One of the main applications of the logic of theory change is to the epistemic analysis of conditionals via the so-called Ramsey test. In the first part of the present note this test is studied in the “limiting case” where the theory being revised is inconsistent, and it is shown that this case manifests an intrinsic incompatibility between the Ramsey test and the AGM postulate of “success”. The paper then analyses the use of the postulate of success, and a weakening (...) of it, generating axioms of conditional logic via the test, and it is shown that for certain purposes both success and weak success are quite superfluous. This suggests the proposal of abandoning both success and weak success entirely, thus permitting retention of the postulate of “preservation” discarded by Gärdenfors. (shrink)
The recent literature offers several models of the notion of matter of fact supposition1 revealed in the acceptance of the so-called indicative conditionals. Some of those models are qualitative [Collins 90], [Levi 96], [Stalnaker 84]. Other probabilistic models appeal either to infinitesimal probability or two place probability functions. Recent work has made possible to understand which is the exact qualitative counterpart of the latter probabilistic models. In this article we show that the qualitative notion of change that thus arises is (...) hypothetical revision, a notion previously axiomatized in [Arló-Costa 97] and [Arló-Costa & Thomason 96]. This notion is incompatible with AGM as well as with other standard methods of theory change. The way in which matter-of-fact supposition is modeled by hypothetical revision is illustrated via examples. The model is compared with other qualitative accounts of the notion of supposition encoded in two-place probability functions, with models of subjunctive supposition, as well as with some of the well know models of learning. Applications in knowledge representation and in the theory of games and decisions are summarized. (shrink)
The paper studies first order extensions of classical systems of modal logic (see (Chellas, 1980, part III)). We focus on the role of the Barcan formulas. It is shown that these formulas correspond to fundamental properties of neighborhood frames. The results have interesting applications in epistemic logic. In particular we suggest that the proposed models can be used in order to study monadic operators of probability (Kyburg, 1990) and likelihood (Halpern-Rabin, 1987).
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.
The article focuses on representing different forms of non-adjunctive inference as sub-Kripkean systems of classical modal logic, where the inference from □A and □B to □A ∧ B fails. In particular we prove a completeness result showing that the modal system that Schotch and Jennings derive from a form of non-adjunctive inference in (Schotch and Jennings, 1980) is a classical system strictly stronger than EMN and weaker than K (following the notation for classical modalities presented in Chellas, 1980). The unified (...) semantical characterization in terms of neighborhoods permits comparisons between different forms of non-adjunctive inference. For example, we show that the non-adjunctive logic proposed in (Schotch and Jennings, 1980) is not adequate in general for representing the logic of high probability operators. An alternative interpretation of the forcing relation of Schotch and Jennings is derived from the proposed unified semantics and utilized in order to propose a more fine-grained measure of epistemic coherence than the one presented in (Schotch and Jennings, 1980). Finally we propose a syntactic translation of the purely implicative part of Jaśkowski's system D₂ into a classical system preserving all the theorems (and non-theorems) explicilty mentioned in (Jaśkowski, 1969). The translation method can be used in order to develop epistemic semantics for a larger class of non-adjunctive (discursive) logics than the ones historically investigated by Jaśkowski. (shrink)
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)
An important trend in contemporary epistemology centers on elaborating an old idea of pragmatist pedigree: theory selection (and in general the process of changing view and fixing beliefs) presupposes epistemic values. This article focuses on analyzing the case where epistemic values are indeterminate or when the sources of valuation are multiple (epistemic values like coherence and simplicity need not order options in compatible ways). According to the theory that thus arises epistemic alternatives need not be fully ordered by an underlying (...) notion of information-value and therefore the usual economic techniques of optimization cannot be applied in order to compute optimal contractions. But in cases of this sort it is still rational to maximize, i.e. to deem an option as choosable when it is not known to be worse that any other. We present here basic results about a notion of liberal contraction based on maximizing quasi-orderings. This requires the previous solution of some open problems in the theory of rational choice functions, namely a full characterization of choice functions rationalizable in terms of maximization of quasi-transitive relations. We conclude by discussing the problem of what is the adequate feasible set for calculating maximizing solutions for contraction problems and by considering the epistemological roots of some counterexamples against the most fundamental axioms on choice functions (like α). While the first part of the paper shows how economic insights can be used to improve our understanding of the principles of belief formation and change, this final section reverses this strategy by showing the utility of epistemological insights and techniques for providing invariance conditions capable of regulating the applicability of the pure principles of choice. (shrink)
Sven-Ove Hansson and Erik Olsson studied in Hansson and Olsson, 103–119 1995) the logical properties of an operation of contraction first proposed by Isaac Levi in Levi. They provided a completeness result for the simplest version of contraction that they call Levi-contraction but left open the problem of characterizing axiomatically the more complex operation of value-based contraction or saturatable contraction. In this paper we propose an axiomatization for this operation and prove a completeness result for it. We argue that the (...) resulting operation is better behaved than various rival operations of contraction defined in recent years. (shrink)
