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Logic
	In this set of great books, the Organon of Aristotle, the Novum Organum of Francis Bacon, Descartes's Discourse on the Method and his Rules for the Direction of the Mind, and Kant's The Critique of Pure Reason indicate or discuss the nature, scope, and divisions of the discipline which has come to be called "logic." Though of all the works mentioned the Organon is perhaps the most extensive treatment of the subject, Aristotle does not use the word "logic" to name the science or art of which he seems to be the inventor-certainly the first systematic expounder-in the tradition of western thought.
	Here as elsewhere Aristotle is indebted to his predecessors for providing him with materials to develop or criticize: to the Sophists for the construction of arguments, for the formulation of methods of disputation, and for the discovery of fallacies; to Plato for the theory of classification and definition, for the root notion of the syllogism and a conception of proof or demonstration, for the general outlines of an intellectual method to which Plato gives the name "dialectic."
	As indicated in the chapter on DIALECTIC, Aristotle uses Plato's name for the whole method of the mind in the pursuit of truth, in order to designate just one part of his method, the part concerned with probability rather than truth. Yet in the Roman and medieval tradition, the words "logic" and "dialectic" come to be used interchangeably. This is exemplified by the Stoic division of the sciences into physics, ethics, and logic or dialectic, and by the medieval enumeration of the liberal arts of the trivium as grammar, rhetoric, and logic or dialectic. So used, these names designate the whole range of discussion to be found in Aristotle's Organon.
	In their opposition to Aristotelian or what they sometimes call "scholastic" logic, modern inventors of new methods, like Bacon or Descartes, tend to restrict the meaning of logic. For them logic is little more than the doctrine of the syllogism. And this they judge to be no part of genuinely fruitful method, or they hold it to be of use mainly as a critical instrument in disputation rather than discovery. Their identification of logic with dialectic (like their association of both with rhetoric) seems to have an intentionally invidious significance.
	But with Kant, who was influenced by the scholasticism of Christian Wolff, "logic" is generally restored as the name for the whole range of materials in Aristotle's Organon, of which dialectic again becomes. a part. In his own Introduction to Logic, Kant speaks of Aristotle as "the father of Logic." Though "logic has not gained much in extent since Aristotle's time," he says, "there are two amongst more recent philosophers who have again brought general logic into vogue, Leibnitz and Wolff." Since their day, and certainly since Kant's, as may be seen from the titles listed under Additional Readings, "logic" prevails as the name for treatises which discuss, in whole or part, the matters treated in Aristotle's Organon.
	"Logic" is also used in modem times as the name for an inquiry or study which bears little resemblance to the discipline expounded in Aristotle's Organon. What is called "modern logic" to distinguish it from the traditional Aristotelian or scholastic logic, is purely a science, and in no sense an organon, methodology, instrument, or art. It does not restrict itself to stating the laws of thought or formulating the rules of inference. In the words of Josiah Royce, it is "the science of order" and it is applicable to the order of things as well as the order of thought. So conceived, the science of logic is sometimes regarded as having the kind of generality which is traditionally assigned to metaphysics; as, for example, by Russell in his essay, "Logic as the Essence of Philosophy."
	But it is mathematics rather than metaphysics with which logic is identified by its modern exponents. "Logistic or mathematical logic," writes Russell, "is mathematical in two different senses: it is itself a branch of mathematics, and it is the logic which is specially applicable to other more traditional branches of mathematics." Since George Boole's Laws of Thought, which, according to Russell, initiates the modern development of mathematical logic, "logic has become more mathematical and mathematics has become more logical. The consequence," he says, "is that it has now become wholly impossible to draw a line between the two; in fact, the two are one."
	"In what sense," Wittgenstein asks, "is logic something sublime?" His answer stresses the universal significance of logic and the fact that it lies "at the bottom of all the sciences... It seeks to see to the bottom of things and is not meant to concern itself whether what actually happens is this or that . . . It takes its rise... from an urge to understand the basis, or essence, of everything empirical." In sharp contrast, the existentialist Heidegger asserts that logic "is only one exposition of the nature of thinking, and one which... is based on the experience of Being as attained in Greek thought."

Aristotle's Organon stands to the tradition of logic as Euclid's Elements stands to the tradition of geometry. In both cases the work of later minds may alter considerably the structure and content of the discipline. In both cases there are modern departures from the earlier tradition. As in the one case we have Descartes's analytic geometry and the various non-Euclidean geometries, so in the other we have Kant's transcendental logic and the various non-Aristotelian logics.
