History of logic
The history of logic deals with the origin and development of logic and all of its sub-disciplines.
Different traditions of logic have developed in different parts of the world. The European-Western logic has its beginning in ancient Greece and can be divided into two currents: the tradition of the Aristotelian - scholastic logic and that of the modern or mathematical logic from 1847. There are also the traditions of Indian and Tibetan, Chinese, Japanese and Arabic logic.
Ancient logic
precursor
The forerunners of ancient logic include the pre-Socratics (6th and 5th centuries BC), the Sophists (from the 5th century BC) and Plato (4th century BC). The sophists taught, mostly for a fee, for example how to make speeches in front of public assemblies or in court and how to persuade interlocutors or listeners. They also taught rhetoric , individual logical devices and sometimes how to use fallacies .
Plato did not leave a logical system and not even a logical script, but there are already numerous passages in his dialogues that deal with topics of logic and that had a strong influence on the founder of logic, his pupil Aristotle . Plato's preoccupation with the order and the laws of thought is probably to be seen as an answer to the arbitrary, often deliberately misleading conceptual and argumentation acrobatics of the sophists that he rejected. The most important logical discovery Plato was probably the term classification ( diaeresis ). This is a method that makes it possible to define a term you are looking for by subsuming lower terms under higher terms . In addition to the Dihairesis, the constant practice discussions of the teachers and students of the Platonic Academy influenced the further history of logic. The first logical writing of the young Aristotle, the Topik , is the formulation of a set of rules for correct argumentation.
Apart from the logical vocabulary that Plato uses for the Dihairesis method (for example definition , difference (for Aristotle, specific difference ), genus , species ), it is worth mentioning that a determination of the statement and the true or false statement can already be found. Plato distinguishes (in the Dialogue Sophistes 261c) a true combination of a noun and verb, “Theaetetus sits”, from a false one, “Theaetetus flies”.
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The Aristotelian conceptual logic
A first system of logic can be found in Aristotle (384–322 BC), who is not only considered the founder of logic, but was also of incomparable importance for the further history of logic and its development. His logical work Organon consists of six individual writings in which all essential parts of logic are dealt with: the “ concept ” ( categories ), the “ statement ” consisting of concepts ( De Interpretatione ) and the “ conclusion ” consisting of statements ( Analytica priora and Analytica posteriora ). The practice of reasoning is also dealt with ( topics and sophistic refutations ), except in the Organon, logical problems are also discussed in the fourth book of metaphysics .
Aristotelian logic is a logical system in which concepts are related to one another. It is therefore not a matter of propositional logic , but of a term or conceptual logic . In the immediate aftermath, Aristotle's logic was quickly forgotten, and Stoic propositional logic dominated until late antiquity. It was not until the Middle Ages that it began to dominate and decisively influence the development of logic.
Categories
In the Scripture Categories , the "words" are divided into ten kinds (the categories ). These ten parts of speech ( Socrates denotes a certain person, person is a general term, white is a property, etc.) differ in such a way that each part of speech can be combined with some of the other parts of speech to form a “sentence”. A sentence consists of at least two words (man walks; Socrates is a man). In contrast to words, sentences are either affirmative or negative. Every affirmation and every negation is either true or false, so sentences have a “ truth value ”. There are also four different types of things , of which one type can only ever function as the subject of a sentence, never as a predicate of a sentence (things that are certain individuals, such as "Socrates"). Others both as a subject and as a predicate of a sentence (e.g. "man" as a subject: "man is a living being" and as a predicate: "Socrates is a person" ").
