O objetivo deste trabalho é investigar o coerentismo, enquanto resposta filosófica às questões da verdade e da justificação epistémica, com particular ênfase na teoria proposta por Donald Davidson. Este trabalho foi desenvolvido no âmbito da disciplina de Filosofia do Conhecimento II, parte do curso de Filosofia da Faculdade de Letras da Universidade do Porto, Portugal.

Neste breve ensaio, exploramos alguns caminhos de uma controvérsia milenar em torno do estatuto dos entes matemáticos e apresentamos alguns argumentos a favor de uma posição platonista, aproximadamente clássica, sobre o tema. Este trabalho foi realizado no âmbito da disciplina de Filosofia das Ciências II, parte do curso de Filosofia da Faculdade de Letras da Universidade do Porto, Portugal.

Neste trabalho abordamos a obra de Francis Bacon e as suas contribuições para a Filosofia da Ciência, incluindo a sua proposta de método científico e o seu posicionamento crítico face à anterior versão aristotélica e a influência que o pensamento baconiano exerceu na promoção de um novo quadro filosófico para o desenvolvimento científico na modernidade. Este trabalho foi realizado no âmbito da disciplina de Filosofia das Ciências I, parte do curso de Filosofia da Faculdade de Letras da Universidade do Porto, (...) Portugal. (shrink)

O foco deste trabalho repousa sobre um certo caminho histórico percorrido pela ciência, como um todo, no sentido desta se despir de qualquer revestimento metafísico e que teve como marco incontornável a criação, em 1929, do Círculo de Viena. Abordamos algumas tendências e limitações desse movimento e argumentamos que o metafísico terá sempre um espaço no seio mais íntimo da reflexão científica. Este trabalho foi realizado no âmbito da disciplina de Filosofia das Ciências I, parte do curso de Filosofia da (...) Faculdade de Letras da Universidade do Porto, Portugal. (shrink)

Neste trabalho abordamos as contribuições de Larry Laudan para a questão do progresso científico. O modelo proposto, baseado na eficácia das teorias na resolução de problemas, serve de ponto de partida para uma breve reflexão sobre a influência contemporânea que as dificuldades de visão do mundo exercem sobre o desenvolvimento das ciências. Este trabalho foi realizado no âmbito da disciplina de Filosofia das Ciências II, parte do curso de Filosofia da Faculdade de Letras da Universidade do Porto, Portugal.

La obra que tenemos entre manos está escrita por Sara Hidalgo García de Orellán, doctora en Ciencias Políticas y licenciada en Historia, cuya línea de trabajo se centra en la historia del movimiento obrero en Vizcaya y el Partido Socialista vasco desde sus inicios a finales del siglo XIX hasta 1915. Tal y como dice la autora, el libro, estructurado en cinco capítulos, pretende estudiar los elementos principales sobre los que se construye la conciencia socialista y el movimiento obrero, (...) pero realiza su investigación desde una perspectiva novedosa, pues la sintetiza con la historia de las emociones, y es esta dirección la que ha tomado para abordar el tema que nos ocupa. (shrink)

The recent distinction between sense of agency and sense of body-ownership has attracted considerable empirical and theoretical interest. The respective contributions of central motor signals and peripheral afferent signals to these two varieties of body experience remain unknown. In the present review, we consider the methodological problems encountered in the empirical study of agency and body-ownership, and we then present a series of experiments that study the interplay between motor and sensory information. In particular, we focus on how multisensory signals (...) interact with body representations to generate the sense of body-ownership, and how the sense of agency modulates the sense of body-ownership. Finally, we consider the respective roles of efferent and afferent signals for the experience of one’s own body and actions, in relation to self-recognition and the recognition of other people’s actions. We suggest that the coherent experience of the body depends on the integration of efferent information with afferent information in action contexts. Overall, whereas afferent signals provide the distinctive content of one’s own body experience, efferent signals seem to structure the experience of one’s own body in an integrative and coherent way. (shrink)

