In this multi-disciplinary investigation we show how an evidence-based perspective of quantification---in terms of algorithmic verifiability and algorithmic computability---admits evidence-based definitions of well-definedness and effective computability, which yield two unarguably constructive interpretations of the first-order Peano Arithmetic PA---over the structure N of the natural numbers---that are complementary, not contradictory. The first yields the weak, standard, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically verifiable Tarskian truth values to the formulas of PA under the interpretation. (...) The second yields a strong, finitary, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically computable Tarskian truth values to the formulas of PA under the interpretation. We situate our investigation within a broad analysis of quantification vis a vis: * Hilbert's epsilon-calculus * Goedel's omega-consistency * The Law of the Excluded Middle * Hilbert's omega-Rule * An Algorithmic omega-Rule * Gentzen's Rule of Infinite Induction * Rosser's Rule C * Markov's Principle * The Church-Turing Thesis * Aristotle's particularisation * Wittgenstein's perspective of constructive mathematics * An evidence-based perspective of quantification. By showing how these are formally inter-related, we highlight the fragility of both the persisting, theistic, classical/Platonic interpretation of quantification grounded in Hilbert's epsilon-calculus; and the persisting, atheistic, constructive/Intuitionistic interpretation of quantification rooted in Brouwer's belief that the Law of the Excluded Middle is non-finitary. We then consider some consequences for mathematics, mathematics education, philosophy, and the natural sciences, of an agnostic, evidence-based, finitary interpretation of quantification that challenges classical paradigms in all these disciplines. (shrink)

This text explores the problem of transcendental stupidity in Sigmund Freud, Gilles Deleuze and Jacques Derrida’s works, seeking to combine it with the paradoxical figure of Oedipus in psychoanalytical and philosophical tradition and the symptomatic situation of some important animals in analyses and therapies. The case of the Man of the Wolves, the case of Mr. Sergei K. Pankejeff described in Aus der Geschichte einer infantilen Neurose, a fundamental dream in contemporary culture history, would be the point of departure.

Modelling became one of the primary tools of mathematical economic research in the twentieth century, but when we look at examples of how nonanalogical models were first built in economics, both the process of making representations and aspects of the representing relation remain opaque. Like early astronomers, economists have to imagine how the hidden parts of their world are arranged and to make images, that is, create models, to represent how they work. The case of the Edgeworth Box, a model (...) widely used for theoretical work in twentieth-century economics, provides a good example to explore the process of making mathematical representations of the economy. It shows how, in making these new representations, conceptual elements were developed which could not have been represented in the older verbal forms of economics. (shrink)

Plural definite descriptions across many languages display two well-known properties. First, they can give rise to so-called non-maximal readings, in the sense that they ‘allow for exceptions’. Second, while they tend to have a quasi-universal quantificational force in affirmative sentences, they tend to be interpreted existentially in the scope of negation. Building on previous works, we offer a theory in which sentences containing plural definite expressions trigger a family of possible interpretations, and where general principles of language use account for (...) their interpretation in various contexts and syntactic environments. Our theory solves a number of problems that these previous works encounter, and has broader empirical coverage in that it offers a precise analysis for sentences that display complex interactions between plural definites, quantifiers and bound variables, as well as for cases involving non-distributive predicates. The resulting proposal is briefly compared with an alternative proposal by Križ, which has similar coverage but is based on a very different architecture and sometimes makes subtly different predictions. (shrink)

In this paper I focus on the impact on structuralism of the quantum treatment of objects in terms of symmetry groups and, in particular, on the question as to how we might eliminate, or better, reconceptualise such objects in structural terms. With regard to the former, both Cassirer and Eddington not only explicitly and famously tied their structuralism to the development of group theory but also drew on the quantum treatment in order to further their structuralist aims and here I (...) sketch the relevant history with an eye on what lessons might be drawn. With regard to the latter, Ladyman has explicitly cited Castellani's work on the group-theoretical constitution of quantum objects and I indicate both how such an approach needs to be understood if it is to mesh with Ladyman's 'ontic' form of structural realism and how it might accommodate permutation symmetry through a consideration of Huggett's recent account. (shrink)

Karl Marx and Frederick Engels wrote upwards of fifty books and articles, and many letters concerning economic and political developments in Ireland after the Great Famine of 1845-49. For the most part, these writings have been ignored, in preference for attention to their more famous economic and philosophical works. In contrast, this study seeks to set the record straight; examining in detail their appraisal of the relationship between Irish nationalism and English socialism, the thesis finds that Marx and Engels' concern (...) was primarily focused in the direction of the latter. Support for Irish self-determination was significant principally in adding to their re-evaluation of Chartism, the English labour movement, and the potential for socialist revolution generally. Moreover, they were not enthusiastic defenders of the Fenians, but quietly sheltered various misgivings concerning their actions, and limited political horizon and effectiveness, which came to light in their applause for Charles S wait Parnell by mid-1870. The thesis seeks to place Marx and Engels' support for Irish independence within a framework of capitalist development as sketched by Karl Marx in Capital. Therein, he discussed the effects of capitalist accumulation upon Ireland, pronouncing that the particular mode of production was responsible for the manner in which English industry reciprocated Irish agriculture. It is claimed in the thesis that Marx's development of the mechanism of capitalist accumulation is an invaluable analysis of that relationship. Nevertheless, one cannot read through Marx and Engels' varied writings without being aware of the many inconsistencies and omissions that abound. Their general ignorance of industrial growth, particularly in Belfast, of great opposition to Home Rule, and of the conservative strength of the tenantry movement are among the most obvious of these. The thesis continually draws attention to these problems, citing data on political and economic developments of the time as evidence of the drawbacks to their analysis. This method purports to consider how well Marx and Engels understood the Irish question. On the other hand, some of their inaccuracies, especially Engels' almost emotional attention to communal, pre-English Ireland, compares favourably with contemporary opinion. In conclusion, then, the thesis ends by glancing at how Marx and Engels' ideas compared with their contemporaries, suggesting that in many ways, they were trapped in their historical time. (shrink)

Fugue and chaos are used in their contemporary meaning. Elements of the fugue, albeit a ‎small number of universals, will be demonstrated in the area of visual and verbal colors. ‎Chaos dominates the internet, fashion, and everyday life. The visual and verbal colors are ‎differentiated and their communicative potential is indicated alongside the diachronic changes. The prototypes of colors are the interface between visual and verbal colors.‎.