Induction

     Like deductive logic, inductive logic is widely studied by logicians. But referring to a logic of evidential support, inductive logic is basic to our ability to get along in the world, and is a backbone of scientific reasoning. Cause-effect inferences, generalizations and applied generalizations, and analogical inferences are recognized as distinct but overlapping kinds of inductive inferences. Each is ubiquitous in human thought, such that inductive, evidence-driven reasoning appears basic to the pursuit of search for knowledge and understanding. As defeasible or non-monotonic reasoning, inductive arguments and inferences cannot satisfy deductive soundness: The relation of one’s conclusion to one’s premises is enlarging or ampliative (Latin ampliare), such that there is no contradiction in the premises of an inductive argument being true, yet the conclusion false. The backside of this enlargement is the recognition of important concerns about the underdetermination of theories by the facts which they purport to explain (the underdetermination problem) and its implications for theories of scientific explanation, and for the aims and goals of scientific practices more generally. Whether the reasoner is rationally entitled to appeal to a principle of induction  --  the uniformity of nature assumption that the future will resemble the past --  or whether our reliance upon it is more a matter of animal faith, has relatedly been given much critical attention. At least since David Hume framed what has come to be known as the problem of induction, inductive skeptics and even philosophers intending to respond to Humean skepticism have taken especial note of the inherent limitations, and many special paradoxes and riddles, which attend our deep dependence upon inductive reasoning. Hume’s problem has many offshoots, and questions either directly about, or referring us back to inductive processes, continue to receive attention among philosophers in ways that extend far beyond logic and science. There are induction-connected problems for epistemologists, the lottery paradox as but one example, and for metaphysicians, as when we reflect upon what justification we have even for belief in other minds. But the very nature of inductive logic as non-monotonic logic, and inductive reasoning as enlarging or ampliative, may be what turns inductive reasoners from sole attention to armchair worries to empirical or evidence-driven research, and to the pursuit of new knowledge and increasing understanding of the natural world and our place within it.

     Early-modern natural philosophers rejuvenated and extended interest in scientific discovery and evidence-driven arguments, and Francis Bacon’s Novum Organum (1620) is one central work reflecting the rise of modern empiricism and the use of inductive reasoning.  In the Second Book of The Advancement of Learning, Bacon diagnoses the many “idols” of the human mind, concluding that “the formation of ideas and axioms by induction is without doubt the proper remedy to be applied for the keeping off and clearing away of idols.” David Hume shared much of Bacon’s empiricism, but while his mitigated skepticism differs quite substantially from radical skepticism, his A Treatise of Human Understanding (1739) articulates deep worries about the principle of induction. Some of the responses to Humean inductive skepticism try to justify the induction principle by appeal to natural kinds (Howard Sankey 2021) or as an inference to the best explanation (David Armstrong, 1983). Other responses have been dissolutionist, allowing that empirical beliefs and beliefs in a material world and other minds cannot have the certainty of necessary truths or deductive soundness, but arguing that this does not make them unreasonable, or that what Hume showed about induction is “inductive fallibilism, but no more” (Okasha 2001, 237). Inductivists have often battled hypothetical-deductivists and others in regard to scientific methods, and these debates boiled over into challenges to logical empiricism around and after mid-20th century. In “Studies in the Logic of Confirmation,” Carl Hempel (1965a) constructed the Raven Paradox as a thought-experiment helping us to constantly probe and test the steps of the established scientific processes. Yet Hempel also concedes in a postscript that Nelson Goodman’s “New Riddle of Induction” (1983; anticipated in 1946) focused around the projectability of predicates refutes his attempt to provide general criteria of confirmation that are similar to the criteria of deduction validity. The study of induction naturally connects with statistics and probability theory, and Bayesian Confirmation Theory (referring back to Reverend Thomas Bayes (c. 1701–61)) makes a stronger reply, however. It develops a formal apparatus for inductive logic, applying it to the study agents’ dispositions to update their beliefs in light of new evidence, and combining induction with theories of decision and action.

Fitelson, Branden. 2006. “Inductive Logic.” In The Philosophy of Science: An Encyclopedia. Vol. 1, A–M. Edited by Sahotra Sarkar and Jessica Pfeifer, 384–394. New York: Routledge.

Hacking, Ian. An Introduction to Probability and Inductive Logic. Cambridge, UK: Cambridge University Press, 2001. DOI: 10.1017/CBO9780511801297

Hawthorne, James, "Inductive Logic", The Stanford Encyclopedia of Philosophy (Spring 2021 Edition), Edward N. Zalta (ed.), URL = .

Skyrms, Brian. Choice and Chance: An Introduction to Inductive Logic. 4th ed. Belmont, CA: Wadsworth/Thomson, 2000.

Vickers, John M. 2018. “Inductive Reasoning,” Oxford Bibliographies. Oxford University Press.

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