Neutrices are convex additive subgroups of the nonstandard space , most of them are external sets. Because of the convexity and the invariance under some translations and multiplications, external neutrices are models for orders of magnitude. One dimensional neutrices have been applied to asymptotics, singular perturbations, and statistics. This paper shows that in , with standard k, every neutrix is the direct sum of k neutrices of . These components may be chosen to be orthogonal.

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)

Selection on grandparental investment is more complex than Coall & Hertwig (C&H) propose. Patterns of investment are subject to an intergenerational conflict over how resources should be distributed to maximize fitness. Grandparents may be selected to distribute resources unevenly, while their descendants will be selected to manipulate investment in their own favor. Here we outline the evolutionary basis of this conflict.

The nonstandard stroboscopy method links discrete-time ordinary difference equations of first-order and continuous-time, ordinary differential equations of first order. We extend this method to the second order, and also to an elementary, yet general class of partial difference/differential equations, both of first and second order. We thus obtain straightforward discretizations and continuizations, even avoiding change of variables. In fact, we create intermediary objects: partial difference equations with S-continuous solutions, which have both discrete and continuous properties.

Meta-theories, base-theories and theories of practice in Pratical Theology The problem of meta-theories and base-theories, their interaction and the influence of each on the scientific process, have widely been debated in practical theology. In South Africa two meta-theories namely the system- theory together with the theory that social science is busy with the study of actions, are having the greater deal of attention. The purpose of this article is to point out the fact that an early and absolute choice of (...) particular meta-theories, restricts the work of practical theology because it will influence your base-theories, and can weaken the theological content of practical theology. An attempt is made to offer a model by which the interaction between, meta-theories, base-theories and theories of practice can he understood and which can also help the theologian, busy with practical theology, to steer clear of problems and understand the meta- influences in his own scientific work. (shrink)

Chervenak and McCullough, authors of the most acknowledged ethical framework for maternal–fetal surgery, rely on the ‘ethical–obstetrical’ concept of the fetus as a patient in order to determine what is morally owed to fetuses by both physicians and the women who gestate them in the context of prenatal surgery. In this article, we reconstruct the argumentative structure of their framework and present an internal criticism. First, we analyse the justificatory arguments put forward by the authors regarding the moral status of (...) the fetus qua patient. Second, we discuss the internal coherence and consistency of the moral obligations those authors derive from that concept. We claim that some of the dilemmas their approach is purported to avoid, such as the debate about the independent moral status of the fetus, and the foundation of the moral obligations of pregnant women (towards the fetuses they gestate) are not, all things considered, avoided. Chervenak and McCullough construct the obligations of physicians as obligations towards entities with equal moral status. But, at the same time, they assume that the woman has an independent moral status while the moral status of the fetus is dependent on the decision of the woman to present it to a physician for care. According to the logic of their own argumentation, Chervenak and McCullough implicitly admit a different moral status of the woman and the fetus, which will lead to different ascription of duties of the physician than those they ascribed. (shrink)

This article focuses on maternal-fetal surgery (MFS) and on the concept of clinical equipoise that is a widely accepted requirement for conducting randomized controlled trials (RCT). There are at least three reasons why equipoise is unsuitable for MFS. First, the concept is based on a misconception about the nature of clinical research and the status of research subjects. Second, given that it is not clear who the research subject/s in MFS is/are, if clinical equipoise is to be used as a (...) criterion to test the ethical appropriateness of RCT, its meaning should be unambiguous. Third, because of the multidisciplinary character of MFS, it is not clear who should be in equipoise. As a result, we lack an adequate criterion for the ethical review of MFS protocols. In our account, which is based on Chervenak and McCullough's seminal work in the field of obstetric ethics, equipoise is abandoned. and RCT involving MFS can be ethically initiated when a multidisciplinary ethics review board (ERB), having an evidence-based assessment of the risks involved, is convinced that the value of answering the research hypothesis, for the sake of the health interests of future pregnant women carrying fetuses with certain congenital birth defects, justifies the actual risks research participants might suffer within a set limit of low/manageable. (shrink)