We investigated how motor agency in the voluntary control of body movement influences body awareness. In the Rubber Hand Illusion , synchronous tactile stimulation of a rubber hand and the participant’s hand leads to a feeling of the rubber hand being incorporated in the participant’s own body. One quantifiable behavioural correlate of the illusion is an induced shift in the perceived location of the participant’s hand towards the rubber hand. Previous studies showed that the induced changes in body awareness are (...) local and fragmented: the proprioceptive drift is largely restricted to the stimulated finger. In the present study, we investigated whether active and passive movements, rather than tactile stimulation, would lead to similarly fragmented body awareness. Participants watched a projected image of their hand under three conditions: active finger movement, passive finger movement, and tactile stimulation. Visual feedback was either synchronous or asynchronous with respect to stimulation of the hand. A significant overall RHI, defined as greater drifts following synchronous than asynchronous stimulation, was found in all cases. However, the distribution of the RHI across stimulated and non-stimulated fingers depended on the kind of stimulation. Localised proprioceptive drifts, specific to the stimulated finger, were found for tactile and passive stimulation. Conversely, during active movement of a single digit, the proprioceptive drifts were not localised to that digit, but were spread across the whole hand. Whereas a purely proprioceptive sense of body-ownership is local and fragmented, the motor sense of agency integrates distinct body-parts into a coherent, unified awareness of the body. (shrink)

In this paper we study a new approach to classify mathematical theorems according to their computational content. Basically, we are asking the question which theorems can be continuously or computably transferred into each other? For this purpose theorems are considered via their realizers which are operations with certain input and output data. The technical tool to express continuous or computable relations between such operations is Weihrauch reducibility and the partially ordered degree structure induced by it. We have identified certain choice (...) principles such as co-finite choice, discrete choice, interval choice, compact choice and closed choice, which are cornerstones among Weihrauch degrees and it turns out that certain core theorems in analysis can be classified naturally in this structure. In particular, we study theorems such as the Intermediate Value Theorem, the Baire Category Theorem, the Banach Inverse Mapping Theorem, the Closed Graph Theorem and the Uniform Boundedness Theorem. We also explore how existing classifications of the Hahn—Banach Theorem and Weak Kőnig's Lemma fit into this picture. Well-known omniscience principles from constructive mathematics such as LPO and LLPO can also naturally be considered as Weihrauch degrees and they play an important role in our classification. Based on this we compare the results of our classification with existing classifications in constructive and reverse mathematics and we claim that in a certain sense our classification is finer and sheds some new light on the computational content of the respective theorems. Our classification scheme does not require any particular logical framework or axiomatic setting, but it can be carried out in the framework of classical mathematics using tools of topology, computability theory and computable analysis. We develop a number of separation techniques based on a new parallelization principle, on certain invariance properties of Weihrauch reducibility, on the Low Basis Theorem of Jockusch and Soare and based on the Baire Category Theorem. Finally, we present a number of metatheorems that allow to derive upper bounds for the classification of the Weihrauch degree of many theorems and we discuss the Brouwer Fixed Point Theorem as an example. (shrink)

The classical Hahn–Banach Theorem states that any linear bounded functional defined on a linear subspace of a normed space admits a norm-preserving linear bounded extension to the whole space. The constructive and computational content of this theorem has been studied by Bishop, Bridges, Metakides, Nerode, Shore, Kalantari Downey, Ishihara and others and it is known that the theorem does not admit a general computable version. We prove a new computable version of this theorem without unrolling the classical proof of the (...) theorem itself. More precisely, we study computability properties of the uniform extension operator which maps each functional and subspace to the set of corresponding extensions. It turns out that this operator is upper semi-computable in a well-defined sense. By applying a computable version of the Banach–Alaoglu Theorem we can show that computing a Hahn–Banach extension cannot be harder than finding a zero in a compact metric space. This allows us to conclude that the Hahn–Banach extension operator is ${\bf {\Sigma^{0}_{2}}}$ -computable while it is easy to see that it is not lower semi-computable in general. Moreover, we can derive computable versions of the Hahn–Banach Theorem for those functionals and subspaces which admit unique extensions. (shrink)

