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Logic

LOGIC

LOGIC. Recent research on the seemingly staid subject of logic has revealed not only that certain topics in logic explained how inductive reasoning came about, but also that logic itself learned to create its own history in which logic arose from simple beginnings, but over time developed ever better ways of thinking, eventually becoming a progressive force in the history of thought. Furthermore, by the eighteenth century, the history of logic served as the structure for the history of philosophy, as well as an encyclopedia of knowledge known as historia literaria.

Although the importance of inductive reasoning to natural philosophy has been acknowledged, other research has shown that the tradition of inductive logic, which historians of the scientific revolution have identified as new, was actually developed by Aristotelian philosophers. The best known of these is the Paduan philosopher Jacobo Zabarella. His logic developed in part as a criticism of Florentine Neoplatonism and the medieval Scotist philosophy. This tradition of logic was taught not only in Italy but also in England, where logic texts by Zabarella have been found to have been used as school texts. Further, in Germany there remain today ninety-seven copies of Zabarella's Opera Logicae. This logic was then adopted by Bartholomew Keckerman for more elementary teaching and finally adopted again during the second half of the seventeenth century in Finland and Scandinavia after the Ramus vogue had run its course. Finally, at Jena, texts by Zabarella and the Coimbra commentators from Portugal were seen to be the beginning of a tradition of logic that led to the philosophy of John Locke (16321704) and Robert Boyle (16271691).

The best way to explain the difference between the Neoplatonic and Scotist approaches to knowledge and logic is to follow the debate around what is now considered a guiding logical and philosophical question between 1500 and 1750: What was the first thing thought? Was it the pure concept of an object or idea as defined by the Neoplatonists and some Scotists, that is, an idea conceived in the mind without recourse to the unreliable senses? Was it being, or ens, as Thomas Aquinas wrote? Or was it a fuzzy notion of a whole object or concept that needed to be examined, carefully defined and refined, and finally, when more was known about it, completely reexamined?

The great innovators of logic in the seventeenth centuryFrancis Bacon (15611626), Pierre Gassendi (15921655), Robert Boyle, and John Lockecontinued and transformed this anti-Platonic, anti-Scotist tradition. These anti-Platonic philosophers held that there were two types of knowledge, divine and human, each with its own method. Divine knowledge was accessed through inspiration; human knowledge, or artificial knowledge, had to be learned through the senses. The anti-Platonists often quoted Aristotle as saying, "There is nothing in the mind that is not in the senses."

Many philosophers did work on inductive reasoning, beginning with the sixteenth-century Aristotelians Benedito Pereira in Rome and Zabarella in Padua. Their work was drawn upon and transformed by Bacon, Boyle, and Locke in England, Gassendi and his followers in France, and members of a new German school of philosophy known as eclecticism. The eclectics, like their counterparts in England and France, were both anti-Platonic and anti-Cartesian. They gave their tradition a historical dimension, writing that since no human being could know everything, philosophers should examine the reasoning of past philosophers, criticize or accept the methods they had used to reach their conclusions, and finally judge the validity of the original concepts. Using improved logic, each philosopher would then add new information to explain his findings. Eclecticism also referred to a Neoplatonic philosophy that tried to unify all knowledge under one idea by such early church fathers as Clement of Alexandria. Although it had the same name, this was very different from German eclecticism.

How is it possible to classify Gassendi, Bacon, and Locke together? Here one can realize the pitfalls of assigning one name to logical schools. For example, Gassendi did write a treatise attacking scholastic logic, Adversus Aristoteleos as he called it. This treatise was really attacking the self-referential syllogistic reasoning of dialectic, and often criticizes the Scotist philosopher Eustachius St. Paul, teacher of Descartes, and quotes Benedito Pereira, the anti-Platonic and anti-Scotist Aristotelian at the Collegio Romano. Gassendi dismissed Eustachius as Scholastic or Aristotelian, while he was developing his own version of the anti-Platonic logic of the sixteenth century that he reworked with his own recreation of Epicurean logic.

A further discussion of logic can be reduced to five points: 1) the use of rhetoric as a tool of persuasion by logicians; 2) the transformation of logic by anti-Platonic Aristotelian philosophers and their development of the question, De primo cognito?, 'What was the first thing thought?'; 3) this orientation of logic leads to the very specific criticism of the Neoplatonic myth of the prisca philosophiae, the 'first philosophers'; 4) the development of a technical vocabulary for natural philosophy that was a direct result of inductive logic: as myth and metaphor were rejected for biblical commentary, so Platonic myth and metaphor was to be shunned for inductive reasoning; 5) the hermeneutic of language for logic, which was then applied to the writings of logicians in the past and provided a tool for judging past thought. Thus the history of philosophy was born, and its midwife was logic.

RHETORIC AND LOGICAL REASONING

The scholarship of Letizia Panizza and Heikki Micheli has made it quite clear that, as Micheli writes, "there is no justification for separating rhetoric from logic." The model of the correct logical proof changed dramatically when techniques of rhetoric were used. As Panizza explains, medieval philosophers "who learned their dialectic mainly from Boethius commentaries on Cicero and manuals of logic did not pay attention to Aristotle and Cicero on the close rapport of dialectic and rhetoric" (Cicero's De Oratore, a work only known after 1421). Panizza also explains that by the end of the fifteenth century, "Aristotle is held up as a model for an orator who wants to unite not only eloquence with philosophy in general, but rhetoric with dialectic."

She goes on to explain that logic was the instrument for philosophical thought, while rhetoric was the technique used to convince the reader. The philosophers adopted the persona of the orator, which was about the only technique used by Renaissance historians. By the time Zabarella (15321589) published De Methodis in 1578, rhetoric was being used to convince the reader of his method. Zabarella began each book of his treatises with a summary statement of method in which he declared his objectivity about his topic and his modesty towards knowledge, just as historians before him had done. After declaring his objectivity, he stated why his method of logic was superior to all others.

But the philosopher's use of the first person, in imitation of the speech of an orator, really developed in France with René Descartes's (15961650) Discourse on Method and Gassendi's persuasive voice in the Syntagma. In his work, Descartes declared the originality of his thoughts. He tended to assert the truth of his logical statements with rhetorically styled sincerity rather than engage in argument. Regius, a fellow philosopher, was so annoyed at the Cartesian use of persuasion rather than logic for proof that he wrote to Descartes, "any mad man can claim he is right." Descartes declared, "I think therefore I am." On the contrary, the first thing thought by Gassendi was not an a priori judgment; to him, thought had a history. He studied what past philosophers had thought, and he judged and critically examined the logic of the position. This led him to write a history of logic, the first comprehensive history up to that time.

