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Summary

     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.

Key works

     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.

Introductions

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.

https://www.oxfordbibliographies.com/view/document/obo-9780195396577/obo-9780195396577-0171.xml

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  1. Theory, Evidence, Data: Themes from George E. Smith.Marius Stan & Christopher Smeenk - forthcoming - Springer.
    A volume of papers inspired by the work of George E. Smith on confirmation and evidence in advanced science—from Newton's gravitation theory to the physics of molecules.
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  2. Making of the Problem: Induction from Socrates to Popper.John P. McCaskey - manuscript
  3. Law without law: From observer states to physics via algorithmic information theory.Markus P. Müller - 2020 - Quantum 4:301.
    According to our current conception of physics, any valid physical theory is supposed to describe the objective evolution of a unique external world. However, this condition is challenged by quantum theory, which suggests that physical systems should not always be understood as having objective properties which are simply revealed by measurement. Furthermore, as argued below, several other conceptual puzzles in the foundations of physics and related fields point to limitations of our current perspective and motivate the exploration of an alternative: (...)
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  4. On Mentioning Belief-Formation Methods in the Sensitivity Subjunctives.Bin Zhao - forthcoming - Ergo: An Open Access Journal of Philosophy.
    According to the sensitivity account of knowledge, S knows that p only if S’s belief in p is sensitive in the sense that S would not believe that p if p were false. The sensitivity condition is usually relativized to belief-formation methods to avoid putative counterexamples. A remaining issue for the account is where methods should be mentioned in the sensitivity subjunctives. In this paper, I argue that if methods are mentioned in the antecedent, then the account is too strong (...)
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  5. Studies in Inductive Probability and Rational Expectation.Theo A. F. Kuipers - 1978 - Dordrecht, Netherland: Reidel.
    3 in philosophy, and therefore in metaphilosophy, cannot be based on rules that avoid spending time on pseudo-problems. Of course, this implies that, if one succeeds in demonstrating convincingly the pseudo-character of a problem by giving its 'solution', the time spent on it need not be seen as wasted. We conclude this section with a brief statement of the criteria for concept explication as they have been formulated in several places by Carnap, Hempel and Stegmiiller. Hempel's account is still very (...)
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  6. Onko tieteellinen strukturalismi mahdollista ilman modaalirealismia?Ilkka Pättiniemi & Ilmari Hirvonen - 2016 - In Ilkka Niiniluoto, Tuomas Tahko & Teemu Toppinen (eds.), Mahdollisuus. Helsinki: Philosophical Society of Finland. pp. 94–102.
    Filosofian piirissä on viime aikoina käyty intensiivistä keskustelua metafysiikan naturalisoinnista ja tieteellisen metafysiikan mahdollisuudesta. Yksi tämän keskustelun keskeisistä teoksista on James Ladymanin ja Don Rossin (sekä osin John Collierin ja David Spurrettin) kirjoittama Every Thing Must Go (2007). Tässä kirjassa Ladyman ja Ross puolustavat, omien sanojensa mukaan, neopositivistista skientismiä. Heidän ohjelmansa on skientistinen, koska Ladymanin ja Rossin mukaan tiede on ainoa tapa tutkia todellisuutta objektiivisesti. Neopositivismi ilmenee puolestaan siinä, että heidän ohjelmansa tukeutuu eräänlaiseen verifikaatioperiaatteeseen. Ladymanin ja Rossin verifikaatioperiaate ei kuitenkaan (...)
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  7. EL FALSACIONISMO POPPERIANO: UN INTENTO INDUCTIVO DE EVADIR LA INDUCCIÓN.Maribel Barroso - 2015 - Episteme NS: Revista Del Instituto de Filosofía de la Universidad Central de Venezuela 36 (1):29-39.
    En el presente trabajo expongo la propuesta falsacionista de Karl Popper como resultado de su solución al problema de la inducción. En este sentido, la analizo bajo sus dos aspectos, el lógico y el metodológico. La idea detrás de ello es mostrar, en primer lugar, que su solución lógica al problema de la inducción es totalmente independiente de los criterios metodológicos que propone para la elección entre teorías rivales, y en segundo lugar, que estos últimos constituyen una transgresión a su (...)
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  8. Summa und System: Historie und Systematik vollendeter bottom-up- und top-down-Theorien.Jens Lemanski - 2013 - Münster, Deutschland: mentis.
    ›Bottom-up‹ und ›top-down‹ sind heutzutage gängige Methodenbezeichnungen in allen Bereichen der Wissenschaft. Dennoch sind beide Methoden keine Entdeckung der Moderne, sondern wurden unter Begriffen wie beispielsweise ›Auf-‹ und ›Abstieg‹, ›Induktion‹ und ›Deduktion‹ in der Wissenschaftsgeschichte häufig verwendet, um komplexe Wissensbestände vollständig aufzuarbeiten und zu strukturieren. Paradigmatisch für eine derartige Aufarbeitung stehen die mittelalterliche Summa und das neuzeitliche System. Aktuellen Studien zufolge hat aber bereits Dionysius Areopagita in der Spätantike eine derartige Summe verfasst, während in der Neuzeit erst J. G. Fichtes (...)
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  9. Gambling with Truth: An Essay on Induction and the Aims of Science.H. B. Enderton - 1967 - Journal of Symbolic Logic 41 (4):791-791.
  10. More on induction in the language with a satisfaction class.Henryk Kotlarski & Zygmunt Ratajczyk - 1990 - Mathematical Logic Quarterly 36 (5):441-454.
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  11. Penny Pinching and Backward Induction.Martin Hollis - 1991 - Journal of Philosophy 88 (9):473.