De interpretations
The essential content of De Interpretatione is an analysis of the logical statement. In the context of this analysis, Aristotle refers to the affirmation (S = P) and the negation (S ≠ P) of the same terms as contradiction . The principle of contradiction (S cannot be P and at the same time not P) has since been considered a fundamental law of logic. What is known today as a quantifier is also introduced: the following quantifiers can be placed in front of general terms : “ every person is a sensory being”, “ no person is a turtle”, “ not every person is called Socrates” or “ some people are called Socrates”. Between the statements “every person is white” and “not every person is white” there is - exactly one of the two is correct - a contradictory contrast; between the statements “every person is white” and “no person is white” there is - both are wrong - a second type of opposition, the contrary opposition . A second logical law, the principle of the excluded third , also appears first in Aristotle. So one of the two contradictory opposite statements S = P and S ≠ P must be true. However, this law does not apply in the following case. Neither of the two contradictory statements "tomorrow this house will collapse" and "tomorrow this house will not collapse" can be described as true or false. For statements that say the future, one could - besides true and false - introduce a third truth value. Aristotle thus anticipated multi- valued logic . The verb is is already addressed in its twofold function by Aristotle: firstly, it is assigned to subjects in order to express their existence: “Socrates is ”, secondly it serves as a connection (today called copula ) between the subject and the predicate of a statement: “Socrates is a human". Further privations (non- human, unjust, odd) distinguished and different types of predicates: predicates as white and well come to the subject person to akzidentiell; Predicates such as bipedal and living beings , on the other hand, essentially belong to the human subject , they can be combined to a definition of the subject. With the introduction of today's so-called modal terms, Aristotle also established the modal logic . Modal terms refer to statements: possible (problematic statement: it is possible that SP is) and necessary (apodictic statement: it is necessary so that SP is).
The analytics
| Megarian logicians | Stoic logicians |
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Eubulides (4th century BC) |
Zenon v. Kition († 264 BC) |
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Diodoros Kronos (4th / 3rd century BC) |
Chrysippus (3rd century BC) |
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Philo v. Megara (4th / 3rd century BC) |
The two extensive analytics are the logical main work . Here Aristotle developed the “ syllogistics ”, his proof and inference, which forms a formal logical system in the modern sense. In a conclusion, a third statement (conclusion) is concluded from two statements (premises). These three statements are in turn composed of three terms (subject - predicate - middle term). An example: from the premises Socrates (subject) is a person (middle term) and all people (M) are living beings (predicate) the conclusion Socrates (S) is a living being (P). Aristotle distinguishes three types of inference (he calls them the three figures), which are now called deduction , induction and abduction .
The mega-stoic propositional logic
Apart from the Aristotelian conceptual logic, the two-valued propositional logic developed first in the Megarian , then in the influential Stoic school of philosophy (4th and 3rd centuries BC). First of all, it must be noted that a conceptual logic of these schools will have existed, but has been lost and, secondly, that Aristotle's pupil Theophrastus expanded the syllogistics to include propositional conclusions. At first only the stoic logic, which disseminated its logic in handbooks, was effective. In the Middle Ages it was almost completely displaced by the Aristotelian-scholastic logic, only to be rediscovered by Łukasiewicz in 1934 . Benson Mates and Michael Frede have written monographs on mega-stoic logic. The sources are bad, one is v. a. dependent on Sextus Empiricus , Diogenes Laertios and Galen .
| Authors | Writings on logic |
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| Cicero († 43 BC) | |
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Apuleius of Madaura († after 170) |
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Porphyrios († between 301 and 305) |
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Marius Victorinus († after 363) |
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| Pseudo-Augustine 4th century |
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Boethius († between 524 and 526) |
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The sections on logic in the encyclopedias of:
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| Various authors also wrote numerous commentaries on logical writings, for example Galen , Alexander von Aphrodisias , Porphyrios , Ammonios Hermeiou and Simplikios . | |
Eubulides was the first to formulate the liar's paradox , Philon the oldest truth table . The combination of statements comes from Philon through the words if and then , the so-called material implication (if A, then B; in words: When Stefan comes to the party, he takes Lukas with him). Other statements come from Chrysippus: the conjunction (A and B; in words: Stefan is coming and Luke is coming), the exclusive disjunction (either A or B; in words: either I will marry you or I will marry Judith). For the Stoics, the inclusive alternative (at least A or B) has also been handed down. Diodoros Kronos, Philon and Chrysipp also made contributions to modal logic . The Stoics developed an axiomatization of their propositional logic.
Comments and collections of material
The Latin tradition of logic begins with Cicero (1st century BC) and his translations into Latin. In Apuleius also many Latin terms and the graphic scheme of go (2nd century) logical square back.
