© 2011 by Oxford University Press. All rights reserved. Results on the observational indistinguishability of spacetimes demonstrate the impossibility of determining by deductive inference which is our spacetime, no matter how extensive a portion of the spacetime is observed. These results do not illustrate an underdetermination of theory by evidence, since they make no decision between competing theories and they make little contact with the inductive considerations that must ground such a decision. Rather, these results express a variety of indeterminism (...) in which a specification of the observable past always fails to fix the remainder of a spacetime. This form of indeterminism is more troubling than the familiar indeterminism of quantum theory. The inductive inferences that can discriminate among the different spacetime extensions of the observed past are here called "opaque," which means that we cannot readily see the warrant that lies behind them. (shrink)

It is widely believed that one should not become more confident that all swans are white and all lions are brave simply by observing white swans. Irrelevant conjunction or “tacking” of a theory onto another is often thought problematic for Bayesianism, especially given the ratio measure of confirmation considered here. It is recalled that the irrelevant conjunct is not confirmed at all. Using the ratio measure, the irrelevant conjunction is confirmed to the same degree as the relevant conjunct, which, it (...) is argued, is ideal: the irrelevant conjunct is irrelevant. Because the past’s really having been as it now appears to have been is an irrelevant conjunct, present evidence confirms theories about past events only insofar as irrelevant conjunctions are confirmed. Hence the ideal of not confirming irrelevant conjunctions would imply that historical claims are not confirmed. Confirmation measures partially realizing that ideal make the confirmation of historical claims by present evidence depend strongly on the (presumably subjective) degree of belief in the irrelevant conjunct. The unusually good behavior of the ratio measure has a bearing on the problem of measure sensitivity. For non-statistical hypotheses, Bayes’ theorem yields a fractional linear transformation in the prior probability, not a linear rescaling, so even the ratio measure arguably does not aptly measure confirmation in such cases. (shrink)

The subject of this paper is the relation of Logical Positivism to Theology. By “Logical Positivism” I mean the doctrine originated by Dr. Wittgenstein and expounded more at length by Professors Carnap, Schlick, and other members of the Viennese Circle in the periodical called Erkenntnis . The clearest account of it in English is that given by Mr. R. B. Braithwaite in the volume called Cambridge University Studies.

The founder of Psychical Research, though he has not yet received the honour due to him, seems to have been King Croesus of Lydia, who reigned from 560 to 546 B.C. He carried out an interesting experiment, recorded in detail by Herodotus,2 to test the clairvoyant powers of a number of oracles. He sent embassies to seven oracles, six Greek and one Egyptian. They all started on the same day. On the hundredth day each embassy was instructed to ask its (...) oracle, “What is King Croesus, the son of Alyattes, now doing?” The answer was to be written down and brought back. The oracle of Delphi replied as follows, in hexameters, as its custom was: “I know the number of the sands and the measures of the sea. I understand the dumb, and I hear him who does not speak.” Then it went on: “There comes to my mind the smell of a strong-shelled tortoise, which is being cooked along with lamb's flesh in a brazen vessel; brass is spread beneath it, and with brass it is covered.” As a matter of fact, this answer was perfectly correct. Herodotus tells us that “having considered what would be the most difficult thing to discover and to imagine,” Croesus “cut up a tortoise and a lamb, and himself boiled them together in a brazen pot.” What happened afterwards illustrates the difficulties of this sort of investigation, difficulties which still perplex us to this day. Croesus argued, reasonably enough, that if the Delphic priestess had clairvoyant powers, she probably also had the precognitive powers, she probably also had the precognitive powers which she claimed to have. But when he consulted the oracle later about his forthcoming expedition against the Persians, he received two answers, one of which was ambiguous—“When Croesus crosses the Halys he shall destroy a great empire”—and the other correct, but too obscure to be easily interpreted. (shrink)

Cosmologists often use certain global properties to exclude "physically unreasonable" cosmological models from serious consideration. But, on what grounds should these properties be regarded as "physically unreasonable" if we cannot rule out, even with a robust type of inductive reasoning, the possibility of the properties obtaining in our own universe?

