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 (1632–1704) and Robert Boyle (1627–1691).
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 century—Francis Bacon (1561–1626), Pierre Gassendi (1592–1655), Robert Boyle, and John Locke—continued 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 (1532–1589) 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 (1596–1650) 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.
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.
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 (1639–1691). 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. 1493–1541), the innovative medical philosopher who developed a vocabulary for spells to use in medicinal cures. Medical doctors like the Swiss Thomas Erastus (1524–1583) 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 (1696–1770). 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 .
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. 35–66. 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.
——. 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.
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. 35–50. Wiesbaden, 2000.
——. "Vocabulary as a Critique of Knowledge: Zabarella and Keckermann—Erastus and Conring." In Philologie und Erkenntnis: Beiträge zu Begriff und Problem Frühneuzeitlicher "Philologie, " edited by Ralph Häfner. Tübingen, 2002.
Panizza, Letizia. "Ermolao Barbaro e Pico della Mirandola tra retorica e dialettica." De genere dicendi philosophorum del 1484, Ermolao Barbaro (1454–1493) Congress, edited by Michela Marangoni. Venice, 1996.
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 (384–322 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 term—predicate 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 conclusion—and 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 metaphysics—a forerunner of Aristotle's treatise of that name.
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 forms—distinguished by Chrysippus. The Stoics had a schematic way of representing the indemonstrables—what 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.
Although Aristotle's pupil and successor, Theophrastus (c. 372–c. 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. 234–c. 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. 480–c. 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, 790–1200
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 1034–1109) 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 (1079–1142), 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, 1200–1500
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" words—words 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.
Logic was no less important for Islamic than for Christian philosophers and theologians. By the time of al-Farabi (c. 878–950), the first important Islamic logician, the whole of Aristotle's logical Organon was available in Arabic—far 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; 980–1037) 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 meanings—so-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 condition—for 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 than—as they often thought with regard to other areas of Aristotelian philosophy—a dangerous rival to it. Particularly important was the endorsement of al-Ghazali (1058–1111): 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 .
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.
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 101–381 contain the most complete available account of medieval logic in the Latin West.
Marenbon, John. Boethius. New York: Oxford University Press, 2003. See pages 17–65. 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. 308–324.
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 knowledge—covering both nature and human relations—on 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 one—which is to say that if the premises are true then the conclusion cannot help but be true—then 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 deduction—which deals with moving from general statements to the particular conclusions that follow from them—with 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:
Kennedy’s tax cut in 1961 stimulated the economy
Reagan’s tax cut in 1981 stimulated the economy
Bush’s 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 one’s 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 sciences—or indeed any fact-based discipline—would 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 science—in particular those of rational choice and game theory—reflect 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 one’s 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 doesn’t matter how beautiful your theory is. If it doesn’t agree with experiment, it’s 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 one’s 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
Haack, Susan. 1978. Philosophy of Logics. Cambridge, U.K.: Cambridge University 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
Classical logicThe term logikḗ was coined by the Greek philosopher Alexander of Aphrodisias in the 3c, but systems of organized thinking had already developed well before this in Greece, India, and China. Western culture has inherited the Greek tradition mainly through Rome and the Arab world. In this tradition, logic is closely linked with grammar and rhetoric, and discussion of one often leads to discussion of the others. For the Greeks, both reasoning and language were encompassed in the word lógos, which they contrasted with mûthos, a term that encompassed words, speech, stories, poems, fictions, and fables. Plato (5c BC) in The Republic represented Socrates as wishing to exclude poetry from the proper education of the young, and after some 2,500 years, this viewpoint still carries weight: logic, science, and reason are commonly set on one side and poetry, art, and myth on the other. To make his case, however, Plato used many devices from poetry and rhetoric: he so structured his dialogues that Socrates always won, often with the help of poetic analogies such as the Simile of the Cave. His pupil Aristotle laid the foundations of logic proper, as the study of inference from propositions arranged as formal arguments.
Grammar and logicBecause logic and GRAMMAR developed together they have overlapping terminologies: both use the term sentence, and deductive logic consists of a logic of propositions (also called sentential logic) and a logic of predicates (also called a logic of noun expressions). Logicians, grammarians, and rhetoricians are all interested in such matters as AMBIGUITY, FALLACY, paradox, syntax, and SEMANTICS, and in such modalities as necessity, possibility, and contingency; linguists who are concerned with grammar, computation, and artificial intelligence take as much interest in logic as in natural language. Logicians and mathematicians have created systems that contain both sets of abstract symbols and the rules necessary for their combination and manipulation in strings. Such symbols, rules, and strings are often idealizations of elements in, or thought to be in, natural language (but isolated from such everyday factors as dialect variation, personal idiosyncrasy, figurative usage, emotional connotation, colloquial idiom, social attitude, and semantic change). When such a system of symbols is adapted to practical ends, however, as in computer technology and artificial intelligence, pure logic becomes applied logic, operating within a real machine intended to do real work in real time.
