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The process by which the human intellect passes from what it already knows to what it does not yet know, without having recourse to new information. Since knowledge is expressed in propositions, reasoning may be characterized also as the process by which the mind passes from two or several propositions, called the premises or the antecedent, to another proposition, called the conclusion or the consequent. It may be noted that passing directly from one proposition to another, e.g., by conversion, is not considered reasoning because the conclusion has the same content as the premise, differing from it only in form; thus no new knowledge results. Only by bringing together two or more knowledge-contents does the mind grasp a new knowledge-content. (The direct passage from one proposition to another is sometimes called immediate inference, although the term "inference" is here used in an improper sense.)

Matter and Form. In reasoning there are two aspects to consider, namely, matter and form. The matter is the content with which the reasoning is concerned, i.e., the objects and properties mentioned in the propositions involved in the reasoning. The form is the manner in which the elements of the reasoning are linked together; it is what characterizes the reasoning when abstraction is made from its content. Corresponding to the distinction between form and matter is that between the validity and the truth of a reasoning process; a consideration of validity and truth may thus assist the understanding of form and matter as they are applied to the reasoning process.

Validity of Reasoning. Reasoning is valid, or correct, when the consequent follows necessarily (with a logical necessity) from the antecedent, i.e., when the antecedent cannot be true without the consequent's being true also. It is then said that the consequent is inferred from the antecedent or that there is an inference (in the strict sense) from the antecedent to the consequent. Valid reasoning thus expresses an inference.

The validity of reasoning depends only on its form. In other words, the validity is independent of the objects and properties about which the reasoning is concerned, and therefore, of the truth or falsity of the propositions involved in it. If, in valid reasoning, each mention of an object or of a property is replaced by the mention of another object or another property, the resulting reasoning also is valid.

Reasoning can be valid even if its conclusion is false, as when one of the premises is false. Again, invalid, or incorrect, reasoning can come to a true conclusion; when this occurs, however, it is by accident and not in virtue of the deductive link the reasoning establishes between true premises and the conclusion drawn. When any given reasoning is incorrect, it is always possible to replace it by another with the same form and with true premises that leads to a false conclusion.

The necessary condition of the validity of a given reasoning process is the following: "in all reasoning having the same form, if the premises are true the conclusion is also true" (Dopp, 15).

Truth of Reasoning. The reasoning process that establishes the truth of a proposition is called demonstration. A proposition is demonstrated to be true only if it expresses the conclusion of a valid reasoning process all of whose premises have been previously recognized as true, i.e., as being evident in themselves or as having in turn been demonstrated. According to Aristotelian doctrine, a distinction must be made between demonstration in the strict sense, which concerns what is necessarily true, and demonstration in the improper sense, which concerns what is only probable. The first leads to science (scientia ) as such, which is knowledge of the necessary, whereas the second pertains to dialectics, which is concerned with probable knowledge.

The study of reasoning can be undertaken from the viewpoint of validity only, which considers form alone, or from the viewpoint of demonstration, which considers form and matter conjointly. The first viewpoint is that of formal logic, the second, that of material logic (see logic).

Evolution of Concept. Various conceptions of reasoning have evolved with the history of logic. According to the scholastic conception, which to a great extent was inherited from Aristotle, logic is the study of acts of the mind that relate to the acquisition of truth. In this view, conditions affecting the validity of reasoning and those affecting its truth are based upon the characteristics of the intellectual acts that are involved in the reasoning process and in demonstration. Since those acts can be attained only through philosophical reflection, logic, in this conception, has a philosophical base.

According to the modern conception, which is at the root of contemporary mathematical logic, formal logic must be considered as a science in the same sense as mathematics and must be developed in abstraction from all philosophical preconceptions. The study of reasoning is there attempted in terms of facts and without reference to acts of the mind; it considers only the properties of the objects of thought. This viewpoint finds its most radical expression in formalism. (see logic, symbolic.)

Scholastic Analysis. It is common scholastic teaching that reason or intellect has three fundamental operations: simple apprehension, judgment, and reasoning. In each, a distinction is made between the operation as such, which is an act of the intellect, and the product of the intellect that results from this operation. This product is to be distinguished from its oral or material expression. The term "reasoning" may denote the operation of the mind in apprehending a group of propositions (the antecedent) as inferring another proposition (the consequent) and concluding from the antecedent to the consequent. It may denote also the product of this operation, called argumentation, which is the logical whole formed by the antecedent and the consequent: "a group of propositions in orderly sequence one of which (the consequent) is posited as inferred by the others (the antecedent)" (Maritain, 154). The term "argumentation" may denote the product of reasoning either as a mental object or as the oral or material expression of this object.

The consequence (consequentia ) is the logical link that the reasoning establishes between the antecedent and the consequent; it is the manifestation of an inference. Reasoning, as an act, is really a motion of the mind, a discursus wherein the mind, perceiving two propositions as true and as standing in some type of mutual relationship, perceives in this very connection the truth of a third proposition, which it itself forms and to which it gives its assent. Thus the mind, put in motion by the antecedent, finds its rest in the consequent. The antecedent may therefore be regarded as a cause of the consequent. The essential law that governs this process is the following: in a correct reasoning, it is impossible that the antecedent be true and the consequent false.