ANTI-PLATONIC PHILOSOPHERS

Charles Schmitt wrote that Zabarella's logic set the stage for the logic used in the seventeenth century. Logic texts quoted Zabarella's attack on a priori reasoning and praised his logical method of setting out information not only in the seventeenth century but into the eighteenth. Johann Syrbius of Jena began his 1715 logic text with a critical history of the attack against a priori reasoning. He begins with a short historical discourse on the proposition that species originated in the mind, beginning with a quote from a commentary on Aristotle's De anima by the Portuguese Coimbra philosopher and Zabarella and ending by having linked the earlier traditions with the contemporary philosophy of John Locke and Robert Boyle. He also criticized Descartes, who believed that the species originated in the mind.

NEOPLATONISM

Not only was a priori reasoning rejected by specific philosophers, but the same anti-Platonic argument was used against the nonhistorical view that the prisci philosophiae or prisci sapientes could have known all of human knowledge without having learned it. For the Neoplatonists there was one truth that could be found in different forms in different religions around the world. This universal truth was proposed in the fifteenth century by Marsilio Ficino and was still of interest in the seventeenth to the Jesuit polymath Athanasius Kircher. Kircher's magnificently illustrated book of Noah's Ark, in which all of the knowledge known intuitively by early man is set out among the rooms, is a delightful visualization of universal knowledge.

There was an encyclopedia based on the other view. Zabarella said that as unlearned men, the prisci only knew what was in their nature. As the first thing thought was only hazily understood and had to be observed, identified, and then named, human civilization followed the same pattern. Initially humans knew nothing and had to understand the world through trial and error. A clever person appeared and made improvements, then others asked to become apprentices so that they could learn the logic of that person's way of working. Finally, all of this knowledge was written down. Adam, Moses, and Hermes Trimegistus are not part of this world: they all had only natural knowledge.

Just as there was not only one universal truth, there was not only one logical method for all disciplines. The greatest and most comprehensive history of disciplines was set out in 1708 in the Polyhistor by Georg Morhof (16391691). He articulated the difference between the disciplines as a logician articulates the difference between different sense impressions in inductive reasoning. Once the field of learning was identified, then the early and unclear beginnings of thought could be described and its history told as the history of the progress of the logic of that field of knowledge.

THE VOCABULARY OF NATURAL PHILOSOPHY

If logic could control the organization of knowledge, it also dictated correct vocabulary. Research has shown that this hermeneutics of language was used as a weapon against Platonic philosophers. Perhaps no one was criticized for his vocabulary more than Paracelsus (c. 14931541), the innovative medical philosopher who developed a vocabulary for spells to use in medicinal cures. Medical doctors like the Swiss Thomas Erastus (15241583) attacked the Paracelsian language of spells for its attempt to be universal. Erastus said that no word is universal, but is particular to the civilization in which it is found. Spells and magic tried to unite heaven and earth into a chain of being that did not exist, Erastus complained. He asserted that there was a separation between the realms.

If natural philosophy and medical science were to improve, logic had to be used. Logic must order sense perceptions in such a way that what is known is recorded and what is unknown discovered. To do this, a precise vocabulary had to be devised. There was such interest in identifying the correct type of vocabulary for inductive reasoning and identifying Platonic or Scotist definitions that at the turn of the seventeenth century Goclenius's Lexicon was published, which set out the different types of words for different types of logic.

APPLICATION OF LOGIC TO THE PHILOSOPHY OF THE PAST

Not long after Zabarella's attack on the logic of prisci sapientes, the various types of logic of the various philosophers came under scrutiny. Anthony Grafton pointed out that Isaac Casaubon discovered that the Neoplatonic texts by Hermes Trismegistus were third-century forgeries. This discovery paved the way for a reassessment of Egyptian civilization. When the logic of earlier philosophers was identified, examined, and judged, an important change occurred: the critical characterization of the logic of past philosophers, the identification of philosophers not chronologically but by the success of their logic, changed the way people viewed past philosophy.

Pierre Gassendi wrote the first history of logic. His little-known work De Logicae Origine et Varietate, published in 1648 as a preface to the Syntagma, took the reader on an intellectual trip from the logic of Adam to the logic of Descartes. Adam, wrote Gassendi, did not have logic when he argued with the snake: "He was merely quibbling." He also argued that none of the patriarchs in the Bible were capable of logic either. Logic began with the Greeks and Zeno. Gassendi then criticized Plato's logic because it depended on a priori thinking and "was too much like theology." Although he admitted there was much to admire in Aristotle's logic, Gassendi wrote that it had been spoiled by his followers.

Gassendi admired the logic of the ancient philosopher Epicurus, based on inductive reasoning. Gassendi constructed a believable Epicurean logic in this text that appeared in student logic texts until the mid-eighteenth century. Jean le Clerc, friend of both Robert Boyle and John Locke, wrote perhaps the most widely used of these logic texts. From Epicurus, Gassendi passed over the Middle Ages, cramming one thousand years into two paragraphs, then began in the early modern period with Francis Bacon and the establishment of inductive reasoning. Bacon, wrote Gassendi, went the "heroic way." Gassendi made Bacon as the hero of contemporary thought. There is a great deal of rhetoric in this history of logic.

Finally, the complete triumph of logic as the history of logic came with the work of the German historian of philosophy Jacob Brucker (16961770). At Jena, Brucker was a student of Johan Jacob Syrbius, who had linked contemporary English inductive reasoning with the earlier logic of the Coimbra commentaries and Zabarella's De Methodis. In 1723, Brucker wrote a history of logic called Historia Philosophia Doctrinae de Ideis. In this work he attacked the prisca philosophiae in the person of Zoroaster. Following Gassendi, whose history of logic he knew, Brucker judged each philosopher by whether he used inductive reasoning. He praised Epicurus among the ancient philosophers and dismissed Renaissance philosophers like Valla and Vives, while praising John Locke and Robert Boyle.

Although the early modern period saw many breaks with past tradition, it did not usher in a new logic all at once. Rather, it was a period in conversation with past philosophy: sometimes it agreed, sometimes it disagreed, and sometimes the philosopher transformed his sources beyond recognition. As the De primo cognito? question was reworked by the anti-Platonic philosophers, the concept of intellectual (as opposed to chronological) progress developed in the sixteenth and seventeenth centuries. Nowhere can the concept of progress be seen more clearly than in the history of logic.

See also Aristotelianism ; Bacon, Francis ; Boyle, Robert ; Cartesianism ; Descartes, René ; Gassendi, Pierre ; Locke, John ; Natural Philosophy ; Neoplatonism ; Philosophy .

BIBLIOGRAPHY

Primary Sources

Brucker, Jacob. Historia Philosophia Doctrinae de Ideis. Augsburg, 1723.

. "De Reformatione Philosophiae Rationalis Recentiori Aetate Tentata." In Historia Critica Philosophiae. 2nd ed. Leipzig, 1754. Reprint with English translations of Brucker's Praefatio and definitions of Eclecticism and Syncretism, edited by Constance Blackwell. Bristol. Forthcoming.