No significant logical texts have survived from the transition period from antiquity to the early Middle Ages, but the focus was on collections of material and commentaries on the logic of Plato, Aristotle and the Stoics. Mention should be made of Galen (2nd century), Alexander von Aphrodisias (2nd / 3rd century) and Porphyrios (3rd century) with his porphyry tree . An extensive work by Diogenes Laertios on the history of philosophy and thus also of logic has come down to us.
Boethius (5th / 6th century) was influential, not only translating older texts, but also dealing independently with logic. Also to be mentioned are Isidore (5th / 6th century) and Cassiodor (6th century).
middle Ages
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| Alcuin († 804) |
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Theodulf of Orléans († 821) |
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| Alcuin's pupil (8th / 9th century) |
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Johannes Scottus Eriugena (9th century) |
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New Year's Eve II († 1003) |
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Abbo of Fleury († 1004) |
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Notker III. († 1022) |
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| Anselm of Canterbury († 1109) |
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Gerlandus of Besançon (12th century) |
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Petrus Abelardus († 1142) |
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| Unknown author (12th century) |
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Robert Kilwardby († 1279) |
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Albertus Magnus († 1280) |
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Lambert of Auxerre (13th century) |
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Johannes Duns Scotus († 1308) |
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Raimundus Lullus († 1316) |
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William of Sherwood († between 1266 and 1272) |
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Petrus Hispanus (13th century) |
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Wilhelm von Ockham († 1347) |
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Johannes Buridan († shortly after 1358) |
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Walter Burley († after 1344) |
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Radulphus Strodus (14th century) |
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Albert of Saxony (14th century) |
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Paulus Venetus († 1429) |
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Petrus Tartaretus († around 1522) |
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Stephanus de Monte (15th century) |
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Vincent Ferrer († 1419) |
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Petrus Ramus († 1572) |
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| Various authors also wrote numerous textbooks as well as commentaries and glossaries on logical scripts. | |
The Middle Ages are also an important epoch in the history of logic. It was strongly influenced by the - u. a. known through the mediation of Arabic logic - the logic of Aristotle. In medieval university life, logic had its place as one of the septem artes liberales in the so-called “ artist faculty ” ( facultas artium ). Studying artes was a requirement for studying at all other faculties. In the early Middle Ages (about before 1100), the focus was initially on the encyclopedic works of late antiquity (by Cassiodor , Isidor , Martianus Capella ). Since the 12th century, the subject matter of logic then comprised three separate text corpora:
- logica vetus : The collection of ancient works on logic that the medieval logicians used up to around 1150 is referred to as “old logic”. The corpus of the logica vetus included at least the Latin translations of the three following writings: the Isagoge of Porphyrios and the Categories and De Interpretations of Aristotle. In the course of the 11th century, three works by Boethius were added: On the categorical syllogism , On hypothetical syllogisms, and On topical differences . De diffinitione by Marius Victorinus and Topika by Cicero also belonged rather loosely to the corpus of logica vetus .
- logica nova : The "new logic" was also based on the now available Aristotelian writings Analytica priora , Analytica posteriora , the topic of the sophistic refutations .
- logica moderna : In the course of medieval logic there were also original medieval logics. In these own creations apart from the ancient models, a whole series of new problems from the areas of logic and semantics was developed and discussed in independent treatises.
Some of the specific medieval logical themes:
- The distinction between syncategorematic and categorematic expressions: suction. Syncategorematic expressions ( each ) mean nothing on their own, but can be added to categorematic expressions ( human ) and thus perform their function ( each human ). The categorical expressions are usually the nouns and verbs.
- Neither ancient nor modern logic is familiar with the theory of supposition : termini (general terms like living beings ) can be used in different ways in sentences. Some types of supposition:
- suppositio materialis: In Mensch has 6 letters , Mensch stands for the word human .
- Suppositio personalis: In The ball was shot into the goal , ball stands for a certain ball, for a single thing.
- suppositio simplex: In the tree is a plant , tree stands for the term tree , which falls under other terms such as plant .
Medieval logic was essentially based on theological scholastic philosophy. One can therefore speak of a “scholastic logic” which incidentally - like scholasticism itself - continues in modern times.
Modern times
As a result of the invention of the printing press, the first logic books appeared in the 16th century that were not written in Latin. The first logic book in German known today dates from 1534, the first in Italian from 1547, the first in English from 1551 and the first in French from 1555. At universities in Europe, however, Latin continued to dominate until around 1700, although there were no native Latin speakers gave.
