### LOGIC
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
II. Historical outline.---
### I. Terminology
The term *l.* (from λόγος, concept, reason, originally an adjective: λόγος ἐπιστήμη, τέχνη, ἀρετή) is probably due to the commentators of Aristotle: “...a peripateticis haec ratio diligens disserendi logice vocatur” (Boeth., *In Top. Ciceronis*, I: PL 64, 1045 A). In Aristotle, however, the two main treatises on *l.* were called, from their content (the analysis of the structure and elements of reasoning), *Analytica* (cf. A. Trendelenburg, *Elementa logicae aristoteleae*, p. 47 ff.). Yet Aristotle had already spoken of προτάσεις λόγικα, distinct from γνώσεις (συνεχείς) (*Top.*, I, 13, 105 b 20). The term is in use among the Stoics: “Tria esse dicunt philosophiae genera: aliam quippe physicen, aliam ethicen, tertiam logicen...” (τὸ δὲ λόγον: Diog. Laert., VII, 39 ff.); it is then common with Cicero: “Iam in altera philosophiae parte, quae est quaerendi et disserendi, quae logice dicitur...” (*De finibus*, I, 7).
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### II. Nature and Problems of Logic
Human thought unfolds through multiple moments and processes in function of the nature of the subject in which it is situated and the diverse contents of reality. Its immanent finalistic tendency, in both the biological and theoretical senses, fundamentally determines it toward an immediate objectivity and truth. Yet in a higher order of knowledge (science and philosophy), thought is not guaranteed in its validity without more rigorous control and a more precise technique of exercise. Logic presents itself, both theoretically and historically, as a systematic analysis of the processes of thought in order to grasp, in a reflective setting, their structure, laws, functionality, and to serve as a means for their valid employment in the most arduous fields of knowledge.
The object of logic is, therefore, as St. Thomas defines it precisely, 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 Anal. post.*, I, lect. 1, 2, ca. initium). But rational activity is the object of logic not from the viewpoint of determining the ontological causes and conditions of thought (metaphysics), nor of its contingent qualifications as an act of the empirical subject (descriptive psychology), nor of its meaning and value as an expression of being (gnoseology). Logic is qualified and specified within the realm of philosophical inquiry (even if this specification was not entirely explicit at the outset and was later obscured or surpassed in various trends of modern philosophy) as the science of rational activity in its structure and internal validity.
More than thinking activity *qua* such, logic takes as its object the product of this activity—thought, its moments, its formulations—and considers its characters, relations, conditions, and norms of legitimacy and validity for its adequate correspondence with the structures of reality, in the various planes in which reality is given to human knowledge. Consequently, logic first presents a theoretical meaning and only secondarily assumes a normative character, inasmuch as, by the general conditions it defines for the functional validity of thought, it tends to ensure its accurate, correct, and vigilant use in the evaluation of reality, facts, and principles. It is in this sense that the qualification, once common, of logic 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 generalization of the common aspects of empirical reality; the judgment as the perception and affirmation of cognitive contents in their essential or existential characters; and inference as the process and dialectic of thought from one position to another, from principles to conclusions, from facts to principles. Logic determines the properties and conditions concerning the cognitive value of the concept in general: clarity, distinctness, definition, positivity, negativity, universality; it proposes the classification of concepts and establishes their possible relations: agreement, opposition, contradiction. It defines the forms and modalities of judgment, the relations of equivalence, inclusion, and opposition of subject and predicate, and thus the formal conditions of mutual implication or exclusion of judgments. Logic establishes the conditions of validity for inference, determining the laws of the syllogism and deduction (v.), clarifying the logical meaning of the process from particular to particular (analogy) or from particular to universal (induction). It also defines the limits of probability that may accompany rational processes and investigates the causes and reasons—predominantly formal—of error in conceptual syntheses, in the formulation of judgments, and in inferential processes (sophistry). Through further elaborations, logic determines the more complex activities of knowledge, particularly the methods of scientific research. It defines the framework and development of theoretical thought in 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, and the conditions that thought must fulfill to construct truth and certainty in the various orders of knowledge.
Logic, therefore, by its very nature, does not have a specifically and immediately inventive function in any particular field of knowledge. Invention and the process of truth occur through the intrinsic forces of thought (*logica naturalis*), which no reflective knowledge of its laws (*logica docens*) nor any, even valid, intellectual discipline (*logica utens*) could supply. The ancient and recent reproaches directed at logic when it is seen as an instrument and almost a thought-producing machine are justified. In this regard, the words of St. Thomas hold: “Logica non continetur sub philosophia speculativa quasi principalis pars, sed quasi quidam instrumentum ad eam, prout ministrat speculanti non instrumenta...” (*In Boeth. De Trinit.*, lect. 2a, q. 1, a. 2 ad 2).
