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)

The traditional understanding of abstraction operates on the basis of the assumption that only entities are subject to thought processes in which particulars are disregarded and commonalities are lifted out (the so-called method of genus proximum and differentia specifica). On this basis Frege criticized the notion of abstraction and convincingly argued that (this kind of) “entitary- directed” abstraction can never provide us with any numbers. However, Frege did not consider the alternative of “property- abstraction.” In this article an argument for (...) this alternative kind of abstraction is formulated by introducing a notion of the “modal universality” of the arithmetical and by developing it in terms of the distinction between type-laws (laws for entities – applicable to a limited class of entities) and modal laws (obtaining for every possible entity without any restriction). In order to substantiate this argument a case is made for the acceptance of an ontic foundation for the arithmetical (and other modes or functions of reality – with special reference to Cassirer, Bernays, Gödel and Wang), which, in the final section, serves to give an ontological account of (i) the connections between the arithmetical and other aspects of reality and (ii) the applicabality of arithmetic. In the course of the argument the impasse of logicism is briefly highlighted, while a few remarks are made with regard to the logical subject- object relation in connection with Frege's view that number attaches to a concept. S. Afr. J. Philos. Vol.22(1) 2003: 63-80. (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)

The recent publication of a special number of the SAJP dedicated to a discussion of Samantha Vice’s thoughts on being a white South African prompted this reflection on justice, equity and the modern idea of the state – against the background of moral feelings of guilt and shame, cultural diversity and merging identities. Its aim is to provide a perspective on the unity of the public legal order of the state, the distinct meaning of citizenship and affirmative action in terms (...) of the distinction between constitutive and regulative legal principles also helping white South Africans to understand how affirmative action relates to injustices of the past. The classical understanding of equity will play a key role in this discussion, aimed at showing how we can avoid the apparent impasse of equality before the law and of “fair discrimination.”. (shrink)

By taking serious a remark once made by Paul Bernays, namely that an account of the nature of rationality should begin with concept-formation, this article sets out to uncover both the restrictive and the expansive boundaries of rationality. In order to do this some implications of the perennial philosophical problem of the “coherence of irreducibles” will be related to the acknowledgement of primitive terms and of their indefinability. Some critical remarks will be articulated in connection with an over-estimation of rationality (...) – concerning the influence of Kant's view of human understanding as the formal law-giver of nature (the supposedly “rational structure of the world”), and the apparently innocent (subjectivist) habit to refer to experiential entities as 'objects'. The other side of the coin will be highlighted with reference to those kinds of knowledge transcending the limits of concept-formation – culminating in formulating the four most basic idea-statements philosophy can articulate about the universe. What is found “in-between” these (restrictive) and (expansive) boundaries of rationality will then briefly be placed within the contours of a threefold perspective on the self-insufficiency of logicality – as merely one amongst many more dimensions conditioning human life. Although the meaning of the most basic logical principles – such as the logical principles of identity, non-contradiction and sufficient reason – will surface in our analysis, exploring some of the complex issues in this respect, such as the relationship between thought and language, will not be analysed. The important role of solidarity – as the basis of critique – will be explained and related both to the role of immanent criticism in rational conversation and the importance of acknowledging what is designated as the principle of the excluded antinomy (which in an ontic sense underlies the logical principle of non-contradiction). The last section of our discussion will succinctly illuminate the proper place of the inevitable trust we ought to have in rationality – while implicitly warning against the rationalistic over-estimation of it (its degeneration into a rationalist “faith in reason”). Our intention is to enhance an awareness of the reality that rationality is embedded in and borders on givens which are not open to further “rational” exploration – givens that both condition (in a constitutive sense) and transcend the limits of conceptual knowledge. Some of the distinctions and insights operative in our analysis are explained in Strauss 2000 and 2003. Yet, most of the systematic perspectives found in this analysis of rationality are only developed in this article for the first time. Since a different study is required to discuss related problems and results found within cognitive science, it cannot be discussed within one article. S. Afr. J. Philos. Vol.22(3) 2003: 247–266. (shrink)