The "traditional logic"
In the 17th century a kind of formal logic developed that is still common today and known as “traditional logic”. The influential Handbook Logic by Port-Royal and the Logica Hamburgensis can be named as representative of the early writings of this trend . In this early classical logic, a ( non-formal logical ) strand developed, which reached its climax with Kant : One began to ask how the knowing subject comes to terms , statements and conclusions at all - that is, about the epistemological prerequisites and implications of logic .
The early modern era and non-formal logics
In general, a certain disinterest in formal logic can be diagnosed for earlier modern philosophy (in Descartes , Spinoza , Locke , Hume , Kant , Hegel , etc.). It was limited to passing on textbook knowledge; And so it is not surprising that important philosophers such as Kant and Hegel used the term “logic” in a way that is misleading today for the deliberately non-formal parts of their systems - transcendental (Kant) and dialectical logic (Hegel). Despite opinions to the contrary, Kant had nothing to object to formal (he says “general”) logic; with his transcendental logic he merely goes beyond this. The traditional - and also taught by - formal logic of his time was also incorporated in many places in his Critique of Pure Reason .
Leibniz
Gottfried Wilhelm Leibniz made important achievements in the field of formal logic in the early modern period . Although he had successors (including Jakob I Bernoulli , Gottfried Ploucquet , Johann Heinrich Lambert , Bernard Bolzano ), since most of his logical writings were published long after his death, he initially had little influence on the history of logic. Mention should be made of v. a. his early attempt to advance logic by means of a specially constructed logical language in which variables are used instead of real terms and statements.
The heyday of classical logic
It was not until the middle of the nineteenth century that formal logic began to attract broader attention again, initially primarily in England. Pointing the way here is George Boole with the shorter treatise "The Mathematical Analysis of Logic" ( 1847 ) and his later major work "Laws of Thought" ( 1854 ). Boole's idea is to see logic as a mathematical calculus that is limited to the values 1 and 0 (true and false). Algebraic operations such as addition, multiplication, etc. can be carried out on class symbols . In this way, Boole develops a complete system of single-digit predicate logic that contains syllogistics as a subsystem. At the same time as Boole, Augustus De Morgan published his work "Formal Logic" in 1847. De Morgan is interested in this among others. a. for a generalization of the syllogistics to statements of the form "Most A are B". Another logician in England is John Venn , who published his book "Symbolic Logic" with the famous Venn diagrams in 1881 . Charles Sanders Peirce in America and Ernst Schröder in Germany are also involved in logical research .
The real breakthrough to modern logic, however, comes from Gottlob Frege , who must be regarded as the most important logician alongside Aristotle. In his conceptual writing ( 1879 ) he presented a full second-order predicate logic for the first time . In addition, he developed the idea of a formal language and, based on this, the idea of formal proof , in which, according to Frege, nothing is "left to the guesswork". It is precisely these ideas that form an essential theoretical basis for the development of modern computer technology and information technology . At first, however, Frege's work was hardly noticed by his contemporaries; this may u. a. due to its very difficult to read logical notation . In the two volumes of the “Basic Laws of Arithmetic” published in 1893 and 1903 , Frege tries to axiomatize all mathematics in a kind of set theory . However, this system contains a contradiction (the so-called Russell's antinomy ), as Frege in a famous letter from Bertrand Russell from the year 1902 must be experienced.
Russell himself reserves the right to present, together with Alfred North Whitehead, in the Principia Mathematica ( 1910 ) the first consistent set-theoretical foundation of mathematics. The authors pay tribute to Frege in the preface, they owe him most of the "logical-analytical questions". In contrast to Frege's work, the Principia Mathematica became a resounding success. One reason for this can u. a. in the notation used by Russell / Whitehead, which is still widely used today. Giuseppe Peano , another important logician of the late 19th century , who Russell met at a congress in 1900 , provided the impetus for this notation . In addition to his thoughts on logical notation, Peano is best known for his axiomatization of number theory (the so-called Peano axioms ).
