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Deductive and Inductive ArgumentsAbstract: A deductive argument's premises provide conclusive evidence for the truth of its conclusion. An inductive argument's premises provide probable evidence for the truth of its conclusion. The difference between deductive and inductive arguments does not specifically depend on the specificity or generality of the composite statements. Both kinds of arguments are characterized and distinguished with examples and exercises.
FIG. 1. Historical Frequency of Use of “deductive argument” and “inductive argument” in Google Books 1700-2008. postscript “This process of drawing conclusions from our principles, by rigorous and unimpeachable trains of demonstration, is termed Deduction. In its due place, it is a highly important part of every science; but it has no value when the fundamental principles, on which the whole of the demonstration rests, have not first been obtained by the induction of facts, so as to supply the sole materials of substantial truth. Without such materials, a series of demonstrations resembles physical science only as a shadow resembles a real object. To give a real significance to our propositions, Induction must provide what Deduction itself cannot supply. From a pictured hook we can only hang a pictured chain.”William Whewell, History of the Inductive Sciences vol. I (London: J.W. Parker, 1837), 16. Deduction and Induction Notes1. Richard Whately pointed out in 1831 that induction can be stated as a syllogism with a suppressed universal major premise which is substantially “what belongs to the individual or individuals we have examined, belongs to the whole class under which they come.” [Richard Whately, Elements of Logic (London: B. Fellowes, 1831), 230.] This influential text led many early logicians (e.g., John Stuart Mill) to think mistakenly that inductive logic can be somehow transformed into demonstrative reasoning. Following, George Henrik von Wright's A Treatise on Induction and Probability (1951 Abingdon, Oxon: Routledge, 2003. doi: 10.4324/9781315823157), logicians have abandoned this program [C.f., 29-30]. There is some controversy in the recent informal logic movement as to whether conductive, abductive, analogical, plausible, and other arguments can be classified as either inductive or deductive. Conductive, abductive and analogical arguments in this course are interpreted and reconstructed as inductive arguments. A conductive argument is a complex argument which provides premises which separately provide evidence for a conclusion — each is independently relevant to the conclusion. Conductive arguments can also provide evidence for and against a conclusion (as in evaluations or decision). Abductive argument is a process of selecting hypotheses which best explain a state of affairs very much like inference to the best explanation. An analogical argument specifies that events or entities alike in several respects are probably alike in other respects as well. See e.g. Yun Xie, “Conductive Argument as a Mode of Strategic Maneuvering,” Informal Logic 37 no. 1 (January, 2017), 2-22. doi: 10.22329/il.v37i1.4696 And Bruce N. Waller, “Classifying and Analyzing Analogies” Informal Logic 21 no. 3 (Fall 2001), 199-218. 10.22329/il.v21i3.2246 ↩ 2. Bryan Skyrms, Choice and Chance: An Introduction to Inductive Logic (Dickenson, 1975), 6-7. Some logicians argue that all arguments are exclusively either deductive or inductive, and there are no other kinds. Also, they claim deductive arguments can only be evaluated by deductive standards and inductive arguments can only be evaluated by inductive standards. [E.g., George Bowles, “The Deductive/Inductive Distinction,” Informal Logic 16 no. 3 (Fall, 1994), 160. doi: 10.22329/il.v16i3.2455] Stephen Barker argues: “Our definition of deduction must refer to what the speaker is claiming, if it is to allow us to distinguish between invalid deductions and nondeductions.” [S.F. Barker, “Must Every Inference be Either Deductive or Inductive?,” in Philosophy in America ed. Max Black (1964 London: Routledge, 2013), 62.] On the one hand, for monotonic reasoning, Barker's definition makes the tail wag the dog since on this view the distinction between the two kinds of arguments depends upon the arbitrary psychological factor of what type of argument someone declares it to be rather than the nature or character of the argument itself. On Barker's view (and many current textbook views), the speaker's claim determines whether an argument is deductive or inductive regardless of the structure of the argument itself. Barker explains the distinction from a dialogical point of view: “Suppose someone argues, ‘All vegetarians are teetotallers, and he's a teetotaller, so I think he's a vegetarian.’ Is this inference a definitely illegitimate deduction, or is it an induction which may possibly be logically legitimate? We cannot decide without considering whether the speaker is claiming that his conclusion is strictly guaranteed by the premises (in which case, the inference is a fallacious deduction) or whether he is merely claiming that the premises supply real reason for believing the conclusion (in which case, the inference is an induction which in an appropriate context might be legitimate).” [Barker, 66.] On Barker's view, an invalid deduction cannot be considered a weak induction since, for him, deduction and induction are exclusive forms of argumentation. This is a popular view, but we do not follow this view in these notes. Trudy Govier points out: “If arguers' intentions are to provide the basis for a distinction between deductive and inductive arguments which will be anything like the traditional one, those arguers will have to formulate their intentions with a knowledge of the difference between logical and empirical connection, and the distinction between considerations of truth and those of validity.” [Trudy Govier, “More on Deductive and Inductive Arguments,” Informal Logic (formerly Informal Logic Newsletter) 2 no. 3 (March, 1979), 8. doi: 10.22329/il.v2i3.2824] This point is obvious for monotonic reasoning where arguments are evaluated independently of claims (1) by the person who espouses them or when (2) arguments are evaluated in terms of the principle of charity. Even for dialogical reasoning, a speaker's intention should not determine the distinction between inductive and inductive arguments, for few speakers are informed of the epistemological differences to begin with.↩ 3. “Intentional account” named by Robert Wachbrit, “A Note on the Difference Between Deduction and Induction,” Philosophy & Rhetoric 29 no. 2 (1996), 168.doi: 10.2307/40237896 (doi link not activated 2022.06.28) ↩ 4. Bertrand Russell, The Analysis of Mind (London: George Allen & Unwin, 1921), 40. ↩ 5. Herbert Spencer, Education: Intellectual, Moral and Physical (New York: D. Appleton, 1860), 45-46. ↩ 6. O.B. Goldman, “Heat Engineering,” The International Steam Engineer 37 no. 2(February 1920), 96.↩ 7. Arguments in statistics and probability theory are mathematical idealizations and are considered deductive inferences since their probable conclusions are logically entailed by their probable premises by means of a “rule-based definitions.” Consequently, even though the premises and conclusion of these arguments are only probable, the probabilistic conclusion necessarily follows from the truth of the probabilistic premises. The inference itself is claimed to be certain given the truth of the premises. In a valid deductive argument the conclusion must be true, if the premises are true. The proper description of the truth value of the conclusion of a valid statistical argument is that the statistical result is true, if the premises are true. The truth of the probability value established in the conclusion is certain given the truth of the data provided in the premises.↩ 8. This inductive argument is suggested by this study: Aris P. Agouridis, Moses S. Elisaf, Devaki R. Nair, and Dimitri P. Mikhailidis, “Ear Lobe Crease: A Marker of Coronary Artery Disease?” Archives of Medical Science 11 no. 6 (December 10, 2015) 1145-1155. doi: 10.5114/aoms.2015.56340> ↩ 9. Friedrich Schlegel, Lectures on the History of Literature: Ancient and Modern trans. Henry G. Bohn (London: George Bell & Sons, 1880), 34.↩ 10. R. Schoeny and W. Farland, “Determination of Relative Rodent-Human Interspecies Sensitivities to Chemical Carcinogens/Mutagens,” Research to Improve Health Risk Assessments (Washington, D.C.: U.S. Environmental Protection Agency, 1990), Appendix D, 44. ↩ 11.Foreign Agriculture Circular (Washington D.C.: U.S. Department of Agriculture, 5 no. 64 (November, 1964), 4.↩ 12. This type of induction describes the most common variety: it's often called “induction by incomplete enumeration.”↩ 13. John Wesley, “10 Ways to Improve Your Mind by Reading the Classics,” Pick the Brain: Grow Yourself (June 20, 2007).↩ 14. Adapted from Nikko Schaff, “Letters: Let the Inventors Speak,” Economist 460 no. 8820 (January 26, 2013), 16.↩ 15. James Ramsay, “Dawkins and Religion,” The Times Literary Supplement 5417 (January 26, 2007), 6.↩ 16. Historically, from the time of Aristotle, the distinction between deduction and induction, more or less, has been described as: “[I]nduction is a progression from singulars to universals … and induction is more calculated to persuade, is clearer, and according to sense more known, and common to many things.” [Aristotle, Top. I.xii 105a12-13;16-19 (trans. Owen) “Induction, then, is that operation of the mind, by which we infer that what we know to be true in a particular case or cases, will be true in all cases which resemble the former in certain assignable respects. In other words, Induction is the process by which we conclude that what is true of certain individuals of a class is true of the whole class, or that what is true at certain times will be true in similar circumstances at all times.” [John Stuart Mill, A System of Logic 2 vols.