There is a disagreement among contemporary commentators about Avicena's view of the theoretical intellect in "Kitāb alnafs". Is its activity performed by an internal sense helped by the intellect, or is it a activity proper of the intellect independently of material forms? Some passages of V.5 and V.6 suggest that both elements are necessary to the knowledge: unifying the multiplicity and multiplying the unity; in others words, it is not enough that the intellect conceptualizes the minor and major terms of (...) the syllogism, it also needs to intuit the middle term. (shrink)

The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical (...) practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of “geometric judgments” from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and re-examine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) “space” should be revisited for the purposes of life sciences. (shrink)