People have disagreed on the significance of Libet-style experiments for discussions about free will. In what specifically concerns free will in a libertarian sense, some argue that Libet-style experiments pose a threat to its existence by providing support to the claim that decisions are determined by unconscious brain events. Others disagree by claiming that determinism, in a sense that conflicts with libertarian free will, cannot be established by sciences other than fundamental physics. This paper rejects both positions. First, it is (...) argued that neuroscience and psychology could in principle provide support for milder deterministic claims that would also conflict with libertarian free will. Second, it is argued that Libet-style experiments—due to some of their peculiar features, ones that need not be shared by neuroscience as a whole—currently do not support such less demanding deterministic claims. The general result is that neuroscience and psychology could in principle... (shrink)
The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (that is, logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special class of multialgebras. The proposed semantical framework generalizes previous aproaches to quantified LFIs presented in the literature. The case of QmbC, (...) the simpler quantified LFI expanding classical logic, will be analyzed in detail. An axiomatic extension of QmbC called QLFI1o is also studied, which is equivalent to the quantified version of da Costa and D'Ottaviano 3-valued logic J3. The semantical structures for this logic turn out to be Tarkian structures based on twist structures. The expansion of QmbC and QLFI1o with a standard equality predicate is also considered. (shrink)
In a previous paper, I argued that neuroscience and psychology could in principle undermine libertarian free will by providing support for a subset of what I called “statements of local determination.” I also argued that Libet-style experiments have not so far supported statements of that sort. In a commentary to the paper, Adina Roskies and Eddy Nahmias accept the claim about Libet-style experiments, but reject the claim about the possibilities of neuroscience. Here, I explain why I still disagree with their (...) conclusion, despite being sympathetic to a lot of what they say in support of it. (shrink)
This paper focuses on Gilberto Gomes’ work on free will. In a series of contributions that have had a significant impact on the respective literature, Gomes developed a conception about free will and argued that its existence is consistent with recent scientific findings, specially in neuroscience. In this paper, I object to a claim of Gomes about his conception of free will, namely the claim that it is a compatibilist conception. I seek to show that Gomes does not use the (...) term ‘compatibilism’ as it is usual in the contemporary literature on free will, i.e., as the thesis that free will can exist even if determinism is true. Moreover, the conception of free will Gomes proposes actually has an incompatibilist commitment. I argue that, more than a mere terminological point, acknowledging the incompatibilist aspect of Gomes’ view motivates important questions about the details of the view and helps to reveal a limitation of his defense of the existence of free will. [Este artigo tem como tema o trabalho de Gilberto Gomes sobre o livre-arbítrio. Em uma série de contribuições que tiveram um impacto significativo na respectiva literatura, Gomes elaborou uma concepção sobre o livre-arbítrio e argumentou que sua existência é consistente com descobertas científicas recentes, especialmente na neurociência. Neste artigo, questiono uma afirmação de Gomes sobre sua concepção sobre o livre-arbítrio, a saber, que se trata de uma concepção compatibilista. Busco mostrar que Gomes não usa o termo ‘compatibilismo’ como é habitual na literatura contemporânea sobre o livre-arbítrio, isto é, como a tese segundo a qual o livre-arbítrio pode existir ainda que o determinismo seja verdadeiro. Ademais, a concepção sobre o livre-arbítrio desenvolvida por Gomes tem, efetivamente, um compromisso incompatibilista. Argumento que, mais do que uma mera elucidação terminológica, reconhecer o elemento incompatibilista presente na proposta de Gomes suscita questões importantes sobre os detalhes da proposta e também ajuda a reconhecer uma limitação de sua defesa da existência do livre-arbítrio.]. (shrink)
Multialgebras have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap structures are given. Specifically, (...) a formal study of swap structures for LFIs is developed, by adapting concepts of universal algebra to multialgebras in a suitable way. A decomposition theorem similar to Birkhoff’s representation theorem is obtained for each class of swap structures. Moreover, when applied to the 3-valued algebraizable logics J3 and Ciore, their classes of algebraic models are retrieved, and the swap structures semantics become twist structures semantics. This fact, together with the existence of a functor from the category of Boolean algebras to the category of swap structures for each LFI, suggests that swap structures can be seen as non-deterministic twist structures. This opens new avenues for dealing with non-algebraizable logics by the more general methodology of multialgebraic semantics. (shrink)