Although many logicians, grammarians, and linguists have been interested in a universal calculus of language (something that would transcend natural language or allow the dispassionate description of all language), they have built their systems out of the natural languages that they know best: Greek for Aristotle and his disciples, Latin for medieval and Renaissance grammarians, and English for such present-day theorists as Noam Chomsky. Both prescriptive and descriptive grammarians of such Western languages as French and English have been influenced by logic and by the languages in which the principles of logic developed. Because it emerged in large part through the use and analysis of language, it has not been difficult to find quasi-logical patterns in language. Some analysts have been inclined to see logical orderliness either as inherent in language or as a reasonable goal of language planning, especially when a language is in the process of being standardized. Everyday language, however, has a persistent (even frustrating) tendency towards the illogical or non-logical, as for example in the use of double negatives (I didn't do nothing, which does not therefore mean ‘I did something’) and in idiomatic expressions (such as it's raining cats and dogs).
All analysts of language work towards orderliness, but some go further and engage in or recommend making certain aspects of language, such as the spelling of English, more ‘regular’ (that is, more rule-governed and therefore more logically consistent). They may also favour an artificial language such as Esperanto or Basic English that is (apparently) free from the illogic of natural language. Interest in such reforms has often gone hand in hand with particular conceptions of and assumptions about, progress, science, efficiency, education, literacy, and standards. Logic has therefore been used as a tool for both the description of natural language and its prescriptive improvement. In the development of the first grammars of English, the model was Latin and the analytical terms were Greek as used by the describers of Latin. Medieval and Renaissance models for vernacular prose as a vehicle of rational discourse were either Latin prose or vernacular prose written in the Latin style. Theories of sentences and parts of speech were those developed by classical grammarians and logicians, often the same people. The analysis of sentences into subjects and predicates, main and subordinate clauses, and the like, has paralleled the logician's view of propositions as the core of language and of binary division as a powerful conceptual tool.
The limits of logicIn the second half of the 20c, ancient practice has gained fresh impetus through the work of Noam Chomsky. Some features of his work are: (1) The definition of a language as a set of well-formed sentences, indefinite in number. (2) Abstract and diagrammatic analyses of sentences of standard written English. (3) The use of quasi-logical symbols such as S for sentence, NP for noun phrase, and VP for verb phrase, to sustain the analysis of such sentences. (4) Logical transformations performed on strings of symbols so as to produce further strings. (5) The creation of a generative grammar, that is, a set of explicit, formal rules that specify or generate all and only the sentences which constitute a language; in so doing, they are seen as demonstrating the nature of the implicit knowledge of that language possessed by an ideal native speaker-hearer. Such an approach has often been taken to be a break with the past, but is rooted in more than two millennia of logical and grammatical system-building. It remains a matter of debate whether natural language can be handled by linguistic theories that derive in the main from or are closely associated with aspects of formal logic. Natural language is a neural mechanism, apparently the result of genetic and social evolution. While it is sometimes regular, logical, and precise, it is as often irregular, non-logical, and imprecise, and oftener still a mix of the two. It blends intellect with instinct, logic with inspiration, and the standard with the varied. Logic is closely associated with language and with its description and discussion in literate societies. As such, it is an essential tool, but one cannot deduce from this usefulness that it is the sole or even primary means by which natural language can be understood.
LOGIC (Heb. חָכְמַת הַדִּבּוּר or מְלֶאכֶת הַהִגַּיוֹן), the study of the principles governing correct reasoning and demonstration. The term logic, according to Maimonides, is used in three senses: to refer to the rational faculty, the intelligible in the mind, and the verbal expression of this mental content. In its second sense, logic is also called inner speech, and in its third, outer speech. Since logic is concerned with verbal formulation as well as mental content, grammar often forms a part of logical writings. Shem Tov ibn *Falaquera, for example, prefaces his Reshit Ḥokhmah with an account of the origin of language, its nature, and its parts. As Maimonides had done in the introduction to the Guide of the Perplexed, Falaquera classifies terms into distinct terms, synonyms, and homonyms, a classification which was very important in the medieval philosophic exegesis of the Bible.
