This approach to the justification of rules of inductive logic without the label "reflective equilibrium"—was proposed by Nelson Goodman in his classic Fact, Fiction, and Forecast (Goodman 1955).
The Islamic world systematized empirical science, introduced quantitative and experimental methods, and refined the rules of inductive and deductive thinking- all more than one thousand years ago.
For example, a moral principle or moral judgment about a particular case (or, alternatively, a rule of inductive or deductive inference or a particular inference) would be justified if it cohered with the rest of our beliefs about right action (or correct inferences) on due reflection and after appropriate revisions throughout our system of beliefs.
Goodman's idea was that we justify rules of inference in inductive or deductive logic by bringing them into reflective equilibrium with what we judge to be acceptable inferences in a broad range of particular cases.
Accordingly, within such a given ethical system, moral reasoning can be justified by the "rules of deductive and inductive inference" (ibid., p. 385) and thus be reconstructed along cognitive, i.e. rational, lines.
Wherein, principle is a rule or law concerning a natural phenomenon, such as the principle of the conservation of mass or the right-hand rule for inductive fields; phenomenon means any state or process known through the senses rather than by intuition or reasoning.
Norton claims that any thought experiment is really a (possibly disguised) argument; it starts with premises grounded in experience and follows deductive or inductive rules of inference in arriving at its conclusion.
The idea of considering introduction rules as meaning-giving rules for atoms is closely related to the theory of inductive definitions in its general form, according to which inductive definitions are systems of rules (see Aczel, 1977).
The project of the Carnapian logic of confirmation was to put inductive reasoning on the sure path of a science; to give a unified and objective account of inductive inference including clear rules of procedure, in close analogy to deductive inference (see Carnap LFP, section 43).
The rules of logic, both deductive and inductive, are rules of the art that has as its end, its cognitive end, the search after truth.
The remaining task is then to explicate the pre-theoretic notion of valid inductive inference by defining rules of inference that can be brought into a reflective equilibrium with intuitive judgments of inductive validity.