Este artigo reconstrói os argumentos de Donald Davidson (1970) em favor de sua teoria do monismo anômalo e revisa as principais críticas que recebeu. Essa teoria é amplamente rejeitada atualmente e, dadas as inúmeras críticas recebidas, é razoável concluir que qualquer tentativa de reabilitação tem um longo caminho pela frente. A diversidade dessas críticas sugere que não há consenso sobre por que exatamente o monismo anômalo fracassa, embora as dificuldades pareçam convergir sobre a justificação e possibilidade da tese monista, e (...) não sobre a anomalia do mental. (shrink)
The aim of the paper is to analyze the expressive power of the square operator of Łukasiewicz logic: ∗x=x⊙x, where ⊙ is the strong Łukasiewicz conjunction. In particular, we aim at understanding and characterizing those cases in which the square operator is enough to construct a finite MV-chain from a finite totally ordered set endowed with an involutive negation. The first of our main results shows that, indeed, the whole structure of MV-chain can be reconstructed from the involution and the (...) Łukasiewicz square operator if and only if the obtained structure has only trivial subalgebras and, equivalently, if and only if the cardinality of the starting chain is of the form n+1 where n belongs to a class of prime numbers that we fully characterize. Secondly, we axiomatize the algebraizable matrix logic whose semantics is given by the variety generated by a finite totally ordered set endowed with an involutive negation and Łukasiewicz square operator. Finally, we propose an alternative way to account for Łukasiewicz square operator on involutive Gödel chains. In this setting, we show that such an operator can be captured by a rather intuitive set of equations. (shrink)
In the last few decades, the literature on moral responsibility has been increasingly populated by scientific studies. Studies in neuroscience and psychology, in particular, have been claimed to be relevant for discussions about moral responsibility in a number of ways. And at the same time, there is not yet a systematic understanding of the sort of questions a science of moral responsibility is supposed to answer. This paper is an attempt to move toward such an understanding. I discuss three models (...) for framing scientific questions relevant to an investigation of moral responsibility. The favored model—the Enhancement model—proposes that a science of moral responsibility has two descriptive tasks. First, science can describe the causes and effects of the many sorts of responses that constitute the human practices of moral responsibility, such as praise, blame, and punishment. And, second, science can describe how modifications aiming at the improvement of such practices can be achieved. Relatively to the other models to be considered, the Enhancement model is broader in scope and less tied to the traditional philosophical agenda on moral responsibility. (shrink)
The dissertation has two parts, each dealing with a problem, namely: 1) What is the most adequate account of fuzziness -the so-called phenomenon of vagueness?, and 2) what is the most plausible solution to the sorites, or heap paradox? I will try to show that fuzzy properties are those which are gradual, amenable to be possessed in a greater or smaller extent. Acknowledgement of degrees in the instantiation of a property allows for a gradual transition from one opposite to the (...) other, each intermediate stage constituting an overlap in certain proportion of both contraries. Hence, degrees in the possession of a property give rise to simple contradictions. The reason why I have chosen those two questions is that they provide the main philosophical motivation for a particular brand of an infinite valued and paraconsistent logic. I will claim that Classical logic (CL) is not adequate to handle fuzzy situations, and, being deficient, is in need of being expanded to make room for degrees of truth and weak contradictions. One can hardly deny the importance of the debate, since what is ultimately at stake is what the limits of truth, rationality, intelligibility and possibility are. The main disciplines within which the research moves are the philosophy of language, philosophy of logic, and ontology. (shrink)
