Logic

LOGIC. - It is the science of the structure and processes of thought in relation to their functional validity.

I. TERMINOLOGY

The term l. (from λόγος, concept, reason, originally an adjective: λογική ἐπιστήμη, τέχνη, ἀρετή) is probably due to Aristotle's commentators: "... a peripateticis haec ratio diligens disserendi logice vocatur" (Boeth., In Top. Ciceronis, I: PL 64, 1045 A). In Aristotle, on the other hand, the two principal treatises of l. were called, from their content (the analysis of the structure and the elements of reasoning) Ἀναλυτικά (cf. A. Trendelenburg, Elementa logicae aristoteleae, p. 47 ff.). But Aristotle had already spoken of προτάσεις λογικαί, distinguished from the ἠθικαί and φυσικαί (Top., I, 13, 105 b 20). The term is in use among the Stoics: "Tripartitam esse dicunt philosophiae rationem: aliam quippe physicen, ethicen aliam, tertiam logicen..." (τὸ δὲ λογικόν: Diog. Laert., VIII, 39 ff.); it is, therefore, common from Cicero onward: "Iam in altera philosophiae parte, quae est quaerendi et disserendi, quae logice dicitur..." (De finibus, I, 7).

II. NATURE AND PROBLEMS OF LOGIC

Human thought unfolds through multiple moments and processes as a function of the nature of the subject in which it is posited and of the different contents of the real. Its immanent finalistic tendency, in the double sense, biological and theoretical, fundamentally determines it toward an objectivity and immediate truth. But in a higher order of knowledge (science and philosophy) thought is not guaranteed in its validity without a more rigorous control and a more careful technique of exercise. L. presents itself, theoretically and historically, as a systematic analysis of the processes of thought in order to grasp in a reflective setting its structure, its laws, its functionality, and to serve as a means of its valid employment in the most arduous fields of knowledge. The object of l. is therefore, as St. Thomas exactly defines it, rational activity, understanding reason in the broadest sense, as the power of conceptualization, assertion, inference: «Haec est ars logica, id est rationalis scientia. Quae non solum rationalis est ex hoc quod est secundum rationem..., sed etiam ex hoc quod est circa ipsum actum rationis sicut circa propriam materiam» (In Anad. post., I, lect. 1°, ca. initium). But rational activity is the object of l. not from the point of view of a determination of the ontological causes and conditions of thought (metaphysics), nor of the contingent qualifications that it assumes as an act of the empirical subject (descriptive psychology), nor even of its meaning and value as an expression of being (epistemology). L. qualifies and specifies itself within the ambit of philosophical inquiry (even if such specification was not entirely explicit at the beginning and was later again obscured and superseded in various currents of modern philosophy) as the science of rational activity in its structure and internal validity. More than thinking activity as such, l. takes as its object the product of this activity, thought, its moments, its formulations; it considers their characters, relations, conditions and norms of legitimacy and validity for their adequation to the structures of the real, on the various planes on which this is given to human knowledge. Consequently l. presents first of all a theoretical meaning and only secondarily assumes a normative character insofar as, through the general conditions that it defines for the functional validity of thought, it tends to guarantee a careful, correct use of it, vigilant of itself in the evaluation of reality, of facts, of principles. It is in this sense that the qualification, once common, of l. as an art can find justification: «ars quaedam... directiva ipsius actus rationis: per quam scilicet homo in ipso actu rationis ordinate et faciliter et sine errore procedat» (ibid.; cf. Sum. Theol., 1a-2ae, q. 57, a. 3 ad 3).

