This chapter examines Wittgenstein’s Tractatus Logico-Philosophicus and its model of logical context. Against readings that see it as purely anti-contextualist, the chapter shows how logic functions as a form of context in early Wittgenstein. Through biographical and historical context, it demonstrates how the Tractatus emerged from and responded to specific intellectual environments, while setting up the book’s broader argument about parallel developments in anthropology and philosophy.

I draw a contrast between what I call a ‘presentational-phenomenological model of apprehension and ultimate evidence’ – which I attribute to Descartes, Locke and Hume – and Leibniz’s ‘logical-conceptual model of apprehension and ultimate evidence’. Although there are different uses of the word ‘concept’, Leibniz’s model, in my view, illustrates the strictest and best notion of the concept of concepts: one that centrally relies on logic.

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.

A variety of digital devices and circuits are introduced. The use of binary numbers in digital electronics is discussed. The AND, OR, XOR, NOT, NAND, NOR, XNOR, and buffer logic gates are presented, followed by a discussion of implementing logical functions. The Karnaugh map and Boolean algebra are introduced. Different ways of constructing logic gates are presented. Half- and full-adder circuits are developed. Several types of flip-flops are discussed. Building on this foundation, we introduce counters, decoders, shift registers, D/A and A/D converters, multiplexers, demultiplexers, memory arrays, automated processing, programmable logic devices, and digital EM communications.

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

This chapter provides a discussion on multivariate random variables, which are collections of univariate random variables. The chapter discusses how the presence of multiple random variables gives rise to concepts of covariance and correlation, which capture relationships that can arise between variables. The chapter also discussed the multivariate Gaussian model, which is widely used in applications.

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.