Modern
| Authors | Writings on logic |
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| Jesuits from the University of Coimbra | lat .: Commentarii Conimbricensis in Dialecticam Aristotelis , 1606 |
| Joachim Jungius | Logica Hamburgensis , 1638 |
| Antoine Arnauld and Pierre Nicole | Logic by Port-Royal , 1662 ( French , English ) |
| Gottfried Wilhelm Leibniz | posthumously published manuscripts from 1679 |
| Georg Wilhelm Friedrich Hegel | Science of Logic , 1832 |
| George Boole | The Mathematical Analysis of Logic , 1847; Laws of Thought , 1854 |
| Augustus De Morgan | Formal Logic , 1847 |
| Thank God Frege | Conceptual writing , 1879 |
| Giuseppe Peano | Calcolo geometrico , 1888 |
| Charles Sanders Peirce | numerous articles from 1867 |
| Ernst Schröder | The Operating Circle of the Logic Calculus , 1877; Lectures on the algebra of logic , 1890–1895 |
| David Hilbert | Fundamentals of Geometry , 1903 |
| Bertrand Russell and Alfred North Whitehead | Principia Mathematica , 1910-1913 |
| Alfred Tarski | The Concept of Truth in Formalized Languages , 1936 |
| Rudolf Carnap | Logical Syntax of Language , 1934 |
| Kurt Gödel | On formally undecidable theorems of Principia Mathematica and related systems I , 1931 |
The propositional fragment of the “Principia Mathematica” serves as the starting point for the development of a whole series of metalogical terms. In his post-doctoral thesis from 1918, Paul Bernays (based on the work of David Hilbert ) shows consistency , syntactic and semantic completeness and decidability and examines the independence of the axioms (whereby he finds that one of the axioms is actually dependent, i.e. superfluous).
In addition to the axiomatic method of the “Principia”, other types of calculus are developed. 1934 presents Gerhard Gentzen his system of natural deduction and the sequent calculus . Building on this, Evert Willem Beth developed the tableau calculus in 1959 . Again, Paul Lorenzen orients himself to this in his dialogical logic .
Modern logic also brings with it the development of semantics of predicate logic . An important preparatory work for this is the famous Löwenheim-Skolem theorem (first proven by Leopold Löwenheim in 1915 , a more general result is shown by Albert Thoralf Skolem in 1920 ). In 1929 Kurt Gödel proves the completeness of the first-order predicate logic ( Gödel's completeness theorem ), in 1930 the incompleteness of the Peano arithmetic ( Gödel's incompleteness theorem ). In 1933 , Alfred Tarski formulated a truth theory for predicate logic.
Other important events in the history of modern logic are the development of intuitionistic logic , modal logic , the lambda calculus , type theory and level logic (higher level logic). An important trend in modern logic is also the development of theorem provers (see also Artificial Intelligence ) and the application of logic in computer science through formal methods .
Logic in non-European philosophies
Contrary to very widespread views, there are also traditions of logical thinking outside of Western philosophy that are based on the same basic laws and basic ideas (theorem of contradiction, theorem of excluded third, logic as the doctrine of valid inference, etc.) and are very independent of the European tradition have reached a high level.
India and Tibet
After some up to the 7th century BC The Nyaya Sutra, which was finally available in the 2nd century AD, and its commentaries form the actual beginning of Indian logic. Between 500 and 1300 the logic was cultivated especially by monks of Mahayana Buddhism , who developed their own scholasticism. The most important logicians are Vasubandhu (4th century), Dignaga (approx. 480-540 AD) and Dharmakirti (7th century AD), and the modern period (from 900 AD) dominated Gangeśa (13th century AD) and the Navya-Nyaya (New Nyaya, the "new logical school").
China
The Chinese tradition of logic begins in the 5th century BC. With Mozi , who founded the mohistic logic. Of the ancient Chinese philosophical schools of the Nine Streams, the school of names that emerged from Mohism , such as the philosopher Hui Shi , dealt with logical questions. After Buddhism penetrated China, writings by Dignaga were also translated into Chinese by Xuanzang and his colleagues in the 7th century AD . Overall, however, the logic in Chinese philosophy has not developed as far as in Europe, India and Japan, despite the suggestions from India.
