We study some operations that may be defined using the minimum operator in the context of a Heyting algebra. Our motivation comes from the fact that 1) already known compatible operations, such as the successor by Kuznetsov, the minimum dense by Smetanich and the operation G by Gabbay may be defined in this way, though almost never explicitly noted in the literature; 2) defining operations in this way is equivalent, from a logical point of view, to two clauses, one corresponding (...) to an introduction rule and the other to an elimination rule, thus providing a manageable way to deal with these operations. Our main result is negative: all operations that arise turn out to be Heyting terms or the mentioned already known operations or operations interdefinable with them. However, it should be noted that some of the operations that arise may exist even if the known operations do not. We also study the extension of Priestley duality to Heyting algebras enriched with the new operations. (shrink)
La noción de sentido común en la obra de Hannah Arendt juega un papel fundamental a la hora de explicar cómo un hombre del tipo de Adolf Eichmann podía mantener una auténtica incapacidad para pensar. No obstante, la manera como esta autora comprende aquella noción no es plenamente clara: el sentido común se halla aparentemente en un punto medio entre la actividad del pensamiento y el conocimiento científico, pues aun cuando el sentido de realidad proporcionado por el sentido común resulta (...) fundamental para ambos, éstos, dada la manera como se oponen entre sí, no se reducen a este mero sentido de realidad. Según creo, la tensión que genera este fenómeno puede ser evaluada con más claridad si se estudia la expresión ‘sentido común’ a partir de dos significados distintos –aunque complementarios– de acuerdo con su carácter pasivo y activo: el sentido común puede ser comprendido desde un punto de vista ‘sensible’ y un punto de vista ‘semántico’, respectivamente. (shrink)
Abstract Since modernity, the concept of subject supposes both an anthropocentric and a dualistic view of life and reality. In this study, we carry out an analytic interpretation of the Descartes’ notion of subject, in order to build a different dimension of the concept of subject. We discuss the activity of computing, as the manner by which the living subject relates with and in-forms the world. We further examine computing in the aging yeast as an example of living subject and (...) we try to comprehend the maturity of the subjectivity in Descartes’ res cogitans and in our proposed res computans . Content Type Journal Article Category Original Paper Pages 1-12 DOI 10.1007/s10516-011-9177-5 Authors María Belén Campero, Center of Philosophical Investigations, CONICET, Buenos Aires, Argentina Cristián Favre, Institute of Experimental Physiology, CONICET, School of Biochemical Sciences, University of Rosario, Suipacha 570, S2002LRL Rosario, Argentina Journal Axiomathes Online ISSN 1572-8390 Print ISSN 1122-1151. (shrink)
The fascination of Velasquez's painting Las Meninas stems largely from the ambiguous relationship between the painting as a whole, viewed by a single perceiver, and the variety of different perceptual viewpoints it invites. This situation resonates strongly with a central puzzle in the study of consciousness: the apparent unity of perceptual experience despite multiple sense modalities. Understanding more of this latter might help to explain the way we respond to the painting.