The fundamental structure of the theoretical activity of reason presents three essential forms: the concept as the categorical expression of being or generalization of the common aspects of empirical reality; the judgment as apperception and affirmation of noetic contents in their essential or existential characters; inference as the process and dialectic of thought from one position to another, from principles to conclusions, from facts to principles. Of the concept l. determines the properties and conditions concerning its noetic value in general: clarity, distinctness, definition, positivity, negativity, universality; it proposes the classification of concepts and further establishes their possible relations: compatibility, opposition, contradiction. Of the judgment it defines the forms and modalities, the relations of equivalence, inclusion and opposition of subjects and predicates, and then the formal conditions of the mutual implication or exclusion of judgments. Of inference l. establishes the conditions of validity, determining the laws of the syllogism and of deduction (v.), clarifying the logical meaning of the process from particular to particular (analogy) or from particular to universal (induction). It further defines the limits of probability that are or can be joined to rational processes, and it investigates the causes and reasons, predominantly formal, of error in conceptual syntheses, in the formulation of judgments, in processes of inference (sophistry). With further elaborations l. determines the more complex activities of knowledge, in particular the methods of scientific research. It defines the framework and the development of theoretical thought in the philosophical sciences, clarifies the various moments of the inductive experimental process (observation, hypothesis, verification, law), the particular inventive technique in the highest mathematical-physical research, the conditions that thought must bring into play in order to construct truth and certainty in the various orders of knowledge.

L. therefore does not have, by its very nature, a specifically and immediately inventive function in any particular field of knowledge. The invention and progress of truth are accomplished through the intrinsic forces of thought (l. naturalis) which no reflective knowledge of its laws (l. docens) and no intellectual discipline, however valid (l. utens), could replace. The ancient and recent reproaches directed at l. when one tends to see in it an instrument and almost a machine producing thought are justified. On this point the words of St. Thomas hold good: «Logica non continetur sub philosophia speculativa quasi principalis pars, sed quasi quidam reductum ad eam, prout ministrat speculationi sua instrumenta...» (In Boeth. De Trinit., lect. 2a, q. 1, a. 1 ad 2).

An adequate conception of l. cannot isolate it into a purely formal study of thought. First of all because thought as pure form is not possible. Thought in fact does not posit itself, in any of its moments, and therefore in the very essential articulations of its dialectic, except as the affirmation of a content, however abstract and universal. Those very things that are called the pure laws of thought, e.g., non-contradiction (which sustains the whole deductive-syllogistic l.), belong to the content of thought, that is, to being, as the most universal formulations of its positivity and truth (cf. St. Thomas, In Met., lect. 11a, ed. Cathala, n. 1898). All the more so can l. not be purely formal when it passes to the determination of scientific procedures: these in fact cannot be analyzed without a continuous reference to the object, in which alone they acquire consistency and concreteness.

Consequently, if the idealistic conception that resolves l. into metaphysics, understanding it as the science of the activity of thought as absolute principle or act, is rightly to be rejected, nevertheless the intrinsic connection of logic with metaphysics itself. Precisely because every objective law of thought (even of thought "thought") is a law of content, it opens by itself, wherever one understands and seeks a definitive validation of it, into a conception of the meaning of the object, and therefore into a metaphysics. The inquiry into the essence, finality, action, and ontological dialectic of the spirit in nature and in the world, if it therefore does not fall formally within logic insofar as the internal validity of thought is describable and stands by itself, is nonetheless within the intrinsic demands of logic itself, insofar as no process of thought is fully clarified except in a determination of the concept of truth and of being. This holds above all for the first principles, the condition of all logicality: their original meaning is in fact metalogical, not determinable except from the metaphysical point of view. For the same reason, that is, because of the objective meaning inherent in the qualifications and conditions of validity of rational processes, the impossibility of resolving logic into psychology is equally manifest (W. Wundt, Th. Lipp, Chr. Sigwart, B. Erdmann, E. Goblot, etc.). The validity of the logical relations concerning the object of thought (as such, that is, the "thought," called by the Scholastics "ens rationis" and "secunda intentio": cf. St. Thomas, In Met., IV, lect. 4a, ed. cit., n. 574) is beyond the laws that govern the psychological activity of thinking. Psychology is fact, history; logic is value, universality. Thought presents, as such, an emergence of meaning that is the universal validity of its form in function of the absolute value of being. If in its historical becoming it cannot escape the incidence of all the psychological determinations of the empirical subject (will, feeling, interest, etc.: and this must be taken into account by a logic that intends to conform to the concreteness of thought), it nonetheless transcends them as universality and necessity. The properly logical laws stand on this plane: immanent to thought, they qualify its nature as a transcendental relation to being. The resolution of logic into psychology (already denied by Kant: Kritik d. r. Vernunft, Transcend. Logik., § 1, and against which, after O. Külpe and E. Husserl, valid modern thinkers reacted together with the entire logico-mathematical trend) presented itself as a consequence of positivism (v.), more unjustified than the general postulates of the system, because of the immediate self-consistency, in their order, of logical values in comparison with metaphysical formulations.

