Induction (1990)

Synthese 85 (1990): 95-114, 1990

This paper begins with a rigorous critique of David Stove's recent book The Rationality of Induction. In it, Stove produced four different proofs to refute Hume's sceptical thesis about induction. I show that Stove's attempts to vindicate induction are unsuccessful. Three of his proofs refute theses that are not the sceptical thesis about induction at all. Stove's fourth proof, which uses the sampling principle to justify one particular inductive inference, makes crucial use of an unstated assumption regarding randomness. Once this assumption is made explicit, Hume's thesis once more survives. The refutation of Stove's fourth proof leads to some observations which relate Goodman's 'grue' paradox with randomness of a sample. I formulate a generalized version of Goodman's grue paradox, and argue that whenever a sample, no matter how large, is drawn from a predetermined smaller interval of a population that is distributed over a larger interval, any conclusion drawn about the characteristics of the population based on the observed characteristics of the sample is fatally vulnerable to the generalized grue paradox. Finally, I argue that the problem of justification of induction can be addressed successfully only from a cognitive point of view, but not from a metaphysical one. That is, we may ask whether an inductive inference is justified or not within the 'theories' or 'cognitive structures' of a subject, but not outside them. With this realization, induction is seen as a cognitive process, not unlike vision, that is useful at times, and yet has its own illusions that may make it a serious obstacle to cognition at other times.

Philosophia, 1998

2003

I argue that if John D. Norton's "Material Theory of Induction" could be combined with a theory of direct inference, then several novel and outstanding issues for his theory could be addressed. Most strikingly, there might be a promising answer to Hume's Problem of Induction, often thought to be a major weakness of Norton's theory.

Stanford Dissertation, 2011

In the first chapter, I explain “Hume’s problem of induction.” Induction cannot be justified a priori, and any argument that the unobserved will resemble the observed, based on observation, would be circular. I distinguish this problem from other forms of skepticism about induction, such as Goodman’s riddle, Hempel’s paradox, and other arguments for inductive skepticism made by Hume. I argue that the theories of Popper, Strawson, and Reichenbach fail to resolve Hume’s problem, arguing that Popper circularly assumes that nature is uniform and Strawson and Reichenbach do not claim, let alone defend, the intuitively indispensable truth that the sun will probably rise tomorrow. In the second chapter, I discuss the closely related concepts ‘probability,’ ‘coincidence,’ and ‘explanation.’ I argue that probability needs no reductive definition, being widely understood and possibly primitive. Not all probability judgments are based on induction, so use of the concept ‘probability’ does not presuppose acceptance of induction. ‘Coincidence’ is identified with a certain sense of ‘unlikely’, and to ‘explain’, in the sense relevant to the topic of this dissertation, means to decrease the amount of coincidence we must accept. In the third chapter, I discuss the family of solutions to Hume’s problem of induction that I endorse, in terms of inference to the best explanation, statistical sampling, and Bayesian reasoning. I summarize the arguments of Bayes/Price, Laplace, Mackie, Blackburn, Williams, Stove, Foster, Armstrong, Bonjour, and others who, I argue, share a common solution to the problem of induction (though they do not all recognize this commonality). Strengths and weaknesses of the various formulations are discussed. In the fourth chapter, I defend my version of the solution, an argument that the future will probably resemble the past which relies on a form of reasoning I call “inference to the only alternative to colossal coincidence” or “inference to lesser coincidence”. I argue that the only alternative to colossal coincidence is that the following principle holds true time-impartially: Regularities that have long persisted until a certain time are likely to continue somewhat further (in the absence of additional cross-inductive information). Colossal coincidence is a priori unlikely, so it is likely that this principle holds true time-impartially. I respond to several objections, including the possibility of time-restricted laws as an alternative explanation of past regularity, the possibility that we have been dealt a biased sample by our past experience, and the possibility that time-impartial dependence relations have either prior probability zero or non-existent prior probability, giving no ground to the Bayesian justification of induction. I conclude with a discussion of the meaning of ‘causation’. The referent of ‘causation’ is whatever turns out to fill the role of preventing the vast regularities of our experience from being colossally coincidental, and has the property of being asymmetric with respect to the two directions of time (earlier-to-later and later-toearlier). It is an open, empirical question, whether all physical dependence is causal.

Philosophy and Phenomenological Research, 1962

Problems of self-reference in philosophy have been at the bottom of many of the now classical paradoxes, and this paper will attempt to show that paradoxical conclusions follow from an analysis of the self-reference of induction. The conditions necessary for the generation of paradoxes always include a negation; for example, in Grelling's paradox of heterological terms, it is only when a term is not descriptive of itself that difficulties arise. Similarly, in this case the paradox rests on the assumption that the principle of induction has not been successfully proven. It has often been remarked that induction cannot be relied upon for a proof of itself; but if other proofs had been successful, the continued reliability of inductive inferences would only serve to confirm the principle more fully. If other proofs are not successful, the continued reliability of inductive inferences is, in a sense, an embarrassment. I shall assume that the latter is the case, and shall try first to formulate the source of embarrassment and second to show that, although some authors have gone to extraordinary lengths to avoid a confession of defeat with respect to induction, capitulation is not as dishonorable as it might seem.

Philosophy of Science, 1997

Attempts to utilize the probability calculus to prove or disprove various inductive or inductive skeptical theses are, I believe, highly problematic. Inductivism and inductive skepticism are substantive (logically consistent) philosophical positions that do not allow of merely formal proofs or disproofs. Often the problems with particular alleged formal proofs of inductive or inductive sceptical theses turn on subtle technical considerations. In the following I highlight such considerations in pointing out the flaws of two proofs, one an alleged proof of an inductive sceptical conclusion due to Karl Popper, the other an alleged proof of an inductivist thesis originally due to Harold Jeffreys and later advocated by John Earman. Surprisingly, in examining Popper's argument it is shown that certain apparently weak premises, often embraced by both inductivists and deductivists, lend themselves to inductive conclusions. However, it is argued, those premises are still philosophically substantive and not amenable to a purely formal demonstration. The lesson to be learnt here is twofold. First, we need to be very careful in determining which formal theses entail, and which are entailed by, inductive skepticism and inductivism. Second, we need to take great care in laying out and examining the assumptions presumed in formal arguments directed for and against such formal theses.

Cahiers du CREA, 17, 1997

This paper argues that a view of science, expounded and defended elsewhere, solves the problem of induction. The view holds that we need to see science as accepting a hierarchy of metaphysical theses concerning the comprehensibility and knowability of the universe, these theses asserting less and less as we go up the hierarchy. It may seem that this view must suffer from vicious circularity, in so far as accepting physical theories is justified by an appeal to metaphysical theses in turn justified by the success of science. But this is rebutted. A thesis high up in the hierarchy asserts that the universe is such that the element of circularity, just indicated, is legitimate and justified, and not vicious. Acceptance of the thesis is in turn justified without appeal to the success of science. It may seem that the practical problem of induction can only be solved along these lines if there is a justification of the truth of the metaphysical theses in question. It is argued that this demand must be rejected as it stems from an irrational conception of science.