Logic

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

SUMMARY:

I. Terminology

II. Nature and problems of logic

III. Historical overview.

I. TERMINOLOGY

The term l. (from λόγος, concept, reason, originally an adjective: λογική ἐπιστήμη, τέχνη, ἀρετή) is probably due to the commentators on Aristotle: «... a peripateticis haec ratio diligens disserendi logice vocatur» (Boeth., In Top. Ciceronis, I: PL 64, 1045 A). In Aristotle, however, the two principal treatises of l. were called, on the basis of their content (the analysis of the structure and 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 L

Human thought unfolds through multiple moments and processes, according to the nature of the subject in which it occurs and the diverse contents of reality. Its immanent purposive tendency, in the twofold biological and theoretical sense, fundamentally determines it toward an immediate objectivity and truth. But in a higher order of knowledge (science and philosophy), thought is not guaranteed in its validity without 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, on the level of reflection, its structure, laws, and functionality, and to serve as a means for its valid application in the more arduous fields of knowledge. The object of l. is therefore, as s. Thomas precisely defines it, rational activity, understanding reason in the broadest sense as the power of conceptualization, assertion, and 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 not the object of l. from the standpoint of determining the ontological causes and conditions of thought (metaphysics), nor of the contingent qualifications it assumes as an act of the empirical subject (descriptive psychology), nor of its meaning and value as an expression of being (epistemology). L. is characterized and specified within the sphere of philosophical inquiry (even though this specification was not entirely explicit at the outset and was later again obscured and superseded in various trends of modern philosophy) as the science of rational activity in its internal structure and validity. Rather than thinking activity as such, l. takes as its object the product of this activity, thought, its moments and formulations; it considers their characteristics, relations, conditions, and norms of legitimacy and validity, for their conformity to the structures of reality on the various levels at which reality is given to human knowledge. Consequently, l. first of all has a theoretical significance and only secondarily assumes a normative character, insofar as, by defining the general conditions for the functional validity of thought, it tends to guarantee its careful, correct, and self-vigilant use in the evaluation of reality, facts, and principles. It is in this sense that the once common designation of l. as an art can be justified: «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 the generalization of the common aspects of empirical reality; judgment, as the apperception and affirmation of noetic contents in their essential or existential characteristics; and inference, as the process and dialectic of thought from one position to another, from principles to conclusions, and from facts to principles. With regard to the concept, l. determines the properties and conditions concerning its noetic value in general: clarity, distinctness, definition, positivity, negativity, and universality; it proposes the classification of concepts and also establishes their possible relations: agreement, opposition, and contradiction. With regard to judgment, it defines the forms and modalities, the relations of equivalence, inclusion, and opposition between subjects and predicates, and hence the formal conditions of the mutual implication or exclusion of judgments. With regard to inference, l. establishes the conditions of validity, determining the deduction (v.), clarifying the logical meaning of the process from particular to particular (analogy) or from the particular to the universal (induction). It also defines the limits of probability that accompany, or may accompany, rational processes, and investigates the predominantly formal causes and reasons for error in conceptual syntheses, in the formulation of judgments, and in processes of inference (sophistry). Through further elaboration, l. determines the more complex activities of knowledge, particularly the methods of scientific inquiry. It defines the structure and 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 employed in the highest mathematical-physical research; and the conditions that thought must put into effect in order to construct truth and certainty within the various orders of knowledge.

L. therefore, by its very nature, has no specifically and immediately inventive function in any particular field of knowledge. The invention and advancement of truth are accomplished through the intrinsic powers of thought (l. naturalis), which no reflective knowledge of its laws (l. docens) and no, however valid, intellectual discipline (l. utens) could replace. The ancient and more recent reproaches directed against l. when it is regarded as an instrument, and almost as a machine producing thought, are justified. In this regard, the words of s. Thomas are pertinent: «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 within a purely formal study of thought. First of all, because thought cannot exist as pure form. Thought, in fact, does not arise, at any of its moments—and therefore not even in the essential articulations of its dialectic—except as the affirmation of a content, however abstract and universal. Those very principles that are called the pure laws of thought, for example, non-contradiction (which governs all deductive-syllogistic l.), belong to the content of thought, that is, to being, as the most universal formulations of its positivity and truth (cf. s. Thomas, In Met., lect. 11a, ed. Cathala, n. 1898). L. is even less capable of being purely formal when it proceeds to the determination of scientific procedures: these, in fact, cannot be analyzed without continual reference to the object, in which alone they acquire consistency and concreteness.