Deduction and Induction. There are two types of reasoning: deduction and induction. In deduction, the mind moves only on the plane of the intelligible; it makes manifest "the truth of the proposition in so far as it is contained in the universal truth from which it is derived" (Maritain, 161). The best known and most celebrated form of deductive reasoning is the assertoric syllogism. This is "an argumentation in which, from an antecedent that unites two terms to a third, a consequent is inferred uniting these two terms to each other" (ibid. 169). Aristotelian and scholastic logicians have considered also other forms of deductive reasoning, in particular those of modal logic and of propositional logic.

In induction, the mind moves from the sensible plane to the intelligible plane. Induction is "an argumentation in which the mind infers an universal truth from sufficiently enumerated singular cases" (ibid. 259).

Analysis and Synthesis. Induction and deduction may be further characterized in terms of analysis and synthesis. analysis, or division, is an operation that resolves a complex whole into its parts; it thus passes from the complex to the simple. synthesis is the reverse of this; it passes from the simple to the complex, from the parts to the whole. Induction may be regarded as a type of analysis: it goes from facts to laws, i.e., to the universal principles upon which the facts depend; these may be regarded as wholes of which the facts are parts. It proceeds by a resolutio materialis, resolving the conclusion into the elements from which the mind has drawn it as from its matter. Deduction, on the other hand, may be regarded as a type of synthesis: it goes from principles to their consequences. It proceeds by a resolutio formalis, resolving the conclusion to the intelligible truths on which it depends and finally to first principles that are self-evident. (It should be noted that not every analysis or synthesis involves reasoning; thus division of a concept is an analysis and judgment is a synthesis.)

Practical Reasoning. Demonstration in the strict sense, founded ultimately on the first principles of intellectual understanding, generates speculative, or theoretical, science. Apart from such science there is also practical science, which has human action and the regulation of this action as its object. Reasoning has a role to play in the practical order because, although human action as such proceeds from the will, the intellect presents the will with its object. And it is the intellect that deliberates, prior to the will's election, so as to make possible a judgment concerning means that can lead to the end proposed by the will (see human act).

Human action is concerned with the particular and the contingent. But there are first principles in the practical order, as in the speculative, and a corresponding habit that enables man to come to knowledge of such principles, namely, synderesis. Right reason (recta ratio ), starting with the principles furnished by synderesis and using the rules of reasoning (exactly as in the speculative order), establishes conclusions that constitute the rules of morality. conscience applies these rules to particular situations, to what must be done by the individual here and now. The judgment of conscience is located between moral science, which is knowledge of the principles and rules of action, and the last practical judgment, which decides the course of action to be taken. The judgment of conscience is directed by prudence, a habit that enables man to judge rightly the data of a practical problem and choose means adequate to the end in view. It makes use also of the cogitative power, an internal sense that enables man to perceive the goodness or harmfulness of an object and thus to make comparisons in the realm of practical knowledge.

Modern Analysis. In recent thought, a clear-cut distinction is made between the philosophical and the formal study of reasoning. Philosophical logic, much like scholastic logic, investigates norms of correct reasoning and the conditions required for the acquisition of truth. But logicians from the 19th century onward, applying mathematical methods to the study of the logical problems, have succeeded in creating a discipline that may be considered as a branch of mathematics, namely, mathematical, or symbolic, logic. H. B. Curry compares the relationship between this logic and philosophical logic to the relationship that exists between geometry considered as a pure mathematical science and geometry considered as a physical theory of real space.

Formal Methods. Mathematical logic investigates certain categories of formal systems considered in themselves and abstracting from particular philosophical positions or problems (see axiomatic system). Such formal methods have shown themselves particularly useful in studying the foundations of mathematics; metatheoretical studies of this type likewise make use of the methods of mathematical logic. Using such methods, for example, important work has been done in the elucidation and resolution of paradoxes (see antinomy). Scholastic logic had already contributed considerably to this subject, but modern logic has undertaken the study with more rigorous and strictly formalized methods.

Study of Content. The procedures of mathematical logic can be used also to study the content of reasoning. Since its beginnings, mathematical logic has been preoccupied chiefly with problems of deduction, and a great variety of deductive systems have been elaborated; these offer a much wider field for deductive reasoning than that provided by traditional logic.

Research on inductive reasoning, although less developed, is pursued in the same manner. Here the notion of probability plays a central role; thus investigations of induction are closely related to studies of the foundations of probability. An allied topic of research is the problem of decision. R. Carnap's work is particularly significant for having elaborated a program of inductive logic in the spirit of mathematical logic.

Finally, modern studies of scientific methodology have successfully employed the methods of formalism to study problems pertaining to the acquisition of truth. Studies of induction are partially concerned with such problems. Important studies have examined also the process of verification, the notion of explanation in modern science, the structure of scientific theories, the role of models, and special problems raised by the particular sciences.

See Also: methodology (philosophy).

Bibliography: m. j. adler, ed., The Great Ideas: A Syntopicon of Great Books of the Western World, 2 v. (Chicago 1952); v. 2, 3 of Great Books of the Western World 2:546568. j. maritain, Formal Logic, tr. i. choquette (New York 1946). i. m. bocheŃski, Formale Logik (Freiburg 1956), Eng. A History of Formal Logic, ed. and tr. i. thomas (Notre Dame, Ind. 1961). j. dopp, Notions de logique formelle (Louvain 1965). h. b. curry, The Foundations of Mathematical Logic (New York 1963). r. carnap, "The Aim of Inductive Logic," in Logic, Methodology and Philosophy of Science: Proceedings of the 1960 International Congress, ed. e. nagel et al. (Stanford 1962) 303318.

[j. a. ladriÈre]