Chapter 58
Logic and the rules of right reasoning; syllogism, fallacy and proof.
89 passages · 28 principal · Covers the 49 volumes of primary texts
Logic, in the sense these books give it, is the art and science of right reasoning. It covers the rules by which names are joined into propositions and propositions into syllogisms, the forms of valid proof, and the catalogue of ways an argument can go wrong. It is a great idea for the Harvard Classics because the collection preserves both its long prestige and its long trial. Through these volumes the syllogism is honoured as the instrument of all philosophy, scorned as the toy of pedants, and rebuilt as a method of discovery. Whatever an author thinks of logic, he reasons in judging it, so the question of logic’s worth is also a question about the powers of the mind that weighs it.
The most austere account of logic’s nature comes from Kant. He calls logic the formal part of philosophy, concerned only with the universal laws of thought and having no empirical part at all1. He uses it as the model for his moral philosophy, comparing general logic to transcendental philosophy as general practical philosophy stands to a metaphysic of morals2, and distinguishing pure logic from applied as a guide to separating pure ethics from its applications3. The ancients placed logic differently. George Long reports that the Stoics treated logic or dialectic as an instrument serving the other parts of philosophy, a position he contrasts with Plato’s4. Hobbes describes the work of logicians as a kind of reckoning, adding names into affirmations, affirmations into syllogisms, and syllogisms into demonstrations5. On his account, reasoning that begins from definitions and connects them into general affirmations is what yields a conclusion6. Berkeley gives the same structure a critical edge. Impossibility is shown by demonstrating a repugnancy between ideas, so where there are no ideas, nothing can be demonstrated either way7. Two writers remind us that this machinery has a history and room to grow. Rousseau supposes that syntax and the method of connecting propositions and arguments, the logic of discourse, required a long development among early men8. Kelvin, a physicist, still reaches for a refinement of the logicians, the quantification of the predicate, when he wants precise statement9. The traditional elements did not always yield understanding, however. Augustine tells how he read Aristotle’s Categories unaided and grasped substance, quality, relation, place and time, and yet found himself no better for it10.
That double verdict, that logic is mastered easily and profits little, opens the controversy over the received logic. Its defenders are fewer but forceful. The fullest is John Stuart Mill. He studied Aristotle’s Organon, the scholastic logicians and Hobbes as a boy, and came to value syllogistic logic through his father’s questioning11. He judged that school logic trains exact thinkers to detect fallacy and vague terms, and that it serves better than mathematics for untangling confused thought12. In On Liberty he extends the claim to “negative logic,” the art of exposing weaknesses in a theory, which he thinks undervalued yet indispensable to any firm positive conviction13. Luther, otherwise hostile to Aristotle’s place in the universities, allows that the Logic is fit for practice in speaking, provided it is read without commentaries and not used for mere disputation14. Emerson records the boldest claim of all, Digby’s view that syllogisms are the steps of all a man’s business and belong to his very nature15. More modestly, Voltaire praises Locke as an acute logician16, and Kelvin applies “a little logic” to argue that the negation of infinitude, not infinitude itself, is what cannot be comprehended17.
Against these stand a long line of detractors, and their charges vary. The earliest is simply indifference. Marcus Aurelius is grateful that he did not waste time on resolving syllogisms18. Montaigne turns indifference into a theory of education. Harsh, thorny precepts quicken nothing in the mind19. The mood names Baroco and Baralipton make students dull20. The quiddities of logic do not amend life, and Aristotle taught Alexander morals, not syllogisms21. He rejects the Aristotelian logical ordinances as useless for his own writing22. Bacon makes the charge epistemological. The aids of logic cannot correct errors that arise from faulty primary notions in the mind23. The received logic is too weak and unsubtle for nature, fit for civil business and opinion, and it perpetuates error more than it finds truth24. It flies from particulars straight to general propositions, a precipitate route suited to disputation25, and its subtlety, applied after the fact, comes too late26. It fixes errors rather than disclosing truth, because the mind is already occupied with unsound doctrines27, and like an athletic art it cannot strengthen the understanding enough28. Descartes agrees in substance. Syllogistic logic, he finds, serves to communicate what is already known rather than to discover the unknown, and its sound precepts are mixed with injurious or superfluous ones29. Pascal complains that logicians bury the true rules among useless ones and barbarous names30, and that names like Barbara and Baralipton do not constitute reasoning31. Locke denies that studying logical formalities teaches anyone to reason rightly and would allow only the shortest systems32. Hume reduces syllogistic reasoning outside quantity and number to mere definition33. Huxley adds a historical complaint: medieval philosophers used logical demonstration only to show why the Church’s teaching must be true34.
The moderns did not merely complain; they proposed replacements. Bacon calls his Interpretation of Nature a kind of logic, but one differing immensely from the ordinary kind in its end, its order of demonstration and its starting point35. He sets aside syllogistic demonstration because it rests on words and hasty notions36, and he holds that a true logic must call the principles of the sciences to account instead of taking them on trust37. Two centuries later Mill attempts a reform that keeps the syllogism while reinterpreting it. With friends he worked through Aldrich, Whately and Hobbes, revising the principles of school logic and the theory of propositions, and this study grew into his System of Logic38. He worked out terms, propositions and the inadequacy of the received account of the syllogism as an explanation of deduction39. He was puzzled by the old paradox of how conclusions already contained in the premises can yield new truths40. The quarrel with Macaulay showed him that his father’s method in politics was mistaken41. It led him to a method for the moral sciences in which geometry proves an inappropriate model for a science of causation42. He then drafted the doctrine of reasoning and the book on induction43, owed to Comte the Inverse Deductive Method for history and statistics44,45, and completed books on language, classification and fallacies46. He credits Whately with reviving logic and notes the reception of his own theory of induction47. Bacon wanted a new logic in place of the old, while Mill sought a deeper account of the old that would make room for the new. In this the ancient instrument survives its moderns, but only by being reinterpreted.