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  12. A note on the $\Pi^0_2$ -induction rule.Ulrich Kohlenbach - 1995 - Archive for Mathematical Logic 34 (4):279-283.
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  13. On Principles of Inductive Definition.Bernhard Banaschewski - 1960 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 6 (15-22):248-257.
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  14. Δ11-Good Inductive Definitions Over The Continuum.Jacques Grassin - 1981 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 27 (1):11-16.
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  15. Sur certains modes de fonder nos jugements concernant les événements futurs.Izydora Dambska - 1963 - Logique Et Analyse 6 (21):232.
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  16. Three Riddles of Induction.David Johnson - 1989 - Dissertation, Princeton University
    There are three riddles of induction. The New Riddle is this: How do we give a definition of 'projectible hypothesis' which is noncircular, and which yet divides all universal hypotheses unerringly into two disjoint classes--the projectible and the unprojectible? This is a purely analytical problem: build a machine which sorts hypotheses in the intuitively correct way, it making no difference why the machine works, so long as it works : Why should we rely on inductions to acquire beliefs about the (...)
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  17. George Couvalis, Philosophy of Science: Science and Objectivity. [REVIEW]A. Manion - 1999 - Australasian Journal of Philosophy 77 (2):234.
  18. The Method of "Grounded Theory" in the Age-Old Debate about Induction.Vincent Rodriguez - 1988 - Epistemologia 11 (2):211.
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  19. Essai Sur L'Induction.Antoine Gratacap - 1869 - Boehm & Fils.
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  20. Induction, Discovery and Imprecise Reasoning: A Dissertation in Applied Recursion Theory.Mark Andrew Changizi - 1997 - Dissertation, University of Maryland, College Park
    The riddle of induction, the logic of discovery, vagueness and the sorites paradox are studied.
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  21. Metaphysics: An Inductive Science.Archie Bahm - 1978 - Southwest Philosophical Studies 3.
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  22. Stoll's Whewell's Philosophy of Induction.Homer H. Dubs - 1931 - Journal of Philosophy 28:385.
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  23. Induction, Probability, and Confirmation.G. Maxwell & R. M. Anderson - 1977 - Philosophical Review 86 (4):576-584.
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  24. Inductive Sociology.F. H. Giddings - 1902 - Philosophical Review 11 (2):206-207.
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  25. Methodologies for Geology: G. K. Gilbert and T. C. Chamberlin.Stephen Pyne - 1978 - Isis 69:413-424.
  26. Transcendental Deductions and Universal Architectures for Inductive Inferences.Kevin T. Kelly & Cory Juhl - 1998 - ProtoSociology 12:158-175.
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  27. Margins of Precision. [REVIEW]A. L. - 1973 - Review of Metaphysics 26 (4):748-749.
    Max Black has included approximately one half of the essays that he has published since Models and Metaphors in this collection entitled Margins of Precision. All but two of the essays have appeared in various professional journals, the two exceptions being Chapter V on "Induction" and Chapter VI on "Probability," which are articles in the Encyclopedia of Philosophy, edited by Paul Edwards. The final chapter, "Wittgenstein’s Views About Language," is an address delivered at the Israel Academy, Jerusalem in 1966 and (...)
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  28. Inductive Probability. [REVIEW]R. W. J. - 1961 - Review of Metaphysics 15 (2):341-341.
    Day argues that the meaning of "probable" is partly evaluative and partly descriptive--to say that a proposition is probable is both to recommend its assertion and to say that a certain procedure shows it to be so. The paradigm of an inductive probability judgment, which is the major concern of the book, is "The fact that all observed A's are B's makes it probable that all A's are B's." Several more complex kinds of probability judgments are distinguished and discussed in (...)
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  29. Induction, Acceptance and Rational Belief. [REVIEW]H. K. R. - 1971 - Review of Metaphysics 24 (4):763-764.
    Papers collected in this volume were originally presented at a symposium held at the University of Pennsylvania in December, 1968 and revised in the light of discussion at the symposium for publication. The contributors hold different views about the role played by induction in theories of knowledge and rational belief but many of the papers are conciliatory, reflecting no doubt a good deal of helpful communication at the symposium. For example, Frederic Schick's clearly written and informative lead article considers subjectivist, (...)
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  30. Inductive Processes.S. Wilfred Mallon - 1925 - Modern Schoolman 2 (2):19-22.
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  31. Induction: Processes of Inference, Learning and Discovery. [REVIEW]David Leiser - 1989 - Journal of Mind and Behavior 10 (3):303-306.
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  32. Semiotic Trees and Classifications for Inductive Learning Systems.Ana Marostica - 1998 - Semiotics:114-127.
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  33. A Quantum Inductive Logic.John D. Norton - unknown