III. HISTORICAL NOTES

The logical problem, not considering here its first expressions in Indian thought (Nyāya), is already present, in its moment of insertion into and continuation with metaphysics, at the beginnings of Greek philosophy. As has been noted elsewhere (v. conoscenza), it seems that at the foundation of the Parmenidean conception of the unity and immobility of being lies the logical exigency of the identity-contradiction relation that the concept of being and non-being asserts in human thought. In its normative-instrumental value, logic had certain partial formulations (theory of proof and of refutation) in Protagoras (cf. Diog. Laert., IX, 51 ff.: among the works of Protagoras are remembered the Ἀντιλογιῶν δύο, ibid., 55). The art of disputation and of proof was moreover taken up by the Sophists also in a pejorative sense as verbal-formalistic argumentation tending to the demonstration of the absurd (cf. Aristotle, De soph. elench., IX and passim). This tendency had further developments in eristic (v.). In Socrates one must note the logical significance of the inductive method as a path to definition (concept) and to science. In Plato the ontological value of the idea (v.) confers on the logical problem also a metaphysical significance. Dialectic indicates the reciprocal relation of identity and otherness of the ideas (Soph., 253 d ff.). This relation is not of a purely abstract-formal order but expresses the real-finalistic nexus of the ideas and at the same time the moments of the determination of the real, that is, the subordinate degrees of their participation (μέθεξις) in the immutable consistency of ideal being. The idea of the good (v.) as summit and center of reality (Resp., 508 b ff.) perhaps expresses the deepest and most absolute sense of Plato's ontological dialectic. With Aristotle logic receives its essential scientific systematization. The pre-existing elements are elaborated, exceptionally enriched and brought to a synthesis still valid today, although incomplete. The aim of Aristotelian logic was to analyze the procedures of scientific thought. Since science is vision of the particular in the universal, Aristotelian logic converges on the syllogism (v.) as demonstrative process (ἀπόδειξις) by which the derivation of the particular from the universal is made clear. The six Aristotelian treatises on logic (later gathered under the title Organon) set out the classification of general concepts and of the relations of predicability (Κατηγορίαι); propositions and their relations according to quality, quantity, modality, opposition (Περὶ ἑρμηνείας); the nature, form, laws and figures of the syllogism (Ἀναλυτικὰ πρότερα); demonstration (Ἀναλυτικὰ ὕστερα); the sources of probable or dialectical argumentation (Τοπικά); sophistic argumentation (Περὶ σοφιστικῶν ἐλέγχων). To these must be added scattered partial references and in particular the profound treatment of the principle of contradiction (v.) in Met., IV, 3 ff. The significance of Aristotelian logic lies in the clear definition of the forms of deductive thought: it is therefore constructed substantially on the relations of identity-coherence-inclusion among ideas and the categorial determinations of the real. Because of the lively sense he had of the effective condition of human knowing, Aristotle did not fail to underline the indispensable function of induction and of sensible knowledge, as a path to the universal and to science: "science is not possible by way of the universal without induction, nor by way of induction without sense" (Anal. post., I, 18, 81 a 2; cf. ibid., II, 19, 100 a 3 ff.; Eth. nic., VI, 12, 1143 b 5 ff.). In this Aristotle condemns in advance the pure formalism later prevalent in logic. Nevertheless in the very conception of science as reduction of the particular to the universal there was also immanent the limit of Aristotelian logic. Being, in fact, in its effective phenomenal reality, does not unfold on the sole basis of the conceptual identity-coherence relation but involves many other relations essential to its structure: finality, causality, efficiency, measurability, number, probability. Aristotelian logic did not develop, nor could it then develop, in this direction, the only valid one for a fruitful science of nature. The crystallization, for centuries, in its first, albeit admirable, formulation (Aristotle was clearly conscious of the originality of his construction: De soph. elench., 34, 183 b 16 ff.) later precluded for Aristotelian logic any useful employment in the experimental sciences.

