Abstract
A traditional way of discussing inductive logic is through contrast with deductive logic. More recently, many philosophers have discussed inductive logic in a more autonomous fashion by constructing various formal systems tailored to fit what their craftsmen have seen as repeatable forms of inductive inference. Many of these forms have displayed no obvious analogy to patterns of deductive inference. I think that failure to think through the relationship of deductive and inductive logic by plunging immediately into topics of confirmation and probabilistic inference is philosophically disastrous. In this paper I want to discuss analogies between deductive logic and inductive logic once more. It will be my contention that close attention to a suitable analogy can demonstrate that much philosophical work on induction has arisen from a mistaken attempt to formalize some essentially intuitive features of inductive reasoning.
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References
This claim has been pressed by L. Jonathan Cohen in his papers ‘What has Confirmation to do with Probabilities?’, Mind 75 (1966) 463–481, and
L. Jonathan ‘A Logic for Evidential Support’, British Journal for the Philosophy of Science 17 (1966) 21–43 and 105–126.
Robert Ackermann, ‘Sortal Predicates and Confirmation’, Philosophical Studies (forthcoming).
The locus classicus is Donald Williams, The Ground of Induction, Cambridge, Mass., 1947. A more succinct presentation and criticism is available in
S. F. Barker, Induction and Hypothesis, Cornell 1957, pp. 62–90.
A number of philosophers have objected to the putative validity of the statistical syllogism, often pointing out that it must be combined with the requirement of total evidence. See, for example, Carl G. Hempel, ‘Inductive Inconsistencies’, Synthese 12 (1960) 439–469. A cogent argument that the syllogism is invalid from the standpoint of probability theory, and that the requirement of total evidence will not save it, is to be found in
Patrick Suppes, ‘Probabilistic Inference and the Concept of Total Evidence’, in Aspects of Inductive Logic (ed. by J. Hintikka), Amsterdam 1966, pp. 49–65.
There is an extensive literature. A sufficient refutation of older accounts of enumera-tive induction can be found in Nelson Goodman, Fact, Fiction, and Forecast, 2nd ed., Indianapolis 1965. More recent attacks on other aspects can be sampled in
Frederick L. Will, ‘Consequences and Confirmation’, Philosophical Review 75 (1966) 34–58,
Arthur W. Collins, ‘Explanation and Causality’, Mind 75 (1966) 482–500, and
Arthur W. Collins, ‘The Use of Statistics in Explanation’, British Journal for the Philosophy of Science 17 (1966) 127–140.
Frederick L. Will, op. cit.
Discussion of this issue runs through debates between Fisherians and neo-Bayesian subjectivists in the statistical literature. The importance of the argument can be approached through F. J. Anscombe, ‘Tests of Goodness of Fit’, Journal of the Royal Statistical Society ser. B 25 (1963) 81–94.
Carnap’s approach is presented in an elementary discussion in Robert Ackermann, Nondeductive Inference, London 1966, pp. 36–58. The important work is
Rudolf Carnap, Logical Foundations of Probability, London 1950, but the recent changes announced in
P. A. Schilpp, The Philosophy of Rudolf Carnap, LaSalle 1963, should be consulted. Hintikka’s proposals, close to Carnap’s in overall approach, but differing considerably in calculated a priori values, may be traced through the relevant papers in Aspects of Inductive Logic (ed. by J. Hintikka), Amsterdam 1966.
It is relevant to know that certain related optimalization problems fail of solution in higher dimensional cases. See Douglass J. Wilde, Optimum Seeking Methods, Englewood Cliffs, N.J., 1964. Sexual mechanisms insure varied adaptational strategies under environmental stress. If evolutionary theory is taken seriously, it may provide an intuitive proof that divergent strategies are important to group or institutional welfare. The relevant biological theory has a vast literature, but the theory is given interesting application for this point in The Genetics of Colonizing Species (ed. by Baker and Stebbins), London 1965.
Nelson Goodman’s theory of projection, offered in Fact, Fiction, and Forecast, 2nd ed., Indianapolis 1965, is an elegant case in point. The projectible hypotheses on that largely informal theory may be regarded as exactly the candidates for inclusion as reasonable disjuncts in the basic inductive premises of a reasonable inductive argument.
A survey of the literature, and a proposal that beliefs be closed under deduction,
is defended in Frederick Schick, ‘Consistency’, Philosophical Review 75 (1966) 467–495.
Frederick Schick: The embeddability notion is explored in J. Hintikka, Knowledge and Belief, Ithaca, N.Y., 1962.
There are two landmark papers. See Frederick Schick, ‘Consistency and Rationality’, Journal of Philosophy 60 (1963) 5–19, and
Isaac Levi, ‘Deductive Cogency in Inductive Inference’, Journal of Philosophy 62 (1965) 68–77. Many of Levi’s ideas are similar to those expressed about the basic inductive premise in this paper.
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© 1969 D. Reidel Publishing Company, Dordrecht, Holland
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Ackermann, R. (1969). Some Problems of Inductive Logic. In: Davis, J.W., Hockney, D.J., Wilson, W.K. (eds) Philosophical Logic. Synthese Library, vol 20. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9614-0_10
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