Japan
The Japanese reception of Buddhism via Chinese and Indian sources developed in the 8th century AD, especially in Buddhist scholasticism (especially in the Sanron-shū ), a highly differentiated tradition of reflection that even exceeded the quality of the Indian standards Logic.
Arabic speaking area
Logic in the Arabic-speaking world has its classic phase in the Middle Ages. It was heavily influenced by Aristotelian logic and, in turn, had an impact on medieval European logic. During the heyday of Islam , al-Kindī (approx. 800–873), Latinized Alkindus, initially based his philosophy on mathematics . Al-Kindī had numerous works by Aristotle and other Greek philosophers translated by collaborators, some of whom were of Greek-Christian origin. He is considered the first great philosopher and logician of Islam and was one of the founders of a mathematical way of thinking in philosophy. Other main representatives were Abu Nasr al-Farabi (approx. 870–950), Avicenna (980–1037) and Averroes (1126–1198).
See also
literature
Overall representations:
- Joseph M. Bocheński : Formal Logic. 2nd, expanded edition. Karl Alber, Freiburg / Munich 1956, 1962 (the later new editions are unchanged).
- Dov M. Gabbay, John Woods (Eds.): The Handbook of the History of Logic . Elsevier, Amsterdam 2004 ff. (11 volumes planned)
- William Kneale , Martha Kneale : The Development of Logic. Clarendon Press, 1962, 2nd edition 1964, ISBN 0-19-824773-7 .
- Jan Łukasiewicz : On the history of propositional logic. In: Knowledge 5, 1935, pp. 111–131 (reprinted in: David Pearce, Jan Wolenski (Ed.): Logical Rationalism . Philosophical Writings of the Lemberg-Warschauer Schule , Frankfurt / Main 1988, pp. 76–91)
- Albert Menne : On logic and its history. In: Philosophia naturalis. Volume 22, 1985, pp. 460-468 (basic explanations on the relationship between logic and logic history).
- Carl Prantl : History of Logic in the Occident. 4 volumes, Munich 1855–1870, reprint: Akademie-Verlag, Berlin 1955 (the first fundamental work on the history of logic, but today it is rated very negatively by all schools of logic)
- Wilhelm Risse, Kuno Lorenz, Ignacio Angelelli, Andrés R. Raggio u. a .: logic. In: Joachim Ritter , Karlfried founder , Gottfried Gabriel (Hrsg.): Historical dictionary of philosophy . Volume 5, Schwabe, Basel 1980, Sp. 357-383. [The Historical Dictionary of Philosophy is a completely revised edition of the 'Dictionary of Philosophical Terms' by Rudolf Eisler in 13 volumes, Schwabe, Basel 1971–2007.]
- Heinrich Scholz : History of Logic. Junker and Dünnhaupt, Berlin 1931 (1959 under “Outline of the History of Logic”, Alber, Freiburg im Breisgau 1959).
- Werner Stelnzer: Logic. In: Hans Jörg Sandkühler (Ed.): Encyclopedia Philosophy. Volume 2, Meiner, Hamburg 2010, pp. 1430–1447, here: 1430–1436
- Friedrich Ueberweg : System of logic and history of logical teachings. 5th edition. Bonn 1882 ( English ).
Antiquity and late antiquity:
- Ernst Kapp : The origin of logic among the Greeks. Vandenhoeck & Ruprecht, Göttingen 1965, 1994, ISBN 3-525-33228-9 .
- Klaus Oehler : The historical place where formal logic emerged. In: Ancient Philosophy and Byzantine Middle Ages. Essays on the history of Greek thought. CH Beck, Munich 1969.
- Benson Mates : Stoic Logic. University of California, Berkeley 1953, ISBN 0-608-11119-8 .
- Lambertus Marie de Rijk: Logica modernorum. a contribution to the history of early terminist logic. 2 volumes, Van Gorcum, Assen 1962–1967. (Wijsgerige teksten en studies 6)
- Klaus Döring : The mega-riders. Annotated collection of the Testimonies Grüner, Amsterdam 1971 (studies on ancient philosophy 2).
- Theodor Ebert : Dialecticians and early Stoics with Sextus Empiricus. Investigations into the emergence of propositional logic. Vandenhoeck & Ruprecht, Göttingen 1991.
- Michael Frede : The stoic logic. Vandenhoeck & Ruprecht 1974.
