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)
In this paper we study the systemsP andP * (see Arruda and da Costa,O paradoxo de Curry-Moh Shaw-Kwei, Boletim da Sociedade Matemtica de São Paulo 18 (1966)) and some related systems. In the last section, we prove that certain set theories havingP andP * as their underlying logics are non-trivial.
Costa uses a symbolic metaphor to 8-10 year-olds with ‘Mr. Potato Head’ to show the value of meaning and how to be unique and true to oneself (metaphysics).
This article discusses Philip Pettit’s neo-republicanism in light of the criterion of self-sustenance: the requirement that a political theory be capable of serving as a self-sustaining public philosophy for a pluralist democracy. It argues that this criterion can only be satisfied by developing an adequate politics of virtue. Pettit’s theory is built around the notion of freedom as non-domination, and he does not say much about the virtues of citizens or the policies the state may employ to encourage their development. (...) In order to explain the motivation to comply with republican laws that promote non-domination, Pettit relies on the phenomenon of civility and the mechanism of the intangible hand. But to understand what underlies an adequate level of robust civility one needs to focus on the more basic phenomenon of personal virtue. Policies that aim to promote non-domination should take into account the need to cultivate virtue among citizens, as well as the full range of conditions that favor its exercise. (shrink)
This paper proposes a new, stronger version of the cluster theory of proper names. It introduces a meta-identifying rule that can establish a cluster's main descriptions and explain how they must be satisfied in order to allow the application of a proper name. At the same time, it preserves some main insights of the causal-historical view. With the resulting rule we can not only give a more detailed reply to the counter-examples to descriptivism, but also explain the informative contents of (...) proper names and why they are rigid designators in contrast with descriptions.1. (shrink)
One of the central elements of John Rawls’ argument in support of his two principles of justice is the intuitive normative ideal of citizens as free and equal. But taken in isolation, the claim that citizens are to be treated as free and equal is extremely indeterminate, and has virtually no clear implications for policy. In order to remedy this, the two principles of justice, together with the stipulation that citizens have basic interests in developing their moral capacities and pursuing (...) their conceptions of the good life, are meant to provide a more precise interpretation of what is involved in treating citizens as free and equal. Rawls’ critics, however, have argued that satisfying the two principles of justice is not the most appropriate or plausible way to respect the status of citizens as free and equal. In relation to this debate, the present paper has two aims. The first is to examine Rawls’ account of the type of freedom that a just society must guarantee equally to its citizens. I will argue that those who think of Rawls as a theorist of freedom as non-interference are mistaken, because his notion of liberty resembles in important respects the republican notion of freedom as non-domination. Second, I will consider the extent to which Rawls’ principles of justice successfully protect the freedom as non-domination of all citizens so as to effectively treat them as free and equal. (shrink)
This article examines the relevance of a theory of the multinational state for the evaluation of claims for self-determination and secession. Considerations of ?ethnocultural justice? imply that the recognition of the multinational character of a state ? or the granting of some of the minority nations' demands ? is a matter of justice. If these requirements are not met, secession could be justified. Indeed, if secession needs a just cause (as it has been argued), a failure to build a truly (...) multinational arrangement can be a valid reason for a minority nation to secede. An approach like the one proposed would also contribute to the resolution of some of the key problems of the three main theories of secession and their appeals to nationalism, choice and remedial rights. (shrink)
This study surveys debates on citizenship, the state, and the bases of political stability. The survey begins by presenting the primary sense of 'citizenship' as a legal status and the question of the sorts of political communities people can belong to as citizens. (Multi)nation-states are suggested as the main site of citizenship in the contemporary world, without ignoring the existence of alternative possibilities. Turning to discussions of citizen identity, the study shows that some of the discussion is motivated by a (...) perceived need for citizens to have a sense of political belonging, on the assumption that such a sense promotes political activity and has other personal and social benefits. But there are serious problems with the strategy of understanding the relevant sense of belonging in terms of identification with the nation-state. The study explores a more promising way to generate this sense of belonging. First, societies should function, to a sufficiently high degree, in accord with political principles of justice and democratic decision making. Second, there should be a general consensus on political principles among citizens, as well as high levels of engagement in democratic deliberation. (shrink)
The recent discovery of a mirror neuron system sets a challenge for a philosophy of experience such as phenomenology, because in humans and monkeys the mirror system seems to transform seen actions into an inner representation of these actions. This paper tries to outline the guidelines of a transcendental-phenomenological analysis of alterity, different from empirical research. The transcendental research must provide a criterion for interpreting the results of empirical science. On this basis the paper compares the phenomenological analysis of alterity (...) with some results of neuroscientific research. It is argued that Edmund Husserl presents an analysis that enables us to avoid misinterpretations of the role and function of the mirror neuron system. (shrink)
In this paper an improved formulation of the classical tripartite view of knowledge is proposed and defended. This formulation solves Gettier's problem by making explicit what is concealed by the symbolic version of the tripartite definition, namely, the perspectival context in which concrete knowledge claims are evaluated.