BackgroundObtaining informed consent for intravenous thrombolysis in acute ischemic stroke can be challenging, and little is known about if and how the informed consent procedure is performed by neurologists in clinical practice. This study examines the procedure of informed consent for intravenous thrombolysis in acute ischemic stroke in high-volume stroke centers in the Netherlands.MethodsIn four high volume stroke centers, neurology residents and attending neurologists received an online questionnaire concerning informed consent for thrombolysis with tissue-type plasminogen activator (tPA). The respondents were (...) asked to report their usual informed consent practice for tPA treatment and their considerations on whether informed consent should be obtained.ResultsFrom the 203 invited clinicians, 50% (n = 101) completed the questionnaire. One-third of the neurology residents (n = 21) and 21% of the neurologists (n = 8) reported that they always obtain informed consent for tPA treatment. If a patient is not capable of providing informed consent, 30% of the residents (n = 19) reported that they start tPA treatment without informed consent. In these circumstances, 53% of the neurologists (n = 20) reported that the resident under their supervision would start tPA treatment without informed consent. Most neurologists (n = 21; 55%) and neurology residents (n = 45; 72%) obtained informed consent within one minute. None of the respondents used more than five minutes for informed consent. Important themes regarding obtaining informed consent for treatment were patients’ capacity, and medical, ethical and legal considerations.ConclusionThe current practice of informed consent for thrombolysis in acute ischemic stroke varies among neurologists and neurology residents. If informed consent is obtained, most clinicians stated to obtain informed consent within one minute. In the future, a shortened information provision process may be applied, making a shift from informed consent to informed refusal, while still considering the patient’s capacity, stroke severity, and possible treatment delays. (shrink)

This article introduces a new hybrid intake procedure developed for posttraumatic stress disorder (PTSD) screening, which combines an automated textual assessment of respondents’ self-narratives and item-based measures that are administered consequently. Text mining technique and item response modeling were used to analyze long constructed response (i.e., self-narratives) and responses to standardized questionnaires (i.e., multiple choices), respectively. The whole procedure is combined in a Bayesian framework where the textual assessment functions as prior information for the estimation of the PTSD latent trait. (...) The purpose of this study is twofold: first, to investigate whether the combination model of textual analysis and item-based scaling could enhance the classification accuracy of PTSD, and second, to examine whether the standard error of estimates could be reduced through the use of the narrative as a sort of routing test. With the sample at hand, the combination model resulted in a reduction in the misclassification rate, as well as a decrease of standard error of latent trait estimation. These findings highlight the benefits of combining textual assessment and item-based measures in a psychiatric screening process. We conclude that the hybrid test design is a promising approach to increase test efficiency and is expected to be applicable in a broader scope of educational and psychological measurement in the future. (shrink)

PurposeThe purpose of this study is to describe the implementation and outcomes of an Eye Movement and Desensitization Reprocessing treatment-program for women with posttraumatic stress disorder after childbirth.MethodsA prospective cohort-study with pre- and post-measurements was carried out in the setting of an academic hospital in the Netherland. Included were women who gave birth to a living child at least 4 weeks ago, with a diagnosis of PTSD, or severe symptoms of PTSD combined with another psychiatric diagnosis. All received up to (...) 8 sessions of EMDR-therapy. The posttraumatic stress disorder Checklist for DSM-5 was administered before and after treatment. Trauma history was assessed before treatment with the Life Events Checklist for the DSM-5, the Childhood Trauma Questionnaire and the Childbirth Perception Scale. Descriptive statistics were used.ResultsForty-four women were referred, 26 met the inclusion criteria. After treatment, none of the women met the criteria for diagnosis of PTSD after on average 5 weekly sessions of EMDR- therapy. These outcomes are promising, as they were achieved in women with relatively high levels of psychiatric comorbidity and high rates of previous mental health treatment.ConclusionImplementing an EMDR-treatment program for women with PTSD after childbirth in the setting of an academic hospital is feasible and effective. Key factors for success include a close collaboration between the relevant hospital departments and a thorough case conceptualization addressing the etiology of the PTSD. (shrink)

