logik im Abendlande (Leizig, 1855) 408. I have generally given at most one ancient source for a doctrine. More information about sources can be found by consulting B. Mates, Stoic logic (2nd ed.) or M. Frede, Die stoische Logik.
(2) Reprinted in J. Łukasiewicz, Selected works, ed. L. Borkowski
(3) I. M. Bochenski, Ancient formal logic (Amsterdam, 1951) 77.
From: Ian Mueller - An introduction to Stoic logic. In The Stoics. Edited by John M. Rist - Berkeley: University of California Press 1978. pp. 1-26
"Zeno, the founder of the Stoic school of philosophy, is said to have been influenced primarily by two of the Socratic schools, the Cynics and the Megarians. (*) From the Cynics, according to the usual account, he took his moral teaching; from the Megarians, his logic. In view of our present subject, we shall omit all discussion of the Cynics and devote our attention to the Megarians.
The Megarian school was founded by Euclid, a follower of Socrates and a somewhat older contemporary of Plato. (See fig. 1.)
Among the pupils of Euclid were: Eubulides, a famous logician to whom the antinomy of The Liar is sometimes ascribed; Ichthyas, the successor of Euclid as head of the school; and Thrasymachus of Corinth, who is known primarily as the teacher of Stilpo. Stilpo, a contemporary of Aristotle, enjoyed a great reputation as a lecturer. He is supposed to have been somewhat influenced by the Cynics. His most famous pupil was Zeno, founder of Stoicism. Another important branch of the Megarian school consisted of Eubulides, Apollonius Cronus, Diodorus Cronus, and Philo, in that order. The latter two are very important in connection with Stoic logic, mainly for their views on the truth-conditions of conditionals.
Diodorus, a native of lasus in Caria, lived at the court of Alexandria in the reign of Ptolemy Soter. His surname or nickname "Cronus" ("old fool") is variously explained. According to one story, it was given to him by Ptolemy on account of his inability to solve a problem of logic put forth by Stilpo at a royal banquet. In fact, Diodorus is said to have taken his defeat so much to heart that he went home, wrote a treatise on the subject, and died in despair. According to another account, Diodorus took the surname from his teacher, Apollonius Cronus. At any rate, Diodorus was certainly not regarded as an old fool in antiquity. On the contrary, he was so celebrated for his dialectical skill that he was called "the logician" and "most logical one". This epithet gradually became a surname, and was even applied to his five daughters, who were also distinguished as logicians.
Little is known of the philosophy of Diodorus save two important definitions (and examples illustrating these): (1) a proposition is possible if and only if it either is true or will be true; (2) a conditional proposition is true if and only if it neither is nor was possible for the antecedent to be true and the consequent false. It is known that he constructed the famous "Master" argument (e) ImpLeigov) to justify his definition of "possible." It is also known that he entered into a controversy with his pupil Philo over the truth-conditions for hypothetical propositions; this controversy was perpetuated and enlarged within the Stoic school.(**)
Philo of Megara, the pupil of Diodorus, was also very famous as a logician. Almost nothing is reported of his life except that he was a friend of Zeno. Chrysippus later wrote treatises against both him and his master. Philo disagreed with Diodorus concerning the nature of possibility and especially concerning the criterion for the truth of conditional propositions. Regarding the first, he thought (as against Diodorus) that a piece of wood at the bottom of the sea should be considered combustible even if it will never be burned. In regard to conditionals, he gave exactly the modern truth-table definition: a conditional is false if it has a true antecedent and a false consequent; in the other three cases it is true.
Zeno himself apparently lived ca. 350-260 B.C., but the dates are very uncertain. Like all the other major Stoic philosophers before the Christian era, he was not a native of Greece proper. (His birthplace was at Citium, in Rhodes.) Few facts are known about him, but where the facts leave off, legend begins. It is said that he was greatly respected for his personal characteristics dignity, modesty, sincerity, affability. Presumably because of a life of moderation, he lived to the ripe old age of ninety-eight, and, as the story has it, he died in the following way. As he was leaving the school one day, he stumbled and broke his toe. Beating his hand upon the ground, he addressed himself to the gods: "I'm coming of my own accord. Why then do you bother to call me?" Then he perished by holding his breath.