This article suggests a ‘best alternative' justification of induction (in the sense of Reichenbach) which is based on meta-induction . The meta-inductivist applies the principle of induction to all competing prediction methods which are accessible to her. It is demonstrated, and illustrated by computer simulations, that there exist meta-inductivistic prediction strategies whose success is approximately optimal among all accessible prediction methods in arbitrary possible worlds, and which dominate the success of every noninductive prediction strategy. The proposed justification of meta-induction is (...) mathematically analytical. It implies, however, an a posteriori justification of object-induction based on the experiences in our world. *Received November 2005; revised March 2008. †To contact the author, please write to: Department of Philosophy, University of Duesseldorf, Universitaetsstrasse 1, Geb. 23.21, Duesseldorf, Germany D-40225; e-mail: [email protected]. (shrink)

The instrumentalist argument from the underdetermination of theories by data runs as follows: (1) every theory has empirically equivalent rivals; (2) the only warrant for believing one theory over another is its possession of a greater measure of empirical virtue; (3) therefore belief in any theory is arbitrary. In this paper, I examine the status of the first premise. Several arguments against the universal availability of empirically equivalent theoretical rivals are criticized, and four algorithms for producing empirically equivalent rivals are (...) defended. I conclude that the case for the first premise of the argument from underdetermination is very strong. The disposition of the argument itself depends on the fate of the second premise. (shrink)

1. Introduction. It is generally admitted that a large part of man's knowledge is based on inductive arguments. Hence any philosophical theory concerning the nature of inductive arguments constitutes an epistemological theory. Any such philosophical theory of induction must, if it is to be satisfactory, take adequate account of Hume's criticism of inductive arguments. One way of treating his criticism is to say that the validity of inductive arguments is in an important sense relative to some broad factual assumptions about (...) the general nature of the universe and that these general factual assumptions are presupposed in a certain way by the users of inductive arguments. Let us call any theory of this general type a postulate theory of induction. (shrink)

In this paper, I examine Cicero’s oft-neglected De Divinatione, a dialogue investigating the legitimacy of the practice of divination. First, I offer a novel analysis of the main arguments for divination given by Quintus, highlighting the fact that he employs two logically distinct argument forms. Next, I turn to the first of the main arguments against divination given by Marcus. Here I show, with the help of modern probabilistic tools, that Marcus’ skeptical response is far from the decisive, proto-naturalistic assault (...) on superstition that it is sometimes portrayed to be. Then, I offer an extended analysis of the second of the main arguments against divination given by Marcus. Inspired by Marcus’ second main argument, I formulate, explicate, and defend a substantive principle of scientific methodology that I call the “Ciceronian Causal-Nomological Requirement” (CCR). Roughly, this principle states that causal knowledge is essential for relying on correlations in predictive inference. Although I go on to argue that Marcus’ application of the CCR in his debate with Quintus is dialectically inadequate, I conclude that De Divinatione deserves its place in Cicero’s philosophical corpus, and that ultimately, its significance for the history and philosophy of science ought to be recognized. (shrink)

The no free lunch theorem is a radicalized version of Hume’s induction skepticism. It asserts that relative to a uniform probability distribution over all possible worlds, all computable prediction algorithms—whether ‘clever’ inductive or ‘stupid’ guessing methods —have the same expected predictive success. This theorem seems to be in conflict with results about meta-induction. According to these results, certain meta-inductive prediction strategies may dominate other methods in their predictive success. In this article this conflict is analyzed and dissolved, by means of (...) probabilistic analysis and computer simulation. (shrink)

In this paper a new conception of foundation-oriented epistemology is developed. The major challenge for foundation-oriented justifications consists in the problem of stopping the justificational regress without taking recourse to dogmatic assumptions or circular reasoning. Two alternative accounts that attempt to circumvent this problem, coherentism and externalism, are critically discussed and rejected as unsatisfactory. It is argued that optimality arguments are a new type of foundation-oriented justification that can stop the justificational regress. This is demonstrated on the basis of a (...) novel result in the area of induction: the optimality of meta-induction. In the final section the method of optimality justification is generalized to deductive and abductive inferences. (shrink)