Consequently, while the idealistic conception that resolves l. into metaphysics—understanding it as the science of the activity of thought insofar as it is an absolute principle or act—must rightly be rejected, it is nevertheless necessary to maintain the

The intrinsic connection of l. with metaphysics itself. Precisely because every objective law of thought (even of “thought thought”) is a law of content, it opens by itself, whenever one understands it and seeks a conclusive validation of it, into a conception of the meaning of the object, and therefore into metaphysics. The inquiry into the essence, purpose, action, and ontological dialectic of the spirit in nature and in the world does not, therefore, formally belong to l., insofar as the internal validity of thought can be described and sustained in its own right; nevertheless, it lies within the intrinsic requirements of l. itself, since no process of thought is fully clarified except through a determination of the concept of truth and of being. This applies above all to the first principles, the condition of all logicality: their original meaning is in fact metalogical, and can be determined only from a metaphysical point of view. For the same reason—namely, the objective meaning inherent in the qualifications and conditions of validity of rational processes—the impossibility of reducing l. to psychology is equally evident (W. Wundt, Th. Lipp, Chr. Sigwart, B. Erdmann, E. Goblot, etc.). The validity of logical relations concerning the object of thought (as such, that is, the “thought,” called by the scholastics “ens rationis” and “secunda intentio”: cf. s. Tommaso, In Met., IV, lect. 4a, ed. cit., n. 574) lies beyond the laws governing the psychological activity of thinking. Psychology is fact and history; l. is value and universality. Thought, as such, presents an emergence of meaning that consists in the universal validity of its form as a function of the absolute value of being. Although, in its historical development, it cannot escape the influence of all the psychological determinations of the empirical subject (will, feeling, interest, etc.—and a l. that intends to correspond to the concreteness of thought must take this into account), it nevertheless transcends the subject as universality and necessity. Properly logical laws belong on this plane: immanent in thought, they characterize its nature as a transcendental relation to being. The reduction of l. to psychology (already rejected by Kant: Kritik d. r. Vernunft, Transcend. Logik., § 1, and opposed, after O. Külpe and E. Husserl, by important modern thinkers together with the entire logical-mathematical tendency) positivism (v.), and was more unjustified than the system’s general postulates, given the immediate self-consistency, within their own order, of logical values in comparison with metaphysical formulations.

III. HISTORICAL OUTLINE

The logical problem, leaving aside here its earliest expressions in Indian thought (Νχάγοι), is already present, at the moment of its insertion into and continuation with metaphysics, at the beginnings of Greek philosophy. As has been noted elsewhere (v. conoscenza), it seems that underlying the Parmenidean conception of the unity and immobility of being is the logical demand of the identity-contradiction relation, which the concept of being and non-being asserts in human thought. In its normative-instrumental significance, logic received certain partial formulations (the theory of proof and refutation) in Protagoras (cf. Diog. Laert., IX, 51 ff.: among Protagoras’ works are listed Ἀντίλογιῶν δύο, ibid., 55). The art of disputation and proof was also adopted by the sophists in a debased sense, as a verbal-formalistic argumentation tending toward the demonstration of the absurd (cf. Aristotle, De soph. elench., IX and passim). This tendency underwent further development in eristic (v.). In Socrates, one should note the logical significance of the inductive method as a path to definition (concept) and science. In Plato, idea (v.) also gives the logical problem metaphysical significance. Dialectic indicates the reciprocal relation of identity and otherness among ideas (Soph., 253 d ff.). This relation is not of a purely abstract-formal order, but expresses the real-finalistic nexus of ideas and, at the same time, the moments in the determination of reality, that is, the subordinate degrees of their participation (μετέξις) in the immutable consistency of ideal being. good (v.), as the summit and center of reality (Resp., 508 b ff.), perhaps expresses the deepest and most absolute meaning of Plato’s ontological dialectic. With Aristotle, logic received its essential scientific systematization. The pre-existing elements were elaborated, exceptionally enriched, and brought into a synthesis that remains valid even today, although incomplete. The aim of Aristotelian logic was to analyze the procedures of scientific thought. Since science is the vision of the particular in the universal, syllogism (v.) as a demonstrative process (ἀπόδειξις) through which the derivation of the particular from the universal is clarified. The six Aristotelian treatises on logic (later brought together under the title Organon) set out the classification of general concepts and relations of predicability (Κατεγορίας); propositions and their relations according to quality, quantity, modality, and opposition (Περὶ ἐξαιρείας); the nature, form, laws, and figures of the syllogism (Ἀναλυτικὰ πρότερα); demonstration (Ἀναλυτικὰ δάτερα); the sources of probable or dialectical argumentation (Τοπικά); and sophistical argumentation (Περὶ σοφιστικῶν ἐκτήρων). One should add scattered partial references and, in particular, the profound contradiction (v.) in Met., IV, 3 ff. The significance of Aristotelian logic lies in its clear definition of the forms of deductive thought: it is therefore constructed essentially upon relations of identity-coherence-inclusion among ideas and the categorial determinations of reality. Because of his lively sense of the actual condition of human knowing, Aristotle did not fail to emphasize the indispensable function of induction and 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, 8 i 2; cf. ibid., II, 19, 100 a 3 ff.; Eth. nic., VI, 12, 1143 b 5 ff.). In this respect Aristotle condemned in advance the pure formalism that later became prevalent in logic. Nevertheless, the limitation of Aristotelian logic was also immanent in the very conception of science as the reduction of the particular to the universal. Being, in fact, in its actual phenomenal reality, is not expressed solely on the basis of the conceptual relation of identity-coherence, but involves many other relations essential to its structure: finality, causality, efficacy, measurability, number, and probability. Aristotelian logic did not, nor could it then, develop in this direction, the only one valid for a fruitful science of nature. Its crystallization, for centuries, in its first and admirable formulation (Aristotle had a clear awareness of the originality of his construction: De soph. elench., 34, 183 b 16 ff.) later precluded any useful employment of Aristotelian logic in the experimental sciences.

