parity of reasoning. We return then to the old view of Aristotle,
that truth is believing in being; that sense is true of its immediate
objects, and reasoning from sense true of its mediate objects;
and that logic is the science of reasoning with a view to truth, or
Logica est ars ratiocinandi, ut discernatur verum a falso. All we
aspire to add is that, in order to attain to real truth, we must
proceed gradually from sense, memory and experience through
analogical particular inference, to inductive and deductive
universal inference or reasoning. Logic is the science of all
inference, beginning from sense and ending in reason.
In conclusion, the logic of the last quarter of the 19th century may be said to be animated by a spirit of inquiry, marred by a love of paradox and a corresponding hatred of tradition. But we have found, on the whole, that logical tradition rises superior to logical innovation. There are two old logics which still remain indispensable, Aristotle’s Organon and Bacon’s Novum Organum. If, and only if, the study of deductive logic begins with Aristotle, and the study of inductive logic with Aristotle and Bacon, it will be profitable to add the works of the following recent German and English authors:—
Authorities.—J. Bergmann, Reine Logik (Berlin, 1879); Die Grundprobleme der Logik (2nd ed., Berlin, 1895); B. Bosanquet, Logic (Oxford, 1888); The Essentials of Logic (London, 1895); F. H. Bradley, The Principles of Logic (London, 1883); F. Brentano, Psychologie vom empirischen Standpunkte (Vienna, 1874); R. F. Clarke, Logic (London, 1889); W. L. Davidson, The Logic of Definition (London, 1885); E. Dühring, Logik und Wissenschaftstheorie (Leipzig, 1878); B. Erdmann, Logik (Halle, 1892); T. Fowler, Bacon’s Novum Organum, edited, with introduction, notes, &c. (2nd ed., Oxford, 1889); T. H. Green, Lectures on Logic, in Works, vol. iii. (London, 1886); J. G. Hibben, Inductive Logic (Edinburgh and London, 1896); F. Hillebrand, Die neuen Theorien der kategorischen Schlüsse (Vienna, 1891); L. T. Hobhouse, The Theory of Knowledge (London, 1896); H. Hughes, The Theory of Inference (London, 1894); E. Husserl, Logische Untersuchungen (Halle, 1891, 1901); W. Jerusalem, Die Urtheilsfunction (Vienna and Leipzig, 1895); W. Stanley Jevons, The Principles of Science (3rd ed., London, 1879); Studies in Deductive Logic (London, 1880); H. W. B. Joseph, Introduction to Logic (1906); E. E. Constance Jones, Elements of Logic (Edinburgh, 1890); G. H. Joyce, Principles of Logic (1908); J. N. Keynes, Studies and Exercises in Formal Logic (2nd ed., London, 1887); F. A. Lange, Logische Studien (2nd ed., Leipzig, 1894); T. Lipps, Grundzüge der Logik (Hamburg and Leipzig, 1893); R. H. Lotze, Logik (2nd ed., Leipzig, 1881, English translation edited by B. Bosanquet, Oxford, 1884); Grundzüge der Logik (Diktate) (3rd ed., Leipzig, 1891, English translation by G. T. Ladd, Boston, 1887); Werner Luthe, Beiträge zur Logik (Berlin, 1872, 1877); Members of Johns Hopkins University, Studies in Logic (edited by C. S. Peirce, Boston, 1883); J. B. Meyer, Ueberweg’s System der Logik, fünfte vermehrte Auflage (Bonn, 1882); Max Müller, Science of Thought (London, 1887); Carveth Read, On the Theory of Logic (London, 1878); Logic, Deductive and Inductive (2nd ed., London, 1901); E. Schröder, Vorlesungen über die Algebra der Logik (Leipzig, 1890, 1891, 1895); W. Schuppe, Erkenntnistheoretische Logik (Bonn, 1878); Grundriss der Erkenntnistheorie und Logik (Berlin, 1894); R. Shute, A Discourse on Truth (London, 1877); Alfred Sidgwick, Fallacies (London, 1883); The Use of Words in Reasoning (London, 1901); C. Sigwart, Logik (2nd ed., Freiburg-i.-Br. and Leipzig, 1889–1893, English translation by Helen Dendy, London, 1895); K. Uphues, Grundlehren der Logik (Breslau, 1883); J. Veitch, Institutes of Logic (Edinburgh and London, 1885); J. Venn, Symbolic Logic (2nd ed., London, 1894); The Principles of Empirical or Inductive Logic (London, 1889); J. Volkelt, Erfahren und Denken (Hamburg and Leipzig, 1886); T. Welton, A Manual of Logic (London, 1891, 1896); W. Windelband, Präludien (Freiburg-i.-Br., 1884); W. Wundt, Logik (2nd ed., Stuttgart, 1893–1895). Text-books are not comprised in this list. (T. Ca.)