The justification of induction is of central significance for cross-cultural social epistemology. Different ‘epistemological cultures’ do not only differ in their beliefs, but also in their belief-forming methods and evaluation standards. For an objective comparison of different methods and standards, one needs (meta-)induction over past successes. A notorious obstacle to the problem of justifying induction lies in the fact that the success of object-inductive prediction methods (i.e., methods applied at the level of events) can neither be shown to be universally (...) reliable (Hume's insight) nor to be universally optimal. My proposal towards a solution of the problem of induction is meta-induction. The meta-inductivist applies the principle of induction to all competing prediction methods that are accessible to her. By means of mathematical analysis and computer simulations of prediction games I show that there exist meta-inductive prediction strategies whose success is universally optimal among all accessible prediction strategies, modulo a small short-run loss. The proposed justification of meta-induction is mathematically analytical. It implies, however, an a posteriori justification of object-induction based on the experiences in our world. In the final section I draw conclusions about the significance of meta-induction for the social spread of knowledge and the cultural evolution of cognition, and I relate my results to other simulation results which utilize meta-inductive learning mechanisms. (shrink)

Reichenbach held that all scientific inference reduces, via probability calculus, to induction, and he held that induction can be justified. He sees scientific knowledge in a practical context and insists that any rational assessment of actions requires a justification of induction. Gaps remain in his justifying argument; for we can not hope to prove that induction will succeed if success is possible. However, there are good prospects for completing a justification of essentially the kind he sought by showing that while (...) induction may succeed, no alternative is a rational way of trying.Reichenbach's claim that probability calculus, especially via Bayes' Theorem, can help to exhibit the structure of inference to theories is a valuable insight. However, his thesis that the weighting of all hypotheses rests only on frequency data is too restrictive, especially given his scientific realism. Other empirical factors are relevant. Any satisfactory account of scientific inference must be deeply indebted to Reichenbach's foundation work. (shrink)

Does the Bayesian theory of confirmation put real constraints on our inductive behavior? Or is it just a framework for systematizing whatever kind of inductive behavior we prefer? Colin Howson (Hume's Problem) has recently championed the second view. I argue that he is wrong, in that the Bayesian apparatus as it is usually deployed does constrain our judgments of inductive import, but also that he is right, in that the source of Bayesianism's inductive prescriptions is not the Bayesian machinery itself, (...) but rather what David Lewis calls the ``Principal Principle''. (shrink)

1. The Problem. In spite of the vast discussion which has been devoted to the theory of probability, the problem of the short run has received surprisingly little attention. Yet, the whole significance of the theory depends upon a solution of this problem, for without an answer to it we cannot say why it is useful to have knowledge of probabilities or why we should take account of this knowledge in making practical decisions. As far as I know, Charles Peirce (...) was the first to appreciate the importance and difficulty of the question, and his characteristically vivid formulation serves as an excellent starting point for its consideration. He says:According to what has been said, the idea of probability essentially belongs to a kind of inference which is repeated indefinitely. An individual inference must be either true or false and can show no effect of probability; and therefore, in reference to a single case considered in itself, probability can have no meaning. Yet if a man had to choose between drawing a card from a pack containing twenty-five red cards and a black one, or from a pack containing twenty-five black cards and a red one, and that of a red one were destined to transport him to eternal felicity, and that of a black one to consign him to everlasting woe, it would be folly to deny that he ought to prefer the pack containing the larger proportion of red cards, although from the nature of the risk, it cannot be repeated. [Collected Papers, 2.652]. (shrink)