Two systems of belief change based on paraconsistent logics are introduced in this article by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic which extends classical logic such that the law of excluded middle holds w.r.t. the paraconsistent negation. The second one, AGMo , is specifically designed for paraconsistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator that allows to recover all the classical inferences. Besides the three usual (...) operations over belief sets, namely expansion, contraction and revision (which is obtained from contraction by the Levi identity), the underlying paraconsistent logic allows us to define additional operations involving (non-explosive) contradictions. Thus, it is defined external revision (which is obtained from contraction by the reverse Levi identity), consolidation and semi-revision, all of them over belief sets. It is worth noting that the latter operations, introduced by S. Hansson, involve the temporary acceptance of contradictory beliefs, and so they were originally defined only for belief bases. Unlike to previous proposals in the literature, only defined for specific paraconsistent logics, the present approach can be applied to a general class of paraconsistent logics which are supraclassical, thus preserving the spirit of AGM. Moreover, representation theorems w.r.t. constructions based on selection functions are obtained for all the operations. (shrink)
In 1988, J. Ivlev proposed some (non-normal) modal systems which are semantically characterized by four-valued non-deterministic matrices in the sense of A. Avron and I. Lev. Swap structures are multialgebras (a.k.a. hyperalgebras) of a special kind, which were introduced in 2016 by W. Carnielli and M. Coniglio in order to give a non-deterministic semantical account for several paraconsistent logics known as logics of formal inconsistency, which are not algebraizable by means of the standard techniques. Each swap structure induces naturally a (...) non-deterministic matrix. The aim of this paper is to obtain a swap structures semantics for some Ivlev-like modal systems proposed in 2015 by M. Coniglio, L. Fariñas del Cerro and N. Peron. Completeness results will be stated by means of the notion of Lindenbaum–Tarski swap structures, which constitute a natural generalization to multialgebras of the concept of Lindenbaum–Tarski algebras. (shrink)
In this paper two systems of AGM-like Paraconsistent Belief Revision are overviewed, both defined over Logics of Formal Inconsistency (LFIs) due to the possibility of defining a formal consistency operator within these logics. The AGM° system is strongly based on this operator and internalize the notion of formal consistency in the explicit constructions and postulates. Alternatively, the AGMp system uses the AGM-compliance of LFIs and thus assumes a wider notion of paraconsistency - not necessarily related to the notion of formal (...) consistency. (shrink)
[Note: articles 1-5 are in English; Intro, Discussion, and Conclusion are in Portuguese.] Responsibility practices that are part of our daily lives involve, among other things, standards about how one should praise, blame, or punish people for their actions, as well as particular acts that follow those standards to a greater or lesser extent. A classical question in philosophy asks whether human beings can actually be morally responsible for what they do. This dissertation argues that addressing this classical question is (...) insufficient if one wants the investigation of moral responsibility to serve the goal of improving ordinary responsibility practices. As an alternative, I offer directions for an interdisciplinary investigation that I take to be in a better position to promote that goal. My argument is developed in five articles and a discussion section. The first four articles describe limitations of skeptical views, which deny the existence of moral responsibility. The first article assesses a skeptical argument based on results from neuroscience that intends to show that there is no free will. I argue that a premise in the argument—which says that choices are determined by events in the brain—is not supported by the available results. The second article argues that, despite the fact that existent results do not show that choices are determined by brain events, further studies in neuroscience could in principle do that. The third article begins the discussion of limitations that concern the implementability of some of the changes in responsibility practices recommended in skeptical approaches. Specifically, I describe challenges that attempts to reduce the severity of legal punishment are likely to face due to psychological facts about belief in free will and desire to punish. The forth article presents results from an original experiment that sought to test a hypothesis about the workings of belief in free will and the desire to punish, namely the hypothesis that the desire to punish causally affects beliefs about free will. Results failed to support the hypothesis. Finally, the fifth article presents what I call the enhancement model, i.e., a proposal about how to structure an interdisciplinary investigation that can promote the enhancement of ordinary responsibility practices. The final discussion section shows how the enhancement model overcomes some of the limitations of recent discussions about the existence of moral responsibility, which includes not just the skeptical views considered in earlier articles, but also views that affirm the existence of moral responsibility and free will. The central claim of this dissertation, therefore, is that the investigation of moral responsibility can be rearranged so as to further the goal of improving ordinary responsibility practices. (shrink)