    But all these innovations, even when they might be described as anti-Aristotelian rather than simply as non-Aristotelian, bear the marks of their traditional origin. Kant, for example, takes pains everywhere to indicate the parallelism between the formulations of his transcendental logic and those of Aristotle's logic. Even the various systems of relational and mathematical logic usually attempt to show that the Aristotelian logic of subject and predicate, of particular and universal propositions, and of syllogisms can be treated as a special case under their own formulations. The proposals of Bacon or J. S. Mill with respect to induction and the method of Descartes, though accompanied in each case by a critique of the syllogism, are less radical departures, for they do not apparently reject Aristotle's basic doctrines of predication and proof.
    Many of these issues in logical theory are dealt with in other chapters, e.g., in DIALECTIC, INDUCTION, and HYPOTHESIS, in IDEA, JUDGMENT, and REASONING. Here we are principally concerned with the conception of logic itself, not with the detailed content of the science as much as with its character as an art or science, its relation to other arts and sciences, its major divisions, and its leading principles. Though such considerations are more explicitly treated by Kant than by Aristotle, the formative influence of the Organon warrants examining it first.

The parts of logic, as Aristotle conceives them, seem to be indicated by the subject matter of the various books which comprise the collection of writings assembled under the title of Organon. That title has a bearing on the question whether logic is a science or an art and on its difference from other sciences and arts. The word "organon" has the meaning of instrument or method. That in turn suggests something to be used as rules of art are used as directions to be followed to produce a certain result.
    Aristotle's own differentiation of the speculative sciences, the practical sciences, and the arts throws light on this view of logic as an art. "The end of theoretical knowledge," he writes, "is truth, while that of practical knowledge is action." In other words, the theoretical, or speculative, sciences differ from the practical sciences in that they are knowledge for its own sake as opposed to knowledge for an ulterior end. According as the ulterior end is the production or "making" of something, as distinct from human action or conduct, art is distinct from the other practical sciences. "Making and acting are different," Aristotle says; "the reasoned state of capacity to act is different from the reasoned state of capacity to make. Hence, too, they are not included one in the other; for neither is acting making nor is making acting." Logic, then, if it is an art, will be concerned with the "making" of something, with producing a work or an effect.
    The way in which Aristotle himself refers to the Organon seems to confirm this view. He regards it as a preparation for work in the theoretical sciences. "Due to a want of training in logic," he writes, some men attempt to discuss the criteria of truth in mathematics or physics at the same time that they are considering the subject matter of these sciences. "They should know these things already when they come to a special study, and not be inquiring into them while they are listening to lectures on it." Logic, in Aristotle's view, trains the mind in the ways of science. Its productive goal as an art is the making of science itself. For this reason, in the medieval period, logic comes to be called a "speculative art" or, with grammar and rhetoric, a liberal art.
    "Even in speculative matters," Aquinas says, "there is something by way of work, e.g., the making of a syllogism, or of a fitting speech, or the work of counting or measuring. Hence whatever habits are ordained to such works of the speculative reason are, by a kind of comparison, called arts indeed, but liberal arts, in order to distinguish them from those arts that are ordained to works done by the body... On the other hand, those sciences which are not ordained to any such work are called sciences absolutely and not arts."
    But though it may not be a science, absolutely speaking, because it is an instrument of intellectual work, logic, in addition to being an art, may also have some of the characteristics of a science. If it is a science, what is the object of its knowledge?
    Aristotle's division of the speculative sciences, which he seems to present as exhaustive, leaves no place for logic. "There are three kinds of theoretical sciences," he writes, "physics, mathematics, theology" or metaphysics, as the last came to be called. Each of these sciences, furthermore, seems to have a distinctive subject matter which is some aspect of reality, such as change, or quantity, or being. But insofar as logic is concerned with the study of terms, propositions, and syllogisms, it deals with elements common to all sciences.
    This suggests that whereas reality is the object of the other sciences, the object of logic as a science is science itself, or more generally the whole of discourse. It considers the elements or patterns of discourse in a formal manner; that is, it considers them apart from their reference to reality or their real significance as the terms, propositions, and syllogisms of particular subject matters or sciences. Because it separates the forms which discursive thought takes from the matter or content it may have, logic is traditionally called a "formal science."

