The major competing statistical paradigms share a common remarkable but unremarked thread: in many of their inferential applications, different probability interpretations are combined. How this plays out in different theories of inference depends on the type of question asked. We distinguish four question types: confirmation, evidence, decision, and prediction. We show that Bayesian confirmation theory mixes what are intuitively “subjective” and “objective” interpretations of probability, whereas the likelihood-based account of evidence melds three conceptions of what constitutes an “objective” probability.

Kant's reasoning in his special metaphysics of nature is often opaque, and the character of his a priori foundation for Newtonian science is the subject of some controversy. Recent literature on the Metaphysical Foundations of Natural Science has fallen well short of consensus on the aims and reasoning in the work. Various of the doctrines and even the character of the reasoning in the Metaphysical Foundations have been taken to present insuperable obstacles to accepting Kant's claim to ground Newtonian science. (...) Gordon Brittan and Gerd Buchdahl, amongst others, have argued that Kant's stated aims in this case are not to be taken at face value, and that prior ontological commitments play a hidden but central role in Kant's special metaphysics. ;Michael Friedman has shown how Kant's stated aims can be taken seriously with his ingenious reconstruction of the Metaphysical Foundations as a demonstration of the a priori basis for our thinking bodies to be in true motion and in absolute space. However, Friedman does not address the issue of matter theory--despite the importance of the issue to Kant. I argue that a strict reading of both the stated aims and doctrines of the Metaphysical Foundations is possible, since much of Kant's reasoning about the empirical concept of matter can be explained by his views on how the construction of empirical concepts is possible. ;Kant's quasi-mathematical constructions are pivotal in Friedman's interpretation. Constructibility is Kant's criterion of acceptability for the concepts of natural science. Yet Kant notoriously fails to construct the dynamical concept of matter, and accepts this failure with an equally notorious complacency. I argue that Kant's criteria of empirical concept construction, apart from any prior ontological commitments, are enough to generate his views on matter. Kant's failure to construct the requisite concept of matter can be ascribed to a missing law of nature, a law of the relation of forces the discovery of which Kant thought imminent. I conclude that matter theory is central to the Metaphysical Foundations, but that this does not undermine Kant's stated aim of giving the a priori ground of Newtonian science. (shrink)

In Chapter I, I discuss Buchdahl’s view that the possibility of empirical lawlikeness could not have been established in the Principles of the Critique given the differences between transcendental, metaphysical and empirical lawlikeness, and the connection between the faculty of Reason and empirical lawlikeness. I then discuss the general conditions for empirical hypotheses according to Kant, which include the justification of the method by which an empirical hypothesis is obtained and the establishment of the general and specific constructability of the (...) empirical concept. -/- *In Chapter II, I discuss the nature of the general construction of concepts which is treated in the Schematism of the Critique, surveying the views of Pippin, Allison, Bennett and Butts in an effort both to make sense of a difficult part of the Critique and to demonstrate that the Schematism is indeed where Kant demonstrates how the construction of empirical concepts in general is possible. -/- *In Chapter III, I discuss Brittan’s and Butts’ views on the nature of the specific construction of empirical concepts, defending Butts’ interpretation as compatible with Buchdahl’s view that gaps exist between kinds of lawlikeness for Kant and, because of its connection with an interpretation of how metaphysical lawlikeness figures in the Metaphysical Foundations of Natural Science, insofar as it helps us to establish the possibility of empirical lawlikeness and natural science. (shrink)