Integrated in certain particular points (hypothetical disjunctive proposition and syllogism: Eudemus, Theophrastus; fourth figure of the syllogism: Galen; relations among propositions and conditional syllogism: the Stoics; while skepticism already contested its heuristic-inventive value: Sextus Empiricus, Pyrrh. hypoth., II, 14); commented on by Alexander of Aphrodisias, Themistius, David the Armenian, Philoponus, Iamblichus, and in particular by Porphyry (Εἰσαγωγὴ εἰς τὰς Ἀριστοτέλους κατηγορίας), Aristotelian logic passed to Scholasticism, in the partial translations and works of Boethius, Martianus Capella, Victorinus first, then in the integral knowledge of the Organon in versions from the Arabic, and then in the text itself. Medieval thought clarified and elaborated the various subjects of the Organon, determined more distinctly the concept of logic, and, principally, developed in a gnoseological-metaphysical sense the doctrine of universals (v.), in which Benedetto Croce himself recognizes no slight advancement of the logical problem (L., 6th ed., Bari 1942, p. 336). Among the logical treatises of Scholasticism there should be remembered: the Liber sex principiorum of Gilbert de la Porrée (on the last six categories of Aristotle), the Metalogicus of John of Salisbury (v.); the Summa totius logicae of Herveus Natalis (v.), formerly attributed to St. Thomas; the commentaries of Albert the Great and of St. Thomas (the latter on the Perihermeneias, partial, and on the Posterior Analytics); the Quaestiones super praedicamenta of Scotus and the Summulae logicales of Peter of Spain (John XXI), which set out in summary all of Aristotelian logic and where there appear for the first time the mnemonic verses indicating the modes of the syllogism. The further Scholastic elaborations of the 14th-15th centuries are characterized by the full fall into verbal-abstractistic formalism (a typical example being the Ars magna of Lull), while with Ockham (v.)

the challenge to the realistic value of concepts, and therefore to the syllogistic process that made use of them, heralds the movement of reaction against scholastic logic (already expressed earlier, on the basis of postulates of another kind, in the anti-Aristotelian orientation of the mystical currents: school of St. Victor, St. Peter Damian). The new concept, which was being elaborated, of science as experimental knowledge contributes to this. Valla, Agricola, Erasmus, Bruno (v.) are in agreement in condemning traditional logic. Peter Ramus (De la Ramée) in his work Institutum dialecticarum libri tres (Paris 1553) maintains the sterility of Aristotelian logic, without however managing any valid innovation. Bacon, while not denying the formal-demonstrative value of the syllogism, affirms the uselessness for science of traditional logic: «Logica quae nunc habetur inutilis est ad inventionem scientiarum» (Novum Organum, I, aph. 11). His appeal to induction is not however exempt from limits, in that it ignores the value of hypothesis and the function of mathematics in the study of nature, which was instead intuited and applied by Galileo. Also for Descartes the logic of the schools «corrupts rather than perfects the mind» in that it serves only to set forth what one already knows and, worse, teaches the manner «of speaking without discernment of things that one does not know» (Princ. philos., preface, ed. C. Adam-P. Tannery, IX, part 2, p. 13, lines 25 ff.; cf. Discours de la méthode, part 2, ed. cit., VI, p. 17, lines 15 ff.). The true logic must instead «direct reason to discover what it does not know». Nevertheless the Logic of Port-Royal (Logique ou l'art de penser, 1662), of Cartesian inspiration, remains substantially Aristotelian. Leibniz (to whom the first attempt at mathematical logic is owed) affirms that the rules of traditional logic must not be despised (Die philosophische Schriften, ed. C. J. Gerhardt, IV, Berlin 1882, pp. 425-26); its value is recognized also by Wolff, who defines logic as: «scientia dirigendi facultatem cognoscitivam in cognoscenda veritate» (Philos. rationalis sive logica, Discursus praelim., § 61, prolegom., § 1). Empiricism (Locke, Berkeley, Hume), on the other hand, develops exclusively in a gnoseological sense, bringing only later, with the work of J. Stuart Mill (A system of logic rationalistic and inductive, London 1843), a direct contribution to the progress of logic, particularly inductive logic.