Also according to the legends, Zeno devoted much thought and energy to proposed reforms in language. This aroused ire in certain quarters, and it was pointed out that he was proposing to reform a language which he himself could hardly speak. As he was fond of coining new words, much of the technical vocabulary of Stoic logic may well be attributed to him. It was said that he used new terms in order to conceal his plagiarism of the views of his predecessors; Cicero repeats this charge at least fourteen times. His writings, which were not numerous and were written in a very poor style, have been lost (excepting, of course, a few fragments).
The second head of the Stoic school was Cleanthes, known throughout antiquity as a man of strong character, great energy, and weak intellect. According to one story, he was a prize fighter who came to Athens with four drachmas in his pocket and entered the school of Zeno. He accepted Zeno's teaching in every detail and passed it on unchanged. At the age of ninety-nine or so, he died by starving himself to death.
Cleanthes was succeeded by Chrysippus, often said to have been the greatest logician of ancient times. Chrysippus was regarded as the second founder of Stoicism; according to an old saying, "If there had been no Chrysippus, there would have been no Stoa." He was born in 280 B.C. in Cilicia; the date of his death may be conjectured as 205 B.C. Without doubt, he was the best student his Stoic professors ever had. While in training, he thought of so many skeptical arguments against Stoicism that he was accused by the later Stoics of supplying Carneades with ammunition for attacking them. Chrysippus wrote 750 books, if the list given by Diogenes can be trusted. Of these we possess only the titles and a small number of fragments. But the titles alone show that he wrote on almost every important aspect of propositional logic. There are many ancient complaints that Chrysippus' books were dry and repetitious, and written in a very poor style. Yet they were widely read. He did not, like Cleanthes, merely repeat the words of his predecessors; there is a story that when he was a student of logic he wrote to Cleanthes, "Just send me the theorems. I'll find the proofs for myself."
It seems likely that Chrysippus was responsible for the final organization of Stoic logic into a calculus. When the five basic undemonstrated argument-types are cited, the name of Chrysippus is usually mentioned; in one place it is expressly stated that Chrysippus restricted the number of these types to five."
(*) For the following account I am indebted to Zeller, Die Philosophie der Griechen, vol. 2, part 1, pp. 244 ff., and vol. 3, part 1, pp. 27-49; William Smith, Dictionary of Greek and Roman Biography and Mythology (Boston, Little, Brown, 1849), 3 vols.
(**) The views of Diodorus will be discussed fully in the sequel, pp. 36-40, 44-51. Cf. my article, "Diodorean Implication."
From: Benson Mates - Stoic logic - Berkeley - University of California Press 1953, pp. 5-7
ANCIENT THEORIES OF MEANING
"There were three ancient theories of meaning:
(1) According to the Peripatetics, words mean thoughts, and thoughts stand for things.
(2) According to the Epicureans, words directly mean things.
(3) According to the Stoics, words mean sayables, (1) and sayables stand for things.
The Stoics agree with the Peripatetics and disagree with the Epicureans in maintaining that a semantic theory must be three-tiered. The Stoics disagree with the Peripatetics insofar as the intermediate items in their three-tiered theory are sayables and not thoughts.
Thus far, mere caricature: each of the theories I have sketched requires further elucidation; and each of the sketches would be regarded as wildly inaccurate by some scholars. I shall not attempt to replace the caricatures by professional portraits; rather, I want to address one particular problem which the caricatures raise. If the Peripatetic and Stoic theories differ insofar as thoughts differ from sayables, then -- we may well wonder -- what exactly is the difference between sayables and thoughts, and how is Stoic saying related to Stoic thinking?