In this paper, we develop an organizational account that defines biological functions as causal relations subject to closure in living systems, interpreted as the most typical example of organizationally closed and differentiated self-maintaining systems. We argue that this account adequately grounds the teleological and normative dimensions of functions in the current organization of a system, insofar as it provides an explanation for the existence of the function bearer and, at the same time, identifies in a non-arbitrary way the norms that (...) functions are supposed to obey. Accordingly, we suggest that the organizational account combines the etiological and dispositional perspectives in an integrated theoretical framework. (shrink)
Two competing accounts of value incomparability have been put forward in the recent literature. According to the standard account, developed most famously by Joseph Raz, ‘incomparability’ means determinate failure of the three classic value relations ( better than , worse than , and equally good ): two value-bearers are incomparable with respect to a value V if and only if (i) it is false that x is better than y with respect to V , (ii) it is false that x (...) is worse than y with respect to V and (iii) it is false that x and y are equally good with respect to V . Most philosophers have followed Raz in adopting this account of incomparability. Recently, however, John Broome has advocated an alternative view, on which value incomparability is explained in terms of vagueness or indeterminacy . In this paper I aim to further Broome’s view in two ways. Firstly, I want to supply independent reasons for thinking that the phenomenon of value incomparability is indeed a matter of the indeterminacy inherent in our comparative predicates. Secondly, I attempt to defend Broome’s account by warding off several objections that worry him, due mainly to Erik Carlson and Ruth Chang. (shrink)
The article will attempt to show that Velasquez's Las Meninas can be viewed as an allegorical enactment of some of the current debates and controversies in the philosophy of cognition and self-representation. I will focus on two very different philosophical trajectories, to which the allegory of the painting can be linked. The first, analytic, trajectory relates Las Meninas to the notion of representation and self-representation in the work of philosophers David Rosenthal, Robert Van Gulick, Uriah Kriegel and Bruce Mangan, and (...) neurologists Bernie Baars and Rodolfo Llinas. The second, continental, trajectory begins by relating to the painting Merleau-Ponty's phenomenological 'embodied self-representation'. This trajectory, which can be further linked to John Ziman's 'second person view' of reality, proceeds to relate Las Meninas to Lacan's 'object gaze' and the 'unbearable fragility of representation', ending with Bataille's (non)concept of 'sovereignty' as essential yet non-representable losses in representation. I will conclude by suggesting that the evolution of the cognitive state experienced by an observer of Las Meninas can be viewed as an 'ontogenetic' recapitulation of the more 'phylogenic' progression of the philosophical history of representation and self-representation alluded to by the canvas. (shrink)
The purpose of this article is to analyze the significance of the absence of the problem of living body in Heidegger's analytic of Dasein. In order to evaluate the occurrences of the problem of the body in Being and Time, I also refer to the context of some of Heidegger's later work where there is to be found a sketch of an ontological investigation of the living body. I analyze then in detail the scarce occurrences of body in the fundamental (...) ontology, showing finally that the lack of a proper phenomenological examination of living body generates a series of conceptual difficulties for the problem of Dasein's death, precisely when the issue of dead body is at stake. (shrink)
John Broome has argued that incomparability and vagueness cannot coexist in a given betterness order. His argument essentially hinges on an assumption he calls the ‘collapsing principle’. In an earlier article I criticized this principle, but Broome has recently expressed doubts about the cogency of my criticism. Moreover, Cristian Constantinescu has defended Broome’s view from my objection. In this paper, I present further arguments against the collapsing principle, and try to show that Constantinescu’s defence of Broome’s position fails.
The idea of a probabilistic logic of inductive inference based on some form of the principle of indifference has always retained a powerful appeal. However, up to now all modifications of the principle failed. In this paper, a new formulation of such a principle is provided that avoids generating paradoxes and inconsistencies. Because of these results, the thesis that probabilities cannot be logical quantities, determined in an objective way through some form of the principle of indifference, is no longer supportable. (...) Later, the paper investigates some implications of the new principle of indifference. To conclude, a re-examination of the foundations of the so-called objective Bayesian inference is called for. (shrink)
