On the basis of an initial reference to a number of critical appraisals of H. Dooyeweerd’s philosophy, this article proceeds by provisionally focusing on the image of Franz Xavier Von Baader1 — who was intellectually active during the first part of the nineteenth century — in secondary literature . The main concern, however, is to enter into a more detailed evaluation of the claim made by J.G. Friesen,2 namely that all the basic systematic insights and distinctions found in the philosophy (...) of Herman Dooyeweerd are already present in the thought of Von Baader. That Dooyeweerd was indeed influenced by numerous philosophers and philosophical insights spanning the entire history of philosophy is beyond doubt. However, that there is any direct influence on his thought from Von Baader cannot be substantiated on the basis of the available sources even though it is not unlikely that he might have been aware of the existence of Von Baader. Both the quotations used by Friesen in support of his thesis and an extensive reading of the original Collected Works of Von Baader serve as a basis for the assessment of the claims made by Friesen. In fact, there are a number of philosophical distinctions found in the original works of Von Baader that, considered in isolation, are much closer to views of Dooyeweerd. However, once these are placed within the context of Von Baader’s thought, the striking and significant distance between the thought of Von Baader and Dooyeweerd once again become apparent. (shrink)

This article sets out to analyse some of the most basic elements of our number concept - of our awareness of the one and the many in their coherence with multiplicity, succession and equinumerosity. On the basis of the definition given by Cantor and the set theoretical definition of cardinal numbers and ordinal numbers provided by Ebbinghaus, a critical appraisal is given of Frege’s objection that abstraction and noticing (or disregarding) differences between entities do not produce the concept of number. (...) By introducing the notion of subject functions, an account is advanced of the (nominalistic) reason why Frege accepted physical, kinematic and spatial properties (subject functions) of entities, but denied the ontic status of their quantitative properties (their quantitative subject function). With reference to intuitionistic mathematics (Brouwer, Weyl, Troelstra, Kreisel, Van Dalen) the primitive meaning of succession is acknowledged and connected to an analysis of what is entailed in the term ‘Gleichzahligkeit’ (‘equinumerosity’). This expression enables an analysis of the connections between ordinality and cardinality on the one hand and succession and wholeness (totality) on the other. The conceptions of mathematicians such as Frege, Cantor, Dedekind, Zermelo, Brouwer, Skolem, Fraenkel, Von Neumann, Hilbert, Bernays and Weyl, as well as the views of the philosopher Cassirer, are discussed in order to arrive at an assessment of the relation between ordinality and cardinality (also taking into account the relation between logic and arithmetic) - and on the basis of this evaluation, attention is briefly given to the definition of an ordered pair in axiomatic set theory (with reference to the set theory of Zermelo-Fraenkel) and to the defmition of an ordered pair advanced by Wiener and Kuratowski. (shrink)