Several scholars, both ancient and modern, have denied that there is any substantive difference between the Peripatetic and the Stoic theories of meaning on the grounds that sayables are simply thoughts under a different name. Thus according to Simplicius, some people held that
the argument <in the Categories> is about thoughts (peri noematon); for Aristotle plainly says that it is about things which are said (peri ton legomenon), and things which are said, or sayables, are thoughts, as the Stoics too held. (in Cat. 10.2-4 = FDS 703) (2)
More recently it has been maintained that a sayable is "that which is merely an expressed thought"; for sayables "exist only insofar as they are thought and expressed in words. As ideas in the mind ... the lekta ... should be interpreted ... as something ... akin to the ideas of, for instance, classical British empiricism -- as a kind of mental images which precede and accompany our words and give them meaning" (3)
A weaker thesis has also found favour: sayables are not to be identified with thoughts, but they are logically dependent upon the activity of thinking. For "every species of lekton requires the utterance of some expressible object present to the mind. Does this entail that lekta only persist as long as the sentences which express them? ... there is no evidence to show that lekta, as distinct from the speaker and his reference, persist outside acts of thought and communication". (4)
These theses about sayables and thoughts are not mere conjectures. For there are several ancient texts which associate sayables with thoughts, and these texts have been taken to support either the strong view that sayables actually are thoughts or the weaker view that sayables are parasitic upon thoughts.
The issues are complicated, both from a philosophical and from an exegetical point of view. I shall first make a few abstract remarks; then look at the Peripatetic theory of meaning; and finally turn to the texts which associate thoughts with sayables." pp. 47-48
(1) I use the unlovely word "sayable" for the Greek lekton. I take it that lekta stand to saying as thoughts stand to thinking; but no decent English word stands to "say" as "thought" stands to "think".
(2) Note that Simplicius does not subscribe to this view of lekta (pace Long [1971] 80): he ascribes it to unnamed interpreters of Aristotle's Categories, and at e.g. in Cat. 397.10-12 he implicitly distinguishes lekta from dianoemata.
(3) Nuchelmans (1973) 52, 55.
(4) Long (1971) 97,98.
From: Jonathan Barnes - Meaning, saying and thinking. In Dialektiker und Stoiker. Zur Logik der Stoa und ihrer Vorläufer. Edited by Klaus Döring and Theodor Ebert - Stuttgart: Franz Steiner 1993 pp. 47-61
STOIC DIALECTIC AND THE DOCTRINE OF LEKTA (SAYABLES)
"In moving from the theory of knowledge to the other topics which the Stoics include within the third branch of their philosophy, it must be noted that they draw a sharp distinction between logic and language. All the remaining topics can be grouped either on one side of this distinction or the other. The Stoics define language as utterance. Language is sound. It is corporeal, material, and sensible. (135) Hence, language is part of the world of real being. Words, real beings themselves, are natural signs of natural objects. Logic, on the other hand, falls within the category of the incorporeals. Logical statements are lekta. (136) They have meaning, but since they are not corporeal, they do not have full being. They exist only intramentally. The lekta include predicates, arguments, syllogisms, and fallacies. They are not natural signs of natural objects.
This classification of logical statements as lekta has important implications for the way in which the Stoics handle dialectic, or logic as a formal branch of philosophical investigation.(137) Their logic is propositional. The variables in Stoic syllogisms are propositions, in contrast to the variables in Aristotelian syllogisms, which tend to be terms and classes. The Stoics are sensitive to the grammatical precision of their logical propositions; they elaborate a more precise way of expressing negation than had been used hitherto, prefixing a negative word to the entire proposition and not just to the verb. Thus, instead of saying "It is not day," they say "Not: it is day." While less idiomatic, this is a more unambiguous way of specifying what is being negated, similar to the usage "Not-p" in modern symbolic logic. Indeed, the technical ingenuity of Stoic logic is considerable, resulting in a number of ideas which had been neglected in Aristotle's logic.
Since lekta are not natural signs of natural objects, the Stoic preference in logic is for hypothetical syllogisms.(138) Unlike the categorical, deductive, or inductive syllogisms used by Aristotle, the hypothetical syllogism does not begin with an axiomatic statement about a general class of beings, nor does it conclude with a statement about the fixed, essential nature of things. For the Stoics, such a procedure would have been in conflict with a propositional logic whose aim is to demonstrate the logical tenability of the conclusions of one's premises, not their empirical or ontological verifiability. At the same time, and although they are lekta, the Stoics' hypothetical syllogisms are compatible with the physics which they espoused, for their syllogisms deal with the changing relations between concrete individual events rather than with a changeless structure of fixed essences.(139) The five main types of syllogisms used by the Stoics may be schematized as follows:
Conditional: "If it is light, it is day."
