In the field of systematic philosophy a key task that Klapwijk took upon himself was that of analyzing and criticizing most cautiously Vollenhoven's early idea of the possibility of an integral Christian philosophy unaccommodated to the ideas of Greek paganism or modern secular humanism undiluted by what Vollenhoven had called "synthesis philosophy", i.e. a mix of Gospel motifs with sophisticated conceptions of a non-Christian origin. For Vollenhoven, this synthesis quality compromises the entirety of the Patristic philosophical theology, contrary to Alfred North Whitehead's appraisal of the same era. (See also the Wiki page for Classical Christian Philosophy, a misnomer.)
Another task that Klapwijk took upon himself was to analyze and evaluate differences between the university's two leading lights, Abraham Kuyper and Herman Bavinck, both now long deceased but both with partisan followers who could live less with the leaders' differences than could those leaders themselves. One of Klapwijk's first attempts to articulate this critical stance for his philosophical community occurred in a widely-read volume edited by Hendrik Hart, Johan van der Hoeven, and Nicholas Wolterstorff, reviewed in Theology Today, by Eugene Osterhaven: "An excellent chapter on 'Rationality in the Dutch Neo-Calvinist Tradition' by Jacob Klapwijk ... treats Abraham Kuyper's doctrines of common grace, and the antithesis, and his failure to harmonize the two, especially when he dealt with human reason. Kuyper's attempts to give the antithesis organizational form is shown to "lead to a dangerous identification of the Christian (or, if you will, Reformed) cause with God's cause" (p. 97). Although Kuyper intended Christian organizations to be a means for Christianizing society, 'the danger was that they were considered not as deficient instruments but as ends in the struggle for the kingdom of God'."
As mentioned by Osterhaven, one major difference in ideas between Bavinck and Kuyper is formulated in terms inherent to the Reformed tradition. It's the contrast between the doctrine of "religioius anthithes' (not only the human soul but all of life in culture and society is to be redeemed) and its counterpart, the doctrine of "common grace" (cultural goods are tokens of God’s grace equally for Christians and non-Christians). How to integrate both perspectives? Bavinck emphasized common grace, while Kuyper, in many of his works, emphasized (sometimes severely) the antithetical attitude, also in terms of separate Christian organisations in public life. A comparison of the two positions, which came to designate two interwoven and contentious traditions in the Christian Reformed Churches in the Netherlands and the Christian movements that flowed from its membership, is presented in one of the three chapters that Jacob Klapwijk contributed to a very important self-critical work of Reformational philosophy, entitled Bringing into Captivity Every Thought (1991). He was one of the three editors of the volume and among nearly a dozen contributors.
The dispute about synthesis and antithesis has incisive consequences for the Christian’s position in culture and society but touches in particular the Christian calling in philosophy. Klapwijk wanted to think of Reformational philosophy not only, not even primarily as "Calvinist" in Vollenhoven's term, not only as "reformational-ecumenical" (in Dooyeweerd's terms), but as a transformational philosophy. He took as an example the Church fathers’ notion of spoliatio Aegyptiorum, the robbery of the Egyptians (see Ex. 12:36). God ordered the Israelites in the great exodus to rob their antagonists from their silver and golden treasures. Yet, it was not for the sake of synthesis and syncretism (‘the golden calf’): the metals were purified and re-used for the service of God in the sanctuary of the desert. This is for Klapwijk a paradigm of the transforming power of a religious belief, also in philosophical discussions. Christian philosophy should overcome the synthesis/antithesis dilemma. It is athletic enough to keep pace with the broader philosophical world, putting the theories of the day to a critical test and using what is valuable in such a way that it can become subservient to a Christian perspective on reality in the realms of theoretical thought.
Hart, Hendrik; Johan van der Hoeven; and Nicholas Wolterstorff (editors, 1983). Rationality in the Calvinian Tradition (Lanham, MD, USA: University Press of America).
Klapwijk, Jacob; Hendrik Hart; and Kor A. Bril (editors, 1973). The Idea of a Christian Philosophy: Essays in Honour of D H Th Vollenhoven (Toronto: Wedge).
Klapwijk, Jacob (1973). "Calvin and Neo-Calvinism on Non-Christian Philosophy," Philosophia Reformata 38 (1973), pp. 43-61.
Klapwijk, Jacob (1983). "Rationality in the Dutch Calvinist Tradition," Rationality in the Calvinian Tradition (eds Hart, Van der Hoeven, Wolterstorff, Lanham, MD, USA: University Press of America), pp. 93-111.
Klapwijk, Jacob (1986). "Antithesis, Synthesis, and the Idea of Transformational Philosophy," Philosophia Reformata 51, pp.138-152.
Klapwijk, Jacob (1987). Kijken naar kopstukken (Amsterdam: Buijten en Schipperheijn).
Klapwijk, Jacob (1987). "Reformational Philosophy on the Boundary between Past and Future," Philosophia Reformata 52, pp 101-134.
Klapwijk, Jacob; Sander Griffioen; and Gerben Groenewoud (editors, 1991). Bringing into Captivity Every Thought: Capita Selecta in the History of Christian Evaluations of non-Christian Philosophy (Lanham, MD, USA: University Press of America).
Klapwijk, Jacob (1991). "Epilogue: the idea of transformational philosophy." Klapwijk, Griffioen, Groenewoud (eds.) Bringing into Captivity Every Thought: Capita Selecta in the History of Christian Philosophy (Lanham, MD, USA: University Press of America), pp. 241-266.
Klapwijk, Jacob (1994). "Pluralism of Norms and Values: On the Claim and Reception of the Universal," Philosophia Reformata 59 (2), pp 158-192.
Klapwijk, Jacob (2008) Purpose in the Living World? Creation and Emergent Evolution. (Cambridge: Cambridge University Press).
Osterhaven, Eugene (1984). Book review: "Rationality in the Calvinian Tradition," Theology Today, October 1984.