Gassendi, Pierre. "De Logicae Origine et Varietate." In Opera Omnia, vol. 1, pp. 3566. Leiden, 1658. Reprint, Stuttgart-Bad, 1994. The English translation, Pierre Gassendi's "Instutio Logica" (1658): A Critical Edition and Introduction by Howard Jones (Assen, 1981) does not include a translation of Gassendi's history of logic.

Syrbius, J. J. Institutiones Philosophiae Primae Novae et Eclecticae. Jena, 1720.

. Institutiones Philosophiae Rationalis Eclectica, in Praefatione Historia Logicae Succincte Delineatur. Jena, 1717.

Toletus, Francescus. Commentaria Una cum Questionibus in Octo Libros Aristotelis de Physica Auscultatione. First edition, Cologne, 1574; last edition, Venice, 1615. Reprint, Hildesheim, 1985.

. Commentaria Una cum Questionibus in Universam Aristotelis Logicam. First edition, Rome, 1572; last edition, Cologne 1615. Reprint, Hildesheim, 1985.

Zabarella, Jacobo. Opera Logica. Frankfurt, 1608 and 1966.

Secondary Sources

Blackwell, Constance. "Epicurus and Boyle, Le Clerc and Locke: Ideas and Their Redefinition in Jacob Brucker's Historia Philosophica Doctrinae de Ideis 1723." In Il vocabolario della République des Lettres: Terminologia filosofica e storia della filosofia, problemi di metodo, in memoriam di Paul Dibon, edited by Marta Fattori. Naples, 1997.

. "The Logic of the History of Philosophy: Morhof's 'De Variis Methodis' and the Polyhistor Philosophicus. " In Mapping the World of Learning: The Polyhistor of Daniel Georg Morhof, edited by Françoise Waquet, pp. 3550. Wiesbaden, 2000.

. "Vocabulary as a Critique of Knowledge: Zabarella and KeckermannErastus and Conring." In Philologie und Erkenntnis: Beiträge zu Begriff und Problem Frühneuzeitlicher "Philologie, " edited by Ralph Häfner. Tübingen, 2002.

Mikkeli, Heiki. An Aristotelian Response to Renaissance Humanism: Jacopo Zabarella on the Nature of the Arts and Sciences. Helsinki, 1992.

Panizza, Letizia. "Ermolao Barbaro e Pico della Mirandola tra retorica e dialettica." De genere dicendi philosophorum del 1484, Ermolao Barbaro (14541493) Congress, edited by Michela Marangoni. Venice, 1996.

Constance Blackwell

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Logic

LOGIC.

Logic is the study of correct reasoning. A host of philosophical themes have clustered around this central concern: the nature of truth and validity, of possibility and necessity; the semantics of words, sentences, and arguments; and even questions about substances and accidents, free will and determinism.

Aristotle

Aristotle (384322 b.c.e.) was the first person to formulate an explicit theory of correct reasoning, as he himself claimed in Sophistical Refutations. He owed a good deal to the exploration into forms of argument carried out in the course of argument contests, such as those illustrated by Plato in some of his Socratic dialogues. Book 8 of his own Topics reads like a handbook for contestants, and the Topics as a whole is designed to teach its readers how to construct "dialectical" arguments: arguments that, in keeping with the idea of a real contest, use generally accepted premises that will be granted by the interlocutor. In an argument, says Aristotle, "when certain things have been laid down, something other than what has been laid down necessarily results from them." This definition captures the idea of logical consequence, and in his Prior Analytics Aristotle develops his "syllogistic," a formal theory of logical consequence, which he applies to "demonstrations," arguments in which the premises must not be merely accepted, but true.

Syllogisms (in the narrow sense considered in the Prior Analytics ) consist of three assertoric sentences, two of them premises, from which the third, the conclusion, follows. In an assertoric sentence, something is "predicated" of a subject, and a predicate can stand in one of just five relations to a subject: it may be its definition, its genus ("Man is an animal"), its differentia (the element of the definition that differentiates things of one species from another: "Man is rational"), an accident (a characteristic the particular thing happens to have: "Socrates is curly-haired"), or its characteristic property (a feature that all and only things of the subject's species have, but is not part of its definition: "Man is able to laugh").

The two premises of a syllogism share a common ("middle") term, and they have "quantity" (universal/particular) and "quality" (affirmative/negative). They may be, then, universal affirmative (A-sentences: "Y belongs to every X"), universal negative (E-sentences: "Y belongs to no X"), particular affirmative (I-sentences: "Y belongs to some X"), or particular negative (O-sentences: "Y does not belong to some X"). Depending on the position of the middle termpredicate of both premises ("third figure"), subject of both premises ("second figure"), or subject of the first, predicate of the second ("first figure")from some combinations of two A, E, I, and O sentences as premises, there follows an A, E, I, or O sentence as a conclusionand this conclusion follows purely in virtue of the form of the argument. (Although ancient logicians rarely used false premises as their examples, they too made their conclusions follow logically.) So, for example, in the first figure, the patterns AAA, EAE, AII, and EIO are valid arguments. First-figure syllogisms were held by Aristotle to be self-evident: for example, Mortal belongs to every man (every man is mortal); man belongs to every philosopher; thus mortal belongs to every philosopher. Aristotle also shows how second-and third-figure syllogisms can be reduced to first-figure ones, using a set of conversion rules.

Aristotle's other logical works both fill in the discussions in the Topics and the Prior Analytics and introduce new philosophical dimensions. On Interpretation discusses assertoric statements and their relations (such as contradiction and contrariety). It also proposes a basic semantics, in which sentences are signs for thoughts, and thoughts for things, and it ventures into difficult questions of possibility and necessity. If it is true that there will be a sea battle tomorrow, then how can we avoid the unpalatable conclusion that it is a matter of necessity that the battle will take place tomorrow? The Posterior Analytics uses the theory of demonstration as a basis for a theory of scientific knowledge. The Sophistical Refutations explore fallacious but apparently valid arguments. The Categories has, in part, the aspect of a preface to the Topics, but it is in part a work of metaphysicsa forerunner of Aristotle's treatise of that name.