Where Aristotle makes his object the elements of discourse (or thought expressed in language), later logicians treat the formal aspect of thought itself. They deal with concepts, judgments, and reasoning instead of with terms, propositions, and syllogisms. This difference results in a definition of logic as the science of thought; the basic formulations of logic are the laws of thought. Thus, for example, Kant says that logic "treats of nothing but the mere forms of thought." Its limits "are definitely fixed by the fact that it is a science which has nothing to do but fully to exhibit and strictly to prove all formal rules of thought."
    The logical principles of identity, excluded middle, and contradiction, as well as the principles of inference, are said to be "laws of thought." William James proposes as the most "fundamental principle of inference" what he calls the "axiom of skipped intermediaries," which states that "skipping intermediary terms leaves relations the same." That "equals of equals are equal" is a special application of this principle in the sphere of quantities. Because it applies to all subject matters equally, James regards the principle as "on the whole the broadest and deepest law of man's thought."
    In either conception of logic as a formal science, questions arise concerning the relation of logic to other sciences. For Aristotle the question is about logic and metaphysics, because both seem to have an unrestricted scope. Metaphysics considers the being of everything which is; logic, the formal components of discourse about anything. Aristotle says of philosophy in relation to dialectic, that both "embrace all things" but that "dialectic is merely critical where philosophy claims to know." The same comparison could apply to metaphysics and logic. Both "embrace all things" but not from the same point of view.
    Aristotle also asks whether it belongs to metaphysics as well as to logic to inquire "into the truths which are called axioms" - especially those which are the first principles of all knowledge or demonstration, not merely the foundations of knowledge about some limited subject matter. "Since these truths clearly hold good for all things qua being," the science which studies being qua being (i.e., metaphysics) must be concerned with them. It also belongs to metaphysics as well as to logic "to inquire into the principles of the syllogism."
    The principles of identity, excluded middle, and contradiction belong to both sciences to the one as the most universal truths about existence, to the other as the basic rules of discourse or the laws of thought. This sharing of a common ground does not seem to Aristotle to violate their separateness; but Bacon charges him with having "corrupted natural philosophy by logic." Of Aristotle's physics, he says that it is built of "mere logical terms," and, Bacon adds, Aristotle "remodelled the same subject in his metaphysics under a more imposing title."
    Whereas Aristotle considers the relation of logic to metaphysics, Kant considers its relation to psychology. Both logic and psychology are concerned with thinking and knowing. Distinguishing between pure and applied logic, Kant says that pure logic "has nothing to do with empirical principles and borrows nothing from psychology." Applied logic depends on psychology. In fact, says Kant in his Introduction to Logic, it is "a psychology in which we consider what is the usual process in our thought, not what is the right one." Applied logic ought not to be called logic at all, for "logic is the science of the right use of the understanding and the reason generally, not subjectively, that is, not according to empirical (psychological) principles, as to how the understanding actually thinks, but objectively, that is, according to a priori principles, as to how it ought to think."
    James also insists upon the distinction be tween psychology and logic. He even uses Kant's terms in calling logic an a priori and psychology an empirical science. What the psychologist calls "laws of thought," such as the laws of the association of ideas, describe the actual flow of thought and connections which depend upon similarity and succession. The laws of logic, in contrast, state reason's perception of the rational structure of thought itself and the relations which must obtain if thought is to be rational.

Returning now to the indication of the parts of logic which may be found in the structure of the Organon, we can see two orders in the books. The first three books-the Categories, On Interpretation, and the Prior Analytics deal with terms, propositions, and syllogisms: with the classification of terms and their re lation to one another; with the classification of propositions and their opposition to one another; with the analysis of the various types of syllogisms and the formulation of the rules of valid inference. Terms are the elements of propositions; terms and propositions are the elements of the syllogism. This seems to determine the order of the first three books.
    The first three books as a whole stand in a certain order to the remaining books. Taking the latter as a group, their differentiation from what precedes them seems to lie in the fact that they deal with terms, propositions, and syllogisms, not abstracted from all considerations of knowledge and truth about reality, but rather with primary emphasis upon the logic of actual knowledge, or on the processes of knowing and arguing about what is true or probable. In the traditional development of Aristotelian logic, this division between the first three and the remaining books of the Organon is sometimes characterized as a distinction between formal and material logic.
