This chapter presents a portrait of study and teaching at the Faculty of Arts in Paris during the first half-century of the university's existence: from enrolment under a master to obtaining a licence, entering the corporation of the Magistri Artium and, eventually, enrolment in one of the higher faculties (theology, canon law or medicine).

This chapter discusses the work of twelfth-century theologians in Paris who laid the foundations for the development of theology as a discipline in the university. These thinkers explored the characteristics and limits of the discourse on God in theological treatises and summae, which employed increasingly sophisticated technical terminology drawn in part from grammar, logic, and rhetoric.

This chapter traces the development of a number of Trinitarian issues throughout the second half of the twelfth century - the classification of theological language, the debate about why we can say 'God begot God' but not 'essence begot essence', and the definition of the personal properties - and show how they shape Lateran IV and continue thereafter. Finally, the chapter indicates some new approaches and areas of focus among theologians writing after the council.

This section offers a review and frequently asked questions regarding ethnography in international business.

In this introduction, we first describe the contents of the Summa Logicae in some detail, situating the work in the larger context of medieval logical texts of the thirteen and fourteenth centuries and explaining why it occupies pride of place in Ockham’s philosophical project. Second, we argue that the Summa Logicae was most likely composed in Avignon between 1324 and 1328 contrary to the accepted view that Ockham wrote it in London over the summer of 1323. Third, we trace the legacy of the Summa Logicae from its first reception in Oxford and Paris in the 1330s, into the Parisian controversies of the 1330s and 1340s, and its dissemination further into Europe over the course of the next century or so. We end this history by noting the 1974 publication of the modern critical edition of the Summa Logicae, which was an enormously significant landmark in Ockham studies.

I first present a model of Ockham’s semantics that puts modality front and center (it is a presheaf semantics over a branching timeline). I then show what kinds of statements about language Ockham’s semantics supports. Finally, I discuss how Ockham’s semantics fares in light of Tarski’s and Montague’s paradoxes.

Chapter 4 introduces students to logical values, a simple data type that can only take values of one and zero. While simple, logical values are essential components of program flow (conditionals, loops) which they will learn next, so mastery of them is essential before tackling those more difficult tools. Logical values can also be used to subset arrays according to their values, making them critical for complex data management tasks. Students new to programming are often unfamiliar with operations that create logical values, or which operate on logical values, so this chapter provides detailed explanations and examples to familiarize students with this new and valuable data type.

Heidegger’s subordination of reason to “care” in Being and Time has exposed him to the charge of irrationalism. Against this view, I argue that Being and Time offers a “normativity-first” account in which reason, as reason-giving (logon didonai), is an ineluctable demand constitutive of authentic selfhood. Examining Heidegger’s rejection of the neo-Kantian equation of reason with logic in his 1929 Kantbuch, I explain the threads that connect what Heidegger calls “pure sensible reason” to his extensive phenomenological account, in Being and Time, of the “everyday” and “authentic” modes of Dasein’s care-structure. As authenticity’s discursive mode, the “call of conscience” is Dasein’s portal into normative space. As the essay “On the Essence of Ground” makes plain, Dasein’s response to the call involves answerability for what it holds to be best in its practical life, hence reason-giving. Such an origin of reason contrasts with rationalism only in eschewing any principle of sufficient reason.

This chapter examines the issue of the “logic” underlying Hegel’s exposition of the “concept of nature.” Given the systematic structure of Hegel’s Philosophy of Nature, which is positioned between the Logic and the Philosophy of Spirit, the problem of the logic guiding the immanent development of nature’s forms as well as the development of the philosophical cognition of them is, in Hegel’s view, a particularly relevant one. At the center of this chapter is the question of whether the “logic of nature” is the same logic presented in the first systematic division of Hegel’s philosophy or rather a modified variant of such a logic. The logic of nature, it argues, combines the determinations of pure speculative thinking (or the determinations of the “absolute idea”) with the specific conditions offered by the concept and by the reality of nature. Crucial to this logic is, first, Hegel’s famous definition of nature as the “idea in the form of otherness.” Such a definition obtains from the end of the Logic, which is be examined in detail, and followed through some crucial passages from the Philosophy of Nature. This chapter follows the development of the logic of nature between two extremes – the “absolute idea” and “spirit” – and concludes with a brief examination of the three syllogisms with which Hegel crowns his encyclopedic system.

Hegel has commonly been ridiculed for views expressed in his 1801 dissertation, On the Orbits of the Planets, in the final pages of which he had adopted a series of numbers from Plato’s Timaeus – a cosmological text earlier taken seriously by Kepler – to account for the ratios of the distances from the sun of the then known six planets of the solar system. While defenders of Hegel have usually toned down the extent of these claims, this chapter argues that Hegel’s reference to Plato’s Pythagorean cosmology must be taken seriously – not as cosmology, however, but as instantiating the logic appropriate for empirically based science. Hegel’s allusion to Plato’s mythologically expressed “syllogism” is consistent with his idea that logic as Plato conceived it allowed its application to the empirical world but that this applicability had been compromised by Aristotle adaptation of it. With the proper grasp of logic’s utilization of the category of “singularity” in its difference to “particularity” – available to Plato but not Aristotle – we can appreciate how, while Kepler’s Laws were empirically based, Newton’s were not as they relied on abstract entities that could not be justified empirically.

This chapter argues that Hegel’s aim in his philosophy of nature is not to compete with natural science but to show that there is reason in nature – reason that science cannot see but that works through the causal processes discovered by science. It considers first the transition from Hegel’s logic to his philosophy of nature and argues that the latter continues the project of the former, starting with reason, or the “absolute idea”, as nature, as sheer externality. It then argues that Hegel derives nature’s categories logically – a priori – from the idea-as-externality, and subsequently matches them with empirical phenomena (rather than constructing categories to fit the latter). It provides an abridged account of Hegel’s physics in order to show how the categories of physical (as opposed to mechanical or organic) nature are derived from one another and how they are embodied in physical phenomena, such as sound, heat, and magnetism. It then concludes by arguing that, contrary to appearances, Hegel’s conception of light complements, and is not simply at odds with, that presented by quantum physics.

This chapter argues that Collingwood’s “logic of question and answer” (LQA) can best be understood in the light of contemporary argumentation theory. Even if Collingwood quite often describes LQA in terms of inner thinking and reasoning, as was still usual in his time, his insistence on the normative (“criteriological”) character of LQA, paired with his attack on the pretensions of psychologists to describe logic (as well as other normative endeavours) in a purely empirical manner, makes clear that LQA has the same aspirations as the rising discipline of formal (mathematical) logic. The concise exposition of the form, content, and application of LQA is supported by references to all the relevant passages in Collingwood’s oeuvre as well as illustrated by means of a concrete example of his way of doing history. Although a recent and still developing discipline, contemporary argumentation theory was born as an attempt to describe and analyze argumentative texts as guided by norms constitutive of our argumentative practices in a way that completely escapes formal logic. It thus provides a place for LQA that has so far been lacking.