II. History
Logic cannot dispense with the light afforded by its history so long as counter-solutions of the same fundamental problems continue to hold the field. A critical review of some of the chief types of logical theory, with a view to determine development, needs no further justification.
Logic arose, at least for the Western world, in the golden age of Greek speculation which culminated in Plato and Aristotle. There is an Indian logic, it is true, but its priority is more than disputable. In any case no influence upon Greek thought can be shown. The movement which ends in the logic of Aristotle is demonstrably self-contained. When we have shaken ourselves free of the prejudice that all stars are first seen in the East, Oriental attempts at analysis of the structure of thought may be treated as negligible.
It is with Aristotle that the bookish tradition begins to dominate the evolution of logic. The technical perfection of the analysis which he offers is, granted the circle of presuppositions within which it works, so decisive, that what precedes, even Plato’s logic, is not unnaturally regarded as merely preliminary and subsidiary to it. What follows is inevitably, whether directly or indirectly, by sympathy or by antagonism, affected by the Aristotelian tradition.
A. Greek Logic
i. Before Aristotle
Logic needs as its presuppositions that thought should distinguish itself from things and from sense, that the problem of validity should be seen to be raised in the field of thought itself, and that analysis of the structure of thought should be recognized as the one way of solution. The physical philosophers. Thought is somewhat late in coming to self-consciousness. Implied in every contrast of principle and fact, of rule and application, involved as we see after the event, most decisively when we react correctly upon a world incorrectly perceived, thought is yet not reflected on in the common experience. Its so-called natural logic is only the potentiality of logic. The same thing is true of the first stage of Greek philosophy. In seeking for a single material principle underlying the multiplicity of phenomena, the first nature-philosophers, Thales and the rest, did indeed raise the problem of the one and the many, the endeavour to answer which must at last lead to logic. But it is only from a point of view won by later speculation that it can be said that they sought to determine the predicates of the single subject-reality, or to establish the permanent subject of varied and varying predicates.[1] The direction of their inquiry is persistently outward. They hope to explain the opposed appearance and reality wholly within the world of things, and irrespective of the thought that thinks things. Their universal is still a material one. The level of thought on which they move is still clearly pre-logical. It is an advance on this when Heraclitus[2] opposes to the eyes and ears which are bad witnesses “for such as understand not their language” a common something which we would do well to follow; or again when in the incommensurability of the diagonal and side of a square the Pythagoreans stumbled upon what was clearly neither thing nor image of sense, but yet was endowed with meaning, and henceforth were increasingly at home with symbol and formula. So far, however, it might well be that thought, contradistinguished from sense with its illusions, was itself infallible. A further step, then, was necessary, and it was taken at any rate by the Eleatics, when they opposed their thought to the thought of others, as the way of truth in contrast to the way of opinion. If Eleatic thought stands over against Pythagorean thought as what is valid or grounded against what is ungrounded or invalid, we are embarked upon dialectic, or the debate in which thought is countered by thought. Claims to a favourable verdict must now be substantiated in this field and in this field alone. It was Zeno, the controversialist of the Eleatic school, who was regarded in after times as the “discoverer” of dialectic.[3]
Zeno’s amazing skill in argumentation and his paradoxical conclusions, particular and general, inaugurate a new era. “The philosophical mind,” says waiter Pater,[4] “will perhaps never be quite in health, quite sane or natural again.” The give and take of thought had by a swift transformation of values come by something more than its own. Zeno’s paradoxes, notably, for example, the puzzle of Achilles and the Tortoise, are still capable of amusing the modern world. In his own age they found him imitators. And there follows the sophistic movement.
- ↑ Cf. Heidel, “The Logic of the Pre-Socratic Philosophy,” in Dewey’s Studies in Logical Theory (Chicago, 1903).
- ↑ Heraclitus, Fragmm. 107 (Diels, Fragmente der Vorsokratiker) and 2, on which see Burnet, Early Greek Philosophy, p. 153 note (ed. 2).
- ↑ e.g. Diog. Laërt. ix. 25, from the lost Sophistes of Aristotle.
- ↑ Plato and Platonism, p. 24.