An adequate conception of logic cannot isolate it as a mere formal study of thought. First, because thought is not possible as pure form. Thought, in any of its moments and thus in the very essential articulations of its dialectic, is not posited except as an affirmation of content, however abstract and universal. Even those laws said to be pure laws of thought, e.g., the principle of non-contradiction (which governs all deductive-syllogistic logic), belong to the content of thought, i.e., to being, as the most universal formal laws, and in a more solid and true manner (cf. St. Thomas, *In Met.*, lect. 11a, ed. Cathala, n. 1898). All the more reason logic cannot be purely formal when it proceeds to the determination of scientific procedures: these, in fact, are not analyzable without continual reference to the object, in which alone they acquire consistency and concreteness.
Consequently, while the idealistic conception that reduces logic to metaphysics—understanding it as the science of the activity of thought as an absolute principle or act—must rightly be rejected, it is nonetheless necessary to affirm
The intrinsic connection of logic with metaphysics itself. Precisely because every objective law of thought (and even of "thought thought") is a law of content, it opens up, if one understands and seeks a decisive validation of it, into a conception of the meaning of the object, and thus into a metaphysics. Research into the essence, purpose, action, and ontological dialectic of the spirit in nature and the world, even if it does not formally belong to logic insofar as the internal validity of thought can be described and sustained on its own, is nevertheless demanded by the intrinsic exigencies of logic itself, since no process of thought is fully clarified except in a determination of the concept of truth and of being. This is especially true of the first principles, which are the condition of all logic: their original meaning is indeed metalogical, determinable only from a metaphysical standpoint.
For the same reason—namely, the objective meaning inherent in the qualifications and conditions of validity of rational processes—it is equally evident that logic cannot be reduced to psychology (W. Wundt, Th. Lipps, Chr. Sigwart, B. Erdmann, E. Goblot, etc.). The validity of logical relations concerning the object of thought (qua object, i.e., the "thought-of," called by the Scholastics *ens rationis* and *secunda intentio*: cf. St. Thomas, *In Met.*, IV, lect. 4a, ed. cit., n. 574) transcends the laws governing the psychological activity of thought. Psychology is fact, history; logic is value, universality. Thought, as such, presents an emergence of meaning: the universal validity of its form in function of the absolute value of being. Although in its historical development it cannot escape the impact of all the psychological determinations of the empirical subject (will, feeling, interest, etc.—and a logic that aims at adequacy to the concreteness of thought must take this into account)—it transcends them as universals and necessities. Properly logical laws are situated on this plane: immanent to thought, they qualify its nature as a transcendental relation to being.
The reduction of logic to psychology (already rejected by Kant: *Critique of Pure Reason*, Transcendental Logic, §1; and opposed, after O. Külpe and E. Husserl, by modern thinkers together with the entire logical-mathematical school) was a consequence of positivism (v.), more unjustified than the general postulates of the system, given the immediate self-consistency, within their own order, of logical values in comparison with metaphysical formulations.
**III. Historical Notes.** — The logical problem, without considering here its earliest expressions in Indian thought (Nyāya), is already present, in its moment of insertion and continuity with metaphysics, at the dawn of Greek philosophy. As has been noted elsewhere (v. Conoscenza), it seems that underlying Parmenides’ conception of the unity and immobility of being is the logical principle of the identity-contradiction relation, which the concept of being-not-being asserts in human thought. In its normative-instrumental value, logic received some partial formulations (theory of proof and refutation) in Protagoras (cf. Diog. Laert., IX, 51 ff.: among Protagoras’ works are mentioned *Antilogiai* in two books, ibid., 55). The art of disputation and proof was also adopted by the Sophists, though in a debased sense, as verbal-formalistic argumentation aimed at demonstrating the absurd (cf. Aristotle, *De soph. elench.*, IX and passim). This tendency found further development in the institution (v.).