(London: Longmans, Green, Reader, and Dyer,) I:333.] “[D]eduction consists in passing from more general to less general truths; induction is the contrary process from less to more general truths.” [W. Stanley Jevons, The Principles of Science 2nd ed. rev. (1887 London: Macmillan, 1913), 11.] This view remains a popular view and does distinguish many arguments correctly. However, since this characterization is not true in all instances of these arguments, this distinction is no longer considered correct in the discipline of logic. William Whewell was perhaps the earliest philosopher to register a correction to the view that induction can be defined as a process of reasoning from specific statements to a generalization. Throughout his writings he explains that induction requires more than simply generalizing from an enumeration of facts. He suggests as early as 1831 that the facts must be brought together by the recognition of a new generality of the relationship among the facts by applying that general relation to each of the facts. See. esp. William Whewell, The Mechanical Euclid (Cambridge: J. and J.J. Deighton, 1837), 173-175; The Philosophy of the Inductive Sciences, vol. 2 (London: J.W. Parker and Sons, 1840), 214; On the Philosophy of Discovery (London: John W. Parker and Son, 1860), 254.↩ 17. Notice that if this argument were to be taken as a syllogism (which will be studied later in the course), it would be considered an invalid deductive argument. A valid deductive argument has its conclusion follow with necessity; when the conclusion does not logically follow as in the “great Greek philosophers” example, there still is some small bit of evidence for the truth of the conclusion, so the argument could be evaluated as an extremely weak inductive argument. No matter what class names (i.e. no matter what subjects and predicates) are substituted into the form or grammatical structure of this argument (assuming the statements themselves are not tautological in some sense), it could never be a valid deductive argument — even when all the statements in it happen to be true.↩ 18. P.F. Strawson distinguishes the particular and the general in this manner:
P.F. Strawson, “Particular and General,” Proceedings of the Aristotelian Society New Series 54 no. 1 (1953-1954), 260. doi: 10.1093/aristotelian/54.1.233 Also by JStor (free access by registration).↩ 19. Bryan Skyrms, Choice and Chance: An Introduction to Inductive Logic (Dickenson, 1975), 7.↩ 20. Adapted from Hermann Hesse, Demian (Berlin: S. Fischer, 1925), 157.↩ 21. Mortimer J. Adler, How to Read a Book (New York: Simon and Schuster: 1940), 89.↩ 22. Marcus Tullius Cicero, Old Age in Letters of Marcus Tullius Cicero with his Treatises on Friendship and Old Age and Letters of Gaius Plinius Caecilius Secundus, trans. E.E. Shuckburgh and William Melmoth, Harvard Classics, vol. 9 (P.F. Collier & Son, 1909), 35.↩ 23. John S. Mbiti, African Religions & Philosophy (Oxford: Heinemann, 1969), 1.↩ 24. Ferdinand E. Marcos, The Democratic Revolution in the Philippines (Englewood Cliffs, NJ: Prentice-Hall, 1974), 93. Also, Ferdinand E. Marcos, Toward the New Society: Essays on Aspects of Philippine Development (Philippines: National Media, 1974), 7.↩ 25. Francine Russo, “The Personality Trait ‘Intolerance of Uncertainty’ Causes Anguish During COVID,” Scientific American Mind 33 no. 3 (May-June 2022), 14. Also, here: Francine Russo, “The Personality Trait ‘Intolerance of Uncertainty’ …” Scientific American (accessed June 25, 2022).↩ 26. Charles Muller, “A Korean Contribution to the Zen Canon; The Oga Hae Seorui (Commentaries of Five Masters on the Diamond Sūtra),” in Zen Classics: Formative Text in the History of Zen Buddhism eds. Steven Heine and Dale S. Wright (Oxford: Oxford University Press, 2006), 54.↩ 27. Barry Hallen, Short History of African Philosophy 2nd.ed. (Bloomington: Indiana University, 2009), 21.↩ Readings on Induction and DeductionS.F. Barker, “Must Every Inference be Either Deductive or Inductive?,” in Philosophy in America ed. Max Black (1964 London: Routledge, 2013), 62. doi: 10.4324/9781315830636 George Bowles, “The Deductive/Inductive Distinction,” Informal Logic 16, no. 3 (Fall 1994), 159-184. doi: 10.22329/il.v16i3.2455 Trudy Govier, “More on Deductive and Inductive Arguments,” Informal Logic (formerly Informal Logic Newsletter) 2 no. 3 (March, 1979), 7-8. doi: 10.22329/il.v2i3.2824 David Hitchcock, “Deduction, Induction and Conduction,” 3 no. 2 Informal Logic (formerly Informal Logic Newsletter) (January, 1980), 7-15. doi: 10.22329/il.v3i2.2786 IEP Staff, “Deduction and Induction,” The Internet Encyclopedia of Philosophy P.F. Strawson, “Particular and General,” Proceedings of the Aristotelian Society New Series 54 no. 1 (1953-1954), 233-260. Also by JStor (free access by registration). doi: 10.1093/aristotelian/54.1.233 Robert Wachbrit, “A Note on the Difference Between Deduction and Induction,” Philosophy & Rhetoric 29 no. 2 (1996), 168-178. doi: 10.2307/40237896 (doi link not activated 2022.06.25) JStor (free with registration) Which terms are used to describe what are the parts of a deductive argument is true or untrue?A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid.
What makes a deductive argument true?The argument's validity depends on whether the conclusion naturally follows from the premises. If the statements offered as premises are true, and the conclusion follows naturally from those premises, then a deductive argument is considered to be valid.
Is deductive reasoning True or false?Deductive arguments aim to show that the conclusion must be true. Inductive arguments aim to show not that the conclusion must be true but rather that it is likely true. Every deductive argument has at least two premises.
What are the three types of deductive arguments?There are three common types of deductive reasoning:. Syllogism.. Modus ponens.. Modus tollens.. |