This paper examines infinity and self-reference from a critique perspective. Starting from an extension of Cantor Paradox that suggests the inconsistency of the actual infinite, the paper makes a short review of the controversial history of infinity and suggests several indicators of its inconsistency. Semantic self-reference is also examined from the same critique perspective by comparing it w...

1 – The mythical and theological origin of physico-mathematical spaces; the geometrization of time Abstract There is no mathematical plane nor space in Euclid's geometry. Lines are traced, extended, intersected on a plane, an “apeiron” (it has no boundary), which is “practiced” but not mathematized. These lines have no thickness, they intersect in a point, that is a sign (“semeion”); they are o...

This paper examines the Kalam cosmological argument, as put forward by William Craig. Craig infers the existence of a personal God from the supposedly finite past of the universe. The temporal finiteness of the universe is based upon philosophical arguments for the presumed impossibility of an actual infinity of past events and is confirmed by two lines of scientific evidence. The arguments aga...

The Infinite is one of the most intriguing ideas in which the human mind has ever engaged. Full of paradoxes and controversies, it has raised fundamental issues in domains as diverse and profound as theology, physics, and philosophy. The infinite, an elusive and counterintuitive idea, has even played a central role in defining mathematics, a fundamental field of human intellectual inquiry chara...

Exosystem: A dynamical system modelling the set of all exogenous inputs (command/disturbances) affecting a controlled plant. Internal Model: A model of the exogenous inputs (command/disturbances) affecting a controlled plant, embedded in the interior of the controller. Generalized Tracking Problem: The problem of designing a controller able to asymptotically track/reject any exogenous command/d...

The investigation of hydrodynamic models with partially penetrable obstacles has been initiated by the recent progress in the development of free flow turbines [l] for the purpose of estimating their efficiency limit [2]. In the previous paper [3], an explicitly solvable analog of the Kirchhoff cavitation flow was obtained. As in the classical situation, the main deficiency of the Kirchhoff mod...

In this short note we first account for Aristotle's views on infinity, by clarifying the way his notion of potential infinity should be understood, in light entelechy. We then present four distinct ways which mathematicians attempted to tame actual and ask question whether they are indeed different ways, or ultimately variations same concept. suggest that what doing is find a construct form sub...

In this paper, several dynamical systems for computing canonical correlations and canonical variates are proposed. These systems are shown to converge to the actual components rather than to a subspace spanned by these components. Using Liapunov stability theory, qualitative properties of the proposed systems are analyzed in detail including the limit of solutions as time approaches infinity.

We apply percolation theory to a recently proposed measure of fragmentation F for social networks. The measure F is defined as the ratio between the number of pairs of nodes that are not connected in the fragmented network after removing a fraction q of nodes and the total number of pairs in the original fully connected network. We compare F with the traditional measure used in percolation theo...