Libraries provide access to large amounts of library metadata. Unfortunately, many libraries only offer textual interfaces for searching and browsing their holdings. Visualizations provide simpler, faster, and more efficient ways to navigate, search and study large quantities of metadata. This paper presents GlamMap, a visualization tool that displays library metadata on an interactive, computer-generated geographic map. We provide detailed discussion of how GlamMap benefits the work of librarians and researchers. We show how geographic representations help librarians to perform tasks such (...) as collection assessment and how geographic information helps researchers to identify important scientific resources. (shrink)

This paper investigates conceptions of explanation, teleology, and analogy in the works of Immanuel Kant (1724-1804) and Georges Cuvier (1769-1832). Richards (2000, 2002) and Zammito (2006, 2012, 2018) have argued that Kant’s philosophy provided an obstacle for the project of establishing biology as a proper science around 1800. By contrast, Russell (1916), Outram (1986), and Huneman (2006, 2008) have argued, similar to suggestions from Lenoir (1989), that Kant’s philosophy influenced the influential naturalist Georges Cuvier. In this article, I wish to (...) expand on and further the work of Russell, Outram, and Huneman by adopting a novel perspective on Cuvier and considering (a) the similar conceptions of proper science and explanation of Kant and Cuvier, and (b) the similar conceptions of the role of teleology and analogy in the works of Kant and Cuvier. The similarities between Kant and Cuvier show, contrary to the interpretation of Richards and Zammito, that some of Kant’s philosophical ideas, whether they derived from him or not, were fruitfully applied by some life scientists who wished to transform life sciences into proper sciences around 1800. However, I also show that Cuvier, in contrast to Kant, had a workable strategy for transforming the life sciences into proper sciences, and that he departed from Kant’s philosophy of science in crucial respects. (shrink)

Introduction to collection of papers by group of scholars and ACO missionaries brought together to discuss the developments within the ACO over the past hundred years during a conference that was organised by Dr Wilbert van Saane of Haigazian University in January 2021. I will briefly summarise what strikes me as characteristic of the ACO on the basis of these articles, and conclude with a discussion of how this may contribute to further reflection in Mission Studies and World Christianity.

There is an increasing body of literature proposing to include animal welfare in the United Nations Sustainable Development Agenda. The main argument is the potential positive effect that improving the welfare of animals could have over the health and welfare of humans. However, recent literature suggests that the welfare interests of animals should also be considered. Based on these premises, an analysis of the practical implications of including animal welfare in the United Nations Sustainable Development Goals is granted. The aim (...) of this study is to address this by applying the case of animals in the agriculture and aquaculture systems. Animal farming inherently affects the welfare of a substantial number of sentient animals while, the welfare of farmed animals has been connected to human wellbeing and several environmental issues. The study highlights the feasibility of incorporating the welfare of farmed animals into a future version of the SDGs. It does so by developing a model based on a set of human-focused (anthropocentric) and animal-focused (sentientistic) targets for each of the 17 goals. It has been argued that expanding the scope of the SDGs from anthropocentrism to sentientism creates a synergy between human and animal welfare and, on top of that, is progress towards sustainability. (shrink)

