In 1947 Donald Cary Williams claimed in The Ground of Induction to have solved the Humean problem of induction, by means of an adaptation of reasoning first advanced by Bernoulli in 1713. Later on David Stove defended and improved upon Williams’ argument in The Rational- ity of Induction (1986). We call this proposed solution of induction the ‘Williams-Stove sampling thesis’. There has been no lack of objections raised to the sampling thesis, and it has not been widely accepted. In our (...) opinion, though, none of these objections has the slightest force, and, moreover, the sampling thesis is undoubtedly true. What we will argue in this paper is that one particular objection that has been raised on numerous occasions is misguided. This concerns the randomness of the sample on which the inductive extrapolation is based. (shrink)

It is well known that there are, at least, two sorts of cases where one should not prefer a direct inference based on a narrower reference class, in particular: cases where the narrower reference class is gerrymandered, and cases where one lacks an evidential basis for forming a precise-valued frequency judgment for the narrower reference class. I here propose (1) that the preceding exceptions exhaust the circumstances where one should not prefer direct inference based on a narrower reference class, and (...) (2) that minimal frequency information for a narrower (non-gerrymandered) reference class is sufficient to yield the defeat of a direct inference for a broader reference class. By the application of a method for inferring relatively informative expected frequencies, I argue that the latter claim does not result in an overly incredulous approach to direct inference. The method introduced here permits one to infer a relatively informative expected frequency for a reference class R', given frequency information for a superset of R' and/or frequency information for a sample drawn from R'. (shrink)

In the middle of last century metaphysics was widely criticized, ridiculed, and committed to the flames. During this period a handful of philosophers, against several anti-metaphysical trends, defended metaphysics and articulated novel metaphysical doctrines. Donald C. Williams was one of these philosophers. But while his contributions to metaphysics are well known his defence of metaphysics is not and yet it played a key part in the development and revival of metaphysics. In this paper I present his defence of metaphysics in (...) its historical context. I also show how his defence is relevant in response to recent attacks on metaphysics. (shrink)

The applicability of Bayesian conditionalization in setting one’s posterior probability for a proposition, α, is limited to cases where the value of a corresponding prior probability, PPRI(α|∧E), is available, where ∧E represents one’s complete body of evidence. In order to extend probability updating to cases where the prior probabilities needed for Bayesian conditionalization are unavailable, I introduce an inference schema, defeasible conditionalization, which allows one to update one’s personal probability in a proposition by conditioning on a proposition that represents a (...) proper subset of one’s complete body of evidence. While defeasible conditionalization has wider applicability than standard Bayesian conditionalization (since it may be used when the value of a relevant prior probability, PPRI(α|∧E), is unavailable), there are circumstances under which some instances of defeasible conditionalization are unreasonable. To address this difficulty, I outline the conditions under which instances of defeasible conditionalization are defeated. To conclude the article, I suggest that the prescriptions of direct inference and statistical induction can be encoded within the proposed system of probability updating, by the selection of intuitively reasonable prior probabilities. (shrink)

It is widely agreed that ‘scientific law’ is one of the key scientific terms which any adequate philosophy of science must attempt to clarify or define. The importance of the concept ‘law’ is made evident by the fact that the distinctive functions of science—explanation and prediction—are usually analyzed with reference to laws. Thus events are explained by showing that descriptions of them are deducible from laws, and laws are utilized in deducing descriptions of unknown future events, thereby permitting their prediction. (...) Moreover, it has recently become clear that the concept ‘law’ is relevant to the analysis of counterfactual conditionals, disposition terms, and the physical modalities. An adequate explication of ‘law’, then, will further the analysis of these important concepts. (shrink)

The aim of this contribution is to provide a rather general answer to Hume's problem, the well-known problem of induction. To this end, it is very useful to apply his differentiation between ``relations of ideas'' and ``matters of fact'', and to reconsider earlier approaches. In so doing, we consider the problem formally, as well as empirically. Next, received attempts to solve the problem are discussed. The basic structure of inductive problems is exposed in chap. 6. Our final conclusions are to (...) the positive, i.e., Hume's problem can be dealt with - solved - in a constructive way. More specifically, bounded generalisations can be justified, and the key to the solution is the concept of information. (shrink)

Summary In chapter one I reject the thesis that a relation of partial entailment holds between probability evidence and conclusion, as also the claim that the propositions of applied geometry are synthetic a priori. By way of balance, I suggest that there may be a sense in which necessary conditions of discourse transcend the distinction between a priori and empirical. In chapter two I reject the claim that logical relations in the form of intrinsic probability enter into the no-miracles argument, (...) which I suggest is frequency-connected in its more systematic applications, so that it belongs within a system. I begin chapter three with a critique of an attempted formal probability solution to Hume’s problem, and I now suggest that inductive inference has application only within a system in which its validity is pre-supposed in its premises, a concomitant of which is that the sceptic about induction cannot stop short of global scepticism. Since my aim is to show that global scepticism is self-refuting, given that intentionality may be analysed in terms of a system, I now develop that analysis by devoting chapter four to an examination of Wittgenstein on meaning and understanding. In chapter five I reject his thesis equating meaning and understanding with use, arguing instead that they are irreducible and subject to dispositionality conditions, and in furtherance of that argument I try to solve the problem of the authoritativeness of belief avowals by showing again that there are necessary conditions of discourse. These are such that selfascribing belief, crediting oneself with understanding and with being suitably disposed, are inherent in reasoning. In chapter six I weave the threads of the previous discussion into a solution by arguing that the sceptic about induction, who is committed to global scepticism, necessarily refutes himself. In chapter seven, on the problem of other minds, I attempt a solution by modifying the arguments used against inductive scepticism. (shrink)