The Stoics

The Stoics developed a logic different from Aristotle's, and to a large extent independently from him. Their greatest logician, Chrysippus, lived from about 280 to 206 b.c.e. and, as with most of the Stoics, his thought has mostly to be reconstructed from reports and fragments in later writers. Whereas Aristotelian syllogistic is a term-logic, Stoic logic was propositional: it explored the relations between what they called "assertibles"that is to say, sentences that can be used to make assertions. Assertibles can be simple ("It is day") or complex ("If it is day, it is light"/ "It is day or it is not light"). The argument forms classified by the Stoics involve one complex and one simple assertible: for example, "If it is day, it is light. It is day. So, it is light." This is the first of five "indemonstrables"basic argument formsdistinguished by Chrysippus. The Stoics had a schematic way of representing the indemonstrableswhat they called their "modes"using ordinal numbers. The four remaining modes of the five indemonstrables are (2) If the first, then the second; not the second; so not the first; (3) Not both the first and the second; the first; so not the second; (4) Either the first or the second; the first; so not the second; (5) Either the first or the second; not the first; so the second. Since the assertibles could be either negative or positive, and the complex assertible could itself include complex assertibles ("If both the first and the second, then the third"), there was quite a wide range of indemonstrable argument schemes. But Stoic logic was not limited to them. Nonindemonstrable forms of argument could be valid, and the Stoics had a theory of "analysis" in which, using certain basic rules (themata ) and, if wanted, additional theorems, the nonindemonstrable arguments were shown to be made up of demonstrable ones or of conversions of them.

Stoic logicians also explored modal concepts. One of their main starting points was provided by the fourth-century b.c.e. Megaric logician Diodorus Cronus, who formulated a "Master Argument," the subject of many attempts at reconstruction by modern historians, which attempts to show that, from the premises that true past propositions are necessary, and that an impossibility never follows from what is possible, it follows that nothing is possible except what is or will be true. The Stoic logicians rejected the argument by querying one or other of its premises, and Chrysippus developed his own understanding of possibility and necessity.

The Neoplatonists

Although Aristotle's pupil and successor, Theophrastus (c. 372c. 287 b.c.e.), wrote extensively on logic, and Alexander of Aphrodisias (fl. c. 200 c.e.) cultivated Aristotelian logic, the most important enthusiasts of Aristotelian logic were, surprisingly, the Neoplatonists, from Porphyry (c. 234c. 305) onward. Porphyry wrote an introduction (Eisagoge) to the Categories, which itself became for later students a part of the Aristotelian logical corpus (known as the Organon ), and he wrote extensive commentaries on Aristotle's logical works. Despite his Platonic metaphysics, Porphyry believed that logic, which is concerned with the world of appearances that is the subject of normal discourse, should be studied in strictly Aristotelian terms. Although later Neoplatonic commentators, following the lead of Iamblichus, tended more to introduce their characteristic metaphysical ideas into discussions of logic, Porphyry's approach was transmitted to the medieval Latin West by Boethius (c. 480c. 524), who translated into Latin most of the Organon and wrote commentaries on some of it and logical textbooks on topical argument (the late ancient development of the Topics ), division, and on syllogisms.

The Medieval Latin West, 7901200

The study of logic was revived in the Latin West at the court of Charlemagne; his adviser, Alcuin, wrote the first medieval logical textbook (On Dialectic ) in about 790. Logic was central to the intellectual life of medieval Europe in a way that it had not been in antiquity, and has not been since the Renaissance. Yet, until the 1130s, medieval logicians made do with what became known as the logica vetus ("old logic"): just Porphyry's Eisagoge, Aristotle's Categories and On Interpretation, and Boethius's commentaries and textbooks. They had only the most limited access to the Stoic tradition, through mentions by Boethius and the On Interpretation of Apuleius (second century c.e.). Ninth-century authors, such as John Scotus Erigena, were interested especially in the Categories its metaphysical aspects and the question, raised by Augustine and by Boethius, of whether any of the ten categories distinguished by Aristotle apply to God. Anselm of Canterbury (1033 or 10341109) was a gifted logician who explored and questioned the Aristotelian doctrine of the Categories and made imaginative use of the ideas on possibility and necessity in On Interpretation.

In the twelfth century, the logica vetus was the central concern of the flourishing Paris schools. Peter Abelard (10791142), the greatest logician of the time, developed a nominalist metaphysics on its basis and elaborated a semantics to explain how sentences that use universal words (such as "Socrates is a man") are meaningful although there are no universal things, only particulars. Abelard also excelled in more purely logical matters. Starting from the hints and misunderstandings he found in Boethius, he rediscovered propositional logic and, in his Dialectica (c. 1116), he explored in great depth the truth conditions for conditional ("if then ") sentences. Abelard was thus able to pioneer the analysis of sentences that are of ambiguous interpretation in terms of propositional logic, an aspect of logic that became especially popular from the 1130s onward, when On Sophistical Refutations and then the rest of Aristotle's logic (the logica nova "new logic") became available. And he is one of the few logicians ever to have examined the logic of impersonal sentences, such as "It is good that he came today."

The Medieval Latin West, 12001500

From the middle of the twelfth century, logicians developed various branches of their subject, known as the logica modernorum ("contemporary logic"), that had not been treated specially, or at all, in antiquity. Peter of Spain's widely read Tractatus (often called Summulae logicales ) illustrates how parts of the logica modernorum had developed up until about the 1230s. There was a lull in interest and innovation in logic for nearly a century, but in the first half of the fourteenth century writers at Oxford, such as Walter Burley (d. 1344/45), William of Ockham (d. ?1349), Thomas Bradwardine (d. 1349), and William of Heytesbury (d. 1372/23), and, in Paris, John Buridan (d. after 1358) revived the branches of the logica modernorum and brought them to new levels of sophistication. The Logica magna (Great logic) of Paul of Venice (d. 1429) is a vast record of these achievements.

Some branches of the logica modernorum grew directly from the mid-twelfth-century interest in fallacies. For example, sophismata were a sort of disputation, involving a master and his pupils, built around sentences that either are apparently false but can be interpreted so as to make them true (e.g., "The whole Socrates is less than Socrates") or at least are open to different interpretations (e.g., "Every man is"). The ambiguities usually centered around the use of what were called "syncategorematic" wordswords other than ordinary nouns, adjectives, and verbs with their own referential content: for instance, "only," "except," "all," "begins," "ceases"and specialized treatises were devoted to studying these syncategoremata. Another type of disputation, "obligations," involved trying to force an opponent who has agreed to defend a particular statement into a self-contradiction, while following a very strict set of rules for what statements may be accepted or must be rejected. Liar paradoxes ("What I am now saying is false")"insolubles"formed another branch of study. In the theory of the "properties of terms" a highly elaborate theory was developed about the reference of words depending on their function within a sentence. Propositional logic was elaborated in treatises on what were called "consequences" (consequentiae ), although it remains questionable how far the approach was purely propositional.

Aristotle's texts and methods were not, however, forgotten in the later Middle Ages. Aristotelian syllogistic, studied earlier through Boethius's textbooks, could now be learned directly from the Prior Analytics. It was a basic tool for almost every medieval philosopher or theologian, and a set of mnemonics ("bArbArA," "cElArEnt," etc.) were devised to enable students to remember the valid patterns. On Interpretation continued to be central to discussions about possibility, necessity, and divine prescience, and the Posterior Analytics provided the criteria for organizing branches of knowledge as diverse as grammar and theology.