Middle Ages:
- Earline J. Ashworth: The Tradition of Medieval Logic and Speculative Grammar from Anselm to the End of the 17th Century. A Bibliography from 1836 Onwards. Pontifical Institute of Medieval Studies, Toronto 1978.
- Philotheus Boehner: Medieval Logic. An Outline of its Development from 1250 - c. 1400 . University of Manchester Press, Manchester 1952.
- Alexander Broadie : Introduction to Medieval Logic. 2nd Edition. Clarendon, Oxford 1993.
- Heinz W. Enders: Linguistic treatises of the Middle Ages and the concept of semantics: a historical-systematic contribution to the question of the semantic foundation of formal systems. Schöningh, Munich 1975, ISBN 3-506-79420-5 (publications of the Grabmann Institute for Research into Medieval Theology and Philosophy, NF 20) (Munich University Writings: Department of Catholic Theology)
- Desmond Paul Henry: Medieval Logic and Metaphysics. A Modern Introduction. Hutchinson, London 1972.
- Gyula Klima: Ars Artium. Essays in Philosophical Semantics, Medieval and Modern. Institute of Philosophy of the Hungarian Academy of Sciences, Budapest 1988.
- Norman Kretzmann , Eleonore Stump (Eds.): The Cambridge Translations of Medieval Philosophical Texts. Vol. 1: Logic and the Philosophy of Language. Cambridge University Press, Cambridge 1988.
- Norman Kretzmann (Ed.): Meaning and Inference in Medieval Philosophy. Kluwer, Dordrecht 1989.
- Lorenzo Minio-Paluello: Twelfth Century Logic . Texts and Studies. Edizioni di Storia e Letteratura, Rome 1956–1958.
- Ernest A. Moody: Truth and Consequence in Mediaeval Logic. Studies in Logic and the Foundations of Mathematics. North Holland, Amsterdam 1953.
- Jan Pinborg: The Development of Language Theory in the Middle Ages . Münster 1985.
- Jan Pinborg: Logic and Semantics in the Middle Ages . An overview. Stuttgart / Bad Cannstatt 1972. (Problemata 10)
Modern times:
- Wilhelm Risse : The logic of the modern age. 2 vols., Frommann, Stuttgart / Bad Cannstatt 1964, 1970.
- PH Nidditch: The Development of Mathematical Logic. New York 1962.
Non-western logic:
- Dov M. Gabbay, John Woods (Eds.): Handbook of the History of Logic. Vol. 1. Greek, Indian and Arabic Logic. Elsevier, Amsterdam 2004, ISBN 0-444-50466-4 .
- Christoph Harbsmeier: Science and civilization in China. Volume 7, Part 1: Language and Logic . Cambridge University Press, Cambridge u. a. 1998.
- Roy W. Perrett (Ed.): Indian Philosophy. Volume 2. Logic and Philosophy of Language. Garland, London / New York 2001.
- Nicholas Rescher: Studies in Arabic Philosophy. University of Pittsburgh Press, 1966.
- Nicholas Rescher: Studies in the History of Arabic Logic. University of Pittsburgh Press, 1963.
- Nicholas Rescher: The Development of Arabic Logic. University of Pittsburgh Press, 1964.
Web links
Overview presentations and bibliographies
- Thomas Case: Logic. In: Encyclopedia Britannica. 1911.
- Raul Corazzon: Ontology and History of Logic. An annotated bibliography.
Antiquity
- Susanne Bobzien : Ancient Logic. In: Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy .
- Norbert Froese: Logical basic principles, the syllogism and ancient philosophy of science . (PDF; 513 kB).
- Klaus Glashoff: Modern Interpretation of Ancient Logic .
middle Ages
- Henrik Lagerlund: Medieval Theories of the Syllogism. In: Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy .
- Catarina Dutilh Novaes: 14th Century Logic after Ockham . (PDF; 452 kB)
- Terence Parsons: Formulating Medieval Logic. ( April 11, 2011 memento on the Internet Archive ) University of California.
18.-20. century
- Volker Peckhaus: Leibniz's Influence on 19th Century Logic. In: Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy .
- Volker Peckhaus: Logic in the 19th Century .