En este artículo me ocupo de la cuestión de cómo en las teorías de proceso dual se puede dar cuenta del autoengaño y su conexión con la racionalidad. Presento las versiones intencionalista y no intencionalista del autoengaño y muestro cómo el debate entre ellas puede dirimirse de manera más completa y satisfactoria en el marco de una teoría dual. En éste suelen aceptarse dos sistemas de razonamiento, uno heurístico y otro analítico, que compiten por el control de nuestras inferencias y (...) acciones, pero a veces interactúan y colaboran entre sí. Se defiende que si predomina la respuesta de S1, se puede ver el patrón del autoengaño como una forma de razonamiento heurístico y no únicamente como un vínculo causal. Se sugiere que las evaluaciones en cuanto a la racionalidad del proceso del autoengaño, dependerá del modo en que intervenga en el patrón de razonamiento y del sistema desde el cual se lleve a cabo. In this paper I discuss the phenomenon of self-deception and its connection with the notion of rationality linked to the dual process theories. I present the intentionalist and nonintentionalist accounts of self-deception and aim to show how the debate between them can be resolved in a more comprehensive and satisfactory manner, if it is placed in the frame of the dual process theories. The dual model usually accepts two kinds of reasoning processes, heuristic and analytic, referred to two different systems, S1 and S2. These processes compete for control of our inferences and actions, but sometimes they interact and collaborate. It is suggested that in a dual model, the evaluations in terms of the rationality of the process will depend on the way in which self-deception participates in the reasoning process and on the system from which the evaluation takes place. (shrink)
Je me propose une évaluation du travail effectué par Jeanne Hersch sur les droits de l�homme. A-t-elle tenté de «fonder» les droits, c�est-a-dire, de développer des argumentations contraignantes qui en établissent la validité ? Elle dérive les droits d�une conception normative de la nature humaine, s�appuyant sur la volonté, qui doit être libre, plutôt que sur la raison. Ses «fondements» ne sont pas des argumentations, mais des présupposés anthropologiques. Elle tente d�expliquer les échecs des droits de l�homme par une analyse (...) de leur tendance naturelle à se multiplier, se différencier, s�opposer l�un à l�autre. (shrink)
RESUMEN:El siguiente escrito ensaya una interpretación del rendimiento del mito de los metales expuesto por Platón en su diálogo llamado Politeia a propósito de la siguiente interrogación: ¿Cómo se constituye el orden social en la pólis platónica? Para responder a esta pregunta debemos esclarecernos respecto de: i) El papel de la educación en la constitución del orden social. ii) La correlación entre el mito de los metales y el orden social. iii) La constitución tripartita de la psykhḗ humana. Una vez (...) aclarado estos distintos puntos podremos comprender la oculta pero significativa función del mito de los metales en la constitución del orden social platónico. ABSTRACT:This article attempts an interpretation of the account of the myth of the metals as expounded by Plato in the Politeia. We address the following question: How is the social order established in the Platonic polis? To answer this question we must clarify: i) the role of education in the constitution of the social order; ii) the correlation between the myth of the metals and the social order; iii) the tripartite constitution of the human psyche. Once these various points have been made clear, we can understand the hidden but significant function of the myth of the metals in the constitution of the Platonic social order. (shrink)
Starting from a historical-juridical study of A. M. de Aldama on the origin and evolution of the reference to the teaching of Christian doctrine to pueri contained in the formula of final vows of all priests in the Society of Jesus, the author investigates the meaning of this ministry and its importance today. In an analytic section, the article traces the historical development of the ministry of education in Christian doctrine to pueri and rudes in the experience of Ignatius and (...) his first companions and in the foundational texts. The theme is treated above all in the light of some questions brought up by the historical data of the past and present. In conclusion the author seeks to reply synthetically to the questions, by showing some essential elements in the significance of the ministry of teaching Christian doctrine to children for an apostle in today's world. (shrink)
S. Jakowski introduced the discussive prepositional calculus D 2as a basis for a logic which could be used as underlying logic of inconsistent but nontrivial theories (see, for example, N. C. A. da Costa and L. Dubikajtis, On Jakowski's discussive logic, in Non-Classical Logic, Model Theory and Computability, A. I. Arruda, N. C. A da Costa and R. Chuaqui edts., North-Holland, Amsterdam, 1977, 37–56). D 2has afterwards been extended to a first-order predicate calculus and to a higher-order logic (cf. the (...) quoted paper). In this paper we present a natural version of D 2, in the sense of Jakowski and Gentzen; as a consequence, we suggest a new formulation of the discussive predicate calculus (with equality). A semantics for the new calculus is also presented. (shrink)
The anti- Humean proposal of constructing desire as belief about what would be good must be abandoned on pain of triviality. Our central result shows that if an agent's belief- desire state is represented by Jeffrey's expected value theory enriched with the Desire as Belief Thesis (DAB), then, provided that three pairwise inconsistent propositions receive non- zero probability, the agent must view with indifference any proposition whose probability is greater than zero. Unlike previous results against DAB our Opinionation or Indifference (...) Theorem is a purely synchronic one that depends in no way of the properties of Jeffrey conditionalization. (shrink)