The philosophy of mathematics has been accused of paying insufficient attention to mathematical practice: one way to cope with the problem, the one we will follow in this paper on extensive magnitudes, is to combine the `history of ideas' and the `philosophy of models' in a logical and epistemological perspective. The history of ideas allows the reconstruction of the theory of extensive magnitudes as a theory of ordered algebraic structures; the philosophy of models allows an investigation into the way epistemology (...) might affect relevant mathematical notions. The article takes two historical examples as a starting point for the investigation of the role of numerical models in the construction of a system of non-Archimedean magnitudes. A brief exposition of the theories developed by Giuseppe Veronese and by Rodolfo Bettazzi at the end of the 19th century will throw new light on the role played by magnitudes and numbers in the development of the concept of a non-Archimedean order. Different ways of introducing non-Archimedean models will be compared and the influence of epistemological models will be evaluated. Particular attention will be devoted to the comparison between the models that oriented Veronese's and Bettazzi's works and the mathematical theories they developed, but also to the analysis of the way epistemological beliefs affected the concepts of continuity and measurement. (shrink)
In this paper, I examine to what extent can a more or less uncontroversial list of human rights ground a liberal notion of toleration that would have as its object nonliberal states. Although it is sometimes taken for granted that respect for human rights should draw the limits of toleration, I argue that the Rawlsian argument for it does not fully work. More exactly, I defend the idea that, although he tries to warrant positive toleration for non-liberal peoples, the concept (...) of human rights can provide an argument only for a negative type of toleration. According to his reasoning, positive toleration would require an argument from the 'primacy of peoples', which unfortunately is implausible. Last but not least, I raise the question regarding the grounding of human rights as a vindicating tool for toleration. Here I argue that such an argument is necessary and propose one to the effect that human rights proper can justify toleration in the same way the harm principle does. Since the harm principle can justify non-interference only, the notion of human rights can ground a negative type of toleration. (shrink)
Interaction mining is about discovering and extracting insightful information from digital conversations, namely those human?human information exchanges mediated by digital network technology. We present in this article a computational model of natural arguments and its implementation for the automatic argumentative analysis of digital conversations, which allows us to produce relevant information to build interaction business analytics applications overcoming the limitations of standard text mining and information retrieval technology. Applications include advanced visualisations and abstractive summaries.
The idea of a probabilistic logic of inductive inference based on some form of the principle of indifference has always retained a powerful appeal. However, up to now all modifications of the principle failed. In this paper, a new formulation of such a principle is provided that avoids generating paradoxes and inconsistencies. Because of these results, the thesis that probabilities cannot be logical quantities, determined in an objective way through some form of the principle of indifference, is no longer supportable. (...) Later, the paper investigates some implications of the new principle of indifference. To conclude, a re-examination of the foundations of the so-called objective Bayesian inference is called for. (shrink)
We make a first attempt to axiomatically formulate the Montevideo interpretation of quantum mechanics. In this interpretation environmental decoherence is supplemented with loss of coherence due to the use of realistic clocks to measure time to solve the measurement problem. The resulting formulation is framed entirely in terms of quantum objects without having to invoke the existence of measurable classical quantities like the time in ordinary quantum mechanics. The formulation eliminates any privileged role to the measurement process giving an objective (...) definition of when an event occurs in a system. (shrink)
Gödel's Incompleteness Theorems have the same scientific status as Einstein's principle of relativity, Heisenberg's uncertainty principle, and Watson and Crick's double helix model of DNA. Our aim is to discuss some new faces of the incompleteness phenomenon unveiled by an information-theoretic approach to randomness and recent developments in quantum computing.
Abstract In the 1920s, Ludwig von Mises argued correctly that the problem of making economic calculations without market?generated prices would be an insuperable difficulty for socialist systems of production. Bryan Caplan is right to argue that there is no theoretical way to infer the magnitude of this difficulty, but he is wrong to insist that the history of poor economic performance displayed by real?world socialism should be attributed not to the ?socialist calculation problem,? but to inadequate work incentives. A state (...) that had solved the calculation problem would have well within its means the solution to the incentives problem, too. (shrink)
We present and discuss various formalizations of Modal Logics in Logical Frameworks based on Type Theories. We consider both Hilbert- and Natural Deduction-style proof systems for representing both truth (local) and validity (global) consequence relations for various Modal Logics. We introduce several techniques for encoding the structural peculiarities of necessitation rules, in the typed -calculus metalanguage of the Logical Frameworks. These formalizations yield readily proof-editors for Modal Logics when implemented in Proof Development Environments, such as Coq or LEGO.