In Socrates, the logical significance of the inductive method stands out as a path to definition (concept) and to science. In Plato, Idea (v.) lends metaphysical meaning even to the logical problem. Dialectic expresses the reciprocal relation of identity and otherness among the Ideas (*Sophist*, 253d ff.). This relation is not merely abstract-formal 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 (*methexis*) in the immutable consistency of ideal being. The Idea of the Good (v.) as the summit and center of reality (*Republic*, 508b ff.) perhaps expresses the deepest and most absolute sense of Plato’s ontological dialectic.
With Aristotle, logic receives its essential scientific systematization. The preexisting elements are elaborated, exceptionally enriched, and brought to a synthesis still valid today, though incomplete. Aristotle’s intent was to analyze the procedures of scientific thought. Since science is the vision of the particular in the universal, Aristotelian logic converges on the syllogism (v.) as a demonstrative process (*apodeixis*) by which the derivation of the particular from the universal is clarified. The six Aristotelian treatises on logic (later gathered under the title *Organon*) develop: the classification of general concepts and relations of predicability (*Categories*); propositions and their relations according to quality, quantity, modality, and opposition (*On Interpretation*); the nature, form, laws, and figures of the syllogism (*Prior Analytics*); demonstration (*Posterior Analytics*); the sources of probable or dialectical argumentation (*Topics*); and sophistical argumentation (*On Sophistical Refutations*). Additional partial references are scattered throughout his works, notably the profound treatment of the principle of contradiction (v.) in *Metaphysics*, IV, 3 ff.
The significance of Aristotelian logic lies in its clear definition of the forms of deductive thought: it is thus substantially constructed upon the relations of identity-coherence-inclusion among ideas and the categorial determinations of the real. Mindful of the actual conditions of human knowing, Aristotle did not fail to emphasize the indispensable function of induction and sensory knowledge as the path to the universal and to science: “Science is not possible through the universal without induction, nor through induction without sensation” (*Posterior Analytics*, I, 18, 81b 2; cf. ibid., II, 19, 100a 3 ff.; *Nicomachean Ethics*, VI, 12, 1143b 5 ff.). In this, Aristotle anticipates the pure formalism later prevalent in logic. Yet within the same conception of science as the reduction of the particular to the universal, the limit of Aristotelian logic was already implicit. For being, in its phenomenal actuality, is not exhausted by the mere relation of identity-coherence but involves other essential relations: finality, causality, efficiency, measurability, number, probability. Aristotelian logic did not, nor could it at the time, develop in this direction—the only one valid for a fruitful science of nature. The centuries-long crystallization of its first, albeit admirable, formulation (Aristotle was clearly aware of the originality of his construction: *On Sophistical Refutations*, 34, 183b 16 ff.) later precluded Aristotelian logic from any fruitful application in the experimental sciences.
and pure nothingness: the third moment, becoming, expresses their dynamic unity, by which, in the rhythm of contradiction and the overcoming of every aspect of fact, the process of the real is realized.
The Hegelian conception was continued by Italian idealism. In Gentile, once the absolute reality is identified with the spiritual act, concrete and real logic 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 logica, I, 3rd ed., Florence 1940, p. 46). Ancient logic took as its object the «abstract logos», the «thought thought», that is, the contents of abstract thought separated from the reality of the spiritual act that posits them (as such it was and remains valid, albeit in the pure order of being and end, this objective); the logic of actuation, instead, is the science of the act understood as pure knowing» (ibid., p. 47), not bound in its absolute creative autonomy to the schemes of the moments 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 cognitive spirit «at every moment elaborates the course of the real» (L., ed. cit., p. 4). Since the spirit is dialectically developed (history) immanent to the real, logic as the science of universal theoretical activity embraces all historical problems and solutions: it thus identifies with philosophy as history (ibid., p. 329; cf. A. Rügge, Windelband, Enc. delle scienze filosofiche, I, Palermo 1914, p. 195).
The second half of the 19th century and the present one have seen a flourishing revival of logical studies both in the traditional sense or close to it (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 deepening of the relationship between logic and language, etc.), which confirm the unfoundedness of the Kantian judgment on the impossibility of progress in logic. Symbolic logic (v.) should be noted, which perfects, with the exactitude 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 logic of potentiation aims to determine the relative variations of entities and their reciprocal potentiation, with a view to a greater adequation of thought to the complex relative structures of the real. It is in this sense that the great contemporary logicians have been developed. They have precisely been the principles of scientific research based on logical procedures corresponding to the dialectical research of discovery in the phenomenal becoming of nature. If the new conception (and realization) of science has imposed going beyond traditional logic in this field, it is clear, however, that it has neither denied nor devalued II. 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.