Gödel’s Disjunction: The Scope and Limits of Mathematical Knowledge

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Religion and Science unification

Speaking for God has been part of religion for many years. However, science has come in the past few years to question that role or even our very ability to speak about God in general. My goal is to show that dogmatism, under any form, is wrong. And even though dogmatism had for a long time been associated with ill-intentioned religion, nowadays science has replaced religion in the throne of doctrinaire thinking. The point of the paper is to illustrate that one-way thinking is never correct – most of the times a combination of science and religion, measurements and theoretical thinking, logic and intuition, is required to draw a conclusion about the most important philosophical questions. The paper establishes that exact sciences can be very useful, but they also have limits. The Religion-vs-Science problem is a pseudo-problem; logic and evidence can easily be used to defend theistic views. Both science and religion use common tools and methods and can be unified in a new way of thinking. This paper sets the foundations on how this can be achieved. The conclusion is that science and religion both complete our knowledge for the world, our understanding of humans and our purpose in life. Speaking about God is part of science as well as of religion. Only when we think of God as theologians and as scientists at the same time can we fully reach Him

Vagueness, Logic and Use: Four Experimental Studies on Vagueness

Although arguments for and against competing theories of vagueness often appeal to claims about the use of vague predicates by ordinary speakers, such claims are rarely tested. An exception is Bonini et al. (1999), who report empirical results on the use of vague predicates by Italian speakers, and take the results to count in favor of epistemicism. Yet several methodological difficulties mar their experiments; we outline these problems and devise revised experiments that do not show the same results. We then describe three additional empirical studies that investigate further claims in the literature on vagueness: the hypothesis that speakers confuse ‘P’ with ‘definitely P’, the relative persuasiveness of different formulations of the inductive premise of the Sorites, and the interaction of vague predicates with three different forms of negatio

A historical reconstruction of the connections between the Viennese neopositivists and the American pragmatists: economic theory in the project for the International Encyclopaedia of Unified Science

Persuaded by the fact that the philosophical debate in Vienna during the 1930s deeply influenced the subsequent American developments of economic theory, my purpose is to reconstruct, from a historical and theoretical point of view, how Austrian interests in economics (which spread in the interwar period) moved to the USA, and what the subsequent developments were. From a historical point of view, I shall focus on the genesis of the International Encyclopaedia of Unified Science promoted by philosophers belonging to the Vienna Circle (Otto Neurath, Rudolph Carnap and Philipp Frank) and American pragmatists (John Dewey and, above all, Charles Morris) between 1938 and 1969. From a theoretical point of view, I shall focus on the development of economic theory within this project, which was regarded as the most important outcome of logical positivism or new empiricism, this being the common philosophical outlook that they shared. The aim of this paper is to show how the original meaning of economics (as formulated by Neurath) within the Vienna Circle was changed in its transition from Vienna to the USA (when the International Encyclopaedia was organized) and was finally radically transformed in the American context during the following decades.

In the Beginning Was the Verb: The Emergence and Evolution of Language Problem in the Light of the Big Bang Epistemological Paradigm.

The enigma of the Emergence of Natural Languages, coupled or not with the closely related problem of their Evolution is perceived today as one of the most important scientific problems. \ud The purpose of the present study is actually to outline such a solution to our problem which is epistemologically consonant with the Big Bang solution of the problem of the Emergence of the Universe}. Such an outline, however, becomes articulable, understandable, and workable only in a drastically extended epistemic and scientific oecumene, where known and habitual approaches to the problem, both theoretical and experimental, become distant, isolated, even if to some degree still hospitable conceptual and methodological islands. \ud The guiding light of our inquiry will be Eugene Paul Wigner's metaphor of ``the unreasonable effectiveness of mathematics in natural sciences'', i.e., the steadily evolving before our eyes, since at least XVIIth century, \ud ``the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics''. Kurt Goedel's incompleteness and undecidability theory will be our guardian discerner against logical fallacies of otherwise apparently plausible explanations. \ud John Bell's ``unspeakableness'' and the commonplace counterintuitive character of quantum phenomena will be our encouragers. And the radical novelty of the introduced here and adapted to our purposes Big Bang epistemological paradigm will be an appropriate, even if probably shocking response to our equally shocking discovery in the oldest among well preserved linguistic fossils of perfect mathematical structures outdoing the best artifactual Assemblers

The limits and basis of logical tolerance: Carnap’s combination of Russell and Wittgenstein

<p><i>Notes</i>: All data series were filtered by 40-yr Butterworth low-pass filter prior to statistical analysis. Differencing:</p>△<p>no difference,</p>α<p>1^stdifference. Significance (2-tailed):</p>∧<p>p<0.1,</p><p>*p<0.05,</p><p>**p<0.01,</p><p>***p<0.001.</p

A Computable Economist’s Perspective on Computational Complexity

A computable economist's view of the world of computational complexity theory is described. This means the model of computation underpinning theories of computational complexity plays a central role. The emergence of computational complexity theories from diverse traditions is emphasised. The unifications that emerged in the modern era was codified by means of the notions of efficiency of computations, non-deterministic computations, completeness, reducibility and verifiability - all three of the latter concepts had their origins on what may be called 'Post's Program of Research for Higher Recursion Theory'. Approximations, computations and constructions are also emphasised. The recent real model of computation as a basis for studying computational complexity in the domain of the reals is also presented and discussed, albeit critically. A brief sceptical section on algorithmic complexity theory is included in an appendix