Ernst Mayr argued that the emergence of biology as a special science in the early nineteenth century was possible due to the demise of the mathematical model of science and its insistence on demonstrative knowledge. More recently, John Zammito has claimed that the rise of biology as a special science was due to a distinctive experimental, anti-metaphysical, anti-mathematical, and anti-rationalist strand of thought coming from outside of Germany. In this paper we argue that this narrative neglects the important role played (...) by the mathematical and axiomatic model of science in the emergence of biology as a special science. We show that several major actors involved in the emergence of biology as a science in Germany were working with an axiomatic conception of science that goes back at least to Aristotle and was popular in mid-eighteenth-century German academic circles due to its endorsement by Christian Wolff. More specifically, we show that at least two major contributors to the emergence of biology in Germany—Caspar Friedrich Wolff and Gottfried Reinhold Treviranus—sought to provide a conception of the new science of life that satisfies the criteria of a traditional axiomatic ideal of science. Both C.F. Wolff and Treviranus took over strong commitments to the axiomatic model of science from major philosophers of their time, Christian Wolff and Friedrich Wilhelm Joseph Schelling, respectively. The ideal of biology as an axiomatic science with specific biological fundamental concepts and principles thus played a role in the emergence of biology as a special science. (shrink)

A shift towards more environmentally friendly and socially responsible food systems is a key step in the achievement of global sustainable development goals. To obtain significant results, however, it is essential to find participative ways to frame food sustainability objectives, so they can speak to a wide array of actors of change. This article addresses the promising potential of empowering actors across the food system to make a shift in their food choices, by facilitating the association of food sustainability values (...) with contemporary moral issues. In this context, a conceptual framework for a transition towards food sustainability is proposed, based upon the concept of the moral circle. This approach transcends the human-centred methods enacted in traditional sustainable development agendas, offering an alternative with a more holistic perspective. It is expected that emphasising moral reflection around sustainability might encourage societal participation in the creation of sustainable, fair and healthier food systems. (shrink)

A shift towards more environmentally friendly and socially responsible food systems is a key step in the achievement of global sustainable development goals. To obtain significant results, however, it is essential to find participative ways to frame food sustainability objectives, so they can speak to a wide array of actors of change. This article addresses the promising potential of empowering actors across the food system to make a shift in their food choices, by facilitating the association of food sustainability values (...) with contemporary moral issues. In this context, a conceptual framework for a transition towards food sustainability is proposed, based upon the concept of the moral circle. This approach transcends the human-centred methods enacted in traditional sustainable development agendas, offering an alternative with a more holistic perspective. It is expected that emphasising moral reflection around sustainability might encourage societal participation in the creation of sustainable, fair and healthier food systems. (shrink)

Kant’s views on animals have received much attention in recent years. According to some, Kant attributed the capacity for objective perceptual awareness to non-human animals, even though he denied that they have concepts. This position is difficult to square with a conceptualist reading of Kant, according to which objective perceptual awareness requires concepts. Others take Kant’s views on animals to imply that the mental life of animals is a blooming, buzzing confusion. In this article I provide a historical reconstruction of (...) Kant’s views on animals, relating them to eighteenth-century debates on animal cognition. I reconstruct the views of Buffon and Reimarus and show that (i) both Buffon and Reimarus adopted a conceptualist position, according to which concepts structure the cognitive experience of adult humans, and (ii) that both described the mental life of animals as a blooming, buzzing confusion. Kant’s position, I argue, is virtually identical to that of Reimarus. Hence Kant’s views on animals support a conceptualist reading of Kant. The article further articulates the historical antecedents of the Kantian idea that concepts structure human cognitive experience and provides a novel account of how the ideas of similarity and difference were conceptualized in eighteenth-century debates on animal cognition. (shrink)

The paper uses the formalism of indexed categories to recover the proof of a standard final coalgebra theorem, thus showing existence of final coalgebras for a special class of functors on finitely complete and cocomplete categories. As an instance of this result, we build the final coalgebra for the powerclass functor, in the context of a Heyting pretopos with a class of small maps. This is then proved to provide models for various non-well-founded set theories, depending on the chosen axiomatisation (...) for the class of small maps. (shrink)