The two mental acts which are basic to logic are conception and judgment. The former is involved in the apprehension of the essence of things, the latter, in deciding whether propositions are true or false.
Maimonides does not consider logic a part of philosophy proper as the Stoics did, but follows the Peripatetics in viewing it as the instrument and auxiliary of all the other sciences.
Although some of the methods of biblical exegesis and legal interpretation (middot) employed by the rabbis of the talmudic period rest upon the rules of logic (see *Hermeneutics), it is doubtful that the rabbis had a formal knowledge of the subject. However, beginning with Saadiah, who refers to Aristotle's categories, proving that they are not applicable to God (Emunot ve-De'ot, 2:8), Jewish thinkers have been acquainted with the Organon – the title traditionally given to the body of Aristotle's logical treatises which formed the basis of logic – as propounded by the logicians of Islam. During the Islamic period, few works on logic were written by Jews. While Isaac *Israeli and Joseph ibn *Ẓaddik appear to have written works on logic, the first extant work on logic written by a Jew is Maimonides' Maqāla fi-Ṣināʿat al-Manṭiq (ed. by M. Turker (1961); Arabic text in Hebrew characters published by I. Efros in: paajr, 34 (1966), 9–42 (Hebrew section); translated by the same into English under the title Maimonides' Treatise on Logic, in: paajr, 8 (1937/38), 34–65). It was only when the setting of Jewish philosophy shifted to Christian countries and Arabic ceased to be the language of the Jews that logical works were translated into Hebrew and a greater number of Hebrew works on logic were written by Jews.
In the Maqāla fi-Ṣināʿat al-Manṭiq Maimonides offers concise exposition of the 175 most important logical, physical, metaphysical, and ethical terms used in the discussion of logical theory. The popularity of this treatise is attested by the fact that it was translated into Hebrew three times, under the title Millot ha-Higgayon or Shemot ha-Higgayon: once in a florid style by *Ahitub, a physician in Palermo in the 13th century; again, by Joseph ben Joshua ibn Vivas (of Lorca) in the 14th century; and by Moses b. Samuel ibn *Tibbon (all three translations appear in: paajr, 8 (1937/38), 23–129). This last translation was by far the most popular and has gone through many editions. Maimonides' work served not only as a handbook of logic, but, until comparatively recent times, also as an introduction to general philosophy. Of the commentaries written on it, those of Mordecai b. Eliezer *Comtino and Moses *Mendelssohn may be singled out.
While there is little information on the logical authorities used by the Jews up until the middle of the 12th century, it is known that by this time al-Fārābī was the acknowledged authority on logic. Maimonides, in a famous letter to Samuel ibn Tibbon, the Hebrew translator of his Guide, advises him to study logic only from the works of al-Fārābī, and, as M. Tucker has shown, Maimonides in his Maqāla fi-Ṣināʿat al-Manṭiq relied heavily on four works by al-Fārābī. During the first half of the 13th century, *Averroes too came to be regarded as an authority on logic, soon superseding al-Fārābī. Thus, Judah ben Samuel ibn *Abbas, in his Ya'ir Nativ, suggested that in order to learn the principles of logic, a student should read the works of al-Fārābī or Averroes.
While it appears that there were no translations into Hebrew of any of the books comprising the Organon, all the commentaries of al-Fārābī and Averroes were translated and annotated. Jacob b. Machir translated Averroes' Epitome of the Organon, and Jacob *Anatoli, Averroes' middle commentaries, which he completed in 1232. *Kalonymus b. Kalonymus and Moses b. Samuel ibn Tibbon were among some of the others who undertook to translate the logical writings of al-Fārābī and Averroes. Anatoli's translation of the middle commentaries was utilized by Joseph *Kaspi in his compendium of logic, entitled Ẓeror ha-Kesef.
The Jews were also familiar with the logical writings of Avicenna. Their knowledge of Avicenna's writings did not come from translations of Avicennian works, but rather through the logical portions of al-*Ghazālī's "Intentions of the Philosophers" (Maqāṣid al-Falāsifa). In addition to the Islamic tradition, a work by a Christian scholar, Peter of Spain's SummulaeLogicales, was also popular, as the four or five Hebrew translations or extracts of it, which are still extant, testify.
