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In this chapter, Talbott considers how, if human psychology were different, it could have been discovered that autonomy was a burden for human beings and thus that human beings should not be guaranteed autonomy rights. Talbott also explains his metaphysical immodesty with an example of why he believes human rights norms apply universally. Talbott ends with a reminder that, in exercising our judgment and our self-determination, all of us play a role in the bottom-up social-historical process of the discovery and development and implementation of human rights.

Many of the perceived failures of Aristotelian natural philosophy in the late 16th and early 17th centuries were put down to his conception of method. In fact, both defenders of Aristotle and his critics took his method of presentation for a method of discovery, the former trying to establish how it could act as a method of discovery, and the latter replacing it with something new. Bacon attempted to provide a radical alternative to Aristotelianism, though in some respects, it was locked into the same programme as Aristotle. Of more immediate significance were disputes over the hypothetical standing of Copernicanism, disputes in which Kepler and Galileo were major players.

Deliberative democrats offer ‘talk as a decision procedure’. This chapter argues that it is a good ‘discovery procedure’, particularly because of the way it expands the agenda; but talk is a flawed ‘decision procedure’ because ‘path dependency’ can render its outcomes indeterminate or arbitrary. A risk of path dependency is inevitable, insofar as talk is a serial process with dynamic updating, as deliberative democrats want it to be. The best way to capture the benefits of ‘talk as a discovery procedure’, while avoiding the risks of ‘talk as a decision procedure’, is to adopt the rule: ‘first talk, then vote’.

Self-knowledge is supposed to be transforming. Yet ordinarily, knowledge by itself has no effect on the object known. This chapter discusses the phenomenon of first-person authority; ‘the ocular view’ of self-knowledge and an alternative account; and self-knowledge with regard to beliefs and to emotions. It argues that self-discovery often requires a dialectic between the first-person and the third-person points of view in relation to one’s self.

This chapter begins by discussing the meaning of data mining, machine learning, and knowledge discovery. Data mining, machine learning, and knowledge discovery refer to research areas which can all be thought of as outgrowths of multivariate statistics. Their common themes are analysis and interpretation of data, often involving large quantities of data, and even more often resorting to numerical methods. The chapter then presents an incomplete survey of the relevant literature following by an introduction to the Python programming language and the Git code management tool. Next, it describes the surveys and data sets used in examples, plotting and visualizing the data in this book, and how to efficiently use this book.

Reasons why Lewis's critics were not looking for a secret layer of meaning. Reasons why Lewis's critics were not interested in astrology. The extent to which Lewis knew about astronomy. The extent to which he believed in astrology. The circumstances in which the donegalitarian discovery was made.

Chapter 1 presents an overview of the two central activities of the scientific process: discovery (learning new things about the world) and credibility (convincing other researchers that the new findings are correct). According to the linear model of research found in science textbooks, these activities are carried out by dispassionate investigators who are guided at every step by objectivity and logic in accordance with the scientific method. By contrast, everyday practice is far more ambiguous. Researchers are influenced by personality and biography; success requires intuition and passion as well as objectivity and logic. Objectivity ultimately depends on individual researchers transcending their subjectivity by turning to the scientific community with the goal of achieving knowledge that is correct for anyone, anywhere, anytime. Diversity in how scientists think and work enhances scientific exploration. When science education focuses solely on the linear model of research, the excitement and adventure of everyday practice are left out.

Chapter 2 describes discovery in science: exploration at the frontiers of knowledge, becoming first to know something new, and establishing intellectual ownership by making public a discovery claim. Every scientist faces Plato's paradox — the tendency to find that for which one is looking. Noticing the unexpected frequently provides the key to transcending this paradox, and unintended experiments often provide the opportunities. Each researcher has a unique thought style that depends on education, experience, and temperament and influences every aspect of discovery: what to study, what experiments to do, what distinguishes data from background noise. Thought styles explain the researcher's courage to pursue convictions despite community skepticism and experimental difficulties. Discovery transforms the researcher's thought style and world view. Collaboration among researchers and introduction of new research technologies enhance possibilities for this transformation to occur.

Chapter 3 describes how, through the credibility process, the individual's mine, here, now transforms into the community's anyone, anywhere, anytime. The possibility of credible knowledge represents a fundamental belief of science that originates in the repeatability, continuity, and intersubjectivity of everyday life experience. The credibility process involves insiders and outsiders with respect to every discovery claim. Interaction and confrontation of their respective thought styles becomes the dialectic of this process. Discovery claims made credible will be incorporated into and refashion the community's prevailing thought style — the more novel a discovery claim, the greater its potential impact. Novelty also challenges intersubjectivity, and highly novel discovery claims sometimes are received with skepticism by the research community. What appears credible one day may be viewed as error the next, and vice versa, hence the self-correcting feature of science.

This chapter shows how, using basic beliefs, one can go on to make a geometrical discovery by visual means in a non-empirical manner. It focuses on a simple example in order to illustrate the general possibility of what Kant would call synthetic a priori judgements in geometry. It attempts to show how such a judgement can be knowledge. It is commonly asserted that diagrams have no non-redundant role in a proof, even in a geometric proof.

Presentations of geometric proofs are often accompanied by diagrams for quick and easy comprehension. But to many people, it seems clear that diagrammatic reasoning cannot be a part of the argument itself, otherwise it would be prey to the very insecurity that we want to eliminate — insecurity from visual thinking — and so the argument would not be able to justify its conclusion; it would not be a proof. This is the line of thought that most strongly supports the widespread belief that diagrams can have no epistemological role in proof. The main aim of this chapter is to investigate this negative view and the argument for it presented in this book.

This chapter explores the vexed question of visual thinking in analysis. Is visualizing in analysis just a facilitator? Or can it have a non-redundant role in discovering truths of analysis? It is argued that its role in discovery is necessarily highly restricted; but several other important functions are fulfilled by visual means in analysis. The chapter also discusses Rolle's Theorem and Bolzano's Theorem.

This chapter explores the nature and uses of visual thinking with symbols in mathematics. It examines visual symbolic thinking, which is more varied than one might expect, to see how it can contribute to discovery, security, illumination, and generality. It also looks at the roles of symbolic thinking in certain algebraic examples.

This chapter argues that Hegel's return to the standpoint of Kantian criticism turns on his belated recognition that the epistemological demand expressed in that project — namely, that we establish the possibility of metaphysical knowledge in a subjective reflection on our cognitive criteria as a condition of the possibility of metaphysics itself — is grounded in the independence (Selbständigkeit) of the knowing subject. Whereas Hegel earlier rejects distinctively modern epistemological projects — prominently Kant's criticism — as inherently subjectivistic, he comes to recognize that the epistemological demand expressed in these projects cannot be dismissed, insofar as it is backed by a distinctively modern self-discovery, the discovery of the individual subject as self-standing. Kant contributes essentially to this discovery with his articulation of the knowing and acting subject as the author of the highest principles of its epistemic and practical activity. With this recognition, Hegel comes to see that modern dualisms and subjectivism cannot be evaded by returning to an ancient model of epistemology that is yet innocent of these.