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)

I argue that Émilie Du Châtelet breaks with Christian Wolff regarding the scope and epistemological content of the principle of sufficient reason, despite his influence on her basic ontology and their agreement that the principle of sufficient reason has foundational importance. These differences have decisive consequences for the ways in which Du Châtelet and Wolff conceive of science.

For Émilie Du Châtelet, I argue, a central role of the principle of sufficient reason is to discriminate between better and worse explanations. Her principle of sufficient reason does not play this role for just any conceivable intellect: it specifically enables understanding for minds like ours. She develops this idea in terms of two criteria for the success of our explanations: “understanding how” and “understanding why.” These criteria can respectively be connected to the determinateness and contrastivity of explanations. The crucial (...) role Du Châtelet’s principle of sufficient reason plays in identifying good explanations is often overlooked in the literature, or else run together with questions about the justification and likelihood of explanations. An auxiliary goal of the article is to situate Du Châtelet’s principle of sufficient reason with respect to some of the general epistemological and metaphysical commitments of her Institutions de Physique, clarifying how it fits into the broader project of that work. (shrink)

The eighteenth-century German rationalist tradition is, broadly speaking, committed to (what I call) ‘the principle of rational cognition’: the grounded must be rationally cognizable from its sufficient ground. Whereas the prevailing view takes the fundamental challenge to rationalist paradise to stem from the principle of sufficient reason, I argue that it instead stems from this principle: How is it possible to rationally cognize anything at all from its ground? By investigating the opposing responses of two of Leibniz’s most influential immediate (...) successors, Christian Wolff and Christian Crusius, we find no easy way to remain in rationalist paradise. (shrink)

In his 1763 Prize Essay, Kant is thought to endorse a version of formalism on which mathematical concepts need not apply to extramental objects. Against this reading, I argue that the Prize Essay has sufficient resources to explain how the objective reference of mathematical concepts is secured. This account of mathematical concepts’ objective reference employs material from Wolffian philosophy. On my reading, Kant's 1763 view still falls short of his Critical view in that it does not explain the universal, unconditional (...) applicability of mathematical concepts. (shrink)