- Johan van Benthem : Logic in Philosophy. (PDF; 139 kB) Draft, In: Dale Jacquette (Ed.): Handbook of the Philosophy of Logic. Elsevier, Amsterdam 2007, pp. 65-100.
- Richard Zach: History of Logic from 1900 to 1935 .
Non-western logics
- Marie-Hélène Gorisse: Bibliography of Indian Logic Literature. (PDF; 71 kB) Lille 2009.
- Tony Street: Arabic and Islamic Philosophy of Language and Logic. In: Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy .
Individual evidence
- ↑ The influence of Dihairesis on Aristotle confirms z. E.g .: Joseph M. Bochenski: Formal Logic , 5th edition, Karl Alber, Freiburg / Munich 1996, p. 46.
- ↑ Klaus Oehler: The historical site of the emergence of formal logic , p. 51.
- ↑ See z. B .: K. Lorenz and J. Mittelstrass: On the theory of true and false sentences in Plato. In: Archive for the History of Philosophy, Volume 48, Issue 1–3, pp. 113–152
- ↑ Klaus Oehler: The historical site of the emergence of formal logic , p. 61.
- ↑ The analytics are discussed in detail in the article Aristotle .
- ↑ Joseph M. Bochenski: Formal Logic , Karl Alber, Freiburg / Munich 1996 (5th edition), p. 122.
- Jump up to: John Marenbon: Logic before 1100: The Latin Tradition . In: Dov M. Gabbay, John Woods (Eds.): Handbook of the History of Logic . Volume 2: Mediaeval and Renaissance Logic , Elsevier, Amsterdam a. a. 2008, pp. 1-64.
- ↑ Susanne Bobzien : Die stoische Modallogik , Königshausen & Neumann, Würzburg 1986. ISBN 3-88479-284-9
- ^ Susanne Bobzien: Stoic Syllogistic , Oxford Studies in Ancient Philosophy, Oxford 1996, ISBN 978-0-19-823670-2 .
- Jump up to: John Marenbon: Logic before 1100: The Latin Tradition . In: Dov M. Gabbay, John Woods (Eds.): Handbook of the History of Logic . Volume 2: Mediaeval and Renaissance Logic , Elsevier, Amsterdam a. a. 2008, pp. 1-64.
- ^ Luce Giard: Du latin médiéval au pluriel des langues, le tournant de la Renaissance . In: Histoire Epistémologie Langage . No. 6, 1984, pp. 35-55, here: p. 48.
- ^ E. Jennifer Ashworth: Developments in the fifteenth and sixteenth centuries . In: Dov M. Gabbay, John Woods (Eds.): Handbook of the History of Logic . Volume 2: Mediaeval and Renaissance Logic , Elsevier, Amsterdam a. a. 2008, pp. 609-644, here: p. 609.
- ↑ Logique du Port Royal , also called Logique ou l'art de penser .
- ↑ On the criticism of the myth of "Eastern thinking" cf. Gregor Paul: The Bad Myth of an Eastern Logic. In: New Realities - Challenge of Philosophy. XVI. German Congress for Philosophy, 20.-24. September 1993. Section contributions I. Ed. Of the General Society for Philosophy in Germany, Berlin 1993, pp. 272–279.
- ↑ Overview presentations by Bocheński 1962 and Jonardo Ganeri: Indian Logic. In: Gabbay / Woods 2004, 66-145; further recent literature selected from Gorisse 2009.
- ↑ Uwe Frankenhauser: The Introduction of Buddhist Logic in China . Harrassowitz, Wiesbaden 1996. (= Opera sinologica; 1.) pp. 213-220.
- ^ Gregor Paul : On Buddhist logic and its history in Japan . OAG, Tokyo 1992. (= German Society for Nature and Ethnology of East Asia: OAG aktuell; 56.)
- ^ Avicenna's Treatise on Logic. Part one of 'Danesh-Name Alai' (A Concise Philosophical Encyclopaedia) and autobiography. ed. and over. from the Persian original by Farhang Zabeeh, 's-Gravenhage 1971.
- ↑ See the description of the allegations and defense of Prantl in Günther Jacoby : The claims of logisticians on logic and its history. A contribution to the discussion . Kohlhammer, Stuttgart 1962, pp. 139ff.