These translations are of great importance because in many instances the original Arabic texts of the commentaries are no longer extant. Moreover, many of these texts were translated from the Hebrew into Latin by Jews who served as the intermediaries between the logicians of Islam and the scholastics. *Levi b. Gershom wrote supercommentaries on the middle commentaries and epitomes of Averroes, as well as an independent work on logic entitled Ha-Hekkesh ha-Yashar ("The Correct Syllogism"), which drew upon itself the attention of gentile scholars and was translated into Latin under the title Liber Syllogismi Recti. In the 15th century, *Judah b. Jehiel Messer Leon wrote a supercommentary on Averroes' middle commentaries which shows the influence of the scholastic Walter Burleigh.
L. Jacobs, Studies in Talmudic Logic and Methodology (1961), 3–50; A. Hyman, in: Actes du quatrième congrès international de philosophie médiévale (1969), 99–110; I. Husik, Judah Messer Leon's Commentary on the "Vetus Logica" (1906); Steinschneider, Uebersetzungen, 43–168; Waxman, Literature, 1 (19602), 319–20; 2 (19602), 213.
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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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 .
- 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.
- a syllogistic argument that refutes a proposition by proving the direct opposite of its conclusion. —elenchic, elenctic , adj.
- 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 .
- 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.
- 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.
- 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 .
- 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.
- 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.
- 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.
- the metaphysics or metaphysical aspects of logic. —metalogical , adj.
- a division of logic devoted to the application of reasoning to science and philosophy. See also 83. CLASSIFICATION ; 301. ORDER and DISORDER . — methodological , adj.
- a multiple dilemma or one with many equally unacceptable alternatives; a difficult predicament.
- a syllogism connected with another in such a way that the conclusion of the first is the premise of the one following.
- the form or character of a syllogism.
- 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.
- 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.
- 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.
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.
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.
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.
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.
Indian thinkers of many traditions, including Buddhism, often maintain that reliable knowledge is the key to spiritual liberation. By the fourth century c.e., many such thinkers were engrossed in an ongoing conversation focused on two interrelated questions: What constitutes reliable knowledge? And what types of reliable knowledge are there? The answers to these questions led to intricate debates on the nature of perception, reason, and language. Buddhists participated prominently in this conversation, but their contribution does not constitute a separate "school" of thought. It is, instead, a style of Buddhist philosophy that eventually gained much sway among Buddhist thinkers in India; Tibetan traditions continue to employ it vigorously to this day. Since Buddhists have no indigenous term for this philosophical style, Western scholars invented the term Buddhist logic to describe especially the formulations initially presented by Dig-nĀga (ca. 480–540 c.e.) and refined by Dharmakirti (ca. 600–670 c.e.).
Dignāga gave the first systematic presentation of Buddhist logic, but Dharmak rti and his followers provided the form that became widespread in India and Tibet. Concerning the types of reliable knowledge, Buddhist logic holds that there are just two kinds, each with a corresponding type of object: (1) perception, which cognizes particulars, and (2) inference, which cognizes universals. A particular is a completely unique, causally efficacious entity that exists for only a moment. We know that particulars are real because they are causally linked, directly or indirectly, to our cognitions of them. Universals, the objects of inference, are concepts that are meant to apply to many particulars. They are causally inert; hence, although we imagine them to be real, they cannot in fact be the causes of any cognition. For this reason, Buddhist logicians maintain that only particulars are truly real; universals may seem real, but they are actually mental fictions that we create through a process of excluding everything that is irrelevant to the context at hand.
To understand the difference between particulars and universals, suppose that this dot ﾀ is a unique particular. It may seem to be the same as this other dot ﾀ, but that sameness is created by associating two unique sensory experiences with a single universal, the concept dot. Each specific instance may also seem to last over time, but the apparent stability of particulars over time is also an illusion created by associating them with a single universal. Moreover, only the actual dot on the page can cause a cognition; the universal dot cannot do so (we can see ﾀ; we cannot see our concept of it).
Buddhist logicians further argue that an instance of reliable knowledge must be an efficacious cognition—efficacious because it enables one to achieve one's goal. Strictly speaking, then, reliable knowledge can be partially defective. For example, a cognition might falsely attribute qualities to a thing but still remain effective: While correctly identifying something as fire, one might incorrectly believe that the observed fire is exactly identical to all other fires. Nevertheless, that cognition is still efficacious because those false attributions do not obstruct one from attaining one's goal: If you seek to warm your hands, then it does not matter whether you falsely believe that the fire in front of you is identical to all others.