    In the Posterior Analytics and the Topics Aristotle considers the discovery and establishment of either the true or the probable. He distinguishes between induction and syllogism (or reasoning) as modes of learning and arguing. The later division of logic into deductive and inductive-sometimes confused with the distinction between formal and material logic-does not seem to correspond to the difference between the Prior and the Posterior Analytics. In the Advancement of Learning, for example, Bacon divides the art of judgment, "which treats of the nature of proof or demonstration," into that which concludes by induction and that which concludes by syllogism; whereas Aristotle appears to treat induction as that upon which syllogistic demonstration depends for its primary and in demonstrable premises.
    The distinction between truth and probability, or between knowledge and opinion, does not affect the formal character of either induction or syllogism. A syllogism may be scientific (i.e., demonstratively certain) or dialectical (i.e., merely probable) according to the character of its premises. In either case its formal structure remains the same. Similarly, the difference between scientific and dialectical induction appears only in its result, i.e., whether it is knowledge or opinion. The Posterior Analytics and the Topics consider the employment of both syllogism and induction. The Posterior Analytics treats them in relation to the development and structure of scientific knowledge. The Topics discusses them in relation to the dialectical procedures of argument and discovery.
    The last book of the Organon, which is concerned with exposing the fallacies in sophistical proofs or refutations, serves to protect both scientific and dialectical reasoning from such sophistry. Unlike the philosopher or the dialectician, the sophist does not aim at the truth. Sophistry misuses the weapons of logic - the same weapons used by the scientist or dialectician - to produce a counterfeit of wisdom or, as Aristotle says, "a wisdom which exists only in semblance." Though the dialectician cannot claim to know, he does, nevertheless, deal with opinions critically and respects the canons of logic as much as the philosopher.
    The art of logic seems to have three main employments. To its use by the scientist and the dialectician, Aristotle adds its utilization by the orator for the purposes of persuasion. The rhetorician and the dialectician are most closely allied because both deal with probabilities and disputable matters concerning which opposite conclusions can be drawn. "As in dialectic, there is induction on the one hand and syllogism... on the other, so it is in rhetoric." Aristotle says that "the enthymeme is a rhetorical syllogism, and the example a rhetorical induction."
    The foregoing suggests that a certain order obtains between two of the three arts traditionally called the trivium. The elements and principles of logic are, in a sense, prior to the rules of rhetoric. The art of rhetoric depends on and uses logic. The third art, that of grammar, seems to serve both logic and rhetoric. It serves the logician in his task of forming terms and propositions out of words, phrases, and sentences. It serves the rhetorician in his effort to make a forceful use of language. This conception of the uses of grammar appears in Aristotle's Rhetoric in his consideration of style, and in the opening books of the Organon in his discussion of univocal and equivocal names, the parts of speech, simple and composite expressions, and the different types of sentences.

Kant seems to diverge from Aristotle both with regard to the unity of logic and with regard to the nature and relation of its parts. Formal or elementary logic, Kant thinks, is not the same as an organon of the sciences. He explains, in his Introduction to Logic, that an organon gives instructions as to "how some particular branch of knowledge is to be attained... An organon of the sciences is therefore not a mere logic, since it presupposes the accurate knowledge of the objects and sources of the sciences... Logic, on the contrary, being the general propaedeutic of every use of the understanding and of the reason, cannot meddle with the sciences and anticipate their matter." Conceding that it may be called an organon so far as it serves, "not for the enlargement, but only for the criticism and correction of our knowledge," Kant insists that "logic is not a general art of discovery, nor an organon of truth; it is not an algebra by the help of which hidden truths may be discovered."
    Aristotle, according to Kant, treats the whole of his logic as an organon, dividing it into an analytic and a dialectical part. As Kant sees it, the dialectical part arises from a misuse of the analytic part. This occurs, he says in The Critique of Pure Reason, when general or elementary logic (i.e., the analytic part) "which is meant to be a mere canon of criticism, is employed as if it were an organon, for the real production of at least the semblance of objective assertions... This general logic," says Kant, "which assumes the semblance of an organon, is called dialectic."
