While standard procedures of causal reasoning as procedures analyzing causal Bayesian networks are custom-built for (non-deterministic) probabilistic structures, this paper introduces a Boolean procedure that uncovers deterministic causal structures. Contrary to existing Boolean methodologies, the procedure advanced here successfully analyzes structures of arbitrary complexity. It roughly involves three parts: first, deterministic dependencies are identified in the data; second, these dependencies are suitably minimalized in order to eliminate redundancies; and third, one or—in case of ambiguities—more than one causal structure is assigned (...) to the minimalized deterministic dependencies. (shrink)

The problem of induction is sometimes motivated via a comparison between rules of induction and rules of deduction. Valid deductive rules are necessarily truth preserving, while inductive rules are not.

The objectivity of Bayesian induction relies on the ability of evidence to produce a convergence to agreement among agents who initially disagree about the plausibilities of hypotheses. I will describe three sorts of Bayesian convergence. The first reduces the objectivity of inductions about simple "occurrent events" to the objectivity of posterior probabilities for theoretical hypotheses. The second reveals that evidence will generally induce converge to agreement among agents on the posterior probabilities of theories only if the convergence is 0 or (...) 1. The third establishes conditions under which evidence will very probably compel posterior probabilities of theories to converge to 0 or 1. (shrink)

Eliminative induction is a method for finding the truth by using evidence to eliminate false competitors. It is often characterized as "induction by means of deduction"; the accumulating evidence eliminates false hypotheses by logically contradicting them, while the true hypothesis logically entails the evidence, or at least remains logically consistent with it. If enough evidence is available to eliminate all but the most implausible competitors of a hypothesis, then (and only then) will the hypothesis become highly confirmed. I will argue (...) that, with regard to the evaluation of hypotheses, Bayesian inductive inference is essentially a probabilistic form of induction by elimination. Bayesian induction is an extension of eliminativism to cases where, rather than contradict the evidence, false hypotheses imply that the evidence is very unlikely, much less likely than the evidence would be if some competing hypothesis were true. This is not, I think, how Bayesian induction is usually understood. The recent book by Howson and Urbach, for example, provides an excellent, comprehensive explanation and defense of the Bayesian approach; but this book scarcely remarks on Bayesian induction's eliminative nature. Nevertheless, the very essence of Bayesian induction is the refutation of false competitors of a true hypothesis, or so I will argue. (shrink)

Even though evidence underdetermines theory, often in science one theory only is regarded as acceptable in the light of the evidence. This suggests there are additional unacknowledged assumptions which constrain what theories are to be accepted. In the case of physics, these additional assumptions are metaphysical theses concerning the comprehensibility and knowability of the universe. Rigour demands that these implicit assumptions be made explicit within science, so that they can be critically assessed and, we may hope improved. This leads to (...) a new conception of science, one which we need to adopt in order to solve the problem of induction. (shrink)

J. Richard Gott III (1993) has used the “Copernican principle” to derive a probability density function for the total longevity of any phenomenon, based solely on the phenomenon’s past longevity. John Leslie (1996) and others have used an apparently similar probabilistic argument, the “Doomsday Argument,” to claim that conventional predictions of longevity must be adjusted, based on Bayes’ Theorem, in favor of shorter longevities. Here I show that Gott’s arguments are flawed and contradictory, but that one of his conclusions—his delta (...) t formula—is mathematically equivalent to Laplace’s famous (and notorious) ‘rule of succession’; moreover, Gott’s delta t formula is a plausible worst-case (if one favors greater longevity) bound in some contexts. On the other hand, the Doomsday Argument is fallacious: the argument’s Bayesian formalism is stated in terms of total duration, but all attempted real-life applications of the argument—with one exception, an application by Gott 1994—actually plug in prior probabilities for future duration; moreover, the Self-Sampling Assumption, an essential premise of the Doomsday Argument, is contradicted by the prior information in all known real-life cases. But rejecting the Doomsday Argument does not entail rejecting the possibility of learning about the future from the past. Applying the work of Bruce M. Hill (1968, 1988, 1993) and Frank P.A. Coolen (1998, 2006) in the field of non-parametric predictive inference, I propose and defend an alternative methodology for quantifying how past longevity of any phenomenon does provide evidence for future longevity. In so doing, I identify an objective standard by which to choose among counting time intervals, counting population, or counting any other measure of past longevity in predicting future longevity. This methodology forms the basis of a calculus of induction. (shrink)

Gott ( 1993 ) has used the ‘Copernican principle’ to derive a probability distribution for the total longevity of any phenomenon, based solely on the phenomenon’s past longevity. Leslie ( 1996 ) and others have used an apparently similar probabilistic argument, the ‘Doomsday Argument’, to claim that conventional predictions of longevity must be adjusted, based on Bayes’s Theorem, in favor of shorter longevities. Here I show that Gott’s arguments are flawed and contradictory, but that one of his conclusions is plausible (...) and mathematically equivalent to Laplace’s famous—and notorious—‘rule of succession’. On the other hand, the Doomsday Argument, though it appears consistent with some common‐sense grains of truth, is fallacious; the argument’s key error is to conflate future longevity and total longevity. Applying the work of Hill ( 1968 ) and Coolen ( 1998 , 2006 ) in the field of nonparametric predictive inference, I propose an alternative argument for quantifying how past longevity of a phenomenon does provide evidence for future longevity. In so doing, I identify an objective standard by which to choose among counting time intervals, counting population, or counting any other measure of past longevity in predicting future longevity. *Received May 2007; revised October 2008. †To contact the author, please e‐mail: pos@ronpisaturo.com. (shrink)

Hilary Kornblith (1993) has recently offered a reliabilist defense of the use of the Law of Small Numbers in inductive inference. In this paper I argue that Kornblith's defense of this inferential rule fails for a number of reasons. First, I argue that the sort of inferences that Kornblith seeks to justify are not really inductive inferences based on small samples. Instead, they are knowledge-based deductive inferences. Second, I address Kornblith's attempt to find support in the work of Dorrit Billman (...) and I try to show that close attention to the workings of her computational model reveals that it does not support Kornblith's argument. While the knowledge required to ground the inferences in question is perhaps inductively derived, Billman's work does not support the notion that small samples provide a reliable basis for our generalizing inferences. (shrink)

Many people argue that history makes a special difference to the subjects of biology and psychology, and that history does not make this special difference to other parts of the world. This paper will show that historical properties make no more or less of a difference to biology or psychology than to chemistry, physics, or other sciences. Although historical properties indeed make a certain kind of difference to biology and psychology, this paper will show that historical properties make the same (...) kind of difference to geology, sociology, astronomy, and other sciences. Similarly, many people argue that nonhistorical properties make a special difference to the nonbiological and the nonpsychological world. This paper will show that nonhistorical properties make the same difference to all things in the world when it comes to their causal behavior and that historical properties make the same difference to all things in the world when it comes to their distributions. Although history is special, it is special in the same way to all parts of the world. (shrink)