Although the controversy between Malthus and Ricardo has long been considered to be an important source for the history of economic thought, it has hardly been the object of a careful study qua controversy, i.e. as a polemical dialogical exchange. We have undertaken to fill this gap, within the framework of a more ambitious project that places controversies at the center of an account of the history of ideas, in science and elsewhere. It is our contention that the dialogical co-text (...) is essential for reconstructing the meaning and the evolution of science. In the present paper we try to substantiate this contention by means of a pragma-rhetorical study of this particular controversy. First, we reconstruct, through an analysis of a chunk of the correspondence, a micro-level of specific moves and countermoves which constitute a sequential structure within which also meta-scientific and meta-controversial considerations play a role. We then move to a macro-level of analysis, looking for recurrent patterns of argumentation. Finally, we draw epistemological conclusions on the nature of rationality and progress as manifested in actual scientific controversies. (shrink)
Boolean-valued models of set theory were independently introduced by Scott, Solovay and Vopěnka in 1965, offering a natural and rich alternative for describing forcing. The original method was adapted by Takeuti, Titani, Kozawa and Ozawa to lattice-valued models of set theory. After this, Löwe and Tarafder proposed a class of algebras based on a certain kind of implication which satisfy several axioms of ZF. From this class, they found a specific 3-valued model called PS3 which satisfies all the axioms of (...) ZF, and can be expanded with a paraconsistent negation *, thus obtaining a paraconsistent model of ZF. The logic (PS3 ,*) coincides (up to language) with da Costa and D'Ottaviano logic J3, a 3-valued paraconsistent logic that have been proposed independently in the literature by several authors and with different motivations such as CluNs, LFI1 and MPT. We propose in this paper a family of algebraic models of ZFC based on LPT0, another linguistic variant of J3 introduced by us in 2016. The semantics of LPT0, as well as of its first-order version QLPT0, is given by twist structures defined over Boolean agebras. From this, it is possible to adapt the standard Boolean-valued models of (classical) ZFC to twist-valued models of an expansion of ZFC by adding a paraconsistent negation. We argue that the implication operator of LPT0 is more suitable for a paraconsistent set theory than the implication of PS3, since it allows for genuinely inconsistent sets w such that [(w = w)] = 1/2 . This implication is not a 'reasonable implication' as defined by Löwe and Tarafder. This suggests that 'reasonable implication algebras' are just one way to define a paraconsistent set theory. Our twist-valued models are adapted to provide a class of twist-valued models for (PS3,*), thus generalizing Löwe and Tarafder result. It is shown that they are in fact models of ZFC (not only of ZF). (shrink)
Diana Pérez (2005) criticizes Davidson’s argument for the thesis that there is no thought without language, and offers an alternative defense of that thesis on the basis of empirical studies on developmental psychology. In this comment I argue that more recent studies do not seem to affect Davidson’s argument in the way Pérez suggests, and that her alternative defense of the thesis that there is no thought without language is insufficient. At the end, I offer a sketch of how a (...) weaker and more tenable version of the argument could be articulated. (shrink)
Free will skepticism is the view that people never truly deserve to be praised, blamed, or punished for what they do. One challenge free will skeptics face is to explain how criminality could be dealt with given their skepticism. This paper critically examines the prospects of implementing legal changes concerning crime and punishment derived from the free will skeptical views developed by Derk Pereboom and Gregg Caruso. One central aspect of the changes their views require is a concern for reducing (...) the severity of current forms of punishment. The paper considers two strategies for pursuing such a reduction. By taking into account evidence from the psychology of belief in free will and desire to punish, it is argued that a strategy aiming at a reduction of people’s natural desire to punish criminals can be successful if capable of providing alternatives to current forms of punishment satisfying three properties: they must be less harmful than current forms of punishment, more effective in preventing crime, and incompatible with current forms of punishment. (shrink)
Tradução de correspondências trocadas entre Descartes e Elisabeth no ano de 1643, nas quais discutem a tese cartesiana da alma como imaterial e inextensa.