    Kant here seems to identify dialectic with what Aristotle calls sophistry. He says of dialectic that "different as are the significations in which the ancients use this name of a science or art, it is easy to gather from its actual employment that with them it was nothing but a logic of semblance. It was a sophistic art of giving to one's ignorance, nay, to one's intentional casuistry, the outward appearance of truth, by imitating the accurate method which logic always requires." When logic is treated as an organon, it "is always an illusive logic, that is, dialectical. For as logic teaches nothing with regard to the contents of knowledge... any attempt at using it as an organon in order to extend and enlarge our knowledge, at least in appearance, can end in nothing but mere talk, by asserting with a certain plausibility anything one likes, or, if one likes, denying it.
    Yet Kant himself retains Analytic and Dialectic as the major divisions of his own transcendental logic, explaining that he employs the title of dialectic, not for the misuse of logic, but rather to signify that portion of logic which is the critique of "dialectical semblance" or sophistry. General or ordinary logic takes no account of the content of knowledge and applies to all objects universally because "it treats of the form of thought in general." Transcendental logic does not entirely ignore the content of knowledge, but only the content of that knowledge which is empirical in origin. If there are transcendental or a priori concepts which do not originate from experience, then there can be a science which treats "of that knowledge which belongs to the pure understanding, and by which we may think objects entirely a priori."
    That is the science Kant calls "transcendental Logic." It deals, he writes, "with the laws of the understanding and reason in so far only as they refer a priori to objects." That part of it "which teaches the elements of the pure knowledge of the understanding, and the principles without which no object can be thought, is the transcendental Analytic." The second part of it is the transcendental Dialectic - "a critique of the understanding and reason with regard to their hyperphysical employment, in order thus to lay bare the false semblance of its groundless pretensions... serving as a protection of the pure understanding against all sophistical illusions."

The issue between Kant and Aristotle cannot be understood if it is read simply as a dispute about the nature and divisions of logic. Their diverse views of logic must be seen against the larger background of their philosophical differences with regard to the nature of the mind, the nature of reality, the origin of knowledge, and the character of its objects. Controversies about logic (and even within logic, about this or that theory of judgment or reasoning) usually reflect fundamental issues in psychology and metaphysics. The attack made by some modem logicians, for example, against the subject-predicate logic of Aristotle cannot be separated from their rejection of his doctrine of substance and accident in physics and metaphysics; even as their own relational logic represents a different view of the structure of reality or the constituents of experience.
    On the other hand, the criticism of Aristotelian logic by Bacon and Descartes seems to be motivated primarily by considerations of method. They do not have a different logic to propose, as do Kant and later symbolic or mathematical logicians. Rather for them logic itself - by which they mean Aristotle's logic and particularly his doctrine of the syllogism appears useless for the purposes of enlarging knowledge, discovering new truths, and developing the sciences. Where Kant criticizes Aristotle for regarding logic as an organon or method for acquiring knowledge, Bacon and Descartes complain that logic does not serve that purpose at all, and therefore a novum organum - not a new logic, but a new method is needed.
    "The present system of logic is useless for the discovery of the sciences," Bacon writes. It "rather assists in confirming and rendering inveterate the errors founded on vulgar notions than in searching after truth, and is therefore more hurtful than useful." The syllogism, for example, "is unequal to the subtlety of nature... Our only hope is in genuine induction." Induction is the key to an art of discovery, and the rules of induction the heart of a fruitful method of inquiry.
    The relation of induction to demonstration in Aristotle's logic, and the difference between Aristotle's and Bacon's theories of induction, are discussed in the chapter on that subject. In Bacon's view, the Novum Organum departs radically from the old Organon. The new can be substituted for the old in its entirety. It may be asked, he says, "whether we talk of perfecting natural philosophy alone according to our method, or the other sciences also, such as logic, ethics, politics." His answer is that "as common logic, which regulates matters by syllogisms, is applied not only to natural, but also to every other science, so our inductive method like wise comprehends them all."
    Demonstration is opposed not only to induction, but to discovery. Accordingly, logic conceived as concerned only with the rules of demonstration is opposed to other methods which aim at directing scientific inquiry and research. The basic contrast is between criticism and construction, or between examining what is offered as knowledge for its validity and developing techniques for adding new knowledge to old. In his Concerning Two New Sciences Galileo says that logic "teaches us how to test the conclusiveness of any argument or demonstration already discovered and completed" but not "to discover correct arguments and demonstrations." It does not, "as regards stimulation to discovery, compare with the power of sharp distinction which belongs to geometry."