Enriched at certain particular points (the proposition and the hypothetical-disjunctive syllogism: Eudemus, Theophrastus; the fourth figure of the syllogism: Galen; relations among propositions and the conditional syllogism: the Stoics; while skepticism had already challenged its heuristic-inventive value: Sextus Empiricus, Pyrrh. hypoth., II, 14); commented upon by Alexander of Aphrodisias, Themistius, David the Armenian, Philoponus, Iamblichus, and especially Porphyry (Βλασιονὴ εἰς τὰς Ἀριστοτέλους κατεγορίας), Aristotelian logic passed into scholasticism, first through the partial translations and works of Boethius, Martianus Capella, and Victorinus, then through the full knowledge of the Organon in translations from Arabic, and finally in the original text. Medieval thought clarified and elaborated the various arguments of the Organon, determined the concept of logic more distinctly, and, above all, developed the doctrine of universals (v.) in a gnoseological-metaphysical direction, in which Benedetto Croce himself recognizes a significant advance in the logical problem (L., 6th ed., Bari 1942, p. 336). Among the logical treatments of scholasticism, one should recall: the Liber sex principiorum of Gilbert Porretanus (on Aristotle’s final six categories), Giovanni di Salisbury (v.); the Summa totius logicae of Hervaeus Natalis (v.), formerly attributed to St. Thomas; the commentaries of Albert the Great and St. Thomas (the latter on the Perihermeneias, partial, and on the Analytici post.); Scoto’s Quaestiones super praedicamenta and Peter of Spain’s (Giovanni XXI) Summulae logicales, which present in summary form the whole of Aristotelian logic and in which the mnemonic verses indicating the modes of the syllogism appear for the first time. The further scholastic elaborations of the fourteenth and fifteenth centuries are characterized by a complete lapse into verbal-abstract formalism (a typical example is Lull’s Ars magna), Occam (v.)

the denial of the realistic value of concepts, and therefore of the syllogistic process that relied upon them, heralds the reaction against scholastic l. (already expressed earlier, on the basis of different postulates, in the anti-Aristotelian orientation of the mystical currents: the school of S. Vittore, s. Pier Damiani). The new concept of science as experimental knowledge, which was gradually taking shape, also contributed to this. Valla, Agricola, Erasmo, BRUGNATO (v.) were unanimous in condemning traditional l. Pietro Ramo (De la Ramée), in the work Institutum dialecticarum libri tres (Paris 1553), argued for the sterility of Aristotelian l., without, however, succeeding in achieving any valid innovation. Bacon, while not denying the formal-demonstrative value of the syllogism, asserted the uselessness of traditional l. for science: «Logica quae nunc habetur inutilis est ad inventionem scientiarum» (Novum Organum, I, af. 11). His appeal to induction was nevertheless not free from limitations, since it ignored the value of the hypothesis and the function of mathematics in the study of nature, which Galileo, on the other hand, intuited and applied. For Descartes, too, the l. of the schools «rather spoils than perfects the mind», since it serves only to expound what one already knows and, worse still, teaches one «to speak without discernment of things one does not know» (Princ. philos., pref., ed. C. Adam-P. Tannery, IX, part 2ª, p. 13, lines 25 ff.; cf. Discours de la méthode, part 2ª, cited ed., VI, p. 17, lines 15 ff.). True l., on the contrary, must «direct reason to discover what is unknown». Nevertheless, the L. of Port-Royal (Logique ou l'art de penser, 1662), of Cartesian inspiration, remains essentially Aristotelian. Leibniz (to whom belongs the first attempt at mathematical l.) maintained that the rules of traditional l. should not be despised (Die philosophische Schriften, ed. C. J. Gerhardt, IV, Berlin 1882, pp. 425-26); its value was also recognized by Wolff, who defined l. as: «scientia dirigendi facultatem conoscitivam in cognoscenda veritate» (Philos. rationalis sive logica, Discursus praelim., § 61, prolegom., § 1). Empiricism (Locke, Berkeley, Hume), on the other hand, developed exclusively in a gnoseological direction, making only later, through the work of J. Stuart Mill (A system of logic rationalistic and inductive, London 1843), a direct contribution to the progress of l., particularly inductive l.