    The material theory of induction requires that good inductive inferences must be warranted by facts within their domain of application. In earlier chapters, we have seen many examples of individual inductive inferences warranted by specific facts. Marie Curie, for example, inferred the crystallographic system of all crystals of radium chloride from inspection of just a few specks of the substance. The inference was warranted by facts contained in crystallographic principles from the preceding century, not by some universal inductive inference schema.
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  34. On the Comparison of Inductive Support with Deontic Requirement.T. R. Girill - 1979 - Grazer Philosophische Studien 9 (1):145-159.
    That the concepts of confirmation and requirement are very similar has recently been suggested by the discovery of four analogies between them. This conjecture is tested by comparing examples of each relation. I show that both of these relations can be "defeated" in two similar ways. But I also argue for two important dissimilarities between them: 1) when faced with certain inconsistencies, requirement suffers much more drastically than confirmation, and 2) confirmation is partiresultant in a sense in which requirement is (...)
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  35. If dancers ate their shoes-information integration in inductive judgments.Rj Sternberg & J. Gastel - 1986 - Bulletin of the Psychonomic Society 24 (5):354-354.
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  36. Popper on Metaphysics and Induction.A. Dinis - 1987 - Epistemologia 10 (2):285-301.
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  37. History, Discovery and Induction: Whewell on Kepler on the Orbit of Mars.A. Lugg - 1989 - Boston Studies in the Philosophy of Science 116:283-298.
    Discussion of William Whewell on Kepler on the orbit of Mars. A paper in *An Intimate Relation*, a volume presented to Robert E. Butts on his 60th Birthday.
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  38. Strategies for hypothesis induction.K. Dunbar, Al Fay & D. Klahr - 1991 - Bulletin of the Psychonomic Society 29 (6):519-519.
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  39. On the controversy between Poincaré and Russell about the status of complete induction.Gerhard Heinzmann - 1994 - Epistemologia 17 (1):35-52.
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  40. John WN Watkins, 1924-1999.Stefano Gattei - 2000 - International Studies in the Philosophy of Science 14 (1):77-82.
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  41. A note on the [mathematical formula]-induction rule.Ulrich Kohlenbach - 1995 - Archive for Mathematical Logic 34 (4):279-283.
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  42. Structural reliabilism: Inductive logic as a theory of justification.Sven Ove Hansson - 2005 - History and Philosophy of Logic 26 (1):71-72.
  43. What’s New about the New Induction?P. D. Magnus - 2006 - Synthese 148 (2):295-301.
    The problem of underdetermination is thought to hold important lessons for philosophy of science. Yet, as Kyle Stanford has recently argued, typical treatments of it offer only restatements of familiar philosophical problems. Following suggestions in Duhem and Sklar, Stanford calls for a New Induction from the history of science. It will provide proof, he thinks, of "the kind of underdetermination that the history of science reveals to be a distinctive and genuine threat to even our best scientific theories" . This (...)
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  44. Complementary frameworks of scientific inquiry: Hypothetico-deductive, hypothetico-inductive, and observational-inductive.T. E. Eastman & F. Mahootian - 2009 - World Futures 65 (1):61-75.
    The 20th century philosophy of science began on a positivistic note. Its focal point was scientific explanation and the hypothetico-deductive (HD) framework of explanation was proposed as the standard of what is meant by “science.” HD framework, its inductive and statistical variants, and other logic-based approaches to modeling scientific explanation were developed long before the dawn of the information age. Since that time, the volume of observational data and power of high performance computing have increased by several orders of magnitude (...)
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  45. "Comments on Salmon's" Inductive Evidence".Henry E. Kyburg - 1965 - American Philosophical Quarterly 2 (4):274-276.
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  46. Assuming, ascertaining, and inductive probability.S. Spielman - 1969 - Studies in the Philosophy of Science. American Philosophical Quarterly Monograph 7.
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  47. Theoretical Terms and Inductive Inference.Keith Lehrer - forthcoming - American Philosophical Quarterly.
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  48. Induction as an obstacle for the improvement of human knowledge.R. M. Swartz - forthcoming - Philosophy of Education.
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  49. Induction from a Single Instance: Incomplete Frames. [REVIEW]Rafal Urbaniak & Frederik Van De Putte - 2013 - Foundations of Science 18 (4):641-653.
    In this paper we argue that an existing theory of concepts called dynamic frame theory, although not developed with that purpose in mind, allows for the precise formulation of a number of problems associated with induction from a single instance. A key role is played by the distinction we introduce between complete and incomplete dynamic frames, for incomplete frames seem to be very elegant candidates for the format of the background knowledge used in induction from a single instance. Furthermore, we (...)
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  50. Between rationalism and romanticism: Whewell's historiography of the inductive sciences.Geoffrey N. Cantor - 1991 - In Menachem Fisch & Simon Schaffer (eds.), William Whewell: A Composite Portrait. Clarendon Press. pp. 67--96.
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