    In the same vein Descartes says of logic that "the syllogisms and the great part of the other teaching serve better in explaining to others those things that one knows... than in learning what is new... This made me feel that some other method must be found." The four rules of the method he then states, which codify the steps he himself has taken to make discoveries in geometry and physics, seem to him a general procedure for insuring the advancement of all fields of learning.
    As his Rules for the Direction of the Mind indicates, Descartes's method does not omit the intuition of principles and the deduction of conclusions therefrom-the apparent equivalents of induction and demonstration in Aristotle's Organon. But he explains why he has "omitted all the precepts of the dialecticians" even though he is himself concerned with improving "our power of deducing one truth from another." Their style of argument, he says, "contributes nothing at all to the discovery of the truth . . . Its only possible use is to serve to explain at times more easily to others the truths we have already ascertained; hence it should be transferred from Philosophy to Rhetoric."
    Furthermore, the forms of the traditional syllogism do not seem able to accommodate the connections in mathematical reasoning or the structure of mathematical proof. "Everyone will perceive in mathematical demonstrations," Locke writes, ''that the knowledge gained thereby, comes shortest and clearest without syllogisms." Locke identifies logic with the doctrine of the syllogism and, even more explicitly than Descartes, rejects it as an aid to reasoning.

The question whether logic is itself a methodology, or includes rules for the discovery as well as the demonstration of truth, is answered in terms of broader and narrower conceptions of the science or art. Those who regard the rules of logic as primarily a canon of criticism, which test the validity of intellectual work, look elsewhere for a method whose rules are productive rather than critical. The question then usually arises whether there is one methodology applicable to all fields of inquiry, or as many distinct methods as there are different disciplines or subject matters.
    The difference between the traditional Aristotelian and the modern mathematical logic suggests that there may be a plurality of logics. The attempts made by the exponents of each to subsume the other as a special case do not seem to be entirely successful. Though Aristotelian logic appears to give a satisfactory account of the forms of judgment and reasoning in certain types of discourse, it cannot, in the opinion of symbolic logicians, be applied to mathematics. "Mathematics consists of deductions, and yet," according to Russell, "the orthodox accounts of deduction are largely or wholly inapplicable to existing mathematics." Symbolic logic, on the other hand, may succeed in formulating the relational structure of modem mathematics, but it does not, in the opinion of its critics, hold for metaphysics at least not the sort of metaphysics which treats relation as a category subordinate to substance.
    As Heisenberg points out, "the mathematical scheme of quantum theory can be interpreted as an extension or modification of classical logic... In classical logic it is assumed that, if a statement has any meaning at all, either the statement or the negation of the statement must be correct." That logical principle must be modified in quantum mechanics to accommodate the principle of indeterminacy.

The difference between the kind of thinking that men do in science and in law suggests another type of diversity among logics. The practical or moral judgment seems to involve a special type of predicate. What Aristotle calls the "practical syllogism" and what Aquinas describes as the process of "determination" - quite distinct from deduction - by which positive laws are derived from natural law, seem to call for a logic of practical thinking, quite distinct from the logic of all the theoretical sciences.
    Using the word "logic" in its broadest sense, we must ask whether there is one logic common to all the sciences; or a logic which fits mathematics but not physics or metaphysics, a logic appropriate to speculative philosophy but not to experimental or empirical research, a logic peculiar to the nature of the practical or moral sciences, such as ethics and politics, or to the work of jurisprudence.
    There is evidence in the great books that sciences as different as mathematics and physics, or as metaphysics and politics, differ in their methods of discovery and demonstration. This may mean that they differ in their logics as well. Yet it also appears to be the case that the principle of contradiction applies in all, that fallacious inference is detected by the same criteria in all, and to this extent all share a common logic. Where alternative methods have been proposed within a single major field - notably in the case of philosophy - this may reflect different conceptions of philosophy itself rather than alternative routes to the same end.
    Because of their relevance to the basic issues about logic (and especially those concerning its scope and unity), the rules of methodology in general and the various methods proposed for particular disciplines are included in this chapter. They are also considered, of course, in chapters devoted to the special disciplines or subject matters, e.g., ASTRONOMY AND COSMOLOGY, HISTORY, MATHEMATICS, METAPHYSICS, PHYSICS, THEOLOGY; and in the chapters on SCIENCE and PHILOSOPHY. What is distinctive about each of these methods is discussed in those chapters in relation to the type of knowledge or inquiry which seems to require a method of its own.