Medieval Islam

Logic was no less important for Islamic than for Christian philosophers and theologians. By the time of al-Farabi (c. 878950), the first important Islamic logician, the whole of Aristotle's logical Organon was available in Arabicfar more material, then, than in the Latin West at this period, especially since the Arabic logicians tended to follow the habit of late antiquity in regarding the Rhetoric and the Poetics as parts of the Organon and assigning to them their own characteristic modes of argument, to contrast with demonstrative argument as taught in the Analytics and dialectical argument in the Topics.

Al-Farabi, who worked in Baghdad, Damascus, and elsewhere, saw his task as a logician to represent Aristotle faithfully, although this task involved him in a number of interpretations that went beyond the letter of the text. He was also concerned to vindicate logic in face of the grammarians, who doubted the need for this additional discipline; earlier in the tenth century, there had been a famous debate between the grammarian Abu Sa'id as-Sirafi and the logician Abu Bisr Matta, in which Abu Sa'id seems to have had the upper hand.

The great Persian philosopher Avicenna (Ibn Sina; 9801037) respected al-Farabi and was also an ardent Aristotelian, but his approach to logic differed. In semantics, he rejected al-Farabi's theory that logic is concerned with expressions insofar as they signify meanings. Rather, he claimed, logic deals with meanings that classify meaningsso-called "second intentions." In his approach to syllogistic, Avicenna was far more inclined than al-Farabi had been to pursue his own train of analysis and accommodate Aristotle to it. For example, in modal logic he proposed a number of different readings of modal sentences: they could be taken absolutely (as in "God exists") or according to a conditionfor example, "while something exists as a substance" (as in "man is necessarily a rational body") or "while something is described in the way it is" (as in "all mobile things are changing").

Logic continued to be studied in Islam because it was accepted by theologians as useful to their discipline rather thanas they often thought with regard to other areas of Aristotelian philosophya dangerous rival to it. Particularly important was the endorsement of al-Ghazali (10581111): whereas he wrote a work specifically designed to attack other areas of Aristotelian philosophy, he was himself the author of two short logical works, based on Avicenna. In the next century, Averroës (Ibn Rushd), who worked in Muslim Spain, followed al-Farabi (and the general direction of all his own work as the commentator par excellence on Aristotle) in seeking a greater fidelity to Aristotle, but it was Avicenna who remained the dominant influence on later Islamic logic.

See also Aristotelianism ; Neoplatonism ; Philosophy ; Philosophy, History of ; Scholasticism ; Stoicism .

bibliography

PRIMARY SOURCES

Aristotle. The Complete Works of Aristotle. Edited by Jonathan Barnes. Vol. 1. Princeton, N.J.: Princeton University Press, 1984.

. Prior Analytics. Translated by Robin Smith. Indianapolis: Hackett, 1989.

Kretzmann, Norman, and Eleonore Stump, eds. Logic and the Philosophy of Language. Vol. 1 of The Cambridge Translations of Medieval Philosophical Texts. Cambridge, U.K.: Cambridge University Press, 1988.

Peter of Spain. Summulae logicales. Translated by Francis P. Dinneen. Amsterdam and Philadelphia: Benjamins, 1990.

SECONDARY SOURCES

Barnes, Jonathan, Suzanne Bobzien, Mario Mignucci, and Dink M. Schenkeveld. "Part 2: Logic and Language." In The Cambridge History of Hellenistic Philosophy, edited by Keimpe Algra et al. Cambridge, U.K.: Cambridge University Press, 1999. Excellent, up-to-date survey.

Kretzmann, Norman, Anthony Kenny, and Jan Pinborg, eds. Cambridge History of Later Medieval Philosophy. Cambridge, U.K.: Cambridge University Press, 1982. Pages 101381 contain the most complete available account of medieval logic in the Latin West.

Marenbon, John. Boethius. New York: Oxford University Press, 2003. See pages 1765. Includes bibliography for Greek Neoplatonic tradition. Martin, C. J. "Embarrassing Arguments and Surprising Conclusions in the Development of Theories of the Conditional in the Twelfth Century." In Gilbert de Poitiers et ses contemporains, edited by Jean Jolivet and Alain De Libera. Naples: Bibliopolis, 1987. Discusses Abelard and the twelfth-century rediscovery of propositional logic.

Smith, Robin. "Logic." In The Cambridge Companion to Aristotle, edited by Jonathan Barnes. Cambridge, U.K.: Cambridge University Press, 1995. Excellent bibliography on pp. 308324.

John Marenbon

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Logic

Logic

BIBLIOGRAPHY

Logic is the study of persuasive reasoning. As such, it concerns arguments that successfully convey credibility from a set of premises to a conclusion. Given this broad definition, there are many possible avenues of discourse and logicians have studied everything from formal inference patterns, to the logic of causation, possibility and necessity, obligation, and inference to the best explanation. Nonetheless, formal deductive and inductive logic are the most historically significant branches of logic, even for the social sciences.

The discipline of logic evolved as a prominent branch of philosophy from the time of Aristotle and marks the first time in history that anyone began to systematize the forms of good reasoning. This systematization was of great benefit to philosophers as they attempted to know the universe of knowledgecovering both nature and human relationson the basis of intuitive thought, rather than empirical analysis. As the sciences eventually pulled away from philosophy (first natural philosophy as it evolved into physics in about the seventeenth century, and then the social sciences arguably following in the eighteenth century, as they too learned that knowledge could be formulated on an empirical basis), it is only natural that they would develop their own methods of inquiry, separate from those of philosophers. Nonetheless, the special relationship of logic to the earliest forms of scientific analysis has survived to the twenty-first century, and has had great influence over the modes of inquiry in economics, history, sociology, anthropology, political science, and psychology, that make up the social sciences.

Logic is logic, whether it is applied to the social sciences, or any other field of inquiry. There is no special type of logic that is particularly suitable to the social sciences, just as there is not one for the natural sciences. The principles of valid reasoning are the same no matter what the subject, and are expressible in symbolic notation that is concerned only with the form, rather than the content, of what is uttered. To say if I have a dollar then I have some money is no different, logically, than to say, If one is president of the United States then one is an American citizen. The form of this type of if, then statement (P Q) is known as a conditional, and, along with not, or, and, and if and only if (-, V, &, ), it forms the backbone of logical syntax. The idea that it is then possible to devise more complex statements using these connectives, to formulate premises and then to draw a conclusion, is to present the form of a valid argument in deductive logic, which is one where the conclusion follows necessarily from the premises. As long as the relationship between the premises and conclusion is a deductive onewhich is to say that if the premises are true then the conclusion cannot help but be truethen the conclusion follows inevitably from the premises, and does not require any sort of empirical data to support it.

If it is raining then the streets will be wet.

It is raining.

Therefore, the streets will be wet.