Buddhist logicians must allow that reliable knowledge may be partially defective because they must make use of language without accepting some characteristics implied by universals. The concept dot, for example, makes us falsely believe that all dots are one; nevertheless, we can successfully use this concept to speak of the (actually unique) dots on this page. Likewise, the concept person falsely makes me believe that I am identical to the infant that I was; nevertheless, we can use person to speak of one who suffers and seeks liberation.
This critical approach to universals creates problems when Buddhist logicians present their theory of logic, which is in fact a detailed theory of inference. Here, the form of an inference is "S is P because E," where the terms are a subject (S), a predicate (P), and the evidence (E). An example would be, "Joe is mortal because of being human." An inference is well formed if three relations hold: the evidence entails the predicate (a human must be mortal); the negation of the predicate entails the negation of the evidence (a nonmortal must be nonhuman); and the evidence is a quality of the subject (Joe is indeed human). For Buddhists who employ this theory of inference, two notable problems persist. First, the inference's terms must be universals, and since universals are strictly speaking unreal, how does one account for relations among them? And second, if one uses an inference to prove that a purely imaginary entity does not exist, how can that purely imaginary entity be the subject of that inference? That is, if one wishes to prove that "an absolute Self is nonexistent," how can an imaginary entity (the absolute Self) bear any predicate? This latter question is particularly acute for Madhyamaka thinkers who employ the Buddhist logicians' theory of inference.
Dreyfus, Georges B. Recognizing Reality: Dharmakīrti's Philosophy and Its Tibetan Interpretations. Albany: State University of New York Press, 1997.
Stcherbatsky, Th. Buddhist Logic, 2 vols. Delhi: Motilal Banarsidass, 1992. Reprint of 1930–1932 edition.
Tillemans, Tom J. F. Scripture, Logic, Language: Essays on Dharmakīrti and His Tibetan Successors. Boston: Wisdom, 1999.
Logic is the study of the formal principles of reasoning. It focuses on how to attain knowledge and how to determine whether statements are true or false. Renaissance humanists* contributed to this science in two ways. First, they studied and taught the ideas of classical* writers, especially the Greek philosopher Aristotle, on the subject of logic. Second, they developed new theories about the purpose of logic.
Traditional Logic. The basis of Renaissance logic was Aristotle's Organon. This important work came to the West in three stages. During the 500s the Roman scholar Boethius translated part of it into Latin, along with an introduction written by another Greek scholar. By about 1280, scholars had translated the rest of the text from Greek and Arabic into Latin. Then, in the 1490s, a new edition of the complete Organon appeared in the original Greek. Around the same time, commentaries on Aristotle's logic by scholars of the late Middle Ages also appeared in print. The recovery of these texts led to a burst of scholarship on the subject of Aristotelian logic. Jacopo Zabarella produced the most extensive works on this topic in the mid-1500s.
Aristotelian logic had a great influence on education. The lectures of the Jesuit* Ludovicus Rugerius show how important logic was to Renaissance scholars. Rugerius taught a three-year course in philosophy in Rome in the 1590s. He devoted the entire first year of this course to logic. Rugerius covered Aristotle's text in detail and also made use of commentaries by Greek, Arab, and Latin scholars, including Zabarella and other researchers of his time.
Scholars at the University of Padua in Italy played a major role in the study of Aristotelian logic. For more than a century, they analyzed and debated a section of the Organon that dealt with scientific reasoning. They focused on the problem of how to use facts to prove conclusions and achieve scientific knowledge. Zabarella provided the essential Renaissance solution to this problem in his Book on the Regress (1578).
Spanish scholars at the University of Paris pursued a different line of study in the early 1500s. They focused on mathematics and on the use of logic in philosophy and theology* rather than in science and medicine. One of these scholars, Domingo de Soto, later taught at the University of Salamanca in Spain, where he published commentaries on Aristotle's logic. His student Franciscus Toletus became a Jesuit and organized the philosophy course at the order's Collegio Romano in Rome. In 1572 Toletus published Commentaries, with Questions, on All of Aristotle's Logic. This work formed the basis of Jesuit teaching in logic until the end of the 1600s.
Humanist Logic. Some Renaissance scholars rejected traditional logic and its formal arguments as sterile and not useful. In its place they created a new logic that emphasized persuasion. They sought to link logic to grammar and rhetoric*.
