The Logic of Success
Relational Epistemology
The problem of induction reminds us that science cannot wait for empirical hypotheses to be verified and Duhem’s problem reminds us that we cannot expect full refutations either. We must settle for something less. The shape of this something less depends on which features of full verification and refutation we choose to emphasize. If we conceive of verification and refutation as arguments in which evidence entails the hypothesis or its negation, then the central problem of the philosophy of science is to explicate a relation of confirmation or support that is weaker than full entailment but which serves, nonetheless, to justify empirical conclusions.
Much standard philosophy of science follows from this simple conception. Justification is a state that obtains when the confirmation relation holds. The precise nature of confirmation is hazy, but it can be explicated from historical examples. Confirmation, like entailment, is a universal concept.
Context-dependencies can be absorbed into the relation so long as sufficient intersubjective force remains to ground scientific forms of argument. Underdetermination is a matter of evidential support.
The realism debate can therefore be settled by showing that one theory is better confirmed than another (Glymour 1981, Friedman 1983). Since confirmation confers justification, it philosophically “screens off” all other considerations. Thus, discovery and computability are irrelevant to epistemology (Laudan 1980) and should be referred to appropriate experts in mathematics, psychology and computer science. The only remaining role for mathematical logic is to help us reason about the nature of the explicated confirmation relation. So if there were no underlying relation of justification to be studied, there would be no logic of science. I will refer to this familiar viewpoint as the relational paradigm.
Computational Epistemology
Verification and refutation may also be conceived of as strict success criteria for procedures rather than as logical relations among propositions. Think of a method not as a relation conferring justification but as a procedure that is supposed to determine whether a given hypothesis is correct. A decision procedure is guaranteed to halt with the right answer (yes or no) over a range of possible situations. A verification procedure is one-sided: it halts with “yes” if the hypothesis is correct but may fail to make an output otherwise. A refutation procedure halts with “no” if the hypothesis is incorrect, but may fail to make an output otherwise. Procedural verification occurs when one’s verification procedure halts with “yes”, and similarly for refutation. Procedural decision, verification, and refutation are, perhaps, the most fundamental concepts in computer science and mathematical logic.
The difference between entailment and procedural verification is barely noticeable, since a verification procedure cannot say “yes” unless receipt of the current inputs entails (relative to the underlying set of possibilities) that the hypothesis is correct, and similarly for refutation. The two approaches diverge, however, when we begin to weaken our ambitions in light of the problems of Hume and Duhem. The relational conception suggests that we retain the short-run perspective and excuse possibilities of error so long as some weakened analogue of the entailment relation obtains. The procedural conception suggests an alternative response: dropping the halting requirement, for after the procedure halts, it cannot retract its opinion and correct it later if its answer is mistaken. Allowing a scientist, community, or learning device to “take back” an answer and replace it with another permits inquiry to get “back on track”. The foundational metaphor of instantaneous, partial, support is replaced, thereby, with the pragmatic metaphor of fallible but self-correcting convergence to a correct answer. Such success provides no sign that the goal has been reached. Nor is there an objective sense of “support” along the way. Short-run justification is supposed to be a kind of static state, like floating on a placid pool of experience. Convergent success is more like surfing on the wave of experience: a dynamical stability that depends as much on the surfer’s ongoing technique as on the shape of the wave. I will refer to this dynamic, procedural conception of scientific method as the computational paradigm.
The computational perspective gives rise to an inverted philosophy of science. Methods are not relations that confer immediate justification on mistaken conclusions; they are procedures for converging to correct outputs. Methods should exploit the special structure of the problems they address so universal recommendations should not be expected and equally good solutions may disagree markedly in the short run. Underdetermination arises when no possible method is guaranteed to converge to at a correct answer. It is not sufficient to observe that we systematically prefer one sort of theory to another. A relevant, realist response is to produce an alternative, plausible, model of the inference problem in question and to show how a particular method solves it. The relational paradigm’s harsh judgments against discovery and computability are also reversed. Computationally speaking, discovery (converging to a correct answer) and test (determining whether an answer is correct) are simply two different types of problems (think of adding x + y to obtain z as opposed to deciding whether x + y = z). If anything, discovery is the more fundamental aim, test being a means for filtering out incorrect answers. Computability is not only relevant, but central, for performance must be judged relative to the best achievable performance. In fact, uncomputability and the problem of induction are more similar than different: both arise from a bounded perspective on a global reality (Kelly and Schulte 1997). Instead of distinguishing formal from empirical inquiry, the computational viewpoint calls for a unified treatment. Such a unified account is provided by mathematical logic and computability theory, which have long guided thinking in the philosophy of mathematics. Computability theory focuses on the solvability of problems rather than on the details of specific procedures. Following that instructive example, we might say that an inductive inference problem consists of
- A set of relevant possibilities, each of which specifies some potentially infinite sequence of inputs to the scientist’s method,
- A question whose potential answers partition the relevant possibilities,
- A convergent success criterion and
- A set of admissible methods.
It was a little review of my, The Logic of Success. thank you for visiting this blog . May be useful for friends and can be a reference for future success . If there are errors in this article . I apologize profusely . If there are criticisms and suggestions , you can attach it below.
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