Conjunctive: "It is light and it is day."
Disjunctive: "Either it is light or it is day."
Causal: "It is light because it is day."
Likely: "It is more likely that it is day than that it is night."
In all cases both the initial premises and whatever conclusions may follow from them refer to transient events. Having demonstrated a proposition by means of these syllogisms, one has still not claimed to have said anything about an enduring natural phenomenon. This is a perfectly reasonable choice for the Stoics given both their physics of dynamic events and their conception of the lekta."
(135) SVF, 1, 74; 2, 140-41, 144a.
(136) See the references cited in note 35 above; Diogenes Laertius, Lives 7. 63-81.
(137) The traditional view of Stoic logic, treating it as beneath consideration because of its departures from Aristotelian logic, is stated clearly by Carl Prantl, Geschichte der Logik im Abendlande (Leipzig, 1927), 1, 401-96. It has been superseded by a positive reinterpretation of Stoic logic, marked by two trends. One understands Stoic logic and its differences from Aristotelian logic in the light of its connections with the rest of the Stoic system. The most important studies in this area are Urs Egli, Zur stoischen Dialektik (Basel, 1967), pp. 93-104; Michael Frede, Die stoische Logik, Abhandlungen der Akademie der Wissenschaften in Göttingen, philosophisch-historische Klasse, 3:88 (Göttingen, 1974); and Virieux-Reymond, La logique et l'épistimologie des Stoïciens. See also Bréhier, Hellenistic and Roman Age, pp. 41 fr.; V. Brochard, Études de philosophie ancienne et de philosophie moderne, nouv. ed. I Paris, 1926), pp. 220-51; Carlo Diano, Forma ed evento: Principii per una interpretatione del mondo greco (Venezia, 1952), pp. 9-20; Edelstein, Meaning of Stoicism, pp. 27-29; Goldshmidt. I.e système stoïcien, pp. 82 83; Josiah 13. Gould, "Chrysippus: On the Criteria for the Truth of a Conditional Proposition," Phronesis, 12 (1967), 152-61; Chrysippus, pp. 66-88; Charles H. Kahn, "Stoic Logic and Stoic LOGOS," Archiv für Geschichte der Philosophie, 51 (1969), 158-72; Lorenzo Pozzi, "Il nesso di implicazione nella logica stoica," Atti del convegno di storia della logica, Parma, 8-10 ottobre 1972 (Padova, 1974), pp. 177-87; Giulio Preti, "Sulla dottrina del semeion nella logica stoica," Rivista critica di storia della filosofia, 2 (1956), 5-14; Reymond, "La logique stoïcienne," Revue de Théologie et de Philosophie, n.s. 17 (1929), 161-71; Carlo Augusto Viano, "La dialettica stoica," Rivista di filosofia, 49 (1958), 179-227; Antoinette Virieux-Reymond, "Le 'sunemménon' stoïcien et la notion de la loi scientifique," Studia Philosophica, 9 (1949), 162-69.
The second group consists of scholars primarily interested in modern logic, who have rediscovered Stoic logic because of the affinities they perceive between it and the school of Carnap and Frege. The essay which began this movement is Jan Łukasiewicz, "Zur Geschichte der Aussagenlogik," Erkenntnis, 5 (1935), 111-31. The most important technical treatment of Stoic logic within this or any other perspective is Benson Mates, Stoic Logic (Berkeley, 1953). See also Nimio de Anquin, "Sobre la logica de los Estoicos," Sapientia, 11 (1956), 166-72; Oskar Becker, Zwei Untersuchungen zur antiken Logik (Wiesbaden, 1957); I. M. Bochenski, Ancient Formal Logic (Amsterdam, 1951), pp. 77-102; William Kneale and Martha Kneale, The Development of Logic (Oxford, 1962), pp. 11376; Leo Lugarini, "L'orizzonte linguistico del sapere in Aristotele e la sua trasformazione stoica," Il Pensiero, 8 (1963), 327-51; Jürgen Mau, "Stoische Logik. Ihre Stellung gegenüber der aristotelische Syllogistik und dem modernen Aussagekalkül," Hermes, 85 (1957), 147-58; Mario Mignucci, Il significato della logica stoica, 2a ed. (Bologna, 1967); Jan Mueller, "An Introduction to Stoic Logic," in The Stoics, ed. Rist, pp. 1-26.