One of the first scholars to pursue this program was Lorenzo Valla, a noted Italian humanist of the 1400s. He rejected Aristotle's concern with formal proof, instead claiming that a sound argument rested on good use of language. However, few philosophers accepted Valla's new system of logic. The work of Dutch humanist Rudolf Agricola was more influential. In his Three Books on Dialectical Invention (1479), Agricola proposed a form of logic based on topics rather than on terms. He argued that the formal proofs of Aristotelian logic were of limited use in debate. Instead, he advised his readers to practice the art of influencing others, to involve opponents in debates, and to aim at likelihood rather than certainty.
In the 1500s French humanist Petrus Ramus proposed another alternative to Aristotelian logic. He divided logic into two parts: invention and arrangement. Invention meant finding the best arguments to use in addressing a particular problem or question. Ramus defined an argument as a relationship between a subject and the facts that can be stated about that subject. For example, in the sentence "Cold causes shivering," the word "causes" lays out the relationship between cold and shivering. The process of arrangement, in turn, involved laying out arguments in a useful order. Ramus proposed using outlines to organize subject matter, with headings moving from general concepts to specific ones. This technique became very popular in textbooks on all subjects through the end of the 1500s.
- * humanist
Renaissance expert in the humanities (the languages, literature, history, and speech and writing techniques of ancient Greece and Rome)
- * classical
in the tradition of ancient Greece and Rome
- * Jesuit
refers to a Roman Catholic religious order founded by St. Ignatius Loyola and approved in 1540
- * theology
study of the nature of God and of religion
- * rhetoric
art of speaking or writing effectively
LOGIC . In the words of Petrus Hispanus, logic is both "ars artium et scientia scientiarum, ad omnium aliarum scientiarum methodorum principia viam habens." Roughly, we may take this to say, in modern terms, that logic concerns itself with the methods of correct statement and inference in all areas of inquiry whatsoever. Traditionally logic has divided into the study of deduction and of induction. The former has had an enormous development in the last hundred years or so, whereas the latter is still lagging behind, awaiting its coming of age.
Deductive logic does not dictate the principles or statements with which a given line of reasoning or inference starts; it takes over after these have been initially decided upon. Such principles or statements are decided upon, in turn, by direct insight, by revelation, by direct experience, by induction from instances, and so on. Deductive logic steps in only in the secondary capacity of directing the course of inferences once the so-called "premises" have been accepted or determined. The principles and rules of correct inference are stated in complete generality and hence are applicable to all kinds of subject matter. They are stated within a limited logical vocabulary—primarily that providing for the notions "not," "and," "or," "for all," "for some," and so on—to which the statements of any discipline must be brought into conformity by the use of suitable nonlogical constants providing for the given subject matter. Logic is thus indeed a kind of straitjacket that enforces correct statement and inference, just as moral norms enforce correct behavior and aesthetic norms enforce the beautiful or the artistically acceptable. In logic, however, there is less variation in the norms than in moral or aesthetic matters. Although many varieties of "deviant" logics have been invented, all of these turn out to be mere applications of the one standard logic. This is essentially the logic of Aristotle, brought up to date with the important contributions of DeMorgan, Boole, Peirce, Frege, Schröder, Whitehead and Russell, and Lesniewski.
Principles of logic have played a central role in theology throughout the long history of both, and each has influenced the other in significant ways. To be noted especially is the development, between roughly 1200 and 1500, of the Scholastic logic that aimed at providing the wherewithal for proofs of God's existence, especially those of Anselm, Thomas Aquinas, and Duns Scotus. In recent years, so-called process theology, stemming from the work of Whitehead, owes its origins to Whitehead's early work in logic, and much of the current discussion of the language of theology, especially in England, has been decisively influenced by the contemporary concern with the logic of natural language. In the East, especially in India, logic began to flourish in the first century ce within the confines of the methodology of theological and moral discussion and had a vigorous development that has persisted to the present day.
Logic, especially in its modern form, is a helpful adjunct to theology and should not be viewed with the fear that it will reduce the subject to a long list of sterile formulas. On the contrary, it should be viewed as an instrument that can help theology regain the high cognitive regality it once had as the queen of the sciences.
Bochenski, Joseph M. The Logic of Religion. New York, 1965.
Carnes, John. Axiomatics and Dogmatics. Oxford, 1982.
Martin, R. M. Primordiality, Science and Value. Albany, N.Y., 1980.
Allen, James. Inference from Signs: Ancient Debates about the Nature of Evidence. New York, 2001.
Bowell, Tracy, and Gary Demp. Critical Thinking: A Concise Guide. London, 2001.
Falmagne, Rachel Joffe, and Marjorie Hass. Representing Reason: Feminist Theory and Formal Logic. Lanham, Md., 2002.
R. M. Martin (1987)