Turing’s famous 1936 paper “On computable numbers, with an application to the Entscheidungsproblem” defines a computable real number and uses Cantor’s diagonal argument to exhibit an uncomputable real. Roughly speaking, a computable real is one that one can calculate digit by digit, that there is an algorithm for approximating as closely as one may wish. All the reals one normally encounters in analysis are computable, like π, √2 and e. But they are much scarcer than the uncomputable reals because, as (...) Turing points out, the computable reals are countable, whilst the uncomputable reals have the power of the continuum. Furthermore, any countable set of reals has measure zero, so the computable reals have measure zero. In other words, if one picks a real at random in the unit interval with uniform probability distribution, the probability of obtaining an uncomputable real is unity. One may obtain a computable real, but that is in- finitely improbable. But how about individual examples of uncomputable reals? We will show two: H and the halting probability Ω, both contained in the unit interval. Their construction was anticipated in.. (shrink)
We carry out a textual analysis of Sraffa's main published contributions to pure economics in order to elaborate a rational reconstruction of an aspect of Sraffa's implicit methodology which has not yet been duly investigated. We refer to the threefold relationship between ?economic reality?, ?the economist/observer? and ?economic theory?. We elucidate the constraints which, for Sraffa, should bind the economists' arbitrariness and we trace the elements of continuity and evolution from the 1925?6 critique of Marshallian economics to Production of Commodities.
The intellectual property regimes we have currently in place are heavily under attack. One of the points of criticism is the interaction between two elements of article 27 of the Universal Declaration of Human Rights, the widely discussed issue of being able to benefit from scientific progress and the less argued for position of having a right to take part in scientific enterprises. To shine light on the question if we should balance the two elements or prioritize one of them, (...) an exploration will be offered on how benefiting from scientific progress and the ability to participate in the advancement of science relate to securing human capabilities. A different perspective to the question will be gained by identifying the problem as an issue of misrecognition, especially the failure to recognize many willing collaboration partners in scientific research as peers. Lastly, I will argue that cooperative justice requires that if we have an innovation incentive system that disproportionally benefits one particular group, a certain duty to counterbalance this advantage exists when we are relying on mutual cooperation for the recognition of intellectual property rights. (shrink)
En este trabajo me propongo analizar algunos de los argumentos de John Rawls en contra de un principio de diferencia internacional, tal como fueron presentados en Un derecho de gentes. Sostengo que estos argumentos son inconsistentes con el principio de diferencia doméstico. Si los aceptamos, entonces tendremos que afrontar el dilema de o bien tener que aceptar dicho principio distributivo en ambos ámbitos (el doméstico y el internacional) o bien tener que rechazarlo por completo. También sostengo que las posibles objeciones (...) de Rawls a esta crítica se basan en la dudosa premisa empírica de que los países son exclusivamente responsables de su propio fracaso. In this paper I will analyze John Rawls's claims against an international difference principle as presented in The Law of Peoples. I argue that these claims are inconsistent with the difference principle itself. If we accept them, then we will face the dilemma of either having to endorse this principle both in the domestic and the international domains or having to reject it completely. I also defend the view that Rawls's possible reply to this objection relies on the dubious empirical premise that countries are blameworthy for their own failure. (shrink)
http://dx.doi.org/10.5007/1808-1711.2008v12n2p193 In this paper I claim that the bias to pass from the acknowledgement of the explanatory virtues of a hypothesis to the belief that it is true or approximate to the truth is so strong that scientific realists can hardly elude that temptation. For that reason, some philosophers, like McMullin and Okasha, following Peirce and Hanson, participate of the conviction that the skill of founding scientific explanations bears the ability of founding true theories. But, this way, they pass the (...) limits that they themselves had fixed and their attempt to overcome objections like the one which was formulated by van Fraassen against the inference to the best explanation fails. (shrink)