We systematically study the completion of choice problems in the Weihrauch lattice. Choice problems play a pivotal rôle in Weihrauch complexity. For one, they can be used as landmarks that characterize important equivalences classes in the Weihrauch lattice. On the other hand, choice problems also characterize several natural classes of computable problems, such as finite mind change computable problems, non-deterministically computable problems, Las Vegas computable problems and effectively Borel measurable functions. The closure operator of completion generates the concept of total (...) Weihrauch reducibility, which is a variant of Weihrauch reducibility with total realizers. Logically speaking, the completion of a problem is a version of the problem that is independent of its premise. Hence, studying the completion of choice problems allows us to study simultaneously choice problems in the total Weihrauch lattice, as well as the question which choice problems can be made independent of their premises in the usual Weihrauch lattice. The outcome shows that many important choice problems that are related to compact spaces are complete, whereas choice problems for unbounded spaces or closed sets of positive measure are typically not complete. (shrink)

We study the uniform computational content of different versions of the Baire category theorem in the Weihrauch lattice. The Baire category theorem can be seen as a pigeonhole principle that states that a complete metric space cannot be decomposed into countably many nowhere dense pieces. The Baire category theorem is an illuminating example of a theorem that can be used to demonstrate that one classical theorem can have several different computational interpretations. For one, we distinguish two different logical versions of (...) the theorem, where one can be seen as the contrapositive form of the other one. The first version aims to find an uncovered point in the space, given a sequence of nowhere dense closed sets. The second version aims to find the index of a closed set that is somewhere dense, given a sequence of closed sets that cover the space. Even though the two statements behind these versions are equivalent to each other in classical logic, they are not equivalent in intuitionistic logic, and likewise, they exhibit different computational behavior in the Weihrauch lattice. Besides this logical distinction, we also consider different ways in which the sequence of closed sets is “given.” Essentially, we can distinguish between positive and negative information on closed sets. We discuss all four resulting versions of the Baire category theorem. Somewhat surprisingly, it turns out that the difference in providing the input information can also be expressed with the jump operation. Finally, we also relate the Baire category theorem to notions of genericity and computably comeager sets. (shrink)

Normative theories of argumentation tend to assume that logical and dialectical rules suffice to ensure the rationality of argumentative discourse. Yet, in everyday debates people use arguments that seem valid in light of such rules but nonetheless biased and tendentious. This article seeks to show that the rationality of argumentation can only be fully promoted if we take into account its ethical dimension. To substantiate this claim, I review some of the empirical evidence indicating that people’s inferential reasoning is systematically (...) affected by a variety of biases and heuristics. Insofar as these cognitive illusions are typically unintentional, it appears that arguers may be biased despite their well-intended efforts to follow the rules of critical argumentation. Nevertheless, I argue that people remain responsible for the rationality of their arguments, given that there are a number of measures that they can (and ought to) take to avoid such distortions. I highlight the importance of argumentational virtues and critical thinking to rational debates, and describe a set of indirect strategies of “argumentative self-control”. (shrink)

