Internal Reconstruction as method
Reductionist philosophy of science has split traditionally between extreme inductivists (Carnap 1963; Russell 1956) and extreme deductivists (Popper 1934/ 1959). An important group of pragmatists (Peirce 1934; Hanson 1968; Lakatos 1978) recognized, however, that in addition to induction and deduction, a third mode of inference, abduction (Aristotle’s apagoge), plays a crucial role in the process of empirical science.
Induction is reasoning from individual cases to the general rule, as in e.g.:
As one can see, the level of certainty assigned to inductive and deductive reasoning is rather different. Inductive reasoning is probabilistic, resting on an act of faith — that past experience will be faithfully upheld by future experience. Or, put another way, that a limited sample faithfully represents the entire population. Indeed, as Peirce (1934) has noted, there is an element of abduction buried inside induction.
Deduction, on the other hand, is logically unassailable. But it carries one major drawback: As Wittgenstein (1918) has pointed out, it produces no new knowledge.
Abduction is reasoning by hypothesis, analogy, and explanation. It is, in a profound way, reasoning toward coherence. Within the scientific process, abduction is the crucial step at many distinct points, but perhaps most saliently in the formation of new hypotheses.
The general form of abductive-hypothetical reasoning may be given as (following Peirce 1934; Hanson 1968):
In science, once a new theory has been hypothesized, one moves on to testing its validity. As Popper (1934/1959) points out, testing must involve a distinct phase of deductive reasoning, through which one generates logical consequences (predictions) of the hypothesized theory. Those consequences, further, must be testable. The logic of the testing process is that of falsification. That is:
Induction typically comes into play as a distinct component of hypothesis testing. Most conspicuously, in sampling the actual facts to see whether the predicted facts (logical consequences) of the new hypothesis are real.
As Popper (1934/1959) points out, one cannot verify a theory in science, but at best only fail to falsify it. Since any non-trivial theory has multiple logical consequences, the process of failing to falsify, again and again and again, has no principled logical closure. One first tests major predictions, but even a lifetime would not suffice to test all. So at a certain point one simply ‘has enough’ and quits, perhaps leaving further attempts at falsification to younger minds, richer purses, or to future generations who may yet come up with brand new facts that may incontrovertibly falsify major tenets of the theory.
In the next section I would like to illustrate how the logical status of Internal Reconstruction is very much like that of abductive/analogical reasoning in hypothesis formation. I will do so by citing a run-of-the-mill cycle of Internal Reconstruction in Swahili grammar.