This is, however, a long way from saying that such an argument is sound (that is, both valid and true) and it is here that the first limit of logic is reached in the social sciences, for as practitioners of an empirical discipline, social scientists are concerned to know whether an argument is sound (for instance whether its premises are true), and not just whether its form is valid. Therefore, we need to gather data in the world to assess this. No matter how powerful the principles of logic, in modern social scientific inquiry logic cannot provide the sole means for testing a theory, since logic is concerned not with truth, but with validity, yet the truth of a theory depends crucially on its conformity with actual experience. Pure logic can be done in an armchair, but science needs to go out into the world (if not for experiment, at least for observation).

In his or her search for causes, it is therefore incumbent upon social scientists to dig deeper into the subject, and find some way to assess whether a statement like if one uses the death penalty then crime will drop is true, and this is a tricky business, which deductive logic, at least, cannot adjudicate. However, there is another branch of logic that deals with inductive inferences that is much more conducive to empirical inquiry, and which some have felt represents the very type of reasoning that is used in science. In contrast to deductionwhich deals with moving from general statements to the particular conclusions that follow from themwith induction one moves from particular statements to a general conclusion, somewhat as if one is gathering data points to see if they form a pattern. This resembles, at least ideally, the form of reasoning that a social scientist uses when he or she is searching for a general regularity. For example, if one were to argue that:

Kennedys tax cut in 1961 stimulated the economy

Reagans tax cut in 1981 stimulated the economy

Bushs tax cut in 2003 stimulated the economy

Therefore, tax cuts always (usually, generally) stimulate the economy

one is engaging in a form of reasoning that is familiar to social scientists, who seek to make causal explanations and to formulate general theories based on historical evidence. The problem, however, is that this form of reasoning is not valid, as has famously been shown by the Scottish philosopher David Hume. Specifically, the above argument has a hidden assumption (common to all inductive arguments), which is to think that there is a relevant similarity between the future and the past. But this assumption does not always hold. Moreover, even if this assumption is borne out in some cases, it is important to recognize that there is a distinction to be made between causation and correlation in the social sciences, such that, no matter how solid ones evidence may be, it is always possible that even the strongest correlation may represent only an accidental connection. Try as one might to obtain the sort of certainty that the necessary connection of deductive logic has provided, the social sciences have found this an elusive goal. This represents no particular flaw in the social sciences, for the natural sciencesor indeed any fact-based disciplinewould also seem to suffer from this same difficulty.

Nonetheless, the social sciences have embraced the power of logic and have used it in various ways throughout their history to bolster their conclusions and to capitalize on the strengths of clear reasoning. The development of modern probability theory, and especially the invention of regression analysis in statistics, has been a very useful tool for social scientists to identify patterns in their data and to make sure that their hypotheses do not outrun them. The models of rationality that have been used throughout economics and political sciencein particular those of rational choice and game theoryreflect another important way that the power of logic has had an impact on research design and model building in modern social science. In psychology, too, where experiments are designed to assess rational cognitive function by using thinly disguised logic games, one sees the influence of logic in social inquiry. Such reliance on logical modes of behavioral analysis, however, has come at a cost, for the new trend of behavioral economics, and the more general movement toward more realistic and experimental models in the social sciences, have revealed limitations in some of the classic theories in social science. Assumptions about rational economic man, for instance, may work ideally in our theoretical models, but break down when faced with the irrationality and fractured logic of everyday human experience that constitutes the subject matter of the social sciences.

In another avenue, however, the principles of logic have been unquestionably useful in the social sciences, and that is in research design, the formulation of hypotheses, and the analysis and synthesis of data and theory in social inquiry. Taking a page from the scientific method that is allegedly used in the natural sciences, some methodologists have argued that, as empirical disciplines, the social sciences should follow the five-step method of observation, hypothesis formulation, prediction, experiment (or learning from experience), and assessment. Despite the storied literature in the philosophy of science, provided by philosophers of science Karl Popper and Thomas Kuhn, that has rightly caused philosophers and others to rethink this simplistic model of scientific method, there is a nugget of truth in it for any discipline that cares to be empirical, which is to be ruthless about the comparison of ones theory to the data. If a theory tells an individual to expect something, and one does not find it, then there is an inescapable problem for the theory. In a statement attributed to American physicist Richard Feynman, It doesnt matter how beautiful your theory is. If it doesnt agree with experiment, its wrong. This form of reasoning is directly related to the conditional in our earlier consideration of valid arguments, for it is trivially true that every conditional statement (if P, then Q) implies (indeed, is equivalent to) its contrapositive (if not Q, then not P). Thus, if ones social scientific theory states, If one is a thirteen-year-old boy then one has had an Oedipus Complex and one finds a thirteen-year-old boy who has not had an Oedipus Complex, then the original theory is wrong. If a theory has even one exception, then it is not universally true and must either be discarded, or modified in some way to deal with this anomaly. As Popper demonstrated, here the power of logical certainty may be appreciated, since the contrapositive relationship is one of deductive, not inductive, reasoning and therefore may be relied upon as rock solid in its epistemological status.

The role of logic in the social sciences is a mixed one. As in the natural sciences one realizes that, if it is to explain the world, any empirical theory must go beyond the homilies of deductive reasoning and venture forth into the world of experience, with the chance of being wrong as the price of expressing a truth that is not trivial. Still, as we have seen, the power and benefits of logic have not been without value to the social sciences.

SEE ALSO Game Theory; Hypothesis and Hypothesis Testing; Rational Choice Theory; Scientific Method; Theory

BIBLIOGRAPHY

Haack, Susan. 1978. Philosophy of Logics. Cambridge, U.K.: Cambridge University Press.

Kneale, William, and Martha Kneale. 1962. The Development of Logic. New York: Oxford University Press.

Kuhn, Thomas. 1962. The Structure of Scientific Revolutions. Chicago: University of Chicago Press.

Little, Daniel. 1990. Varieties of Social Explanation. Boulder, CO: Westview Press.

Martin, Michael, and Lee McIntyre, eds. 1994. Readings in the Philosophy of Social Science. Cambridge, MA: MIT Press.

Popper, Karl. 1965. Conjectures and Refutations: The Growth of Scientific Knowledge. New York: Harper Torchbooks.

Rosenberg, Alexander. 1988. The Philosophy of Social Science. Boulder, CO: Westview Press.