(138) SVF, 2, 182, 207-08, 213, 215, 241-42, 245.
(139) For the parallels in physics see SVF, 2, 13, 114, 395-97. Good analyses of this point can be found in Jacques Brunschwig, "Le modèle conjonctif," Les Stoiciens et leur logique, Actes du Colloque de Chantilly, 18-22 septembre 1976 (Paris, 1978), pp. 61-65; Edelstein, Meaning of Stoicism, pp. 27-29; Michael Frede, "Stoic vs. Aristotelian Syllogistic," Archiv für Geschichte der Philosophie, 56 (1974), 1-32; Goldschmidt, Le système stoïcien, pp. 82-83; Gould, "Chrysippus," Phronesis, 12 (1967), 152-61; Chrysippus, pp. 66-88; A. A. Long, "Dialectic and the Stoic Sage," in The Stoics, ed. Rist, pp. 101-24; Virieux-Reymond, "Le 'sunemménon' stoicien," Studia Philosophica, 9 (1949), 162-69. William H. Hay, "Stoic Use of Logic," Archiv für Geschichte der Philosophie, 51 (1969), 145-57 argues unconvincingly that the Stoic syllogisms also reflect an interest in abstract subjects and universal conclusions.
(140) SVF, 2, 368-75. On the other hand, Andreas Graeser, "The Stoic Categories," Les stoiciens et leur logique, pp. 199-221; "The Stoic Theory of Meaning," in The Stoics, ed. Rist, p. 78 sees the categories as linguistic expressions signifying syntactical classifications.
(141) SVF, I, 91.
From: Marcia L. Colish - The Stoic tradition from Antiquity to the early Middle Ages. I. Stoicism in Classical Latin literature - Leiden, Brill 1985, pp. 53-55
THE LEKTON AS WHAT IS SAID OR PREDICATED OF SOMETHING
"4.1.1 According to SVF 1, 89, Zeno of Citium, the founder of the Stoic school, made a distinction between a cause, which is a body or soma, and that of which it is the cause, which is called symbebekos, consequence, or kategorerna, predicate. Stobaeus, who gives this information, cites as examples of causes or bodies practical wisdom (phronesis), the principle of life (psyche), and self-control (sophrosyne); and as examples of what is caused by these bodies being wise (phronein), living (zen), and being temperate (sophronein). For the Stoics a body or soma is everything that acts or undergoes action (SVF II, 336, 340). What is done or undergone by such agents or patients, the action or passion, is a kategorema, which in contrast with the somatic agents or patients is characterized as asomatic (asomaton) Sextus M IX, 211) gives the following examples. The lancet and the flesh are bodies; the lancet is the cause of an asomatic kategorema, namely being cut, with respect to the flesh. Fire and wood are bodies; the fire is the cause of an asomatic kategorema, namely being burnt, with respect to the wood. Further examples can be found in SVF II, 349, where it is also added that the flesh is the cause of the cutting with respect to the lancet.
The verbal character of that which is caused was stressed by the Stoics against those who maintained that it could be indicated by nominal expressions (SE, PH III, 14). If the sun or the sun's heat makes the wax melt, we have to say that the sun is the cause, not of the melting of the wax (tes chyseos), but of the wax being melted, of a kategorema which is indicated by an infinitive (tou cheisthai). Clement of Alexandria (SVF III, 8, p. 263) even makes an explicit distinction, in a somewhat similar context, between 'is cut' (temnetai), which is the actual kategorema, and the infinitive 'to be cut', which is the name (ptiptosis) of the katkategorema." pp. 45-46
(...)
