Scientific reasoning is—and ought to be—conducted in accordance with the axioms of probability. This Bayesian view—so called because of the central role it accords to a theorem first proved by Thomas Bayes in the late eighteenth ...

From Descartes to Popper, philosophers have criticized and tried to improve the strategies of reasoning invoked in science and in everyday life. In recent years leading cognitive psychologists have painted a detailed, controversial, and highly critical portrait of common sense reasoning. Stephen Stich begins with a spirited defense of this work and a critique of those writers who argue that widespread irrationality is a biological or conceptual impossibility.Stich then explores the nature of rationality and irrationality: What is it that distinguishes (...) good reasoning from bad? He rejects the most widely accepted approaches to this question approaches which unpack rationality by appeal to truth, to reflective equilibrium or conceptual analysis. The alternative he defends grows out of the pragmatic tradition in which reasoning is viewed as a cognitive tool. Stich's version of pragmatism leads to a radical epistemic relativism and he argues that the widespread abhorrence of relativism is ill founded. (shrink)

An examination of Galileo's thought and work that focuses on his contributions to modern science.

This article begins by outlining some of the history—beginning with brief remarks of Quine's—of work on conditional assertions and conditional events. The upshot of the historical narrative is that diverse works from various starting points have circled around a nexus of ideas without convincingly tying them together. Section 3 shows how ideas contained in a neglected article of de Finetti's lead to a unified treatment of the topics based on the identification of conditional events as the objects of conditional bets. (...) The penultimate section explores some of the consequences of the resulting logic of conditional events while the last defends it. (shrink)

Epistemic conditionals have often been thought to satisfy the Ramsey test : If A, then B is acceptable in a belief state G if and only if B should be accepted upon revising G with A. But as Peter Gärdenfors has shown, RT conflicts with the intuitively plausible condition of Preservation on belief revision. We investigate what happens if RT is retained while Preservation is weakened, or vice versa. We also generalize Gärdenfors' approach by treating belief revision as a relation (...) rather than as a function.In our semantic approach, the same relation is used to model belief revision and to give truth-conditions for conditionals. The approach validates a weak version of the Ramsey Test — essentially, a restriction of RT to maximally consistent belief states. (shrink)

My title is intended to recall Terence Fine's excellent survey, Theories of Probability [1973]. I shall consider some developments that have occurred in the intervening years, and try to place some of the theories he discussed in what is now a slightly longer perspective. Completeness is not something one can reasonably hope to achieve in a journal article, and any selection is bound to reflect a view of what is salient. In a subject as prone to dispute as this, there (...) will inevitably be many who will disagree with any author's views, and I take the opportunity to apologize in advance to all such people for what they will see as the narrowness and distortion of mine. (shrink)

The familiar theories of physics have the feature that the application of the theory to make predictions in specific circumstances can be done by means of an algorithm. We propose a more precise formulation of this feature—one based on the issue of whether or not the physically measurable numbers predicted by the theory are computable in the mathematical sense. Applying this formulation to one approach to a quantum theory of gravity, there are found indications that there may exist no such (...) algorithms in this case. Finally, we discuss the issue of whether the existence of an algorithm to implement a theory should be adopted as a criterion for acceptable physical theories.“Can it then be that there is... something of use for unraveling the universe to be learned from the philosophy of computer design?” —J. A. Wheeler(1). (shrink)

How to accept a conditional? F. P. Ramsey proposed the following test in (Ramsey 1990).(RT) If A, then B must be accepted with respect to the current epistemic state iff the minimal hypothetical change of it needed to accept A also requires accepting B.

How to accept a conditional? F. P. Ramsey proposed the following test in . 'If A, then B' must be accepted with respect to the current epistemic state iff the minimal hypothetical change of it needed to accept A also requires accepting B. In this article we propose a formulation of , which unlike some of its predecessors, is compatible with our best theory of belief revision, the so-called AGM theory , chapters 1-5 for a survey). The new test, which, (...) we claim, encodes some of the crucial insights defended by F. P. Ramsey in , is used to study the conditionals epistemically validated by the AGM postulates. Our notion of validity is compared with the notion of negative validity used by Gärdenfors in . It is observed that the notions of PV and NV will in general differ and that when these differences arise it is the notion of PV that is preferable. Finally we compare our formulation of the Ramsey test with a previous formulation offered by Gärdenfors . We show that any attempt to interpret as delivering acceptance conditions for Ramsey's conditionals is doomed to failure. (shrink)

In this sequence of philosophical essays about natural science, the author argues that fundamental explanatory laws, the deepest and most admired successes of modern physics, do not in fact describe regularities that exist in nature. Cartwright draws from many real-life examples to propound a novel distinction: that theoretical entities, and the complex and localized laws that describe them, can be interpreted realistically, but the simple unifying laws of basic theory cannot.

This paper argues that when used judiciously Bayes's law has a role to play in the evaluation of scientific hypotheses. Several examples are presented in which a rational response to evidence requires a judgement whether to apply Bayes's law or whether, for example, to redistribute prior probabilities. The paper concludes that reflection on Bayes's law illustrates how an adequate account of the rational evaluation of hypotheses requires an account of judgement--a point which several philosophers have noted despite few attempts to (...) develop an adequate theory of judgement. (shrink)

Professor Brown describes and criticises the major classical model of rationality and offers a new model of this central concept in the history of philosophy and of science.

