We shall discuss the idea of finding all rational points on a curve C by first finding an associated collection of curves whose rational points cover those of C. This classical technique has recently been given a new lease of life by being combined with descent techniques on Jacobians of curves, Chabauty techniques, and the increased power of software to perform algebraic number theory. We shal...

Abstract Marsilio Ficino’s view on ensoulment, which can be extrapolated from his critique of natal astrology, relies the relations metaphysical proportion between different levels life and being are central to Platonic philosophy. Drawing primarily Plotinus, Ficino describes emergence in embryo as a process World Soul is true agent. For him, ‘human nature’ that present developing attracts into...

creativity or uncreativity of the rational soul is one of the oldest problem of philosophy. ibn sina by giving some proofs has proven the creativity of the rational soul. fakhr ad-din ar razi has propsed several critics to each of the avecina’s argument. in this article, we are going to prove that, the origin of razi’s critics is his misunderstanding in ibn sina’s philosophical views in potenti...

Motivated by real life decision problems, we model a boundedly rational choice procedure, called choice by iterative elimination, where an alternative might not be compared by all available alternatives. Our decision maker continues her limited search until she finds an alternative which is optimal within its consideration set. We study properties of this procure and provide a full characteriza...

Modelling real world problems using rational agents has been heavily investigated over the past two decades. BDI (Beliefs, Desires, and Intentions) Logic has been widely used to represent and reason about rational agency. However, in the real world, we often have to deal with different levels of confidence in the beliefs we hold, desires we have, and intentions that we commit to. This paper pro...

We define parallelograms of base a and b in a group. They appear as minimal relators in a presentation of a subgroup with generators a and b. In a Lie group they are realized as closed polygonal lines, with sides being orbits of left-invariant vector fields. We estimate the number of sides of parallelograms in a free nilpotent group and point out a relation to the rank of rational series. 1 Int...

When people use mathematics to model real-life situations, their modeling is often mediated by semantic alignment (Bassok, Chase, & Martin, 1998): The entities in a problem situation evoke semantic relations (e.g., tulips and vases evoke the functionally asymmetric “contain” relation), which people align with analogous mathematical relations (e.g., the noncommutative division operation, tulips/...