We prove that the Weihrauch lattice can be transformed into a Brouwer algebra by the consecutive application of two closure operators in the appropriate order: first completion and then parallelization. The closure operator of completion is a new closure operator that we introduce. It transforms any problem into a total problem on the completion of the respective types, where we allow any value outside of the original domain of the problem. This closure operator is of interest by itself, as it (...) generates a total version of Weihrauch reducibility that is defined like the usual version of Weihrauch reducibility, but in terms of total realizers. From a logical perspective completion can be seen as a way to make problems independent of their premises. Alongside with the completion operator and total Weihrauch reducibility we need to study precomplete representations that are required to describe these concepts. In order to show that the parallelized total Weihrauch lattice forms a Brouwer algebra, we introduce a new multiplicative version of an implication. While the parallelized total Weihrauch lattice forms a Brouwer algebra with this implication, the total Weihrauch lattice fails to be a model of intuitionistic linear logic in two different ways. In order to pinpoint the algebraic reasons for this failure, we introduce the concept of a Weihrauch algebra that allows us to formulate the failure in precise and neat terms. Finally, we show that the Medvedev Brouwer algebra can be embedded into our Brouwer algebra, which also implies that the theory of our Brouwer algebra is Jankov logic. (shrink)

Introduction -- Why understanding the nature of science is important -- Case study of the age of the earth -- Science and true knowledge -- The nature of scientific logic -- Resolving the great paradox.

In this article, we propose to question the accuracy of Jean Wahl’s definition of Vladimir Jankélévitch’s Philosophie Première (1953) as one of the “ultimate efflorescences of negative theology.” In fact, we maintain that—although conceiving the apophatic discourse as a necessary (but insufficient) stepping-stone to the absolute—the aforementioned work constitutes, if anything, an effort to overcome it by means of what we shall call a tesiphatic philosophy, i.e., one that identifies the first principle, not as the absolute negation of being, but (...) as the absolute position of being. To defend our thesis, we shall start by discussing the meaning of the five divine names that Jankélévitch bestows upon his absolute, namely, (1) the “totally-other-order,” (2) the “super-truth,” (3) “the itself,” (4) the “I-know-not-what,” and (5) the “almost-nothing.” In this section of our paper, we will try to show how Jankélévitch’s discourse is, in fact, shaped by the whole negative theology tradition (from Plotinus to Nicholas of Cusa). Finally, in the last part of our paper, we will strive to reflect upon Jankélévitch’s interpretation of the limits of a apophatic metaphysical discourse, questioning whether his Philosophie Première effectively overcomes negative theology’s conception of the absolute. (shrink)

In this paper we study a reducibility that has been introduced by Klaus Weihrauch or, more precisely, a natural extension for multi-valued functions on represented spaces. We call the corresponding equivalence classes Weihrauch degrees and we show that the corresponding partial order induces a lower semi-lattice. It turns out that parallelization is a closure operator for this semi-lattice and that the parallelized Weihrauch degrees even form a lattice into which the Medvedev lattice and the Turing degrees can be embedded. The (...) importance of Weihrauch degrees is based on the fact that multi-valued functions on represented spaces can be considered as realizers of mathematical theorems in a very natural way and studying the Weihrauch reductions between theorems in this sense means to ask which theorems can be transformed continuously or computably into each other. As crucial corner points of this classification scheme the limited principle of omniscience LPO, the lesser limited principle of omniscience LLPO and their parallelizations are studied. It is proved that parallelized LLPO is equivalent to Weak Kőnig's Lemma and hence to the Hahn—Banach Theorem in this new and very strong sense. We call a multi-valued function weakly computable if it is reducible to the Weihrauch degree of parallelized LLPO and we present a new proof, based on a computational version of Kleene's ternary logic, that the class of weakly computable operations is closed under composition. Moreover, weakly computable operations on computable metric spaces are characterized as operations that admit upper semi-computable compact-valued selectors and it is proved that any single-valued weakly computable operation is already computable in the ordinary sense. (shrink)

Phenomenology of the Cultural Disciplines is an interdisciplinary study, reflecting the recent emergence of various particular forms of `phenomenological philosophy of ...'. Included are such fields as psychology, social sciences and history, as well as environmental philosophy, ethnic studies, religion and even more practical disciplines, such as medicine, psychiatry, politics, and technology. The Introduction provides a way of understanding how these various developments are integrated. On the basis of a Husserlian notion of culture, it proposes a generic concept of `cultural (...) disciplines' (which is broader than but inclusive of `human sciences') which subsumes the more specific concepts of `cultural sciences', `axiotic disciplines' (e.g. architecture), and `practical disciplines'. (shrink)