This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one of (...) its axiomatic bases), that fails to imply the proposition being eliminated. In the present paper, the authors study a broader class, including contraction functions that may be less than maximal. Specifically, they investigate "partial meet contraction functions", which are defined to yield the intersection of some nonempty family of maximal subsets of the theory that fail to imply the proposition being eliminated. Basic properties of these functions are established: it is shown in particular that they satisfy the Gardenfors postulates, and moreover that they are sufficiently general to provide a representation theorem for those postulates. Some special classes of partial meet contraction functions, notably those that are "relational" and "transitively relational", are studied in detail, and their connections with certain "supplementary postulates" of Gardenfors investigated, with a further representation theorem established. (shrink)

The standard use of the propositional calculus ('P.C.?) in analyzing the validity of inferences involving conditionals leads to fallacies, and the problem is to determine where P.C. may be ?safely? used. An alternative analysis of criteria of reasonableness of inferences in terms of conditions of justification rather than truth of statements is proposed. It is argued, under certain restrictions, that P. C. may be safely used, except in inferences whose conclusions are conditionals whose antecedents are incompatible with the premises in (...) the sense that if the antecedent became known, some of the previously asserted premises would have to be withdrawn. (shrink)

This edited volume of articles provides a state-of-the-art description of research in logic-based approaches to knowledge representation which combines approaches to reasoning with incomplete information that include partial, modal, and nonmonotonic logics. The collection contains two parts: foundations and case studies. The foundations section provides a general overview of partiality, multi-valued logics, use of modal logic to model partiality and resource-limited inference, and an integration of partial and modal logics. The case studies section provides specific studies of issues raised in (...) the foundations section. Several of the case studies integrate modal and partial modal logics with nonmonotonic logics. Both theoretical and practical aspects of such integration are considered. Knowledge representation issues such as default reasoning, theories of action and change, reason maintenance, awareness, and automation of nonmonotonic reasoning are covered. (shrink)

Are there scientific problems that cannot be solved? Mathematics is riddled with such problems, but can we pose analogous questions outside of mathematics? Does nature itself impose fundamental limits on our knowledge of the universe? Despite the work of some of the greatest minds of the twentieth century, no one really knows.In May 1995 this profound and far-reaching concern brought together a small but select group of scientists in a remote scientific outpost in Abisko, Sweden, a village far north of (...) the Arctic Circle. Boundaries and Barriers captures the spirit—and the content—of the talks given at the meeting. Included are contributions by John Barrow on the limits of science, John Casti on the search for the “unknowable” in science, James Hartle on quantum cosmology, Harold Morowitz on complexity and epistemology, and six more fascinating chapters that illuminate the possible limits to what we can know by using the tools of science. The issues discussed here challenge the very foundations of science, but the conclusions are optimistic. When the dust clears, science remains standing-our best bet for understanding the way the world works. (shrink)

Nonmonotonic reasoning in its broadest sense is reasoning to conclusions on the basis of incomplete information. Given more information, previously drawn inferences may be retracted. Commonsense reasoning has a nonmonotonic component; it has been argued that almost all commonsense inferences are of this sort. From the end of the 1980s to the present there has been an explosion in research in nonmonotonic reasoning. It is now possible to understand more clearly the properties of the major formalisms from a metatheoretical point (...) of view, the relationships among the formalisms and their connection to independently developed proof methods. The goal of this monograph is to make this understanding more accessible. (shrink)

There is currently no viable alternative to the Bayesian analysis of scientific inference, yet the available versions of Bayesianism fail to do justice to several aspects of the testing and confirmation of scientific hypotheses. Bayes or Bust? provides the first balanced treatment of the complex set of issues involved in this nagging conundrum in the philosophy of science. Both Bayesians and anti-Bayesians will find a wealth of new insights on topics ranging from Bayes's original paper to contemporary formal learning theory. (...) In a paper published posthumously in 1763, the Reverend Thomas Bayes made a seminal contribution to the understanding of "analogical or inductive reasoning." Building on his insights, modem Bayesians have developed an account of scientific inference that has attracted numerous champions as well as numerous detractors. Earman argues that Bayesianism provides the best hope for a comprehensive and unified account of scientific inference, yet the presently available versions of Bayesianisin fail to do justice to several aspects of the testing and confirming of scientific theories and hypotheses. By focusing on the need for a resolution to this impasse, Earman sharpens the issues on which a resolution turns. John Earman is Professor of History and Philosophy of Science at the University of Pittsburgh. (shrink)

Frank Ramsey was the greatest of the remarkable generation of Cambridge philosophers and logicians which included G. E. Moore, Bertrand Russell, Ludwig Wittgenstein and Maynard Keynes. Before his tragically early death in 1930 at the age of twenty-six, he had done seminal work in mathematics and economics as well as in logic and philosophy. This volume, with a new and extensive introduction by D. H. Mellor, contains all Ramsey's previously published writings on philosophy and the foundations of mathematics. The latter (...) gives the definitive form and defence of the reduction of mathematics to logic undertaken in Russell and Whitehead's Principia Mathematica; the former includes the most profound and original studies of universals, truth, meaning, probability, knowledge, law and causation, all of which are still constantly referred to, and still essential reading for all serious students of these subjects. (shrink)