G.J. van der Heiden

Local–global problem for Drinfeld modules

Let K be a function field with an A-algebra structure. The ring A arises in the definition of the Drinfeld module phi over K. By E(K) we denote K together with the A-module structure induced on it by phi. For any principal prime ideal (a) subset of A, we study the question whether an element x is an element of E(K) which is an a-fold in E(K-nu) for every place nu of K, is an a-fold in E(K). In particular, we study the group S(a, K) := ker E(K)/aE(K) --> Pi(nu) E(K-nu)/aE(K-nu) for Drinfeld modules of rank 2. We show that this finite group is trivial in many cases, but can become arbitrarily large

The Voice of the Past in the Present: On Dialogue and Testimony

A dialogue is not only concerned with speaking with other people about something, but also includes a speaking for those who can no longer speak as well as for their opinions. In this first part of this essay, in discussion with authors such as Gadamer, Ricoeur and Derrida, I will show in which sense the dimension of speaking for... is part of a hermeneutic conception of dialogue and in which sense this speaking for... helps me in applying the model of dialogue to relation of the historian to the past. In the second part of this essay, I develop this model of dialogue to account for the historian’s activity in terms of the notions of testimony and witnessing. I show how these notions determine the course of Ricoeur’s later reflections on the philosophy of history and why these reflections may benefit from a reconsideration of Gadamer’s conception of generosity and experience.

Factoring polynomials over finite fields with drinfeld modules

In the following, we describe a way of factoring polynomials in Fq[X] with Drinfeld modules. We furthermore analyse the complexity of the algorithm and compare it to the well-known Cantor-Zassenhaus algorithm.

Addendum to "Factoring polynomials over finite fields with Drinfeld modules"

After my paper [2] was electronically published by Mathematics of Computation, I came across the PhD thesis of professor I. Y. Potemine [6]. In Section 4.3 of his thesis, an algorithm for factoring polynomials is proposed which is equivalent to the algorithm discussed in my paper. Potemine’s algorithm is acknowledged in my PhD thesis [1]. Our algorithms were found independently, both as analogues of H. W. Lenstra’s well-known Elliptic Curve Method for factoring integers; cf. [3]. Professor Potemine informed me that there are two even earlier publications in which his algorithm is described; namely [5] and [4]. Nevertheless, a complexity analysis and a comparison with the well-known Cantor–Zassenhaus algorithm can only be found in [2] and [1].

The dialectics of Paul: on exception, grace, and use in Badiou and Agamben

The remarkable philosophical present-day turn to Paul pays a lot of attention to the particular role played by the famous distinctions that structure Paul’s rhetoric such as the distinction between...ABSTRACT The remarkable philosophical present-day turn to Paul pays a lot of attention to the particular role played by the famous distinctions that structure Paul’s rhetoric such as the distinction between faith and law, life and death, and spirit and flesh. These distinctions lead to the question of whether Paul (or the philosophers’ Paul) endorses a dualism or not. In this essay, the author investigates Badiou’s and Agamben’s readings of Paul and asks whether one cannot find a form of dialectics rather than dualism in these readings. The concept of the exception seems to corroborate this suggestion. To examine whether this suggestion makes sense, the author first discusses Badiou’s focus on the antidialectics of death and resurrection as well as the dialectical remnants in Badiou’s reading of Paul. Subsequently, the author analyses Agamben’s dialectical account of the Pauline terms katargein (to deactivate), chrēsis (use) and charis (grace).

Attitudes to Life: The Apostle Paul and Contemporary Philosophy

The remarkable attention to Saint Paul in continental philosophy today originates in the 1990s. In a period of less than 10 years, Jacob Taubes’ lectures on Paul from 1987 were published in 1993 under the title Die politische Theologie des Paulus; Martin Heidegger’s lectures on Paul from 1920 to 1921, were (only) published in 1995 as the first part of the volume Phänomenologie des religiösen Lebens; Alain Badiou’s Saint Paul: La fondation de l’universalisme appeared in 1997, establishing him as one of the new key philosophers in continental thought; and Giorgio Agamben’s The Time That Remains: A Commentary on the Letter to the Romans appeared in 2000, discussing the three aforementioned books. These four books together with other reflections on Paul’s letters, set continental philosophy on fire, opening up a fertile and intriguing conversation with theologians and ancient philosophers, as some volumes on the relation of Paul and continental thought attest to. Confronted with the vast amount of literature that already appeared on Paul and present-day philosophy, it may not make much sense to add one more special issue on this particular topic. Yet, what is and remains important to do in our reflection on and appropriation of this remarkable turn to Paul is to understand why this turn has taken place. To this question, several answers have already been given. Especially the political–theological dimension of the readings of Taubes, Badiou, Agamben and others often push the answers to this question in the direction of political philosophical considerations. Answers in this direction are of great importance, but different answers may be given and different motives deserve our attention as well. In this special issue, we want to explore one of these alternative routes through the landscape of the philosophers’ Paul. Our alternative route is concerned with the question of life and, in particular, with the question of the attitude or way of life that is at stake in the turn to Paul and that allows us to explicate some of the crucial connections with new testamentary and ancient philosophical concerns. The question of the attitude of life is first and foremost concerned with the question of ethos. The Hellenistic schools of ancient philosophy were mainly concerned with, as Foucault called it following Hadot, the care of the self: for these schools, philosophy was never a purely theoretical activity, but rather an activity by which humans redirect their attitude or ethos towards themselves and the world so that they may experience and live their lives differently. This particular attention to the attitude of life is also present in the letters of Paul. As the contributions of this special issue will show, the question of the attitude of life is one of the shared,

