This term, derived from the Greek λόγὶος, λογικη, has been the subject of numerous definitions. By different authors and schools it has been defined as the art of convincing, the art of thinking, the art of discovering truth, the right use of reason, the science and art of reasoning, the science of deductive thinking, the science of the laws of thought as thought, and the science of the laws of discursive thought. These specimen definitions indicate in some degree the diverse conceptions of the subject which have prevailed at different periods and in different circles. Aristotle, whom Sir William Hamilton extravagantly calls the author and finisher of the general science under consideration, had no single name for it. He treated of its principal parts as analytic, apodeictic, and topic. In the latter he included the dialectic of Plato and the sophistic of the Sophists. Notwithstanding the honor credited to Aristotle, he himself says that Zeno the Eleatic was the inventor of dialectics.

Thus we are taken back to the early Greek philosophers for the first formal discussions of what is now universally denominated Logic. They, in successive generations, developed with more or less clearness its principal elements. Socrates illustrated induction; Euclid, deduction. Plato treated of mental images as the results of sensation, of notions as the product of the understanding, and of ideas as the product of reason. Aristotle formulated syllogisms, and defined their principal laws. He taught analysis. He devised a system of categories. He enumerated the five predicables, genus, species, difference, property, and accident. In short, he reduced to a system the fragmentary discoveries in the philosophy of mind of those who had gone before him, and embodied them in works destined to exert a great influence upon after ages. Like many other great men, Aristotle was but indifferently appreciated by his contemporaries. Even after his death, his logical system produced but little influence upon his countrymen the Greeks. Several of the Christian fathers, however, give evidence of having profited by its study, and of desiring to use the knowledge they had thus acquired in propagating the truth of Christianity. Justin Martyr, Tatian, Athenagoras, Clement, and others, both used and defended such dialectics as they had learned in the Grecian schools. On the other hand, as the same style of dialectics had been closely identified with the pernicious vagaries of heathen philosophy, Tertullian, Irenaeus, Arnobius, and Lactantius considered its use as unfavorable to the interests of Christianity, and destructive of true science and wisdom. Augustine also wrote in the same spirit against the academicians.

Bible concordance for LOG.

Nevertheless, speculative studies held a relative prominence in the learning of Greece and Rome during the early Christian centuries; and when, owing to the barbarian irruptions, learning and civilization declined, dialectical science remained in more general cultivation than almost any other of the higher species of knowledge. Having its subject matter in the human mind, it was not dependent for perpetuity upon those external circumstances which influenced the conditions of general literature. Boethius, who has been called the last of the ancient philosophers, and the connecting link between the classical and the medieval age, made a translation of Aristotle's categories into Latin. His contemporaries of the 6th century, Cassiodorus, Capella, and Isidore of Seville, together with several Byzantine writers, e.g. George Pachymera, Theodorus Metachita, and Michael Psellus, formed meager compendiums of logic and rhetoric, without any clear distinction between the two. These manuals superseded or rather substituted the use of the ancient authors on both these subjects, and, imperfect as they were, became the oracles of that long and dismal period in which the trivium (grammar, logic, and rhetoric) and quadrivium (music, arithmetic, geometry, and astronomy) were the chief topics of study and instruction. The ignorance consequent upon such a condition of things continued for the long period of five centuries without material variation.

In the latter part of the 11th century commenced a period of literary awakening known to history as the first aera of scholasticism. SEE SCHOLASTICISM. This movement was characterized by attempts to construct systems of theology on the traditional basis with strict dialectical form and method. Paris was the chief seat of the movement. Anselm, an abbot at Bec in 1078, and late in life an archbishop of Canterbury, made the first vigorous attempt in harmony with logical forms, on the basis of credo ut intelligam. Abelard opposed him, on the principle that understanding should precede faith. Thisas the period of Nominalism and Realism, and also of the foundation of universities. Among the most prominent of the great names of this period is that of Roscelinus of Compeigne, who is celebrated as having been the first to revive the question of the reality of universal ideas, and William of Champeaux, who opened a school of logic in Paris in 1109. The fame of the latter was soon eclipsed by that of Peter Abelard, who was able to invest logical disputation with such fascinations as to make it the favorite occupation of the most intelligent minds for generations following.

Definition of log

The 13th century is counted as the second period of scholasticism, durinlg which the leading dialecticians were Bonaventura, Albertus Magnus, Thomas Aquinas, and Duns Scotus. During this period scholasticism reached its climax. The 14th century, as the third period of scholasticism, witnessed its sensible decline under the protracted but bitter wranglings of the Thomists (Realists) and Scotists (Nominalists).

Notwithstanding an attempt by the Medici of Florence to revive the Platonic philosophy in opposition to that of Aristotle, the latter prevailed in the chief universities of Europe, and the corruptions of it which had been countenanced by scholasticism began to pass away under the influence of more intelligent discussion. In the 16th century, after the invention of printing, the logical and philosophical works of the Stagirite were issued in a purer text and more accurate versions, and largely engaged public criticism.