"The strongest proof that the term lekton was used to designate that which is said or predicated of something, as a synonym of kategorema and in the typical frame of the Stoic theory of predication, is the fact that it is so often qualified by the attribute asomaton. In many contexts one can make sense of this characterization only by taking lek ton as standing for the action or passion, the pragma which is signified by the verb, in contrast with the somata which perform or undergo the action. It is therefore time to try to throw more light upon the ontological and psychological aspects of that which the Stoics called asomaton.
4.1.5. As for the ontological aspects, I shall confine myself to a rough outline; for details and controversial points I refer to Bréhier (1962), Goldschmidt (1969), Hadot (1968 and 1969), and Rist (1969). At the top of the Stoics' ontological hierarchy we find the ti. These somethings are divided into the on and the me on, the sphere of the existent and the sphere of the non-existent. To the on belong the somata, the things that can perform or undergo actions. In terms of the Stoic categories a soma is composed of hyle, matter, and poiotes, determining quality. To the me on belong the void, place, time, and the lekta. These four asomata do not have an independent existence of their own; they are only thought and said. A lekton, as we have seen, belongs to a soma (hyparchein) when the soma actually performs or undergoes the action concerned, but in itself it does not have the same kind of existence as a soma has. What is predicated of a soma is an event that occurs at the periphery of the domain in which bodies act and are acted upon; the actuality of the event entirely derives from the body by which it is caused. In terms of the Stoic categories the lekton has to be associated with the pos echon, the ways of behaving of a body, and the pros ti pa's echon, its ways of behaving in relation to something else.
4.1.6. Turning now to the psychological side of the aromatic lekton, I first call attention to a passage (DL VII, 51) in which two divisions of presentations (phantasiai) are mentioned. One is into those of living beings possessed of reason and speech (logikai) and those of living beings that are deprived of these faculties (alogoi). The presentations of the first group are also called noeseis, in a broad sense of that word (Cf. SVF II, 89). The second division divides presentations into those of sense-perception (aisthetikai) and those of thought in the narrower sense (dia tes dianoias). To the latter group belong the presentations of asomata and of the other things that are apprehended only by means of the logos. Parallel to this second division into presentations of sense-perception and presentations of thought we often find a distinction between periptosis and metabasis: between direct acquaintance by means of the senses (for instance, with something white or black, sweet or bitter) and the formation of ideas, which consists in a kind of transition from sense-perception to something else. The metabasis is characteristic of man (SE, AM VIII, 276, 288; Epictetus, Dissertationes I, 6, 10). This creative power of the human mind amounts, however, to no more than the faculty of compounding, transposing, augmenting, or diminishing the materials afforded us by the senses; it is impossible to find in thought anything which one does not possess as known by experience (SE, AM VIII, 58, 60). Sextus gives the following examples of metabasis (AM I, 25, III, 40, VIII, 59, IX, 393, XI, 250). Because of a likeness of Socrates, which has been seen, we conceive of Socrates, who has not been seen. Starting from the common man we move on to a conception of a giant. By decreasing the size of the common man we grasp a conception of a pygmy. By way of composition we derive from man and horse the conception of a thing we have never perceived, a centaur. DL VII, 52-53, gives a more extensivie list of possibilities. The queer thing is that he contrasts periptosis not with metabasis generally, but with such species of metabasis (in Sextus's sense) as resemblance, analogy, transposition, composition, and opposition. Metabasis occurs as one of the species: some ideas are formed by transition, for instance lekta and place, both asomata. This may be just a mistake; or the word metabasis may have been used by some in a generic sense and by others in a more special sense, without much further difference of meaning.
