A Christian approach to scholarship, directed by the central biblical motive of creation, fall and redemption and guided by the theoretical idea that God subjected all of creation to His Law-Word, delimiting and determining the cohering diversity we experience within reality, in principle safe-guards those in the grip of this ultimate commitment and theoretical orientation from absolutizing or deifying anything within creation. In this article my over-all approach is focused on the one-sided legacy of mathematics, starting with Pythagorean arithmeticism (“everything (...) is number”), continuing with the geometrization of mathematics after the discovery of irrational numbers and once again, during the nineteenth century returning to an arithmeticistic position. The third option, never explored during the history of mathematics, guides our analysis: instead of reducing space to number or number to space it is argued that both the uniqueness of these two aspects and their mutual coherence ought to direct mathematics. The presence of different schools of thought is highlighted and then the argument proceeds by distinguishing numerical and spatial facts, while accounting for the strict correlation of operations on the law side of the numerical aspect and their correlated numerical subjects (numbers). Discussing the examples of 2 + 2 = 4 and the definition of a straight line as the shortest distance between two points provide the background for a brief sketch of the third alternative proposed (inter alia against the background of an assessment of infinity and continuity and the vicious circles present in contemporary mathematical arithmeticistic claims). (shrink)

An overview of the history of the concept of matter highlights the fact that alternative modes of explanation were successively employed. With the discovery of irrational numbers the initial conviction of the Pythagorean School collapsed and was replaced by an exploration of space as a principle of understanding. This legacy dominated the medieval period and had an after-effect well into modernity—for both Descartes and Kant still characterized matter in spatial terms. However, even before Galileo the mechanistic world view slowly entered (...) the scene—the world as chaos, particles in motion. Elevating movement to become the guiding principle in our understanding of matter dominated the main tendency of modern physics until the (end of the) 19th century. The discovery of irreversible processes (radio-activity for example) directed 20th century physics towards an exploration of the meaning of energy-operation. It turned out that even within 20th century physics long-standing legacies prevailed, because an account of the nature of matter continued to be torn apart by atomistic and holistic views—confronted by the problem of constancy and change (radical transformability versus persistence). Concrete, material reality exceeds the scope of any single mode of explanation—an insight that also serves a better understanding of the wave-particle duality. (shrink)

This paper addresses the question of normativity in Hegel by examining the role of ‘undialectical’ resistance to dialectical development. Beginning with a general overview of dialectical normativity and what it might mean to be ‘undialectical,’ the focus then shifts to a privileged example in Hegel’s writings: Sophocles’ Antigone. The central claim of the paper is the following: The very contradictions that fuel dialectical normativity can also trap individuals within an obsolete actuality, without immediate hope of escape. Indeed, the irreducible dependence (...) of dialectical thinking upon the actions and decisions of individual consciousness expose it to the threat of continual stasis or regression. This ineliminable possibility of failure is what is here called the ‘undialectical’ moment of the dialectic, which Hegel understands rather as a negative condition of possibility of freedom and rationality. (shrink)