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The authority of Aristotle had been so long supreme in the continental universities, and the union between what passed for his philosophy and the errors of the Church of Rome had been so long established, that it was only natural for Luther and Melancthon, at the beginning of the Reformation, to inveigh strongly against the Aristotelian logic and metaphysics. As time passed on, however, it became apparent that the work of the Reformers had largely to be done through the agency of that same Aristotelian logic. Melancthon was not slow to perceive this, and subsequently became an acknowledged follower of Aristotle as to dialectics, and even influenced Luther to retract some of his severer utterances. He introduced into the University of Wittenberg, to which Protestant Germany looked up, a scheme of dialectics and physics founded upon the Aristotelian theory. He also imitated the Stagirite philosopher by teaching logic with constant reference to rhetoric. The advocacy and influence of Melancthon secured the preponderance of the Aristotelian dialectics in the Protestant schools of Germany for more than a century.

About the middle of the 16th century a formidable opposition to the authority of Aristotle sprang up at the University of Paris, under the leadership of Peter Ramus, a scholar of great natural acuteness, and of an intrepid, though somewhat arrogant spirit. He published his Institutiones Dialecticae in 1543. His system, founded with much ingenuity on the writings of Plato, notwithstanding violent opposition, prevailed so far as to greatly weaken the influence of the Aristotelian philosophy. The heads of the university, alarmed at this innovation, made complaint against Ramus to Parliament. The king himself interfered, and appointed a public trial of the rival systems of logic. As might have been expected, a majority of the judges favored the established system. Ramus was consequently ordered to desist from teaching, and an order passed for the suppression of his book. That order was subsequently removed, and Ramus again became popular as a teacher. He treated logic as merely the art of arguing, and was very severe on the dry and tedious formalities of the schoolmen. His system embraced invention and proofs, and thus blended with rhetoric. In 1551, through the influence of the cardinal of Lorraine, Ramus became royal professor of rhetoric and philosophy, in which capacity he made many proselytes. Having adhered to the Huguenot party, he was killed in the massacre of St. Bartholomew. But he had already traveled and taught in Germany, where his system found no little favor. In Italy it secured a few disciples. but many more in France, England, and Scotland. Andrew Melville introduced the logic of Ramus at Glasgosw, and it ultimately became popular in all the Scottish universities. The logical writings of the remainder of the 16th century, and somewhat later, were filled with the Ramist and anti-Ramist controversy, which, though of little permanent importance, doubtless prepared the way for a better comprehension of the true principles and processes of logic in later periods.

In the 17th century the writings of lord Bacon formed another epoch in the history of logic. SEE BACON. Logic, according to lord Bacon, comprised the sciences of invention, judging, retaining, and delivering the conceptions of the mind. We invent or discover new arts and arguments. We judge by induction or syllogism, and we may improve memory by artificial modes. The first book of the Novuma Organum developed his celebrated and peculiar division of fallacies, viz. idola tribes, idola splecus, idola fori, and idola theatri. The second book sought to apply the principles of induction to the interpretation of nature. Although, from a defective knowledge of natural phenomena incident to his times, the author's illustrations were far from perfect, and although many logicians have disputed the correctness of his principles, it cannot be questioned that the Baconian logic and method of study exerted a powerful influence upon his own and after times in stimulating thought and discovery. The remaining authors of the 17th century whose writings influenced the study and methods of logic were Des Cartes, Arnauld, author of L'Art de Pense, and Locke, of England. Probably the most influential treatise on the direct subject was Arnauld's Art of Thinking, commonly called the Port-Royal Logic. It attacked the Aristotelian system, and, being written in a modern language, had the advantage over the heavy Latinity of previous books. In this respect it became an example to subsequent writers, who, from the beginning of the 18th century, were numerous if not influential. But, with all that was written respecting it, the study of logic failed to command general attention. It had few attractions for the popular mind, and its special devotees were seldom able to place it in successful competition with philosophy, natural science, and general literature. Although prescribed in every system of academic study, and at once the agency and topic of ceaseless wrangling among professed scholars, yet its influence upon human life and public opinion was infinitesimally small.