The investigation of computational properties of discontinuous functions is an important concern in computable analysis. One method to deal with this subject is to consider effective variants of Borel measurable functions. We introduce such a notion of Borel computability for single-valued as well as for multi-valued functions by a direct effectivization of the classical definition. On Baire space the finite levels of the resulting hierarchy of functions can be characterized using a notion of reducibility for functions and corresponding complete functions. (...) We use this classification and an effective version of a Selection Theorem of Bhattacharya-Srivastava in order to prove a generalization of the Representation Theorem of Kreitz-Weihrauch for Borel measurable functions on computable metric spaces: such functions are Borel measurable on a certain finite level, if and only if they admit a realizer on Baire space of the same quality. This Representation Theorem enables us to introduce a realizer reducibility for functions on metric spaces and we can extend the completeness result to this reducibility. Besides being very useful by itself, this reducibility leads to a new and effective proof of the Banach-Hausdorff-Lebesgue Theorem which connects Borel measurable functions with the Baire functions. Hence, for certain metric spaces the class of Borel computable functions on a certain level is exactly the class of functions which can be expressed as a limit of a pointwise convergent and computable sequence of functions of the next lower level. (shrink)

Matthias Schröder has asked the question whether there is a weakest discontinuous problem in the topological version of the Weihrauch lattice. Such a problem can be considered as the weakest unsolvable problem. We introduce the discontinuity problem, and we show that it is reducible exactly to the effectively discontinuous problems, defined in a suitable way. However, in which sense this answers Schröder’s question sensitively depends on the axiomatic framework that is chosen, and it is a positive answer if we work (...) in Zermelo–Fraenkel set theory with dependent choice and the axiom of determinacy $\mathsf {AD}$. On the other hand, using the full axiom of choice, one can construct problems which are discontinuous, but not effectively so. Hence, the exact situation at the bottom of the Weihrauch lattice sensitively depends on the axiomatic setting that we choose. We prove our result using a variant of Wadge games for mathematical problems. While the existence of a winning strategy for Player II characterizes continuity of the problem (as already shown by Nobrega and Pauly), the existence of a winning strategy for Player I characterizes effective discontinuity of the problem. By Weihrauch determinacy we understand the condition that every problem is either continuous or effectively discontinuous. This notion of determinacy is a fairly strong notion, as it is not only implied by the axiom of determinacy $\mathsf {AD}$, but it also implies Wadge determinacy. We close with a brief discussion of generalized notions of productivity. (shrink)

We study the computational content of the Brouwer Fixed Point Theorem in the Weihrauch lattice. Connected choice is the operation that finds a point in a non-empty connected closed set given by negative information. One of our main results is that for any fixed dimension the Brouwer Fixed Point Theorem of that dimension is computably equivalent to connected choice of the Euclidean unit cube of the same dimension. Another main result is that connected choice is complete for dimension greater than (...) or equal to two in the sense that it is computably equivalent to Weak Kőnig’s Lemma. While we can present two independent proofs for dimension three and upward that are either based on a simple geometric construction or a combinatorial argument, the proof for dimension two is based on a more involved inverse limit construction. The connected choice operation in dimension one is known to be equivalent to the Intermediate Value Theorem; we prove that this problem is not idempotent in contrast to the case of dimension two and upward. We also prove that Lipschitz continuity with Lipschitz constants strictly larger than one does not simplify finding fixed points. Finally, we prove that finding a connectedness component of a closed subset of the Euclidean unit cube of any dimension greater than or equal to one is equivalent to Weak Kőnig’s Lemma. In order to describe these results, we introduce a representation of closed subsets of the unit cube by trees of rational complexes. (shrink)