The Contaminated Wound: Derrida on the Language of Levinas

To capture the relation between Derrida and Levinas, one could commence as Simon Critchley does in his impressive study The Ethics of Deconstruction. To establish that it makes sense to approach Derrida’s deconstruction from the perspective of Levinas’ ethics, he quotes the former’s comment when “challenged by André Jacobs to specify what intellectual distance he maintains with respect to Levinas’ work.”1 Derrida famously responds: “Devant une pensée comme celle de Lévinas, je n’ai jamais d’objection. Je suis prêt à souscrire à tout ce qu’il dit.”2 From this, one could conclude, as Critchley does, that it is justified to assume a definite affinity between Derrida’s and Levinas’ thought. One could argue that even Derrida’s determination of the difference between his and Levinas’ work supports this conclusion since he determines it as a difference of idiom, language, and writing, and these, as he assures us, do not give rise to “philosophical differences.”3 Although this is a striking comment, it is important to remember that idiom, language, and writing are central themes in Derrida’s work. Consequently, the scope of these differences might be more profound than Derrida’s remarks in this discussion indicate. The question he asks—“what do differences of idiom, language or writing mean?”—may at first sight appear to be a rhetorical one but is in fact the crucial question to be answered if one wants to understand the relation between Derrida and Levinas. Clearly, Critchley is aware of this. In The Ethics of Deconstruction, he even adds that one should “be cautious about such remarks because they were transcribed from an oral, improvised debate.”4 Nevertheless, he pushes these objections aside and argues that Derrida’s remarks on the difference with

The Letter and the Witness: Agamben, Heidegger, and Derrida

In Remnants of Auschwitz, Agamben introduces a particular conception of bearing witness to overcome the problems contained in an account of language that depends on the voice or the letter. From his earlier work, it is clear that his critique of the voice and the letter is not only directed to ancient and medieval metaphysics, but also concerns Heideggers account of the voice and Derridas account of the letter and writing. Yet, if Agamben is correct in claiming that bearing witness offers an alternative to Heideggers voice and Derridas letter, it is remarkable – a fact unnoticed in the available literature – that Agamben does not discuss how these conceptions of the voice and the letter are intrinsically connected to the problem of testimony for Heidegger as well as Derrida. To show how this lack of attention to bearing witness in Heidegger and Derrida affects Agambens critique, this article proceeds as follows. First, we interpret Agambens critique of Heideggers conception of the voice and Derrida...In Remnants of Auschwitz, Agamben introduces a particular conception of bearing witness to overcome the problems contained in an account of language that depends on the voice or the letter. From his earlier work, it is clear that his critique of the voice and the letter is not only directed to ancient and medieval metaphysics, but also concerns Heideggers account of the voice and Derridas account of the letter and writing. Yet, if Agamben is correct in claiming that bearing witness offers an alternative to Heideggers voice and Derridas letter, it is remarkable – a fact unnoticed in the available literature – that Agamben does not discuss how these conceptions of the voice and the letter are intrinsically connected to the problem of testimony for Heidegger as well as Derrida. To show how this lack of attention to bearing witness in Heidegger and Derrida affects Agambens critique, this article proceeds as follows. First, we interpret Agambens critique of Heideggers conception of the voice and Derridas conception of writing in terms of the presuppositional constitution of metaphysics. Second, we describe Agambens concept of the witness and indicate how it offers an alternative to this presuppositional constitution of metaphysics. Finally, we show which role bearing witness plays in Heideggers voice and Derridas letter, and how our analysis presents a more precise version of Agambens critique.

Hermeneutics and the Provisional Character of Dialogue

The model of dialogue has been of crucial importance for the philosophical-hermeneutic account of interpretation ever since Schleiermacher. In this essay we investigate how contemporary hermeneutics accounts for this model in terms of provisionality and how the attention to provisionality marks the contemporary hermeneutic conception of interpretation. We will do so by first exploring how the theme of provisionality arises in Martin Heidegger’s work on interpretation: provisionality appears out of Heidegger’s concern with the primacy of anticipation in interpretation. Subsequently, we will show how Hans-Georg Gadamer’s attention to dialogue incorporates the theme of provisionality: since no dialogue ever truly comes to an end, every dialogue invites its own continuation. Finally, we will discuss how Jacques Derrida’s account of dialogue radicalizes the conception of this provisionality: despite its invitation for continuation, dialogues are radically interrupted; consequently, an additional work of interpretation is needed to continue a dialogue beyond these interruptions.

In Dialogue with the Past: Reflections on a Metaphor

Once upon a time, it was not uncommon for historians to describe their engagement with relics from the past – medieval charters unearthed in a badly lit archive, or hand-written letters barely rescued from the moist of a smelly town hall cellar – in truly anthropomorphic terms. No one less than Leopold von Ranke, for instance, wrote the Countess of Arnim in 1828 that amidst his medieval source material in Italy, he met “many princesses, possibly beautiful, all under a curse and needing to be saved.” In almost erotic language, he referred to “virgins” and “objects of love” in Italian archives, whom he longed to meet in the hope of producing “a beautiful Roman-German prodigy.”1 In equally anthropomorphic terms, the French historian Jules Michelet expressed his desire to bring the past to life again. Surrounded by ancient papers and parchments, Michelet addressed these relics as if they were dead bodies waiting for some miraculous resurrection: “Softly my dear friends, let us proceed in order if you please . . . [A]s I breathed their dust, I saw them rise up. They rose from the sepulcher . . . as in the Last Judgment of Michelangelo or in the Dance of Death.”2 It is not merely the exalted prose of these romantic historians that makes us, modern philosophers of history, smile. Its epistemological subtext, too, differs significantly from how we have come to understand the historian’s attempt