(1) Deduction, yielding necessary truth (e.g., various types of syllogism)Induction is the main form of non-deductive reasoning, and, although there are some philosophers following Popper who maintain that Hume’s problem of induction is unsolvable and science can do without induction (Musgrave 1999; Musgrave 2004), these Popperian philosophers are firmly in the minority in their views on induction.
(2) Induction, yielding probable truth, and further divided into(1) induction by simple enumeration;(3) Inference to the best explanation (similar to abduction), yielding probable truth.
(2) inductive argument by analogy;
(3) statistical syllogism, and
(4) induction to a particular.
The general type of induction is “universal inference” or “universal generalisation” (the old Latin term for this was a particulari ad universale), but there are many more types of inductive reasoning.
At (3), we have “inference to the best explanation,” an expression with its origin in Harman (1965), and with good accounts of this given in Lipton (2004) and (2007). This is frequently considered a form of inductive argument, but some classify it as a sui generis form of reasoning, so I have put it in a separate category. Whatever the classification one choices, however, inference to the best explanation is widely regarded as an important and legitimate form of reasoning and firmly in the same general category as induction as a method of argument that yields non-necessary truth.
The inference to the best explanation starts out with an event, an effect or phenomenon a, and looks at the explanations that are possible, and judges that an explanation or theory b is the most probable explanation of a because it is the best and most powerful explanation as opposed to its competitors.
In that sense, inference to the best explanation moves from facts (or effects considered as facts) to a probable explanation of them.
There can be many criteria for deciding which explanation is best, such as if it is observed in similar cases to the one at hand, whether it can make accurate predictions and retrodictions, whether it has the virtue of greater simplicity as opposed to competing theories.
Inference to the best explanation provides the best type of argument for defending an indirect realist ontology of the external world, the real existence of the past, the principle of the uniformity of nature, and as a way of overcoming Hume’s problem of induction. Curiously, the most prominent critics of inference to the best explanation are anti-realists (e.g., van Fraassen 1980).
Although inference to the best explanation seems similar to Charles Sanders Peirce’s principle of abduction, the latter is perhaps best considered an early version of inference to the best explanation, but not exactly the same thing (Campos 2011; Hintikka 1998; Minnameier 2004).
“Abduction,” Stanford Encyclopedia of Philosophy, March 9, 2011
Campos, Daniel. 2011. “On the Distinction between Peirce’s Abduction and Lipton’s Inference to the Best Explanation,” Synthese: An International Journal for Epistemology, Methodology and Philosophy of Science 180.3: 419–442.
Ennis, Robert H. 1968. “Enumerative Induction and Best Explanation,” The Journal of Philosophy 65.18: 523–529.
Fumerton, Richard. 2010. “Inference to the Best Explanation,” in Jonathan Dancy, Ernest Sosa and Matthias Steup (eds.), A Companion to Epistemology (2nd edn.). Wiley-Blackwell, Malden, MA. 445–447.
Harman, Gilbert H. 1965. “The Inference to the Best Explanation,” The Philosophical Review 74.1: 88–95.
Harman, Gilbert H. 1968. “Enumerative Induction as Inference to the Best Explanation,” The Journal of Philosophy 65.18: 529–533.
Hintikka, Jaakko. 1998. “What is Abduction? The Fundamental Problem of Contemporary Epistemology,” Transactions of the Charles S. Peirce Society 34.3: 503–533.
Lipton, Peter. 2004. Inference to the Best Explanation (2nd edn.). Routledge, London.
Lipton, Peter. 2007. “Précis of Inference to the Best Explanation, 2nd Edition,” Philosophy and Phenomenological Research 74.2: 421–423.
Minnameier, Gerhard. 2004. “Peirce-Suit of Truth: Why Inference to the Best Explanation and Abduction ought not to be Confused,” Erkenntnis 60.1: 75–105.
Musgrave, Alan. 1988. “The Ultimate Argument for Scientific Realism,” in R. Nola (ed.), Relativism and Realism in Science. Kluwer Academic Press, Dordrecht. 229–252.
Musgrave, Alan. 2004. “How Popper [Might Have] Solved the Problem of Induction,” Philosophy 79.307: 19–31.
Musgrave, Alan. 2006. “The ‘Miracle Argument’ For Scientific Realism,” Rutherford Journal 2
Okasha, S. 2000. “Van Fraassen’s Critique of Inference to the Best Explanation,” Studies in History and Philosophy of Science 31: 691–710.
Ostien, Philip A. 1974. “God, Other Minds, and the Inference to the Best Explanation,” Canadian Journal of Philosophy 4.1: 149–162.
Peirce, C. S. 1955. “Abduction and Induction,” in J. Buchler (ed.), Philosophical Writings of Peirce. Dover, New York. 150–156.
van Fraassen, Bas C. 1980. The Scientific Image. Clarendon Press, Oxford.
Vogel, Jonathan. 1990. “Cartesian Skepticism and Inference to the Best Explanation,” The Journal of Philosophy 87.11: 658–666.
Weintraub, Ruth. 2013. “Induction and Inference to the Best Explanation,” Philosophical Studies 166.1: 203–216.