This is a follow-up article of Strauss 2011. In order to transcend the shortcomings present in the dialectical legacy regarding normativity, this article further explores key elements within the dialectical tradition focused on the basic motive of nature and freedom and the effect it had on modern social contract theories which aimed at reconstructing human society from its “atoms,” the individuals. The transition to an alternative approach commences with a discussion of the distinction between conditions and what is conditioned. It (...) concerns a correlation found within all aspects of reality, namely that between the law side or norm side on the one hand and the factual side on the other. The basic assumption of this alternative view is found in the idea of ontic normativity which is rooted in a non-reductionist ontology. Against this broader background shortcomings in Kelsen’s theory of law are briefly traced to the dialectic of the causal and non-causal, before a positive characterization of the concept of a principle is given. It turned out that it is a compound basic concept in which terms from different modal aspects of reality are encapsulated at once. The recognition of ontic normativity therefore also enables a distinct methodology, the transcendental-empirical method, which makes it possible to distinguish between the pre-positive nature of a principle, as a universal and constant starting-point for human action, and the historically varying ways in which such a principle can be made valid, through a competent organ disposing over an accountable will and capable to interpret the unique historical circumstances in which the principle has to be positivized . The nature of modal norms is highlighted in terms of various examples, such as jural, historical, logical and aesthetic principles, with special reference to Derrida’s understanding of credit as economic trust or economic faith. In order to make this transcendental-empirical method understandable a more detailed account of the nature of modal aspects is given. The emphasis on ontic normativity also helps us to steer clear of conceptions of natural law, historicism and the shortcomings present in the idea of a social construction of the world. The guiding perspective flowing from this analysis is that modal norms can be articulated through an analysis of analogical structural moments on the law sides of the normative aspects. The last part of this article briefly introduces the distinction between modal and typical norms without entering into a discussion of the latter. (shrink)

Ignoring primitive terms leads to an infinite regress. The alternative is to account for an intuitive understanding into the meaning of such terms. The current investigation proceeds on the basis of an idea of the structure of the various modes of being within which concrete entities function. Examples of primtive terms are given from disciplines such as mathematics, physics and logic and they are related to the general idea of a modal aspect. It is argued that primitive terms are not (...) isolated but reveal their meaning only through their interconnections with other primitive terms that are embedded in other modal aspects. However, although primitive terms are found within the various aspects, the meaning of an aspect only comes to expression through its coherence with other aspects, evinced in modal analogies that are qualified by the core meaning of an aspect. There appears to be two options, either reduce what is irreducible or merely provide synonymous terms for given primitives. The former happens when other unique terms are used to define a specific one and the latter when the attempted ‘definitions’ revert to terms with which the original terms could be meaningfully replaced. It is been pointed out that the coherence between primitives invites every academic discipline to account for the meaning attached to the analogies of primitive terms it is employing, without exploring this additional theme any further. (shrink)

Since the discovery of the paradoxes of Zeno, the problem of infinity was dominated by the meaning of endlessness—a view also adhered to by Herman Dooyeweerd. Since Aristotle, philosophers and mathematicians distinguished between the potential infinite and the actual infinite. The main aim of this article is to highlight the strengths and limitations of Dooyeweerd’s philosophy for an understanding of the foundations of mathematics, including Dooyeweerd’s quasi-substantial view of the natural numbers and his view of the other types of numbers (...) as functions of natural numbers. Dooyeweerd’s rejection of the actual infinite is turned upside down by the exploring of an alternative perspective on the interrelations between number and space in support of the idea of infinite totalities, or infinite wholes. No other trend has succeeded in justifying the mathematical use of the actual infinite on the basis of an analysis of the intermodal coherence between number and space. (shrink)

The Systems Theory is a complex theory (yet it is not identical to recent theories of complexity). The intention of this qualification is to demonstrate that the concept of a system is a complex basic concept of scientific thinking. This means that it is defined in terms of various elementary basic concepts brought together in its explication. The definition given by Von Bertalanffy to the concept of a system employs conceptual elements coming from at least five prominent conceptual clusters. In (...) order to highlight the nature and interrelations between these clusters this article focuses upon perennial philosophical issues which present themselves within the definition of a system. They are those of stability and change, the one and the many (unity and multiplicity), the whole and its parts, and the relation between the material and the vital. An analysis of the interrelations between these clusters provides the basis for an assessment of the scope and limitations Von Bertalanffy's concept of a system. S. Afr. J. Philos. Vol.21(3) 2002: 163-179. (shrink)

Because Gadamer is very sensitive to the role of history, tradition and authority within human life, the overall intention of this article will be to unveil major elements of modern philosophy which exerted an influence upon his thought. In this sense it can be seen as applying his notion of 'Wirkungsgeschichte' to an assessment of certain aspects of his own thought. Particularly in his view on causality and history Gadamer illustrates the intimate connection of his thought with the dialectics of (...) nature and freedom. S. Afr. J. Philos. Vol.21(4) 2002: 291-305. (shrink)