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Abduction, Deduction, Induction

• Charles Sanders Peirce: Scientific Method
• Abductive reasoning

• Pragmatism begins with the idea that belief is that on which one is prepared to act. (Taking a stand)

Scientific method

Insofar as clarification by pragmatic reflection suits explanatory hypotheses and fosters predictions and testing, pragmatism points beyond the usual duo of foundational alternatives: deduction from self-evident truths, or rationalism; and induction from experiential phenomena, or empiricism.

Based on his critique of three modes of argument and different from either foundationalism or coherentism, Peirce's approach seeks to justify claims by a three-phase dynamic of inquiry:

• Active, abductive genesis of theory, with no prior assurance of truth;
• Deductive application of the contingent theory so as to clarify its practical implications;
• Inductive testing and evaluation of the utility of the provisional theory in anticipation of future experience, in both senses: prediction and control.

Thereby, Peirce devised an approach to inquiry far more solid than the flatter image of inductive generalization simpliciter, which is a mere re-labeling of phenomenological patterns. Peirce's pragmatism was the first time the scientific method was proposed as an epistemology for philosophical questions.

A theory that succeeds better than its rivals in predicting and controlling our world is said to be nearer the truth. This is an operational notion of truth used by scientists.

Peirce extracted the pragmatic model or theory of inquiry from its raw materials in classical logic and refined it in parallel with the early development of symbolic logic to address problems about the nature of scientific reasoning.

Abduction, deduction, and induction make incomplete sense in isolation from one another but comprise a cycle understandable as a whole insofar as they collaborate toward the common end of inquiry. In the pragmatic way of thinking about conceivable practical implications, every thing has a purpose, and, as possible, its purpose should first be denoted. Abduction hypothesizes an explanation for deduction to clarify into implications to be tested so that induction can evaluate the hypothesis, in the struggle to move from troublesome uncertainty to more secure belief. No matter how traditional and needful it is to study the modes of inference in abstraction from one another, the integrity of inquiry strongly limits the effective modularity of its principal components.

Peirce's outline of the scientific method in §III–IV of "A Neglected Argument"[111] is summarized below (except as otherwise noted). There he also reviewed plausibility and inductive precision (issues of critique of arguments).

• 1. Abductive (or retroductive) phase. Guessing, inference to explanatory hypotheses for selection of those best worth trying. From abduction, Peirce distinguishes induction as inferring, on the basis of tests, the proportion of truth in the hypothesis. Every inquiry, whether into ideas, brute facts, or norms and laws, arises from surprising observations in one or more of those realms (and for example at any stage of an inquiry already underway). All explanatory content of theories comes from abduction, which guesses a new or outside idea so as to account in a simple, economical way for a surprising or complicated phenomenon. The modicum of success in our guesses far exceeds that of random luck, and seems born of attunement to nature by developed or inherent instincts, especially insofar as best guesses are optimally plausible and simple in the sense of the "facile and natural", as by Galileo's natural light of reason and as distinct from "logical simplicity".[112] Abduction is the most fertile but least secure mode of inference. Its general rationale is inductive: it succeeds often enough and it has no substitute in expediting us toward new truths.[113] In 1903, Peirce called pragmatism "the logic of abduction".[114] Coordinative method leads from abducting a plausible hypothesis to judging it for its testability[115] and for how its trial would economize inquiry itself.[116] The hypothesis, being insecure, needs to have practical implications leading at least to mental tests and, in science, lending themselves to scientific tests. A simple but unlikely guess, if not costly to test for falsity, may belong first in line for testing. A guess is intrinsically worth testing if it has plausibility or reasoned objective probability, while subjective likelihood, though reasoned, can be misleadingly seductive. Guesses can be selected for trial strategically, for their caution (for which Peirce gave as example the game of Twenty Questions), breadth, or incomplexity.[117] One can discover only that which would be revealed through their sufficient experience anyway, and so the point is to expedite it; economy of research demands the leap, so to speak, of abduction and governs its art.[116]
• 2. Deductive phase. Two stages:
  • i. Explication. Not clearly premised, but a deductive analysis of the hypothesis so as to render its parts as clear as possible.
  • ii. Demonstration: Deductive Argumentation, Euclidean in procedure. Explicit deduction of consequences of the hypothesis as predictions about evidence to be found. Corollarial or, if needed, Theorematic.
• 3. Inductive phase. Evaluation of the hypothesis, inferring from observational or experimental tests of its deduced consequences. The long-run validity of the rule of induction is deducible from the principle (presuppositional to reasoning in general) that the real "is only the object of the final opinion to which sufficient investigation would lead";[103] in other words, anything excluding such a process would never be real. Induction involving the ongoing accumulation of evidence follows "a method which, sufficiently persisted in", will "diminish the error below any predesignate degree". Three stages:
  • i. Classification. Not clearly premised, but an inductive classing of objects of experience under general ideas.
  • ii. Probation: direct Inductive Argumentation. Crude or Gradual in procedure. Crude Induction, founded on experience in one mass (CP 2.759), presumes that future experience on a question will not differ utterly from all past experience (CP 2.756). Gradual Induction makes a new estimate of the proportion of truth in the hypothesis after each test, and is Qualitative or Quantitative. Qualitative Gradual Induction depends on estimating the relative evident weights of the various qualities of the subject class under investigation (CP 2.759; see also Collected Papers of Charles Sanders Peirce, 7.114–120). Quantitative Gradual Induction depends on how often, in a fair sample of instances of S, S is found actually accompanied by P that was predicted for S (CP 2.758). It depends on measurements, or statistics, or counting.
  • iii. Sentential Induction. "...which, by Inductive reasonings, appraises the different Probations singly, then their combinations, then makes self-appraisal of these very appraisals themselves, and passes final judgment on the whole result".