Biology in the Critical Philosophy and the Opus postumum Hein van den Berg. Parts of Chap. 2 have been previously published in Hein van den Berg (2011), “ Kant's Conception of Proper Science.” Synthese 183 (1): 7–26. Parts of Chap.
Kant is well known for his restrictive conception of proper science. In the present paper I will try to explain why Kant adopted this conception. I will identify three core conditions which Kant thinks a proper science must satisfy: systematicity, objective grounding, and apodictic certainty. These conditions conform to conditions codified in the Classical Model of Science. Kant’s infamous claim that any proper natural science must be mathematical should be understood on the basis of these conditions. In order to substantiate (...) this reading, I will show that only in this way it can be explained why Kant thought (1) that mathematics has a particular foundational function with respect to the natural sciences and (2) as such secures their scientific status. (shrink)
We propose a new method for the history of ideas that has none of the shortcomings so often ascribed to this approach. We call this method the model approach to the history of ideas. We argue that any adequately developed and implementable method to trace continuities in the history of human thought, or concept drift, will require that historians use explicit interpretive conceptual frameworks. We call these frameworks models. We argue that models enhance the comprehensibility of historical texts, and provide (...) historians of ideas with a method that, unlike existing approaches, is susceptible neither to common holistic criticisms nor to Skinner's objections that the history of ideas yields arbitrary and biased reconstructions. To illustrate our proposal, we discuss the so-called Classical Model of Science and draw upon work in computer science and cognitive psychology. (shrink)
This is a précis of my book Kant's Radical Subjectivism, to be published as part of a symposium dedicated to the book, with critics Hein van den Berg, Karin de Boer, Henny Blomme en Joris Spigt, including a reply by me. The symposium is in Dutch, but the pre-print uploaded here is in English!
Kant’s teleology as presented in the Critique of Judgment is commonly interpreted in relation to the late eighteenth-century biological research of Johann Friedrich Blumenbach. In the present paper, I show that this interpretative perspective is incomplete. Understanding Kant’s views on teleology and biology requires a consideration of the teleological and biological views of Christian Wolff and his rationalist successors. By reconstructing the Wolffian roots of Kant’s teleology, I identify several little known sources of Kant’s views on biology. I argue that (...) one of Kant’s main contributions to eighteenth-century debates on biology consisted in demarcating biology from metaphysics. Kant rejected Wolffian views on the hierarchy of sciences, according to which propositions specifying the functions of organisms are derived from theological truths. In addition, Kant argued that organic self-organization necessitates a teleological description in order to show that self-organization does not support materialism. By demarcating biology and metaphysics, Kant made a small yet important contribution to establishing biology as a science. (shrink)
This is the first in a series of papers on Predicative Algebraic Set Theory, where we lay the necessary groundwork for the subsequent parts, one on realizability [B. van den Berg, I. Moerdijk, Aspects of predicative algebraic set theory II: Realizability, Theoret. Comput. Sci. . Available from: arXiv:0801.2305, 2008], and the other on sheaves [B. van den Berg, I. Moerdijk, Aspects of predicative algebraic set theory III: Sheaf models, 2008 ]. We introduce the notion of a predicative category (...) with small maps and show that it provides a sound and complete semantics for constructive set theories like IZF and CZF. The main technical contribution of this paper is that it shows in detail that such categories can always be conservatively embedded in categories that are exact. These exactness properties play a crucial rôle in showing that predicative categories with small maps contain models of set theory and that they are closed under sheaves and realizability. We will prove the former statement in this paper as well, leaving a proof of the closure properties to the papers on realizability and sheaves as mentioned above. (shrink)
Van den Berg, I.P., Extended use of IST, Annals of Pure and Applied Logic 58 73–92. Internal Set Theory is an axiomatic approach to nonstandard analysis, consisting of three axiom schemes, Transfer , Idealization , and Standardization . We show that the range of application of these axiom schemes may be enlarged with respect to the original formulation. Not only more kinds of formulas are allowed, but also different settings. Many examples illustrate these extensions. Most concern formal aspects of (...) nonstandard asymptotics. (shrink)