In abstract algebraic logic, many systems, such as those paraconsistent logics taking inspiration from da Costa's hierarchy, are not algebraizable by even the broadest standard methodologies, as that of Blok and Pigozzi. However, these logics can be semantically characterized by means of non-deterministic algebraic structures such as Nmatrices, RNmatrices and swap structures. These structures are based on multialgebras, which generalize algebras by allowing the result of an operation to assume a non-empty set of values. This leads to an interest in (...) exploring the foundations of multialgebras applied to the study of logic systems. -/- It is well known from universal algebra that, for every signature Sigma, there exist algebras over Sigma which are absolutely free, meaning that they do not satisfy any identities or, alternatively, satisfy the universal mapping property for the class of Sigma-algebras. Furthermore, once we fix a cardinality of the generating set, they are, up to isomorphisms, unique, and equal to algebras of terms (or propositional formulas, in the context of logic). Equivalently, the forgetful functor, from the category of Sigma-algebras to Set, has a left adjoint. This result does not extend to multialgebras. Not only multialgebras satisfying the universal mapping property do not exist, but the forgetful functor U, from the category of Sigma-multialgebras to Set, does not have a left adjoint. -/- In this paper we generalize, in a natural way, algebras of terms to multialgebras of terms, whose family of submultialgebras enjoys many properties of the former. One example is that, to every pair consisting of a function, from a submultialgebra of a multialgebra of terms to another multialgebra, and a collection of choices (which selects how a homomorphism approaches indeterminacies), there corresponds a unique homomorphism, what resembles the universal mapping property. Another example is that the multialgebras of terms are generated by a set that may be viewed as a strong basis, which we call the ground of the multialgebra. Submultialgebras of multialgebras of terms are what we call weakly free multialgebras. Finally, with these definitions at hand, we offer a simple proof that multialgebras with the universal mapping property for the class of all multialgebras do not exist and that U does not have a left adjoint. (shrink)
From Gadamer's Habilitation thesis, “Plato’s dialectical ethics. Phenomenological Interpretations Relating to the Philebus” (1928), this article seeks to highlight the fundamental lines of Plato’s image, outlined in that author’s first philosophical publication (1931). The confrontation with the themes of ethics and dialectic, in the current state of Platonic studies, indicates that in Plato’s image drawn in the early confrontation with the Philebus, clearly influenced by the phenomenological notion of Dasein, one already finds the fundamental features of what will become Gadamer's (...) philosophical hermeneutics, fully emancipated from Heideggerian tutelage. (shrink)
The dissertation has two parts, each dealing with a problem, namely: 1) What is the most adequate account of fuzziness -the so-called phenomenon of vagueness?, and 2) what is the most plausible solution to the sorites, or heap paradox? I will try to show that fuzzy properties are those which are gradual, amenable to be possessed in a greater or smaller extent. Acknowledgement of degrees in the instantiation of a property allows for a gradual transition from one opposite to the (...) other, each intermediate stage constituting an overlap in certain proportion of both contraries. Hence, degrees in the possession of a property give rise to simple contradictions. The reason why I have chosen those two questions is that they provide the main philosophical motivation for a particular brand of an infinite valued and paraconsistent logic. I will claim that Classical logic (CL) is not adequate to handle fuzzy situations, and, being deficient, is in need of being expanded to make room for degrees of truth and weak contradictions. One can hardly deny the importance of the debate, since what is ultimately at stake is what the limits of truth, rationality, intelligibility and possibility are. The main disciplines within which the research moves are the philosophy of language, philosophy of logic, and ontology. (shrink)
This paper reviews the central points and presents some recent developments of the epistemic approach to paraconsistency in terms of the preservation of evidence. Two formal systems are surveyed, the basic logic of evidence (BLE) and the logic of evidence and truth (LET J ), designed to deal, respectively, with evidence and with evidence and truth. While BLE is equivalent to Nelson’s logic N4, it has been conceived for a different purpose. Adequate valuation semantics that provide decidability are given for (...) both BLE and LET J . The meanings of the connectives of BLE and LET J , from the point of view of preservation of evidence, is explained with the aid of an inferential semantics. A formalization of the notion of evidence for BLE as proposed by M. Fitting is also reviewed here. As a novel result, the paper shows that LET J is semantically characterized through the so-called Fidel structures. Some opportunities for further research are also discussed. (shrink)
Abstract: The Pull Bayesian Significance Test (FBST) for precise hy- potheses is applied to a Multivariate Normal Structure (MNS) model. In the FBST we compute the evidence against the precise hypothesis. This evi- dence is the probability of the Highest Relative Surprise Set (HRSS) tangent to the sub-manifold (of the parameter space) that defines the null hypothesis. The MNS model we present appears when testing equivalence conditions for genetic expression measurements, using micro-array technology.
