According to the approach made famous by Alchourrón, Gärdenfors and Makinson (1985), revision is a transformation K*h of a potential belief state K by adding h yielding another potential belief state.1 This AGM revision transformation is a composition of two other transformations: contraction and expansion. K*h = [K-~h]+h. This is the expansion by adding h of the contraction K-~h of K by removing ~h.
Corrigibilism without solidarity -- Inquiry, deliberation, and method -- Pragmatism and change of view -- Beware of syllogism : statistical reasoning and conjecturing according to Peirce -- Dewey's logic of inquiry -- Wayward naturalism : saving Dewey from himself -- Seeking truth -- The logic of consistency and the logic of truth -- Belief, doubt, and evidentialism -- Induction, abduction, and oracles -- Knowledge as true full belief.
This paper seeks to defend the following conclusions: The program advanced by Carnap and other necessarians for probability logic has little to recommend it except for one important point. Credal probability judgments ought to be adapted to changes in evidence or states of full belief in a principled manner in conformity with the inquirer’s confirmational commitments—except when the inquirer has good reason to modify his or her confirmational commitment. Probability logic ought to spell out the constraints on rationally coherent confirmational (...) commitments. In the case where credal judgments are numerically determinate confirmational commitments correspond to Carnap’s credibility functions mathematically represented by so—called confirmation functions. Serious investigation of the conditions under which confirmational commitments should be changed ought to be a prime target for critical reflection. The necessarians were mistaken in thinking that confirmational commitments are immune to legitimate modification altogether. But their personalist or subjectivist critics went too far in suggesting that we might dispense with confirmational commitments. There is room for serious reflection on conditions under which changes in confirmational commitments may be brought under critical control. Undertaking such reflection need not become embroiled in the anti inductivism that has characterized the work of Popper, Carnap and Jeffrey and narrowed the focus of students of logical and methodological issues pertaining to inquiry. (shrink)
Hans Herzberger's 1973 essay 'Ordinal Preference and Rational Choice' is a classic milestone in the erosion of the idea that rational agents are maximizers of utility. By the time Herzberger wrote, many authors had replaced this claim with the thesis that rational agents are maximizers of preference. That is to say, it was assumed that at the moment of choice a rational agent has a weak ordering representing his or her preferences among the options available to the agent for choice (...) and that the rational agent restricts choice to one of the optimal options. Such an option is an available option judged at least as good as any other.Herzberger explored the prospects of weakening this ordinalist view of maximizing .. (shrink)
We present a decision-theoretically motivated notion of contraction which, we claim, encodes the principles of minimal change and entrenchment. Contraction is seen as an operation whose goal is to minimize loses of informational value. The operation is also compatible with the principle that in contracting A one should preserve the sentences better entrenched than A (when the belief set contains A). Even when the principle of minimal change and the latter motivation for entrenchment figure prominently among the basic intuitions in (...) the works of, among others, Quine and Ullian (1978), Levi (1980, 1991), Harman (1988) and Gärdenfors (1988), formal accounts of belief change (AGM, KM – see Gärdenfors (1988); Katsuno and Mendelzon (1991)) have abandoned both principles (see Rott (2000)). We argue for the principles and we show how to construct a contraction operation, which obeys both. An axiom system is proposed. We also prove that the decision-theoretic notion of contraction can be completely characterized in terms of the given axioms. Proving this type of completeness result is a well-known open problem in the field, whose solution requires employing both decision-theoretical techniques and logical methods recently used in belief change. (shrink)
We present a decision-theoretically motivated notion of contraction which, we claim, encodes the principles of minimal change and entrenchment. Contraction is seen as an operation whose goal is to minimize loses of informational value. The operation is also compatible with the principle that in contracting A one should preserve the sentences better entrenched than A (when the belief set contains A). Even when the principle of minimal change and the latter motivation for entrenchment figure prominently among the basic intuitions in (...) the works of, among others, Quine and Ullian (1978), Levi (1980, 1991), Harman (1988) and Gärdenfors (1988), formal accounts of belief change (AGM, KM -- see Gärdenfors (1988); Katsuno and Mendelzon (1991)) have abandoned both principles (see Rott (2000)). We argue for the principles and we show how to construct a contraction operation, which obeys both. An axiom system is proposed. We also prove that the decision-theoretic notion of contraction can be completely characterized in terms of the given axioms. Proving this type of completeness result is a well-known open problem in the field, whose solution requires employing both decision-theoretical techniques and logical methods recently used in belief change. (shrink)
An argument is advanced to show why E-admissibility should be preferred over maximality as a principle of rational choice where rationality is understood as minimal rationality. Consideration is given to the distinction between second best and second worst options in three way choice that is ignored according to maximality. It is shown why the behavior exhibited in addressing the problems posed by Allais (Econometrica 21:503–546, 1952) and by Ellsberg (Q Econ 75:643–669, 1961) do not violate the independence postulate according to (...) minimal rationality. (shrink)
This is a collection of Isaac Levi’s philosophical papers. Over the period represented by the work here, Professor Levi has developed an interrelated set of views, in the tradition of Peirce and Dewey, on epistemology and the philosophy of science and social science. This focus has been on the problem of induction and the growth of knowledge, the foundations of probability and the theory of rational decision-making. His most important essays in these areas are assembled here, with an introduction setting (...) out their main themes and connections. As a whole the volume presents a coherent, elaborated position which will be of great interest to a range of philosophers, decision theorists, welfare and social choice theorists and cognitive scientists. (shrink)