The ongoing global economic and financial crisis has exposed the risks of considering market and business organizations only as instruments for creating economic wealth while paying little heed to their role in ethics and values. Catholic Social Teaching (CST) could provide a useful contribution in rethinking the role of values in business organizations and markets because CST puts forward an anthropological view that involves thinking of the marketplace as a community of persons with the aim of participating in the Common (...) Good (CG) of society. In the light of the CST tradition, and in particular Caritas in Veritate , this article investigates the thinking of some of the historical scholars of the Italian Economia Aziendale ( EA ), by focusing on the concept of azienda , in order to reinterpret in a more humanistic way the role of business organizations in society. By linking CST and EA , the dichotomy between for-profit and not-for-profit organizations and the stereotype of the so-called business amorality that has, for a long time, driven business managers can be transcended. The conclusions imply a forward-looking application of the ethical concepts embedded in the Italian science of EA. (shrink)
We offer a probabilistic model of rational consequence relations (Lehmann and Magidor, 1990) by appealing to the extension of the classical Ramsey–Adams test proposed by Vann McGee in (McGee, 1994). Previous and influential models of non-monotonic consequence relations have been produced in terms of the dynamics of expectations (Gärdenfors and Makinson, 1994; Gärdenfors, 1993).Expectation is a term of art in these models, which should not be confused with the notion of expected utility. The expectations of an agent are some form (...) of belief weaker than absolute certainty. Our model offers a modified and extended version of an account of qualitative belief in terms of conditional probability, first presented in (van Fraassen, 1995). We use this model to relate probabilistic and qualitative models of non-monotonic relations in terms of expectations. In doing so we propose a probabilistic model of the notion of expectation. We provide characterization results both for logically finite languages and for logically infinite, but countable, languages. The latter case shows the relevance of the axiom of countable additivity for our probability functions. We show that a rational logic defined over a logically infinite language can only be fully characterized in terms of finitely additive conditional probability. (shrink)
An improvement on Horwich's so-called pseudo-proof of Russell's principle of induction is offered, which, we believe, avoids certain objections to the former. Although strictly independent of our other work in this area, a connection can be made and in the final section we comment on this and certain questions regarding rationality, etc.
Earlier, we have studied computations possible by physical systems and by algorithms combined with physical systems. In particular, we have analysed the idea of using an experiment as an oracle to an abstract computational device, such as the Turing machine. The theory of composite machines of this kind can be used to understand (a) a Turing machine receiving extra computational power from a physical process, or (b) an experimenter modelled as a Turing machine performing a test of a known (...) physical theory T. (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.
An appropriately unprejudiced logical investigation of causation as a type of implication relation is undertaken. The implication delineated is bounded syntactically. The developing argument then leads to a very natural process analysis, which demonstrably captures the established syntactical features. Next relevantly-based semantics for the resulting logical theory are adduced, and requisite adequacy results delivered. At the end of the tour, further improvements are pointed out, and the attractive terrain beyond present developments is glimpsed.
This paper aims at showing that Hobbes's theory of language, which allows men to communicate among themselves like no other animal species, is an importante factor in the integration of modern states. Both his nominalism and the fact that he considers language previous to reason play a role in the formation of social groups. This leads him, as Johnston points out, to make political order depend upon linguistic order. In consequence, Hobbes aims at building a political philosophy by introducing a (...) suitable vocabulary and setting basic propositions from which to deduce valid conclusions, proceding more geometrico . He also points out the importance of language for men to emerge from the state of nature and to draw a compact for peace and security. He also stresses the relation between language and power. Biblical references are included to reinforce the role of language in society, It is also shown that occasionally language may be a disgregating factor. Examples are put rather to show the integrating force of language. (shrink)
In his thesis Para uma Teoria Geral dos Homomorfismos (1944), the Portuguese mathematician José Sebastiāo e Silva constructed an abstract or generalized Galois theory, that is intimately linked to F. Klein's Erlangen Program and that foreshadows some notions and results of today's model theory; an analogous theory was independently worked out by M. Krasner in 1938. In this paper, we present a version of the theory making use of tools which were not at Silva's disposal. At the same time, we (...) tried to keep in mind, so much as possible, the gist of his standpoint. (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).
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)
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)
A critical review of what I see as a controversial interpretation of the nature and aims of Darwin’s rhetorical strategy and a narrow and controversial naturalist manifesto.
This paper illustrates the main features of Luigi Ferrajoli’s theoretical approach to law, as they are developed in his Principia Juris . These include his opposition to the traditional perspective of natural law; his anti-cognitivist orientation; and, finally, his fundamentally normative approach. Among the numerous problems discussed in Ferrajoli’s compendious book, the paper focuses on his definition of constitutional democracy. In particular, the paper discusses the way in which Ferrajoli defines the complementarity between democracy and rights; Ferrajoli’s own criticism of (...) T. H. Marshall’s idea of citizenship; and the importance that the distinction between ‘decidable’ and ‘non-decidable’ rights have in Ferrajoli’s own system. Other issues of interests that are briefly discussed include the constitutionalisation of private law, and the defence of different kinds of liberty-rights. (shrink)
This paper is a summary of a lecture in which I presented some remarks on Gödel’s incompleteness theorems and their meaning for the foundations of physics. The entire lecture will appear elsewhere. doi: http://dx.doi.org/ 10.5007 / 1808-1711.2011v15n3p453.
What is a person? What is the self? In the essay, I try to explore the historical roots of contemporary anxieties over the impact that the novel neurotechnologies and the new, rapidly accumulating scientific knowledge of the brain may have on our sense of self. My conclusion is that the allegedly novel situation is not so novel, after all, and that, in fact, we are still moving along a track opened long ago by early-modern transformations in Western culture. This, of (...) course, does not mean that we are not going to face serious problems, but only that we already have the intellectual resources to cope with them effectively (in so far as we consider them to be manageable issues). In the end, neuroethical dilemmas will turn out to be another variety of modern metaphysical and moral quandaries. (shrink)
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)