Marcelo Fischborn discusses the significance of neuroscience for debates about free will. Although he concedes that, to date, Libet-style experiments have failed to threaten “libertarian free will”, he argues that, in principle, neuroscience and psychology could do so by supporting local determinism. We argue that, in principle, Libet-style experiments cannot succeed in disproving or even establishing serious doubt about libertarian free will. First, we contend that “local determination”, as Fischborn outlines it, is not a coherent concept. Moreover, determinism is (...) unlikely to be established by neuroscience in any form that should trouble compatibilists or libertarians—that is, anyone who thinks we might have free will. We conclude that, in principle, neuroscience will not be able undermine libertarian free will and explain why these conclusions support a coherent compatibilist notion of causal sourcehood. (shrink)
In this paper we propose a very general de nition of combination of logics by means of the concept of sheaves of logics. We first discuss some properties of this general definition and list some problems, as well as connections to related work. As applications of our abstract setting, we show that the notion of possible-translations semantics, introduced in previous papers by the first author, can be described in categorial terms. Possible-translations semantics constitute illustrative cases, since they provide a new (...) semantical account for abstract logical systems, particularly for many-valued and paraconsistent logics. (shrink)
In this paper the class of Fidel-structures for the paraconsistent logic mbC is studied from the point of view of Model Theory and Category Theory. The basic point is that Fidel-structures for mbC (or mbC-structures) can be seen as first-order structures over the signature of Boolean algebras expanded by two binary predicate symbols N (for negation) and O (for the consistency connective) satisfying certain Horn sentences. This perspective allows us to consider notions and results from Model Theory in order to (...) analyze the class of mbC-structures. Thus, substructures, union of chains, direct products, direct limits, congruences and quotient structures can be analyzed under this perspective. In particular, a Birkhoff-like representation theorem for mbC-structures as subdirect poducts in terms of subdirectly irreducible mbC-structures is obtained by adapting a general result for first-order structures due to Caicedo. Moreover, a characterization of all the subdirectly irreducible mbC-structures is also given. An alternative decomposition theorem is obtained by using the notions of weak substructure and weak isomorphism considered by Fidel for Cn-structures. (shrink)
In this paper the propositional logic LTop is introduced, as an extension of classical propositional logic by adding a paraconsistent negation. This logic has a very natural interpretation in terms of topological models. The logic LTop is nothing more than an alternative presentation of modal logic S4, but in the language of a paraconsistent logic. Moreover, LTop is a logic of formal inconsistency in which the consistency and inconsistency operators have a nice topological interpretation. This constitutes a new proof of (...) S4 as being "the logic of topological spaces", but now under the perspective of paraconsistency. (shrink)
The paper is a comparative study of the methodologies of Malthus and Ricardo. Its claims are: (i) economic laws almost always admit of exceptions for Malthus; for Ricardo even contingent predictions allow no exception apart from random temporary variations; (ii) both rely on the prestigious Newtonian paradigm, while interpreting it according to two distinct methodological traditions (the one deriving from MacLaurin, the other from Priestley); (iii) the choice of stressing what happens during intervals or in permanent states leads to opposing (...) definitions of the main problem of economic science in so far as equilibrium is always already given for Ricardo and is never given for Malthus; (iv) their use of the ambiguous notion of "tendency" leaves unclear for both the degree of predictive power with which theories are endowed; (v) what both share is the idea of a natural order and this idea is the source of both shortcomings and endless disagreement. -/- . (shrink)
In 2001, W. Carnielli and Marcos considered a 3-valued logic in order to prove that the schema ϕ ∨ (ϕ → ψ) is not a theorem of da Costa’s logic Cω. In 2006, this logic was studied (and baptized) as G'3 by Osorio et al. as a tool to deﬁne semantics of logic programming. It is known that the truth-tables of G'3 have the same expressive power than the one of Łukasiewicz 3-valued logic as well as the one of Gödel (...) 3-valued logic G3. From this, the three logics coincide up-to language, taking into acccount that 1 is the only designated truth-value in these logics. -/- From the algebraic point of view, Canals-Frau and Figallo have studied the 3-valued modal implicative semilattices, where the modal operator is the well-known Moisil-Monteiro-Baaz Δ operator, and the supremum is deﬁnable from this. We prove that the subvariety obtained from this by adding a bottom element 0 is term-equivalent to the variety generated by the 3-valued algebra of G'3. The algebras of that variety are called G'3-algebras. From this result, we obtain the equations which axiomatize the variety of G'3-algebras. Moreover, we prove that this variety is semisimple, and the 3-element and the 2-element chains are the unique simple algebras of the variety. Finally an extension of G'3 to ﬁrst-order languages is presented, with an algebraic semantics based on complete G'3-algebras. The corresponding soundness and completeness theorems are obtained. (shrink)
Sendo a fenomenologia um modo não-especulativo de pensar, o artigo põe a questão sobre a possibilidade de descrever a metafísica em regime de redução fenomenológica, ou seja, a partir de uma atitude que não pretende discursar sobre o ser enquanto ser, mas sim a partir dos diferentes “modos de aparecer” dos principais “objetos” da metafísica: alma, mundo e Deus. Neste caso, que sentido deverá possuir, para o modo fenomenológico de pensar, o metá, presente na palavra metafísica?