A practical or pragmatic justification applies to actions. The action concerned in the case of induction is the making of predictions, and—philosophically of prime importance—the adoption of such rules of procedure as will make the predictions maximally successful. Clearly all ordinary cases of the justification of actions utilize, and in this sense presuppose, inductions. When philosophers ask for a ground of induction in general the answer cannot be inductive evidence. This would be plainly circular or lead to an infinite regress. (...) Hence we are here dealing with a limiting or degenerate case of justification. It is true that one important component of the meaning of such words as “reasonable” or “rational” is indeed the employment of inductive procedures. Many analytic philosophers rest their case right here and consider the quest for a justification of induction as a pseudo problem because, in their view, this quest comes down to asking “is it reasonable to be reasonable?” But—because of an ambiguity of the term “reasonable”—it is precisely here where the distinction between validation and vindication is helpful and points the way to one more step that can be taken in the overall justification of inductive inference. (shrink)

The subject of this paper is the relation of Logical Positivism to Theology. By “Logical Positivism” I mean the doctrine originated by Dr. Wittgenstein and expounded more at length by Professors Carnap, Schlick, and other members of the Viennese Circle in the periodical calledErkenntnis. The clearest account of it in English is that given by Mr. R. B. Braithwaite in the volume calledCambridge University Studies.

According to the paradigm of adaptive rationality, successful inference and prediction methods tend to be local and frugal. As a complement to work within this paradigm, we investigate the problem of selecting an optimal combination of prediction methods from a given toolbox of such local methods, in the context of changing environments. These selection methods are called meta-inductive strategies, if they are based on the success-records of the toolbox-methods. No absolutely optimal MI strategy exists—a fact that we call the “revenge (...) of ecological rationality”. Nevertheless one can show that a certain MI strategy exists, called “AW”, which is universally long-run optimal, with provably small short-run losses, in comparison to any set of prediction methods that it can use as input. We call this property universal access-optimality. Local and short-run improvements over AW are possible, but only at the cost of forfeiting universal access-optimality. The last part of the paper includes an empirical study of MI strategies in application to an 8-year-long data set from the Monash University Footy Tipping Competition. (shrink)

This paper is an attempt at a vindication of induction. The point of departure is that induction requires a justification and that the only kind of justification possible is a vindication. However traditional vindications of induction have rested on unjustified assumptions about the aim of induction. This vindication takes the end pursued in induction simply to be correct prediction. It is argued that induction is the only reasonable way of pursuing this end because induction is the only objective method of (...) predicting. While objectivity is not a necessary condition for successful predicting, it is a sufficient condition for the possession of a property that is, in turn, a necessary condition for correct predicting; and further there could be no reason to expect any non-objective method to possess this necessary condition for success. Induction is the only objective method of predicting for it alone uses facts which must be identified by any predicting method based on rules; and it alone uses these facts according to a relationship that must hold between facts and any meaningful empirical statement. Any alternative to induction must assume that the factual regularities that have been detected will alter in the future and the way they are expected to alter must be arbitrary. It is further claimed that this vindication is proof against the criticisms that have been advanced against practicalist justifications of induction. (shrink)

In this paper I offer a coherentist justification of induction along the lines of a Sellarsian coherence theory. On this coherence theory, a proposition is justified if we can answer all objections raised against it in our social practice of demanding justification and responding to such demands. On the basis of this theory of justification, I argue that we are justified in accepting the uniformity of nature partly because we have no alternative but to accept it for rationally pursuing our (...) epistemic goal. In addition, my coherentist view explains which inductive inferences it is rational to accept. Furthermore, my coherentist view also explains why we can hardly determine a particular numerical value x such that we can draw the conclusion ‘it is rational to accept that p’ from the premise ‘the numerical probability of p is greater than or equal to x’. (shrink)

This chapter explores in more detail two different ways of providing a context to the reading of Cicero's philosophy: the tradition of Academic scepticism in philosophy, inaugurated by Plato, which stressed the open-endedness of philosophical enquiry; and also Cicero's own ambivalence about the relevance of philosophy to public life and politics. The chapter examines the concept of compensation: how philosophy acted as a compensation for Cicero's marginalization from the world of politics. The effect of such compensation on the character of (...) the philosophy is ambiguous. Close reading suggests a constant awareness of the mismatch between Cicero's literary and political ambitions, and that Cicero was under no illusions as to the marginal relationship between philosophy and Roman history. Rhetoric is a central element in this ambiguous relationship. (shrink)