Lee C. McIntyre

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Logic

250. Logic

See also 21. ARGUMENTATION ; 262. MATHEMATICS ; 312. PHILOSOPHY ; 393. THINKING ; 402. TRUTH and ERROR .

a posteriori
the process of reasoning from effect to cause, based upon observation.
apriorism
1. the method of a priori reasoning, i.e., deductive reasoning, from cause to effect or from the general to the particular.
2. an a priori principle.
Barbara
a mnemonic word to represent a syllogistic argument in the first figure, in which there are two universal affirmative premises and a universal affirmative conclusion.
Barmalip, Bramantip
a mnemonic word to represent a syllogistic argument in the fourth figure, in which there are two universal affirmative premises and a particular affirmative conclusion.
Baroco
a mnemonic word to represent a syllogistic argument in the second figure, in which there is one universal affirmative and one particular negative premise and a particular negative conclusion.
Bocardo
a mnemonic word to represent a syllogistic argument in the third figure, in which there is one particular negative and one universal affirmative premise and a particular negative conclusion.
Camestres
a mnemonic word to represent a syllogistic argument in the second figure, in which there is one universal affirmative and one universal negative premise and a universal negative conclusion.
Celarent
a mnemonic word to represent a syllogistic argument in the first figure, in which there is one universal negative and one universal affirmative premise and a universal negative conclusion.
Cesare
a mnemonic word to represent a syllogistic argument in the second figure, in which there is one universal negative and one universal affirmative premise and a universal negative conclusion.
Darapti
a mnemonic word to represent a syllogistic argument in the third figure, in which there are two universal affirmative premises and a particular affirmative conclusion.
Darii
a mnemonic word to represent a syllogistic argument in the first figure, in which there is one universal affirmative and one particular affirmative premise and a particular affirmative conclusion.
Datisi
a mnemonic word to represent a syllogistic argument in the third figure, in which there is one universal affirmative and one particular affirmative premise and a particular affirmative conclusion.
definiendum
1. an expression that has to be defined in terms of a previously defined expression.
2. anything that has to be defined. definienda , n., pl.
Dimaris
Dimatis.
Dimatis
a mnemonic word to represent a syllogistic argument in the fourth figure, in which there is one universal affirmative and one affirmative premise and a particular affirmative conclusion. Also called Dimaris .
Disamis
a mnemonic word to represent a syllogistic argument in the third figure, in which there is one particular affirmative and one universal affirmative premise and a particular affirmative conclusion.
elenchus
a syllogistic argument that refutes a proposition by proving the direct opposite of its conclusion. elenchic, elenctic , adj.
epicheirema
a syllogism in which the truth of one of the premises is confirmed by an annexed proposition (prosyllogism), thus resulting in the formation of a compound argument. See also prosyllogism .
equipollence, equipollency
equality between two or more propositions, as when two propositions have the same meaning but are expressed differently. See also 4. AGREEMENT .
Felapton
a mnemonic word to represent a syllogistic argument in the third figure, in which there is one universal negative and one universal affirmative premise and a particular negative conclusion.
Ferio
a mnemonic word to represent a syllogistic argument in the first figure, in which there is one universal negative and one particular affirmative premise and a particular negative conclusion.
Feriso
a mnemonic word to represent a syllogistic argument in the third figure, in which there is one universal negative and one particular affirmative premise and a particular negative conclusion. Also Ferison .
Ferison
Feriso.
Fesapo
a mnemonic word to represent a syllogistic argument in the fourth figure, in which there is one universal negative and one universal affirmative premise and a particular negative conclusion.
Festino
a mnemonic word to represent a syllogistic argument in the second figure, in which there is one universal negative and one particular affirmative premise and a particular negative conclusion.
Fresison
a mnemonic word to represent a syllogistic argument in the fourth figure, in which there is one universal negative and one particular affirmative premise and a particular negative conclusion.
metalogic
the metaphysics or metaphysical aspects of logic. metalogical , adj.
methodology
a division of logic devoted to the application of reasoning to science and philosophy. See also 83. CLASSIFICATION ; 301. ORDER and DISORDER . methodological , adj.
polylemma
a multiple dilemma or one with many equally unacceptable alternatives; a difficult predicament.
prosyllogism
a syllogism connected with another in such a way that the conclusion of the first is the premise of the one following.
schematism
the form or character of a syllogism.
sorites
an elliptical series of syllogism, in which the premises are so arranged that the predicate of the first is the subject of the next, continuing thus until the subject of the first is united with the predicate of the last. soritical, soritic , adj.
syllogism
a form of reasoning in which two propositions or premises are stated and a logical conclusion is drawn from them. Each premise has the subject-predicate form, and each shares a common element called the middle term.
syntheticism
the principles or practice of synthesis or synthetic methods or techniques, i.e., the process of deductive reasoning, as from cause to effect, from the simple elements to the complex whole, etc.

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logic

logic, the systematic study of valid inference. A distinction is drawn between logical validity and truth. Validity merely refers to formal properties of the process of inference. Thus, a conclusion whose value is true may be drawn from an invalid argument, and one whose value is false, from a valid sequence. For example, the argument All professors are brilliant; Smith is a professor, therefore, Smith is brilliant is a valid inference, but the argument All professors are brilliant; Smith is brilliant; therefore, Smith is a professor is an invalid inference, even if Smith is a professor.

Aristotelian Logic

In Western thought, systematic logic is considered to have begun with Aristotle's collection of treatises, the Organon [tool]. Aristotle introduced the use of variables: While his contemporaries illustrated principles by the use of examples, Aristotle generalized, as in: All x are y; all y are z; therefore, all x are z. Aristotle posited three laws as basic to all valid thought: the law of identity, A is A; the law of contradiction, A cannot be both A and not A; and the law of the excluded middle, A must be either A or not A.

Aristotle believed that any logical argument could be reduced to a standard form, known as a syllogism. A syllogism is a sequence of three propositions: two premises and the conclusion. By varying the form of the proposition and the modifiers (such as all, no, and some), a few specific forms may be delimited. Although Aristotle was concerned with problems in modal logic and other minor branches, it is usually agreed that his major contribution in the field of logic was his elaboration of syllogistic logic; indeed, the Aristotelian statement of logic held sway in the Western world for 2,000 years. Nonetheless, various logicians did, during that time, take issue with parts of Aristotle's thought.

Post-Aristotelian Logic

One of Aristotle's tacit assumptions was that there is a correspondence linking the structures of reality, the mind, and language (and hence logic). This position came to be known in the Middle Ages as realism. The opposing school of thought, nominalism, is exemplified by William of Occam, a medieval logician, who maintained that the structure of language and logic corresponds only to the structure of the mind, not to that of reality. Since knowledge is a study of generalizations, while nature occurs in myriad single instances, the distinction between the world and our conception of it is stressed by the nominalists.

Inductive Reasoning

In the 19th cent. John Stuart Mill noticed the same dichotomy between man's generalizations and nature's instances, but moved toward a different conclusion. Mill held that the scientist or experimenter is not interested in moving from the general to the specific case, which characterizes deductive logic, but is concerned with inductive reasoning, moving from the specific to the general (see induction). For example, the statement The sun will rise tomorrow is not the result of a particular deductive process, but is based on a psychological calculation of general probability based on many specific past experiences. Mill's chief contribution to logic rests on his efforts to formulate rules of inductive logic. Although since the criticisms of David Hume there has been disagreement about the validity of induction, modern logicians have argued that inductive logic does not need justification any more than deductive logic does. The real problem is to establish rules of induction, just as Aristotle established rules of deduction.