We examine the most famous controversy between economists as a means of shedding fresh light on the current debate about economic methodology. By focusing on the controversy as the primary unit of analysis, we show how methodological considerations are but one of a whole set of stratagems strategically employed by each opponent. We argue that each opponent's preference for a particular kind of stratagems expresses his own specific scientific style (within the general scientific and cultural style of an age). We (...) also describe a dynamic dimension of the controversy, independent of the participants' intentions. Such a dimension is analysed in a "cycle" of the controversy, which begins with a well-defined issue and expands to additional topics, without reaching a "solution" to the initial issue. The definition and re-definition of the issue(s) at stake and of the difference between both participants is an essential and recurrent feature of such cycles; the conclusion of a cycle does not imply a real "closure" of the controversy, but only that each opponent has reached a satisfying degree of self-clarification. The controversy, thus, does not yield persuasion -- its ostensible aim. Rather, its "benefit" seems to lie in an unintended result -- clarification and deepening of contrasting approaches to the discipline -- due to its peculiar dynamics. In so far as the history of a discipline requires a reconstruction of such contrasts, it is indispensable for it to take into account the controversies where they emerge, and to view both the positive doctrines and the methodological posture of the contenders as parts of a wider framework, that is a scientific style. (shrink)
A topos version of Cantor’s back and forth theorem is established and used to prove that the ordered structure of the rational numbers (Q, <) is homogeneous in any topos with natural numbers object. The notion of effective homogeneity is introduced, and it is shown that (Q, <) is a minimal effectively homogeneous structure, that is, it can be embedded in every other effectively homogeneous ordered structure.
One of the most expected properties of a logical system is that it can be algebraizable, in the sense that an algebraic counterpart of the deductive machinery could be found. Since the inception of da Costa's paraconsistent calculi, an algebraic equivalent for such systems have been searched. It is known that these systems are non self-extensional (i.e., they do not satisfy the replacement property). More than this, they are not algebraizable in the sense of Blok-Pigozzi. The same negative results hold (...) for several systems of the hierarchy of paraconsistent logics known as Logics of Formal Inconsistency (LFIs). Because of this, these logics are uniquely characterized by semantics of non-deterministic kind. This paper offers a solution for two open problems in the domain of paraconsistency, in particular connected to algebraization of LFIs, by obtaining several LFIs weaker than C1, each of one is algebraizable in the standard Lindenbaum-Tarski's sense by a suitable variety of Boolean algebras extended with operators. This means that such LFIs satisfy the replacement property. The weakest LFI satisfying replacement presented here is called RmbC, which is obtained from the basic LFI called mbC. Some axiomatic extensions of RmbC are also studied, and in addition a neighborhood semantics is defined for such systems. It is shown that RmbC can be defined within the minimal bimodal non-normal logic E+E defined by the fusion of the non-normal modal logic E with itself. Finally, the framework is extended to first-order languages. RQmbC, the quantified extension of RmbC, is shown to be sound and complete w.r.t. BALFI semantics. (shrink)
There are two foundational, but not fully developed, ideas in paraconsistency, namely, the duality between paraconsistent and intuitionistic paradigms, and the introduction of logical operators that express meta-logical notions in the object language. The aim of this paper is to show how these two ideas can be adequately accomplished by the Logics of Formal Inconsistency (LFIs) and by the Logics of Formal Undeterminedness (LFUs). LFIs recover the validity of the principle of explosion in a paraconsistent scenario, while LFUs recover the (...) validity of the principle of excluded middle in a paracomplete scenario. We introduce definitions of duality between inference rules and connectives that allow comparing rules and connectives that belong to different logics. Two formal systems are studied, the logics mbC and mbD, that display the duality between paraconsistency and paracompleteness as a duality between inference rules added to a common core– in the case studied here, this common core is classical positive propositional logic (CPL + ). The logics mbC and mbD are equipped with recovery operators that restore classical logic for, respectively, consistent and determined propositions. These two logics are then combined obtaining a pair of logics of formal inconsistency and undeterminedness (LFIUs), namely, mbCD and mbCDE. The logic mbCDE exhibits some nice duality properties. Besides, it is simultaneously paraconsistent and paracomplete, and able to recover the principles of excluded middle and explosion at once. The last sections offer an algebraic account for such logics by adapting the swap-structures semantics framework of the LFIs the LFUs. This semantics highlights some subtle aspects of these logics, and allows us to prove decidability by means of finite non-deterministic matrices. (shrink)
