Related papers: Goedel's other legacy and the imperative of a self…
We attempt to provide a comprehensive model of evolution of science across millennia taking into account the contributions of other intellectual traditions, cultural value system and increasing in sophistication of humans in their study of…
This article explores the metaphor of Science as provider of sharp images of our environment, using the epistemological framework of Objective Cognitive Constructivism. These sharp images are conveyed by precise scientific hypotheses that,…
Scientific progress has long been understood as recombinant, with breakthroughs arising when existing ideas are joined in new ways. Empirical work in this tradition has focused on the inputs to discovery, asking whether a paper draws…
This paper has two goals. The first goal is to show how an extension of second-order logic is a natural framework to formalize portions of Aristotle's \emph{Topics} and to bring to the foreground the logical, linguistic and philosophical…
There is knowledge. There is belief. And there is tacit agreement.' 'We may talk about objects. We may talk about attributes of the objects. Or we may talk both about objects and their attributes.' This work inspects tacit agreements on…
G\"odel's argument for the First Incompleteness Theorem is, structurally, a proof by contradiction. This article intends to reframe the argument by, first, isolating an additional assumption the argument relies on, and then, second, arguing…
From the perspective of the physics of complex systems (1) we deal with the current state of mod-ern physics including the crisis in physics demonstrated through its epistemological, psychological, economical as well as the social context;…
Self-similarity is the property of a system being similar to a part of itself. We posit that a special class of behaviourally self-similar systems exhibits a degree of resilience to adversarial behaviour. We formalise the notions of system,…
In 1710, George Berkeley, philospher and scientist, discovered that the directions in which we see (sightlines) are tilted 45 degrees towards the past from the directions in which we look. Looking north from the 3-d present we see to the…
We advance a famous principle - causality principle - but under a new view. This principle is a principium automatically leading to most fundamental laws of the nature. It is the inner origin of variation, rules evolutionary processes of…
Godel numbering is an arithmetization of sintax which defines provability by coding a primitive recursive predicate, Pf(x,v). A multiplicity of researches and results all around this well-known recursive predicate are today widespread in…
In this paper we sketch how some fundamental concepts of modern topology (as well as logic and category theory) can be understood philosophically in the light of Hegel's Science Logic as well how modern topological concepts can provide…
The initial techniques developed in Euclid's Elements, well before the use of the parallel postulate, are reexamined in order to clarify even the most obscure details, particularly those related to equality, superposition and angle…
National science systems have become embedded in global science and countries do everything they can to harness global knowledge to national economic needs. However, accessing and using the riches of global knowledge can occur only through…
The book "A Course in Constructive Algebra" (1988) shows the way of understanding classical basic algebra in a constructive style similar to Bishop's Constructive Mathematics. Classical theorems are revisited, with a new flavour, and become…
G\"odel's Dialectica has been introduced and developed in the tradition of the so-called functional interpretations. Only recently has it been related with the a priori unrelated notion of differentiation, by taking a program-theoretic…
We introduce some early considerations of physical and mathematical impossibility as preludes to the Goedel incompleteness theorems. We consider some informal aspects of these theorems and their underlying assumptions and discuss some the…
This book is an introductory course to basic commutative algebra with a particular emphasis on finitely generated projective modules, which constitutes the algebraic version of the vector bundles in differential geometry. We adopt the…
Dictionaries are inherently circular in nature. A given word is linked to a set of alternative words (the definition) which in turn point to further descendants. Iterating through definitions in this way, one typically finds that…
The main goal of this article is to use the epistemological framework of a specific version of Cognitive Constructivism to address Piaget's central problem of knowledge construction, namely, the re-equilibration of cognitive structures. The…