A comparison is made between the criterion of choice of E-admissibility I proposed in Levi, 1974 and elaborated in Levi, 1980 and 1986, and the ideas about norms elaborated by Alchourrón and Bulygin (1971 and 1981) with an emphasis on the fact that choice cannot always be evaluated in terms of binary comparisons as the distinction between second worst and not second worst illustrates. Se establece una comparación entre el criterio de E-admisibilidad propuesto en Levi,1974 y elaborado en Levi,1980 y (...) 1986 y las ideas sobre normas elaboradas por Alchourrón y Bulygin (1971 y 1981) enfatizando el hecho de que una elección no puede siempre ser evaluada en términos de comparaciones binarias como lo ilustra la distinción entre "second worst" y "not second worst". (shrink)
Isaac Levi's new book develops further his pioneering work in formal epistemology, focusing on the problem of belief contraction, or how rationally to relinquish old beliefs. Levi offers the most penetrating analysis to date of this key question in epistemology, offering a completely new solution and explaining its relation to his earlier proposals. He mounts an argument in favor of the thesis that contracting a state of belief by giving up specific beliefs is to be evaluated in terms of the (...) value of the information lost by doing so. The rationale aims to be thoroughly decision theoretic. Levi spells out his goals and shows that certain types of recommendations are obtained if one seeks to promote these goals. He compares his approach to his earlier account of inductive expansion. The recommendations are for "mild contractions." These are formally the same as the "severe withdrawals" considered by Pagnucco and Rott. The rationale, however, is different. A critical part of the book concerns the elaboration of these differences. The results are relevant to accounts of the conditions under which it is legitimate to cease believing and to accounts of conditionals. Mild Contraction will be of great interest to all specialists in belief revision theory and to many students of formal epistemology, philosophy of science, and pragmatism. (shrink)
I respond to Erik Olsson's critique of my account of contraction frominconsistent belief states, by admitting that such contraction cannot be rationalized as adeliberate decision problem. It can, however, be rationalized as a routine designed prior toinadvertent expansion into inconsistency when the deliberating agent embraces a consistent point of view.
David Makinson has argued that the compelling character of counterexamples to the Recovery Condition on contraction is due to an appeal to justificational structure. In “naked theories” where such structure is ignored or is not present, Recovery does apply. This note attempts to show that Makinson is mistaken on both counts. Recovery fails when no appeal is made to justificational structure.
Leeds (1990) levels an objection against the criterion of rational choice I have proposed (Levi 1997, Ch. 6; 1980; 1986), pointing out that the criterion is sensitive to the way possible consequences are partitioned. Seidenfeld, Kadane and Schervish (1989) call into question the defense of the cross product rule by appeal to Pareto Unanimity Principles that I had invoked in my 1986. I offer clarifications of my proposals showing that the difference between my views and those of my critics concerns (...) the extent to which full belief, probabilistic belief, and value judgment are separable. (shrink)
Isaac Levi is one of the preeminent philosophers in the areas of pragmatic rationality and epistemology. This collection of essays constitutes an important presentation of his original and influential ideas about rational choice and belief. A wide range of topics is covered, including consequentialism and sequential choice, consensus, voluntarism of belief, and the tolerance of the opinions of others. The essays elaborate on the idea that principles of rationality are norms that regulate the coherence of our beliefs and values with (...) our rational choices. The norms impose minimal constraints on deliberation and inquiry, but they also impose demands well beyond the capacities of deliberating agents. This major collection will be eagerly sought out by a wide range of philosophers in epistemology, logic, and philosophy of science, as well as economists, decision theorists, and statisticians. (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.
This book by one of the world's foremost philosophers in the fields of epistemology and logic offers an account of suppositional reasoning relevant to practical deliberation, explanation, prediction and hypothesis testing. Suppositions made 'for the sake of argument' sometimes conflict with our beliefs, and when they do, some beliefs are rejected and others retained. Thanks to such belief contravention, adding content to a supposition can undermine conclusions reached without it. Subversion can also arise because suppositional reasoning is ampliative. These two (...) types of nonmonotonic logic are the focus of this book. A detailed comparison of nonmonotonicity appropriate to both belief contravening and ampliative suppositional reasoning reveals important differences that have been overlooked. (shrink)
There is an important class of conditionals whose assertibility conditions are not given by the Ramsey test but by an inductive extension of that test. Such inductive Ramsey conditionals fail to satisfy some of the core properties of plain conditionals. Associated principles of nonmonotonic inference should not be assumed to hold generally if interpretations in terms of induction or appeals to total evidence are not to be ruled out.
Isaac Levi's new book is concerned with how one can justify changing one's beliefs. The discussion is deeply informed by the belief-doubt model advocated by C. S. Peirce and John Dewey, of which the book provides a substantial analysis. Professor Levi then addresses the conceptual framework of potential changes available to an inquirer. A structural approach to propositional attitudes is proposed which rejects the conventional view that a propositional attitude involves a relation between an agent and either a linguistic entity (...) or some other intentional object such as a proposition or set of possible worlds. The last two chapters offer an account of change in states of full belief understood as changes in commitments rather than changes in performance; one chapter deals with adding new information to a belief state, the other with giving up information. The book builds upon topics discussed in some of Levi's earlier work. It will be of particular interest to discussion theorists, epistemologists, philosophers of science, computer scientists, and cognitive psychologists. (shrink)