For Kant, traditional l., insofar as it «sets forth and proves only the formal rules of thought», was to be regarded as perfect and complete since Aristotle (Krit. d. r. Vernunft, preface to the 2ª ed.). But precisely because it concerns only the logical form of thought in general and has no relation to the objects of knowledge, it «constitutes almost nothing more than the vestibule of the sciences» (ibid.; cf. part 2ª, L. trascendentale, intr., § 1). The new Kantian concept of science as the a priori objectivity of the mind also determines the meaning of the new transcendental l.: it «is the science of pure understanding and rational knowledge», insofar as it investigates the a priori forms according to which objects are thought, and therefore defines the origin, scope, and validity of all a priori knowledge. Transcendental l. (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 by the object, and at the same time as a determination of the objective a priori conditions of science (ibid.; § 11 ff.), and consequently with a metaphysical-gnoseological significance.

Idealism, elevating reason to absolute reality and autonomy, further developed l. in the sense of a metaphysics of thought and its forms, and therefore of reality and history. In Hegel, l. 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 one truth and the supreme reality» (Philos. d. Gesch., intr., § 1; Italian trans. Calogero-Fatta, Florence 1941, p. 9), l. coincides with metaphysics (Enz., § 24). In determining the internal dialectic of spirit, through which truth constructs itself in absolute immanence and autonomy, l. therefore describes the constitutive moments and categories of reality. The first forms of dialectic are pure being and pure nothingness: the third moment, becoming, expresses their dynamic unity, through which, in the rhythm of contradiction and the overcoming of every aspect of the finite, the process of the real is actualized.

The Hegelian conception was continued by Italian idealism. In Gentile, once absolute reality had been identified with the spiritual act, concrete and real l. is precisely the science of thought in act which, in its freedom and creativity, «constructs the object as the concreteness of its own being» (Sistema di l., 1, 3ª ed., Florence 1940, p. 46). Ancient l. 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, although within the pure order of objective abstractness); the l. 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, l. is «the science of the pure and concrete concept», that is, of the universal theoretical form in which the knowing spirit «at every moment elaborates the course of the real» (L., cited ed., p. 4). Since spirit is dialectical development (history) immanent in the real, l., as the science of universal theoretical activity, embraces all historical problems and 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 nineteenth century and the present century have witnessed a flourishing revival of logical studies, both in the traditional sense or in directions 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, neopositivism, to which we owe a deeper investigation of the relation between l. and language, etc.), confirming the groundlessness of Kant’s judgment concerning the impossibility of progress in l. Symbolic l. (v.) should be mentioned, as it perfects, through the precision of the symbol, the logical methods of verification and proof and tends toward a more accurate expression of scientific thought. In Italy, A. Pastore’s l. of potentiation proposes the determination of the relative variations of entities and of their reciprocal potentiation, with the aim of bringing thought into greater adequation with the complex relative structures of the real. It is chiefly in this direction that current logical studies are developing. They have been promoted by the very refinement of scientific research, founded upon logical procedures corresponding to the rich dialectic discovered in the phenomenal becoming of nature. If the new conception (and realization) of science has made it necessary, in this field, to go beyond traditional l., it is nevertheless clear that it has neither denied nor devalued II. The laws of logical-deductive thought remain, for the ultimate investigation and determination of the real (metaphysics), which is also the most essential to the human problem, the irreplaceable path 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. II. 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. II. 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