The AGM theory of belief contraction is extended tomultiple contraction, i.e. to contraction by a set of sentences rather than by a single sentence. There are two major variants: Inpackage contraction all the sentences must be removed from the belief set, whereas inchoice contraction it is sufficient that at least one of them is removed. Constructions of both types of multiple contraction are offered and axiomatically characterized. Neither package nor choice contraction can in general be reduced to contractions by single (...) sentences; in the finite case choice contraction allows for reduction. (shrink)
The thesis that every truth is knowable is usually glossed by decomposing knowability into possibility and knowledge. Under elementary assumptions about possibility and knowledge, considered as modal operators, the thesis collapses the distinction between truth and knowledge (as shown by the so-called Fitch-argument). We show that there is a more plausible interpretation of knowability—one that does not decompose the notion in the usual way—to which the Fitch-argument does not apply. We call this the potential knowledge-interpretation of knowability. We compare our (...) interpretation with the rephrasal of knowability proposed by Edgington and Rabinowicz and Segerberg, inserting an actuality-operator. This proposal shares some key features with ours but suffers from requiring specific transworld-knowledge. We observe that potential knowledge involves no transworld-knowledge. We describe the logic of potential knowledge by providing models for interpreting the new operator. Finally we show that the knowability thesis can be added to elementary conditions on potential knowledge without collapsing modal distinctions. (shrink)
In this paper we set out a semantics for relevant (counterfactual) conditionals. We combine the Routley-Meyer semantics for relevant logic with a semantics for conditionals based on selection functions. The resulting models characterize a family of conditional logics free from fallacies of relevance, in particular counternecessities and conditionals with necessary consequents receive a non-trivial treatment.
Semantics are given for modal extensions of relevant logics based on the kind of frames introduced in . By means of a simple recipe we may obtain from a class FRM (L) of unreduced frames characterising a (non-modal) logic L, frame-classes FRM (L.M) characterising conjunctively regular modal extensions L.M of L. By displaying an incompleteness phenomenon, it is shown how the recipe fails when reduced frames are under consideration.
With each proposition P we associate a set of proposition (a hyperproposition) which determines the order in which one may retreat from accepting P, if one cannot fully hold on to P. We first describe the structure of hyperpropositions. Then we describe two operations on propositions, subtraction and merge, which can be modelled in terms of hyperpropositions. Subtraction is an operation that takes away part of the content of a proposition. Merge is an operation that determines the maximal consistent content (...) of two propositions considered jointly. The merge operation gives rise to an inference relation which is, in a certain sense, optimally paraconsistent. (shrink)
The paradox of propositions, presented in Appendix B of Russell's The Principles of Mathematics, is usually taken as Russell's principal motive, at the time, for moving from a simple to a ramified theory of types. I argue that this view is mistaken. A closer study of Russell's correspondence with Frege reveals that Russell carne to adopt a very different resolution of the paradox, calling into question not the simplicity of his early type theory but the simplicity of his early theory (...) of propositions. (shrink)
The paper presents the main ideas of Ultrafilter Logic (UL), as introduced by Veloso and others. A new proposal, Normality Logic (NL), is outlined for expanding the expressive power of UL. The system NL appears to offer a simpler solution to the problem of expressive power than the sorting strategy of Carnielli and Veloso. Interpretations of NL are discussed and an important point of contact to Hansson's notion of non-prioritized belief revision is observed.
In Appendix B of Russell's The Principles of Mathematics occurs a paradox, the paradox of propositions, which a simple theory of types is unable to resolve. This fact is frequently taken to be one of the principal reasons for calling ramification onto the Russellian stage. The paper presents a detaiFled exposition of the paradox and its discussion in the correspondence between Frege and Russell. It is argued that Russell finally adopted a very simple solution to the paradox. This solution had (...) nothing to do with ramified types but marked an important shift in his theory of propositions. (shrink)
The causal/explanatory exclusion argument is one of the principal weapons against the possibility of mental causes/explanations having genuine causal/explanatory power. I argue that the causal and the explanatory versions of the exlusion argument should be distinguished. There are really two arguments, one of them perhaps successful, the other one not.