Mathematics and Logic

With the development of symbolic logic by George Boole and Augustus De Morgan in the 19th cent., logic has been studied in more purely mathematical terms, and mathematical symbols have replaced ordinary language. Reference to external interpretations of the symbols (formulated in ordinary language) was also rejected by the formalist movement of the early 20th cent. Bertrand Russell and Alfred North Whitehead, in Principia Mathematica (3 vol., 1910–13), attempted to develop logical theory as the basis for mathematics. Pure formal logic attempts to prove that a logical system is dependent only on the perceptual recognition and valid manipulation of symbols and requires no interpretive reference to content.

Intuitionism, rejecting such formalism, holds that words and formulas have significance only as a reflection of activity in the mind. Thus a theorem has meaning only if it represents a mental construction of a mathematical or logical entity. Kurt Gödel, in the 1930s, brought forth his "incompleteness theorem," which demonstrates that an infinitude of propositions that are underivable from the axioms of a system nevertheless have the value of true within the system. Neither these Gödel Propositions, as they are called, nor their negations are provable. One implication for the modern logician is that Aristotle's law of the excluded middle (either A or not A) is neither so simple nor so self-evident as it once seemed.

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logic

log·ic / ˈläjik/ • n. 1. reasoning conducted or assessed according to strict principles of validity: experience is a better guide to this than deductive logic he explains his move with simple logic the logic of the argument is faulty. ∎  a particular system or codification of the principles of proof and inference: Aristotelian logic. ∎  the systematic use of symbolic and mathematical techniques to determine the forms of valid deductive argument. ∎  the quality of being justifiable by reason: there's no logic in telling her not to hit people when that's what you're doing. ∎  (logic of) the course of action or line of reasoning suggested or made necessary by: if the logic of capital is allowed to determine events. 2. a system or set of principles underlying the arrangements of elements in a computer or electronic device so as to perform a specified task. ∎  logical operations collectively. DERIVATIVES: lo·gi·cian / ləˈjishən; lō-/ n.

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logic

logic Branch of philosophy that deals with the processes of valid reasoning and argument. Logic defines the way in which one thing may be said to follow from, or be consequent upon, another. This is known as deductive logic. Inductive logic is when a general conclusion is drawn from a particular fact or facts. Although logical systems were devised in China and India, the history of logic in the West began in the 4th century bc with the Greek philosopher Aristotle. In the Middle Ages, Arab scholars rediscovered logic and in Europe Pierre Abélard used logic in the synthesis of ideas that was the goal of scholasticism. Various post-Renaissance scholars, including Leibniz, developed the foundations of modern logic. In the 19th century, George Boole outlined symbolic (mathematical) logic, and Gottlob Frege developed the system. Modern formal logic or symbolic logic utilizes symbols to represent precisely defined classes of proposition connected to each other by such operators as ‘and’, ‘or’, ‘if… then’.

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logic

logic
1. A knowledge representation and reasoning formalism originally developed by mathematicians to formalize mathematical reasoning. In mathematical logic the investigation involves mathematical methods taken from algebra or the theory of algorithms. The two most common systems are propositional calculus and predicate calculus.

Logic has been widely adopted within artificial intelligence, for example as an alternative to production rules in expert systems and for representing the meaning of natural language statements (see natural-language understanding). Many alternative logics have been developed in artificial intelligence to represent the vagueness and uncertainty of common sense (as opposed to mathematical knowledge) and to represent the tentative nature of common-sense reasoning; these include nonmonotonic reasoning and uncertain reasoning (see uncertainty).

2. See digital logic, computer logic.

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logic

logic reasoning conducted or assessed according to strict principles of validity; a particular system or codification of the principles of proof and inference. In the Middle Ages, logic was one of the seven liberal arts.
logic bomb in computing, a set of instructions secretly incorporated into a program so that if a particular condition is satisfied they will be carried out, usually with harmful effects.
logic chopping the practice of engaging in excessively pedantic argument. The expression chop logic is recorded from the early 16th century, and originally meant ‘exchange or bandy logical arguments’; in later use, chop was wrongly understood as meaning ‘cut, split’.

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Logic

Logic. An activity both condemned and justified in the history of Buddhist thought. While the Buddha discouraged vain philosophical speculation, there is no evidence that he disapproved of logic as such. The Abhidhammic literature, with its listing of Buddhist concepts, is presented in a vaguely logical manner; and the Theravādin Kathāvatthu is an attempt to refute logically more than 200 propositions held by opposing schools. See also TARKA.

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logic

logic science that treats of forms of thinking XIV; logical argumentation XVII. — (O)F. logique — late L. logica — Gr. logikḕ, for hḕ logikḕ tékhnē the art of reasoning; logiké, fem. of logikós, f. lógos reasoning, discourse (see LOGOS).
So logical XVI. — medL. logician XIV. — (O)F.

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"logic." The Concise Oxford Dictionary of English Etymology. . Retrieved August 22, 2017 from Encyclopedia.com: http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/logic-3

logic

logicbathypelagic, magic, tragic •neuralgic, nostalgic •lethargic, Tajik •Belgic •paraplegic, quadriplegic, strategic •dialogic, ethnologic, hydrologic, isagogic, logic, monologic, mythologic, pathologic, pedagogic, teleologic •georgic • muzhik •allergic, dramaturgic •anarchic, heptarchic, hierarchic, monarchic, oligarchic •psychic • sidekick • dropkick •synecdochic • Turkic •Alec, cephalic, encephalic, Gallic, intervallic, italic, medallic, mesocephalic, metallic, phallic, Salic, tantalic, Uralic, Vandalic •catlick • garlic •angelic, archangelic, evangelic, melic, melick, philatelic, psychedelic, relic •Ehrlich • Gaelic •acrylic, bibliophilic, Cyrillic, dactylic, exilic, idyllic, imbecilic, necrophilic •niblick • skinflick •acyclic, cyclic, polycyclic •alcoholic, anabolic, apostolic, bucolic, carbolic, chocoholic, colic, diabolic, embolic, frolic, hydraulic, hyperbolic, melancholic, metabolic, parabolic, rollick, shambolic, shopaholic, symbolic, vitriolic, workaholic •saltlick • cowlick • souslik • gemütlich •public • Catholic

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"logic." Oxford Dictionary of Rhymes. . Encyclopedia.com. 22 Aug. 2017 <http://www.encyclopedia.com>.

"logic." Oxford Dictionary of Rhymes. . Encyclopedia.com. (August 22, 2017). http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/logic-1

"logic." Oxford Dictionary of Rhymes. . Retrieved August 22, 2017 from Encyclopedia.com: http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/logic-1