For Kant traditional logic, in that it «sets forth and proves only the formal rules of thought», is to be considered perfect and complete from Aristotle onward (Krit. d. r. Vernunft, preface to the 2nd ed.). But it, precisely because it concerns only the logical form of thought in general and has no relation to the objects of knowledge, «constitutes almost nothing other than the vestibule of the sciences» (ibid.; cf. part 2, Transcendental Logic, intr., § 1). The new Kantian concept of science as the a priori objectivity of the mind also determines the meaning of the new transcendental logic: it «is the science of the pure understanding and of rational knowledge» in that it seeks the a priori forms according to which objects are thought, and therefore defines the origin, the extent and the validity of all a priori knowledge. Transcendental logic (analytic and dialectic: the latter precisely as the science of the limits of rational knowledge) thus presented itself as an analysis of the internal structure of thought presupposed to the object, and at the same time as the determination of the a priori objective conditions of science (ibid.; § 11 ff.), with therefore a metaphysical-gnoseological meaning.

Idealism, elevating reason to absolute reality and autonomy, further developed logic in the sense of a metaphysics of thought and of its forms and therefore of reality and of history. In Hegel logic is «the science of the pure Idea, that is, of the Idea in the abstract element of thought» (Enz., § 19). It therefore concerns the forms of the Absolute insofar as it is pure thought. Since thought is «the unique truth and the supreme reality» (Philos. d. Gesch., intr., § 1; Ital. trans. Calogero-Fatta, Florence 1941, p. 9), logic coincides with metaphysics (Enz., § 24). In the determination of the internal dialectic of the spirit by which, in absolute immanence and autonomy, truth is constructed upon itself, logic accordingly describes the moments and the categories constitutive of reality. The first forms of the dialectic are pure being and pure nothing: the third moment, becoming, expresses their dynamic unity, by which, in the rhythm of contradiction and of the overcoming of every aspect of the finite, the process of the real is brought about.

The Hegelian conception is continued by Italian idealism. In Gentile, absolute reality having been identified with the spiritual act, concrete and real logic is precisely the science of thought in act which, in its freedom, is creativity and «constructs the object as the concreteness of its own being» (Sistema di l., 1, 3rd ed., Florence 1940, p. 46). Ancient logic took as its object the «abstract logos», «thought thought», that is, the contents of thought abstracted from the reality of the spiritual act that posits them (as such it was and remains valid, though in the pure order of objective abstractness); the logic of actualism, on the other hand, «is the science of the act understood as pure knowing» (ibid., p. 47), not bound in its absolute creative autonomy to the schemas of the moments that it posits and resolves in its becoming. For Croce logic is «the science of the pure and concrete concept», that is, of the universal theoretical form in which the knowing spirit «elaborates at every moment the course of the real» (L., ed. cit., p. 4). Since the spirit is dialectical development (history) immanent to the real, logic as the science of universal theoretical activity embraces all problems and historical solutions: it therefore identifies itself with philosophy as history (ibid., p. 329; cf. A. Rüge-G. Windelband, Enc. delle scienze filos., I, Palermo 1914, p. 195).