Este artículo pretende analizar la particular relación de imbricación que Michel Foucault y Giorgio Agamben han venido a establecer entre la vida humana y el poder. A tal fin, se propone un recorrido por los dos momentos centrales de su producción que permiten dar cuenta de dicha imbricación: en el caso de Agamben, el referido a la investigación “homo sacer” y, en el de Foucault, el de su investigación en torno de la biopolítica como acontecimiento decisivo de la modernidad. Ambas (...) investigaciones han redundado, entre otros aspectos, pero de manera central, en la configuración de la vida humana en su relación con el poder. En cada uno de los momentos elegidos en las producciones de los filósofos, se analizan las nociones centrales que componen cada investigación: nuda vida, “homo sacer”, estado de excepción y “oikonomía”, en el primer caso; y biopolítica y gubernamentalidad, en el segundo. Finalmente, se contrastan ambas formulaciones filosóficas a fin de sopesar los alcances y las potencialidades que implican frente al análisis que proponen. Este breve ejercicio de análisis sobre la relación entre la vida y el poder en los dos filósofos, pretende poner en evidencia los riesgos a los que nos exponen ciertos presupuestos frecuentes que fundamentan y dan sentido a las ideas y a las prácticas políticas contemporáneas. (shrink)
A graph-theoretic account of logics is explored based on the general notion of m-graph (that is, a graph where each edge can have a finite sequence of nodes as source). Signatures, interpretation structures and deduction systems are seen as m-graphs. After defining a category freely generated by a m-graph, formulas and expressions in general can be seen as morphisms. Moreover, derivations involving rule instantiation are also morphisms. Soundness and completeness theorems are proved. As a consequence of the generality of the (...) approach our results apply to very different logics encompassing, among others, substructural logics as well as logics with nondeterministic semantics, and subsume all logics endowed with an algebraic semantics. (shrink)
Dugundji proved in 1940 that most parts of standard modal systems cannot be characterized by a single finite deterministic matrix. In the eighties, Ivlev proposed a semantics of four-valued non-deterministic matrices (which he called quasi-matrices), in order to characterize a hierarchy of weak modal logics without the necessitation rule. In a previous paper, we extended some systems of Ivlev’s hierarchy, also proposing weaker six-valued systems in which the (T) axiom was replaced by the deontic (D) axiom. In this paper, we (...) propose even weaker systems, by eliminating both axioms, which are characterized by eight-valued non-deterministic matrices. In addition, we prove completeness for those new systems. It is natural to ask if a characterization by finite ordinary (deterministic) logical matrices would be possible for all those Ivlev-like systems. We will show that finite deterministic matrices do not characterize any of them. (shrink)
Much forensic inference based upon DNA evidence is made assuming Hardy-Weinberg Equilibrium (HWE) for the genetic loci being used. Several statistical tests to detect and measure deviation from HWE have been devised, and their limitations become more obvious when testing for deviation within multiallelic DNA loci. The most popular methods-Chi-square and Likelihood-ratio tests-are based on asymptotic results and cannot guarantee a good performance in the presence of low frequency genotypes. Since the parameter space dimension increases at a quadratic rate on (...) the number of alleles, some authors suggest applying sequential methods, where the multiallelic case is reformulated as a sequence of “biallelic” tests. However, in this approach it is not obvious how to assess the general evidence of the original hypothesis; nor is it clear how to establish the significance level for its acceptance/rejection. In this work, we introduce a straightforward method for the multiallelic HWE test, which overcomes the aforementioned issues of sequential methods. The core theory for the proposed method is given by the Full Bayesian Significance Test (FBST), an intuitive Bayesian approach which does not assign positive probabilities to zero measure sets when testing sharp hypotheses. We compare FBST performance to Chi-square, Likelihood-ratio and Markov chain tests, in three numerical experiments. The results suggest that FBST is a robust and high performance method for the HWE test, even in the presence of several alleles and small sample sizes. (shrink)
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