This article explains Kant’s claim that sciences must take, at least as their ideal, the form of a ‘system’. I argue that Kant’s notion of systematicity can be understood against the background of de Jong & Betti’s Classical Model of Science (2010) and the writings of Georg Friedrich Meier and Johann Heinrich Lambert. According to my interpretation, Meier, Lambert, and Kant accepted an axiomatic idea of science, articulated by the Classical Model, which elucidates their conceptions of systematicity. I show that (...) Kant’s critique of the mathematical method is compatible with his adherence to this axiomatic conception of science. I further show that systematicity furthers traditionally accepted logical ideals of scientific knowledge, which explains why Meier and Kant think that sciences must be ‘systematic’. (shrink)

We argue that an adequate treatment of verb phrase anaphora must depart in two major respects from the standard approaches. First of all, VP anaphors cannot be resolved by simply identifying the anaphoric VP with an antecedent VP. The resolution process must establish a syntactic/semantic parallelism between larger units that the VPs occur in. Secondly, discourse structure has a significant influence on the reference possibilities of VPA. This influence must be accounted for. We propose a treatment which meets these requirements. (...) It builds on a discourse grammar which characterizes discourse cohesion by means of a syntactic/semantic matching procedure which recognizes parallel structures in discourse. It turns out that this independently motivated procedure yields the resolution of VPA as a side effect. (shrink)

This paper analyzes the historical context and systematic importance of Kant's hypothetical use of reason. It does so by investigating the role of hypotheses in Kant's philosophy of science. We first situate Kant’s account of hypotheses in the context of eighteenth-century German philosophy of science, focusing on the works of Wolff, Meier, and Crusius. We contrast different conceptions of hypotheses of these authors and elucidate the different theories of probability informing them. We then adopt a more systematic perspective to discuss (...) Kant's idea that scientific hypotheses must articulate real possibilities. We argue that Kant's views on the intelligibility of scientific hypotheses constitute a valuable perspective on scientific understanding and the constraints it imposes on scientific rationality. (shrink)

We introduce constructive and classical systems for nonstandard arithmetic and show how variants of the functional interpretations due to Gödel and Shoenfield can be used to rewrite proofs performed in these systems into standard ones. These functional interpretations show in particular that our nonstandard systems are conservative extensions of E-HAω and E-PAω, strengthening earlier results by Moerdijk and Palmgren, and Avigad and Helzner. We will also indicate how our rewriting algorithm can be used for term extraction purposes. To conclude the (...) paper, we will point out some open problems and directions for future research, including some initial results on saturation principles. (shrink)

Within eighteenth-century debates on animal cognition we can distinguish at least three main theoretical positions: (i) Buffon’s mechanism, (ii) Reimarus’ theory of instincts, and (iii) the sensationalism of Condillac and Leroy. In this paper, I adopt a philosophical perspective on this debate and argue that in order to fully understand the justification Buffon, Reimarus, Condillac, and Leroy gave for their respective theories, we must pay special attention to the theoretical virtues these naturalists alluded to while justifying their position. These theoretical (...) virtues have received little to no attention in the literature on eighteenth-century animal cognition, but figure prominently in the justification of the mechanist, instinctive, and sensationalist theories of animal behavior. Through my philosophical study of the role of theoretical virtues in eighteenth-century debates on animal cognition, we obtain a deeper understanding of how theoretical virtues were conceptualized in eighteenth-century science and how they influenced the justification of theories of animal cognition. (shrink)

In the present paper I investigate the role that analogy plays in eighteenth-century biology and in Kant’s philosophy of biology. I will argue that according to Kant, biology, as it was practiced in the eighteenth century, is fundamentally based on analogical reflection. However, precisely because biology is based on analogical reflection, biology cannot be a proper science. I provide two arguments for this interpretation. First, I argue that although analogical reflection is, according to Kant, necessary to comprehend the nature of (...) organisms, it is also necessarily insufficient to fully comprehend the nature of organisms. The upshot of this argument is that for Kant our understanding of organisms is necessarily limited. Second, I argue that Kant did not take biology to be a proper science because biology was based on analogical arguments. I show that Kant stemmed from a philosophical tradition that did not assign analogical arguments an important justificatory role in natural science. Analogy, according to this conception, does not provide us with apodictically certain cognition. Hence, sciences based on analogical arguments cannot constitute proper sciences. (shrink)

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.