This essay presents a brief survey on some of the basic questions concerning the Philosophy of Technology, including the different historical perspectives regarding the part played by technology in human life and societies. From the historical debate between the more pragmatic and the more skeptical sides, the optimistic and pessimistic views, an answer is proposed, finding support in a sociological point of view in what can be interpreted as a contemporary marxist approach on these problems. This work was developed in (...) the context of the course \textit{An Introduction to the History of Science} given by Professor Luca Maria Possati, part of the Philosophy degree at the Faculty of Arts and Humanities of University of Porto, Portugal. (shrink)

Given a program of a linear bounded and bijective operator T, does there exist a program for the inverse operator T−1? And if this is the case, does there exist a general algorithm to transfer a program of T into a program of T−1? This is the inversion problem for computable linear operators on Banach spaces in its non-uniform and uniform formulation, respectively. We study this problem from the point of view of computable analysis which is the Turing machine based (...) theory of computability on Euclidean space and other topological spaces. Using a computable version of Banach’s Inverse Mapping Theorem we can answer the first question positively. Hence, the non-uniform version of the inversion problem is solvable, while a topological argument shows that the uniform version is not. Thus, we are in the striking situation that any computable linear operator has a computable inverse while there exists no general algorithmic procedure to transfer a program of the operator into a program of its inverse. As a consequence, the computable version of Banach’s Inverse Mapping Theorem is a powerful tool which can be used to produce highly non-constructive existence proofs of algorithms. We apply this method to prove that a certain initial value problem admits a computable solution. As a preparation of Banach’s Inverse Mapping Theorem we also study the Open Mapping Theorem and we show that the uniform versions of both theorems are limit computable, which means that they are effectively -measurable with respect to the effective Borel hierarchy. (shrink)

We discuss computability properties of the set of elements of best approximation of some point xX by elements of GX in computable Banach spaces X. It turns out that for a general closed set G, given by its distance function, we can only obtain negative information about as a closed set. In the case that G is finite-dimensional, one can compute negative information on as a compact set. This implies that one can compute the point in whenever it is uniquely (...) determined. This is also possible for a wider class of subsets G, given that one imposes additionally convexity properties on the space. If the Banach space X is computably uniformly convex and G is convex, then one can compute the uniquely determined point in . We also discuss representations of finite-dimensional subspaces of Banach spaces and we show that a basis representation contains the same information as the representation via distance functions enriched by the dimension. Finally, we study computability properties of the dimension and the codimension map and we show that for finite-dimensional spaces X the dimension is computable, given the distance function of the subspace. (shrink)

In a previous work, we have shown that the null result of the Michelson–Morley experiment in vacuum is deeply connected with the notion of time. The same is true for the postulate of constancy of the two-way speed of light in vacuum in all frames independently of the state of motion of the emitting body. The argumentation formerly given is very general and has to be true not only within Special Relativity and its “equivalence” of all inertial frames, but as (...) well as in Lorentz-Poincaré scenario of a preferred reference frame. This paper is the second of a trilogy intending to revisit the foundations of Special Relativity, and addresses the question of the constancy of the one-way speed of light and of the differences and similarities between both scenarios. Although they manifestly differ in philosophy, it is debated why and how the assumption of a “special system of reference experimentally inaccessible” is indeed compatible with Einstein’s Special Relativity, as beautifully outlined and discussed by Bell [Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1988)]. This rather trivial statement is still astonishing nowadays to a big majority of scientists. The purpose of this work is to bring such assertion into perspective, widening the somewhat narrow view of Special Relativity often presented in textbooks and scientific papers. (shrink)

The author argues that given the dominant logic of the projects of the United States security apparatuses, realities such as Abu Ghraib and Camp X-Ray cannot be considered merely aberrations, but rather are the logical manifestations of security. In order to make this argument the author explores the concepts of sovereignty, the exception, and homo sacer in the works of Carl Schmitt and Giorgio Agamben.