The second half of the 19th century and the present one have seen a luxuriant reflowering of logical studies both in a traditional sense or close to the traditional one (W. Hamilton, F. Überweg, A. Trendelenburg, W. Windelband, etc.), and in other directions (B. Bolzano, E. Boutroux, H.-L. Bergson, E. Husserl, neo-positivism, to which an in-depth study of the logic-language relationship is owed, etc.) which confirm the groundlessness of the Kantian judgment on the impossibility of progress in logic. Mention must be made of symbolic logic (v.), which perfects, with the exactness of the symbol, the logical methods of verification and proof and tends toward a more accurate expression of scientific thought. In Italy the logic of potentiation of A. Pastore proposes the determination of the relative variations of entities and of their reciprocal potentiation, with the aim of a greater adequation of thought to the complex relative structures of the real. It is in this sense that present-day logical studies are predominantly developing. They have been promoted by the very refinement of scientific research set upon logical procedures responding to the rich dialectic discovered in the phenomenal becoming of nature. If the new conception (and realization) of science has imposed the need to go beyond, in this field, traditional logic, it is clear nevertheless that it has neither denied nor devalued it. The laws of logical-deductive thought remain, for the ultimate research and determination of the real (metaphysics), which is also the most essential to the human problem, the irreplaceable itinerary and norm of reason.

York 1942; L. Gabriel, Vom Brahma zur Existenz. Gesch. der Logik u. Philos., Vienna 1948. Indicazioni storiche generali e su singoli autori in Überweg, IV, pp. 666, 679, 682, 704. Ampia bibl. storica recente in G. A. De Bric, Bibli. philosophica 1934-45, I, Bruxelles 1950, pp. 12-14, 29, 66, 187-88, 641 (sulla l. indiana). Opere sistematiche. Fra le principali: B. Condillac, Logique, Parigi 1781; H. Lotze, Logik, Lipsia 1843; A. Rosmini, L. Torino 1854; ed. nazionale, 2 voll., Milano 1942-43; W. Hamilton, Lectures on metaph. and logic, 4 voll., Londra 1859-60; W. S. Jevons, Elementary lessons of logic, ivi 1870, trad. it. di G. Capone-Braga, Padova 1948; A. Trendelenburg, Logische Untersuchungen, 2 voll., 3ª ed., Berlino 1870; ed., Elementa logica aristotelicae, 6ª ed., ivi 1892; E. Husserl, Die logischen Untersuchungen, 2 voll., Halle 1900-1901; 2ª ed. rifatta, ivi 1913-22; H. Joseph, An introduction to logic, 2ª ed., Oxford 1916; W. Wundt, Logik, 5ª ed., 3 voll., Stoccarda 1919-24; F. Bradley, The principles of logic, 2 voll., 2ª ed., Londra 1922; Chr. Sigwart, Logik, 5ª ed., Tubinga 1924; E. Gublot, Traité de logique, 2ª ed., Parigi 1929; J. Dewey, Logic, the theory of inquiry, Nuova-York 1933, trad. it. Torino 1948; A. Pastore, La l. del potenziamento, Napoli 1935; F. Orestano, Nuove vedute logiche, Milano 1939. Fra i neoscolastici: G. Coffey, The science of logic, 2 voll., rist. Londra 1918; T. Pesch, Institutions logicales, 3 voll., Friburgo 1868, 12ª ed. ivi 1919; D. Mercier, Logique, 7ª ed., Lovanio 1922; G. Joyce, Principles of logic, Londra 1926; J. Maritim, Elements de philosophie, II, Petite logique, Parigi 1933; J. Fröbes, Traité de logique, Roma 1940; U. Viglino, L., ivi 1941; J. Dopp, Lexum de logique formelle, Lovanio 1950. Ottimo sempre: Job. a S. Thoma, Cursus philos. thomisticus, Torino 1930. - Fra le opere recenti: H. Lefebure, Logique formelle, Logique dialectique (marxista), Parigi 1947; S. Lupasco, Logique et contradiction, ivi 1947; U. Künzel, Traditionelle und philos. Logik, Amburgo 1948; M. Granel, Logica, Madrid 1949; J. Piaget, Traité de logique, Parigi 1949; M. Prot, Langage et logique, Vers une logique nouvelle, ivi 1949; A. Sesmat, Logique, ivi 1950; V. W. Quine, Foundations of logic, Nuova York 1950; M. Beardsley, Practical logic, ivi 1950.

Ugo Viglino