The limits of this article do not admit of a detailed notice of all the logicians and logical systems of modern times, but only of allusion to a few of the most influential. In Germany, more than in all other countries, the study of logic has within the last hundred years assumed new phases and developed new doctrines, more especially in connection with the various systems of idealistic philosophy. Of that philosophy Immanuel Kant, SEE KANT, may be considered the inaugurator, and his first philosophical production commenced with the study of logic. As early as 1762 he published a treatise on the "False Subtlety of the Four Syllogistic Figures," in which he maintained that only the first is pure, and the others ratiocinia hybrida. From this point he went on developing his system, till in 1781 he published his Kritik of Pure Reason, to which in 1790 he added his Kritik of the Judgment. Kant claimed to have subjected the human mind to a new analysis, from which he determined the three comprehensive functions of sense, understanding, and reason. His general scheme is summed up as follows:

I. Doctrine of the transcendental elements of knowledge.

A. Transcendental aesthetics. B. Transcendental logic. a. Transcendental analytics. b. Transcendental dialectics.

II. The transcendental mlethod.

Not to mention the numerous defenders and modifiers of the Kantian system, we pass to G.W.F. Hegel, SEE HEGEL, the publication of whose Wissenschaft der Logik in 1812 marks another epoch in German metaphysics. Hegel employed the term logic in a very extended sense. Not confining it to abstract forms of thought and the laws of ideas, he considered it the science of the self-sufficient and self-determining idea — the science of truth and reality. From his fundamental principle that thought and substance are identical, it followed that what is true of one is true also of the other, and that the laws of logic are ontological. His system claimed to develop the idea of the absolute by antagonisms through all its successive stadia. With him the primary element of logic consisted in the oneness of the subjective and objective. Instinctive knowledge only regards the object without considering itself. But consciousness, besides the former, contains a perception of itself, and embraces, as three stages of progress, consciousness, self-consciousness, and reason. Pure logic, according to Hegel, is divided into,

1. The logic of being; 2. The logic of qualified nature; 3. The logic of the idea.

In 1825, Richard Whately, afterwards archbishop of Dublin, published an article in the Encyclopaedia Metropolitana, which, having been expanded and printed as his Elements of Logic, was soon after extensively adopted as a text-book both in England and America. This publication has justly been considered as constituting an Vera in the study of logic in English-speaking countries. The principles of Kant's Kritik of Pure Reason were not extensively introduced into Great Britain until after 1836, when Sir William Hamilton began his lectures in the University of Edinburgh. SEE HAMILTON. Although Hamilton took opposite ground to Whately in reference to the essential character of logic, yet both were admirers and exponents of the Analytic of Aristotle. Thus the reawakened taste for logical studies during the current century arose from a restoration, by different methods, of the old logic which had come down from the early ages, and survived all the opposition and ridicule of the modern centuries. It is worthy of especial note that none of the systems put forth by Ramus, Descartes, Locke, or Condillac, and their several modifiers, has been able to stand the test of time like that of the old philosophers and schoolmen. This fact may be accepted as proving that the syllogism indicates substantially the process which takes place in all minds in the act of reasoning. Notwithstanding this small demonstration, and a few other points of general concurrence, the science of logic, which has been the subject of human study for more than two thousand years, remains still incomplete. Many of its principles and processes are yet in continued and active dispute. Since Whately and Hamilton, Mr. John Stuart Mill has written an elaborate work in which he depreciates the syllogism and magnifies induction. But his theories in reference to both bear the stamp of Comte's empirical positivism.

The chief logical discussion of the present day revolves around the "New Analytic of Logical Forms," or the quantification of the predicate introduced by Sir William Hamilton. This new analytic, which is chiefly valuable for its enlargement of the hitherto narrow sphere of formal logical praxis, is an emanation from the metaphysics of Kant, being grounded upon certain principles of the Kritik of Pure Reason. Its theory, although illustrated by an ingenious system of notation, was left in a somewhat crude state by Hamilton, but has been ably elaborated by Mansel and Thomson, of England, and Bowen and Mahan. of America. While these writers seem to think that they have attained the end of all logical perfection, Dr. M'Cosh, of Princeton, charges their whole system with fundamental error in presupposing "that there are forms in the mind which it imposes on objects as it contemplates them." To explode this error is the avowed object of M'Cosh's recent treatise, in which, while he falls back for confirmation upon the old logic, he claims to unfold laws which were not noticed by the old logicians. The characteristic of his work is a more elaborate treatment of the notion than has taken place since the publication of the Port-Royal Logic. Thus logic seems destined to pass down to coming centuries as it has descended from the past, a subject of endless debate, but one from which each successive generation derives its advantage in the very process of debate.

See Hallam's Literature of Europe; Blakey's Historical Sketch of Logic; Kant's Kritik; Hegel's Wissenschaft der Logik; Whately's Elements of Logic; Sir William Hamilton's Lectures on Logic; Mansel's Prolegomena Logica; Thomson's Laws of Thought; Eleements of Logic, by H.P. Tappan, by W.D. Wilson, by C.K. True, by H. Coppee, by J.R. Boyd, by H.N. Day, by A. Schuyler, by L.H. Atwater; System of Logic, by John Stuart Mill; Science of Logic, by Asa Mahan; Formal Logic, by James M'Cosh. (D.P.K.)

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