Now the lekton was defined as that which exists kata logiken phantasian, by way of a presentation which is typical of a living being possessed of reason and speech (DL VII, 63; SE, AM VIII, 70). Sextus adds that a logike phantasia is a presentation in which it is possible to set the thing presented before the mind by means of speech (logos). This can be connected with what DL,
VII, 49, says: first comes the presentation and then follows thought (dianoia), which is capable of expressing things in speech (eklaletike) and expresses that which it undergoes by the influence of the presentation, by means of an utterance. From elsewhere (SVF II, 236) we know that the Stoics called the noemata by the name of ekphorika, things capable of being expressed in words.
The view that the thinking faculty is capable of forming, on the basis of the materials offered by sense-perception, new presentations which are arrived at by a process of metabasis and exist only in so far as they are thought and expressed in words, was illustrated by means of the following simile (SE, AM VII, 409). A trainer or drill-sergeant who is teaching a boy rhythm and how to make certain motions sometimes takes hold of the boy's hands and at other times stands at a distance and offers himself as a model for the boy's imitations, by making certain rhythmical motions. In the same way some of the objects presented produce the impression in the soul as it were by touching and contact with it (such as white and black and somata generally),
whereas others are not of this nature, since in their case the principal part of the soul has presentations which are not caused by them but are formed on the occasion of their occurrence (tou hegemonikou ep'autois phantasioumenou kai ouch hyp'auton), as is the case with asomatic lekta. Sextus cites this simile in connection with the question of how presentations of asomatic lekta are possible. Since an asomaton neither effects nor suffers anything, it cannot produce presentations in the soul. The Stoics apparently solved this problem by pointing out that just as the boy makes both movements which are caused by the trainer and spontaneous movements, so the soul has both presentations that are caused by somata and spontaneous presentations — for instance, of lekta. The lekta do not cause their presentations, but those presentations are produced by the soul itself, although this spontaneous production is limited to certain operations on the impressions of sense-perception.
That lekta are merely thought and that nothing directly corresponds to them in the world of existing somata is confirmed by SVF II, 521. The Stoics considered time and asomata generally as existing only in thought, without the reality of bodies which consists in causal activity. It looks as if this were contradicted by a passage in Plutarch (De communibus notitiis contra Stoicos 1084 c), where such activities as walking and dancing (ton peripaton, ten orchesin) are counted among the somata. This can be connected with what Seneca (Epistula 113, 23; SVF II, 836) tells us about a controversy between Cleanthes and Chrysippus concerning the nature of walking (ambulatio). Cleanthes contended that it is pneuma which has been sent down from the principal part of the soul into the feet; Chrysippus maintained that it is the principal part of the soul itself (a soma). To solve the apparent contradiction we probably have to distinguish between the Om as far as it is in a certain state or is disposed in a certain way (pos echon) and that state itself, considered on its own. If the action or passion is regarded as realized in a soma, it is, as it were, an aspect of that soma. This point of view was strongly emphasized by Chrysippus, here and elsewhere. But if the action or passion is contrasted with the soma, as that which is caused or undergone by it, it is seen to have a status of its own; from this point of view it is something asomatic and a mere product of thought.
4.1.7. It may be concluded, I think, that at least one of the ways in which the word lekton was used by Stoic philosophers was to designate that which is said or predicated of something. The lekton or kategorema is an asomatic pragma, an action or passion which is performed or undergone by a soma. From an ontological point of view the lekton-kategorema-pragma is totally
different from the soma. Somata are the real things which are characterized by their capacity of acting and being acted upon. The actions or passions themselves are merely thought and expressed in words; they are presentations which are spontaneously formed by a transition from sense-experience and made known by spoken sounds, without having a direct counterpart in somatic reality. Given this ontological and psychological peculiarity of the lekton, it is not unlikely that almost from the beginning the word lekton could also be taken as referring to that which is only (thought and) said. If the lekton as such does not really exist and is nothing but a spontaneous product of thought, it is quite natural to see it not only as that which is said of a soma, but also as that which is merely an expressed thought, only something said." pp. 51-55
From: Gabriel Nuchelmans - Theories of proposition. Ancient and medieval conceptions of the bearers of truth and falsity. Amsterdam: North-Holland 1973.
The Stoic Theory of Categories and Plotinus' Criticism
Last modified: Tuesday, March 09, 2010