1. Parsing Categories of Belief Why Early Modern M&E divides belief into two types: Sensory & Mathematical

2. Ways to Categorize Beliefs According to subject matter (e.g., theological, scientific, aesthetic, political, practical, philosophical, anthropological, etc.) According to evaluative criteria (e.g., stupid, crazy, misguided, well-founded, hard-headed, logical, rational, self-evident, etc.) According to the means by which the beliefs are formed (e.g., a posteriori/sensory beliefs, a priori/mathematico-logical beliefs)

3. Why the Early Moderns Chose Door #3 Early modern thinkers had the following insight: given that all our beliefs about ourselves, our minds, and the world around us, are built upon a foundation if ideas (i.e., their content is produced by an act of judgment that combines ideas into the form of judgments/propositions/ assertions), if we knew how we come to have all the different kinds of ideas we in fact do have, then we would then be able to answer the primary question in epistemology: “how are justified true beliefs possible/actual?” AND, answering that question would allow us to answer the main question of metaphysics: “What exists, and what is the nature of its existence [i.e., how is the determinable determined?]?

4. Thus, Descartes, Locke, Leibniz, Hume, Berkeley, Kant, Malebranche, Wolff, Reid, Rousseau, et al., thought that first philosophy = the pursuit of a true theory of mind/mental content. It is for this reason that my question (“What are the two kinds of beliefs that are required in order to pursue the scientific study of nature?”) is answered by Early Modern Philosophers this way: 1) sensory beliefs, and 2) mathematical beliefs.

5. And why is access to the formation of true instances of these two kinds of beliefs a necessary condition of doing the kind of natural science being pursued by Newton, Galileo, Brahe, LaPlace, et al.? Because that kind of science, and any kind of science based on the scientific method, depends on 1) formulating hypotheses [often using mathematical descriptions to express them], which are tested using 2) observations [entirely available to human minds by means of sense perception] to explain natural phenomena associated with those observations.

6. The Primary Early Modern Philosophical Project To discover a model of mind that offers the correct etiology of all ideas used to formulate true beliefs about 1) sensory experience, and 2) mathematical propositions and reasoning. It was believed that this model of mind would provide a foundation for the primary assumptions on which any science of nature that tests theory on the basis of observation is grounded. This model will establish how, where, when and why some of our ideas accurately represent the world outside our minds, and how we can be sure that our beliefs based on these ideas also reflect the objective state of affairs in that world.

7. Three Approaches to this Project Rationalism (heyday: 1640-1700) Proponents: Descartes, Spinoza, Leibniz, Arnauld, Malebranche, and Wolff. Empiricism (heyday: 1690-1780) Proponents: Locke, Berkeley, Hume, Hobbes, and Reid. Transcendental Idealism (heyday: 1780-1800) Proponents: Kant (and also, Fichte)

8. What Distinguuishes Each Approach Rationalism—patterns philosophical knowledge after mathematical beliefs: the same rigorous order of reasons and consequences, the same certainty and independence of all contingency, that could be found in Euclid, these thinkers sought to bring to philosophy. Basic principle: innate ideas available to the mind by means of pure reason are more likely to reflect the character of the world as it is, and hence reason is the proper faculty of knowledge. Empiricism—patterns philosophical knowledge after empirical beliefs. Basic principle: only beliefs using ideas drawn from sense perception can be trusted to represent the world accurately, since sense perception is our only means of access to the world we hope to comprehend and explain, and hence, sense perception is the proper faculty of knowledge. Transcendental Idealism—both traditions make a common mistake (assuming that there is only one faculty of knowledge) while promoting one truth missing from its competitor (both reason and sense perception are necessary if knowledge of the objects of experience is to be possible), and hence, experience, and so knowledge of nature, depends on: sense perception + structures of the mind.