The present study examined the costs and benefits of native language similarity for non-native vocabulary learning. Because learning a second language is difficult, many learners start with easy words that look like their native language to jumpstart their vocabulary. However, this approach may not be the most effective strategy in the long-term, compared to introducing difficult L2 vocabulary early on. We examined how L1 orthographic typicality affects pattern learning of novel vocabulary by teaching English monolinguals either Englishlike or Non-Englishlike pseudowords (...) that contained repeated orthographic patterns. We found that overall, the first words that individuals learned during initial acquisition influenced which words they acquired later. Specifically, learning a new word in one session made it easier to acquire an orthographically similar word in the next session. Similarity among non-native words interacted with native language similarity, so that words that looked more like English were easier to learn at first, but they were less effective at influencing later word learning. This demonstrates that although native language similarity has a beneficial effect early on, it may reduce learners' ability to benefit from non-native word patterns during continued acquisition. This surprising finding demonstrates that making learning easier may not be the most effective long-term strategy. Learning difficult vocabulary teaches the learner what makes non-native words unique, and this general wordform knowledge may be more valuable than the words themselves. We conclude that native language similarity modulates new vocabulary acquisition and that difficulties during learning are not always to be avoided, as additional effort early on can pay later dividends. (shrink)

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)

Recently, the second author, Briseid, and Safarik introduced nonstandard Dialectica, a functional interpretation capable of eliminating instances of familiar principles of nonstandard arithmetic—including overspill, underspill, and generalizations to higher types—from proofs. We show that the properties of this interpretation are mirrored by first-order logic in a constructive sheaf model of nonstandard arithmetic due to Moerdijk, later developed by Palmgren, and draw some new connections between nonstandard principles and principles that are rejected by strict constructivism. Furthermore, we introduce a variant of (...) the Diller–Nahm interpretation with two different kinds of quantifiers, similar to Hernest’s light Dialectica interpretation, and show that one can obtain nonstandard Dialectica by weakening the computational content of the existential quantifiers—a process called herbrandization. We also define a constructive sheaf model mirroring this new functional interpretation, and show that the process of herbrandization has a clear meaning in terms of these sheaf models. (shrink)

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)

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)

In this interview with Jan Hendrik van den Berg, the Dutch phenomenologist and psychiatrist addresses the origins of his work, his most significant influences, and the purpose of metabletic phenomenology in the modern age. In the course of the interview. Dr. Van den Berg provides a basic overview of his work, and highlights the central finding of his metabletic analyses: a loss of wonder before nature, which results from the more fundamental loss of genuine spirituality in the modern (...) world. (shrink)

In this paper, we analyse conceptions of induction and certainty in Wolff and Crusius, highlighting their competing conceptions of physics. We discuss (i) the perspective of Wolff, who assigned induction an important role in physics, but argued that physics should be an axiomatic science containing certain statements, and (ii) the perspective of Crusius, who adopted parts of the ideal of axiomatic physics but criticized the scope of Wolff’s ideal of certain science. Against interpretations that take Wolff’s proofs in physics to (...) be based on empirical statements that are probable, we show how inductively established statements, coupled with assumptions concerning the uniformity of nature, can be certain according to Wolff. We examine Crusius’ little known work on physics and show that he attacked Wolff, arguing that many statements of physics are probable. We provide a discussion of the reception of methodological rules similar to Newton’s Regulae Philosophandi, discussing different interpretations of such rules. We conclude by briefly hinting at how the debate between Wolff and Crusius provides historical context for understanding Kant’s philosophy of natural science. (shrink)