A different line of criticism doubts not logic’s method but its rank. Carlyle grants that logic is good but denies that it is best. The man of logic and the man of insight are separable, he argues, and the schoolmen’s syllogisms made no progress48. The poets and aestheticians press the contrast harder. Goethe’s Mephistopheles ridicules logic, likening thought to a weaver’s web and the syllogism to a mechanical first, second, third, and he suggests that dissecting thought kills its living spirit49. Schiller speaks of the abstract mind bound by the fetters of logic50, and of an understanding that dissects beauty into parts for fear of losing the distinctness of its concept51. Shelley distinguishes poetry from logic because poetry is not controlled by the active powers of the mind52. Mill, logic’s champion, confesses that the discipline of mere logic and analysis worked against ideal nobleness of feeling53. From another quarter, Emerson praises English logic as practical, tied to facts and results, the logic of cooks and carpenters rather than of syllogisms54. Burke draws the boundary in politics. A sophistry that serves as accomplice to theft and murder is answered by the executioner’s lash, not by syllogism55.
Even the critics, however, assume that reasoning can go wrong in identifiable ways, and the doctrine of fallacy is where logic’s usefulness is least disputed. Descartes is at pains to deny that he commits the logicians’ fallacy of the circle56. Berkeley warns his opponents against petitio principii and ignoratio elenchi in their objections to immaterialism57. Dryden turns against Collier the maxim that an argument from abuse to use is invalid, since immoral plays do not prove that there should be no plays58. Mill reports writing commentary on the fallacies of speakers, following Bentham’s Book of Fallacies59. Lowell observes that the inference from an attack on slavery to a right of resistance satisfies minds untrained to detect fallacy60, which is itself an argument for the very training Mill commended.
Sophistry is fallacy used on purpose. Plutarch tells how Philotas silenced a rival physician with a sophistical syllogism about fever and cold water61. Dante gives logic a grim role at judgment, where a devil argues that one cannot repent of sin and will it at once, since that is a contradiction62. Montaigne’s advice is to mock such syllogisms rather than answer them, citing Chrysippus’s view that they are tricks for children63. Pascal laments the licence of logicians who have broken so many just barriers64, but he trusts that true method banishes the sophists’ cavils and equivocations65. Burke detects a political sophistry in metaphysical propositions declared with universal consequences and then limited by despotism66. Thackeray shows that the same gravity can be turned to satire. Swift argues monstrous propositions with perfect logic67, developing an absurd premise gravely until wonderful absurdities follow68.
Pascal also supplies the most positive alternative to the logicians’ rules. He sets out formal rules of definition, axiom and demonstration as a method of certain proof69. There are eight rules, five of them essential, and the art of persuading consists in defining every term and proving by substituting definitions for the things defined70. To the objection that these rules are commonplace, he answers that logicians state them but only geometricians practise them, which is why false reasoning abounds71. The logicians borrowed geometry’s rules without grasping their force, and only geometricians attain the method of not erring72. Geometry marks precisely the two true paths of definition and demonstration that the logicians obscure30. His rules of order govern both proving truths and discriminating between them73. Locke’s counsel is humbler: proceed from general to particular or the reverse, and distinguish notions carefully74. Pascal’s confidence in geometry contrasts sharply with Mill’s later judgment that geometry is the wrong model for sciences of causation42. Where Pascal saw the perfection of method, Mill saw a limit.
These disputes shaped schooling. Harrison records logic, rhetoric, philosophy and mathematics as the course of the first degree in Elizabethan England75. Milton objects that beginners are thrust into the abstractions of logic and metaphysics before the easy sensible arts76, yet he keeps logic, “so much as is useful,” before rhetoric77. Locke thinks abstract logic amuses rather than informs young minds and discourages them78. Luther, as noted, would keep Aristotle’s Logic for practice in speaking14.
Literature, finally, made scholastic logic a comic type. Thomas à Kempis dismisses talk of genus and species as useless questioning79. More’s Utopians know nothing of second intentions and cannot see man in common80. Marlowe’s Faustus judges disputing well too small an end81, while Wagner parodies scholastic argument82. Shakespeare’s gravedigger reasons by a mock “argal”83. Jonson’s Subtle teaches quarrelling in the jargon of moods, predicaments and the four causes84. Burns waves logic-chopping away as moonshine85. Manzoni’s Don Ferrante proves by substance and accident that contagion cannot exist86, and in the novel the plague goes on regardless. Montaigne’s dull students20 and Goethe’s dissected spirit49 belong to the same family of portraits.
Several questions remain open across these texts. One is whether logic’s rules are laws of thought, as Kant held1, or instruments to be judged by what they find, as Bacon insisted35. Another is whether the syllogism can yield new truth, the puzzle Mill wrestled with40. A third is whether exactness of reasoning forms the mind or narrows it, the division between Mill’s praise12 and Carlyle’s doubt48. The satirists mocked the forms of logic, yet their jokes depend on readers seeing where the reasoning fails. The ridicule thus presupposes the very discipline it mocks.
Introductory essay written by Claude Opus 5.5 from the outline and the notes on every passage below; quotations are checked against this edition.
See also: Science 2a · Mind 6c
See also: Induction 1b
See also: Mathematics 2b
See also: Reasoning, Mathematics, Philosophy, Science, Education, Principle