The paper presents the main ideas of Ultrafilter Logic, as introduced by Veloso and others. A new proposal, Normality Logic, is outlined for expanding the expressive power of UL. The system NL appears to offer a simpler solution to the problem of expressive power than the sorting strategy of Carnielli and Veloso. Interpretations of NL are discussed and an important point of contact to Hansson's notion of non-prioritized belief revision is observed.
We defend J. Kim's principle of explanatory exclusion from a recent criticism advanced by A Marras. We show that the principle follows from a less controversial principle of causal exclusion together with the assumption that claims of explanation are factual. We resolve the tension produced by Marras' argument by drawing a distinction between causal and explanatory relevance. In cross-level explanations the explanans property is not causally but explanatorily relevant to the explanandum. This calls for an account of how explanatorily relevant (...) properties are grounded in causally relevant properties which in turn ultimately depend on causally efficacious properties. A. (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.
The sentential logic S extends classical logic by an implication-like connective. The logic was first presented by Chellas as the smallest system modelled by contraining the Stalnaker-Lewis semantics for counterfactual conditionals such that the conditional is effectively evaluated as in the ternary relations semantics for relevant logics. The resulting logic occupies a key position among modal and substructural logics. We prove completeness results and study conditions for proceeding from one family of logics to another.
John Horty has proposed an approach to reasoning with ought-propositions which stands in contrast to the standard modal approach to deontic logic. Horty’s approach is based on default theories as known from the framework of Default Logic. It is argued that the approach cannot be extended beyond the most simple kinds of default theories and that it fails in particular to account for conditional obligations. The most plausible ways of straightening out the defects of the approach conform to a simple (...) theory of default reasoning in standard deontic language. (shrink)
The process [by which any individual settles into new opinions] is always the same. The individual has a stock of old opinions already, but he meets a new experience that puts them to a strain…. The result is an inward trouble to which his mind till then had been a stranger, and from which he seeks to escape by modifying his previous mass of opinions. He saves as much of it as he can, for in this matter of belief we (...) are all extreme conservatives. So he tries to change first this opinion, and then that (for they resist change very variously), until at last some new idea comes up which he can graft upon the ancient stock with a minimum of disturbance of the latter, some idea that mediates between the stock and the new experience and runs them into one most felicitously and expediently.The new idea is then adopted as the true one. It preserves the older stock of truths with a minimum of modification, stretching them just enough to make them admit the novelty, but conceiving that in ways as familiar as the case leaves possible. (William James, Lectures on Pragmatism, 1907). (shrink)
The paradox of propositions, presented in Appendix B of Russell’s The Principles of Mathematics, is usually taken as Russell’s principal motive, at the time, for moving from a simple to a ramified theory of types. I argue that this view is mistaken. A closer study of Russell’s correspondence with Frege reveals that Russell came to adopt a very different resolution of the paradox, calling into question not the simplicity of his early type theory but the simplicity of his early theory (...) of propositions. (shrink)
: Pragmatist truth - as advocated e.g. by Peirce and James - is usually taken to integrate four key elements: the value of truth is likened to some kind of utility; truth is naturally taken to consist in correspondence; truth is essentially linked to the possibility of knowledge; truth is not relative but absolute. Critics have never tired to question the individual and collective consistency of these four constraints. The principal challenge issued to pragmatists always consisted in developing viable interpretations (...) of the key notions utility, correspondence, knowability and absoluteness that would render the pragmatist proposal at least consistent. I shall take up that challenge developing some ideas of James in a contemporary garb.Keywords: Truth. Utility. Knowledge. JamesResumo: Verdade pragmatista - como defendida por Peirce e James, por exemplo - da forma como é considerada usualmente, integra quatro elementoschave: o valor da verdade é assemelhado a algum tipo de utilidade; a verdade é naturalmente considerada como consistindo de correspondência; a verdade está essencialmente ligada à possibilidade de conhecimento; a verdade não é relativa e sim absoluta. Os críticos nunca se cansam de questionar a consistência individual e coletiva dessas quatro limitações. O principal desafio lançado aos pragmatistas , sempre envolveu o desenvolvimento de interpretações viáveis das noções-chave: utilidade, correspondência, cognoscibilidade e integridade, que tornariam a proposta pragmatista, ao menos, consistente. Aceitarei o desafio, desenvolvendo algumas idéias de James sob uma roupagem contemporânea.Palavras-chave: Verdade. Utilidade. Conhecimento. James. (shrink)