Related papers: Infinity and the Sublime
Classical computation, grounded in formal, logical systems, has been the engine of technological progress for decades, excelling at problems that can be described with unambiguous rules. This paradigm, however, leaves a vast ocean of human…
Information is everywhere in nature which is very uncertain and unpredictable. But information, in itself, is a very ambiguous term. In this cursory write-up, we attempt to understand the formal meaning of information by quantifying…
Computability logic is a formal theory of (interactive) computability in the same sense as classical logic is a formal theory of truth. This approach was initiated very recently in "Introduction to computability logic" (Annals of Pure and…
At a first glance the Theory of computation relies on potential infinity and an organization aimed at solving a problem. Under such aspect it is like Mendeleev theory of chemistry. Also its theoretical development reiterates that of this…
This article is an introduction to formal languages from the point of view of combinatorial group theory. Group theoretic applications are included and language classes are defined algebraically.
The goal of this paper is to experiment new math concepts and theories, especially if they run counter to the classical ones. To prove that contradiction is not a catastrophe, and to learn to handle it in an (un)usual way. To transform the…
The classical logical antinomy known as Richard-Berry paradox is combined with plausible assumptions about the size i.e. the descriptional complexity of Turing machines formalizing certain sentences, to show that formalization of language…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
Type theories, logical frameworks and meta-languages form a common foundation for designing, implementing, and reasoning about formal languages and their semantics. They are central to the design of modern programming languages, certified…
The aim of this paper is to study the historical evolution of mathematical thinking and its spatial spreading. To do so, we have collected and integrated data from different online academic datasets. In its final stage, the database…
These notes are an elaboration on: (i) a short course that I gave at the IPhT-Saclay in May-June 2012; (ii) a previous letter on reversibility in quantum mechanics. They present an introductory, but hopefully coherent, view of the main…
In this short presentation, we address two somewhat separate issues. The first one deals with the establishment (vs discovery) of what we call "physical laws". The discussion runs on a "successive approximations" approach, suited to our own…
This is a philosophy-intense physics article, or, if you wish, a physics-intense philosophy article. Also, being a mathematician, I tend to view the physics, in particular the essence of quantum physics, in emphasizing the mathematical…
The notions of formal contexts and concept lattices, although introduced by Wille only ten years ago, already have proven to be of great utility in various applications such as data analysis and knowledge representation. In this paper we…
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…
In his late work (De venatione sapientiae), Cusanus unfolded basic ideas of his brilliant theology. After a long period, this ingenious teaching became clearly recognizable especially in our time. Forward with his face to the back, modern…
How does scientific knowledge grow? This question has occupied a central place in the philosophy of science, stimulating heated debates, but yielding no clear consensus. Many explanations can be understood in terms of whether and how they…
Scientific cosmology has now reached its period of maturity with the establishment of a standard model, which is the theory of an expanding universe. The question of whether this expansion resolves itself, in the past, into a singularity…
I have developed a pedagogy and textbook for teaching logic centered on what I call "logical worldviews". A logical worldview examines the close connection between philosophical commitments and the logical principles and method for a…
Enormous questions still loom for the emerging science of spontaneous thought: what, exactly, is spontaneous thought? Why does our brain engage in spontaneous forms of thinking, and when is this most likely to occur? And perhaps the…