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The Mathematical Origins of Nineteenth-Century Algebra of Logic

Volker Peckhaus

in The Development of Modern Logic

This chapter discusses the complex conditions for the emergence of 19th-century symbolic logic. The main scope will be on the mathematical motives leading to the interest in logic; the philosophical ... More

This chapter discusses the complex conditions for the emergence of 19th-century symbolic logic. The main scope will be on the mathematical motives leading to the interest in logic; the philosophical context will be dealt with only in passing. The main object of study will be the algebra of logic in its British and German versions. Special emphasis will be laid on the systems of George Boole (1815–1864) and above all of his German follower Ernst Schröder (1841–1902).Less

Introduction

Leila Haaparanta

in The Development of Modern Logic

This introductory chapter begins with a discussion of the concept of logic, focusing on Aristotelian logic and symbolic logic. It then discusses the concept of modern logic, and the uses of the terms ... More

This introductory chapter begins with a discussion of the concept of logic, focusing on Aristotelian logic and symbolic logic. It then discusses the concept of modern logic, and the uses of the terms “logic,”, “philosophical logic”, and “philosophy of logic.”.Less

Reasoning and Belief in Victorian Mathematics

Daniel J. Cohen

in The Organisation of Knowledge in Victorian Britain

This chapter focuses on the progress of mathematics in the nineteenth century. British mathematicians of this period showed interest in the formal aspects of mathematics, particularly in symbolic ... More

This chapter focuses on the progress of mathematics in the nineteenth century. British mathematicians of this period showed interest in the formal aspects of mathematics, particularly in symbolic logic. Bertrand Russell and Alfred North Whitehead were among the most highly influential figures in Victorian mathematical circles due to their wide-ranging thought and institutional positions. Principia Mathematica (1910–1913), in which Russell and Whitehead equated logic and mathematics at the deepest level possible, was a culmination of the innovative mathematical research of the Victorian age.Less

Logic and Intuition

Michael Heim

in The Metaphysics of Virtual Reality

Infomania does not merely place additional tools at the tip of a man's fingertips; it builds a new environment and alters his psychic framework. The chapter argues that thinking in front of a ... More

Infomania does not merely place additional tools at the tip of a man's fingertips; it builds a new environment and alters his psychic framework. The chapter argues that thinking in front of a computer is different from thinking in front of a pencil and paper. With the magnitude of information that it can deliver, the computer system must operate under a search system which allows a person to scan through the voluminous computer files with tremendous efficiency. The Boolean logic is one of the most applied systems in computer search technology. The gains of infomania however comes at the price of a researcher's direct involvement with things where he is alienated and abstracted from the subject matters he is trying to explore. The chapter juxtaposes the alienating logic of infomania to the intuitive encounters that a person experiences through the reading of books.Less

Logic

Amirouche Moktefi

in The Mathematical World of Charles L. Dodgson (Lewis Carroll)

This chapter discusses Dodgson’s work on syllogisms (a topic that can be traced back to Aristotle and Ancient Greece) and how to solve them systematically using a marked board and some counters. His ... More

This chapter discusses Dodgson’s work on syllogisms (a topic that can be traced back to Aristotle and Ancient Greece) and how to solve them systematically using a marked board and some counters. His method is explained in detail in this chapter. Dodgson introduced it in his Game of Logic, which he used to teach syllogisms to children, and which he then developed in his Symbolic Logic, Part I. The rest of the chapter is concerned with further work that Dodgson carried out, but which was not published at the time because of his premature death at the age of 65.Less

Algebra: Symbolic Logic and the Logic of Symbolism

Andrea Henderson

in Algebraic Art: Mathematical Formalism and Victorian Culture

The difference between the transcendent Coleridgean symbol and the unreliable conventional symbol was of explicit concern in Victorian mathematics, where the former was aligned with Euclidean ... More

The difference between the transcendent Coleridgean symbol and the unreliable conventional symbol was of explicit concern in Victorian mathematics, where the former was aligned with Euclidean geometry and the latter with algebra. Rather than trying to bridge this divide, practitioners of modern algebra and the pioneers of symbolic logic made it the founding principle of their work. Regarding the content of claims as a matter of “indifference,” they concerned themselves solely with the formal interrelations of the symbolic systems devised to represent those claims. In its celebration of artificial algorithmic structures, symbolic logician Lewis Carroll’s Sylvie and Bruno dramatizes the power of this new formalist ideal not only to revitalize the moribund field of Aristotelian logic but also to redeem symbolism itself, conceived by Carroll and his mathematical, philosophical, and symbolist contemporaries as a set of harmonious associative networks rather than singular organic correspondences.Less

The Erotic Ontology of Cyberspace

Michael Heim

in The Metaphysics of Virtual Reality

How does the metaphysical laboratory fit into human inquiry as a whole? What status do electronic worlds have within the entire range of human experience? What perils haunt the metaphysical origins ... More

How does the metaphysical laboratory fit into human inquiry as a whole? What status do electronic worlds have within the entire range of human experience? What perils haunt the metaphysical origins of cyberspace? These are some of the questions that this chapter poses. By exploring various philosophies, the chapter seeks to give an account of the way entities exist in cyberspace and their ontological status. Describing a human's relationship with computers, the chapter introduces the concept of Eros where man searches for a home for his heart and mind and becomes spiritually dependent upon machines. In the end, we are faced with an amoral indifference to human relationships, an online existence that is intrinsically ambiguous. The chapter advises us that while we enter into the future of cyberspace, we must not lose touch of the body people who remain rooted in the energies of the earth.Less

Symbolic Logic on the Social Plane of Alice’s Adventures in Wonderland

Anna Kornbluh

in The Order of Forms: Realism, Formalism, and Social Space

This chapter asks what a nonsense novel reveals about realism. It shows that Wonderland’s overarching concerns with sovereignty, execution, and social ordering cohere with its commitment to nonsense, ... More

This chapter asks what a nonsense novel reveals about realism. It shows that Wonderland’s overarching concerns with sovereignty, execution, and social ordering cohere with its commitment to nonsense, semantic games, and the development of symbolic logic. Presenting symbolic logic as a type of political theory elaborating the minima of social cohesion, the book does not merely think about logic. It constructs its own form as a symbolic logicization—a reduction to the letter—of literary realism. Along the way, the analysis considers photography and graphic textual design. Emulating the distinct form of its subject matter, this chapter proceeds through a series of syllogisms.Less

Intelligent Systems

William B. Rouse

in Computing Possible Futures

This chapter addresses the ways in which human intelligence in routine and partly routine jobs can be augmented rather than replaced. The design of aids should begin with defining the user ... More

This chapter addresses the ways in which human intelligence in routine and partly routine jobs can be augmented rather than replaced. The design of aids should begin with defining the user experience, proceed to designing the user interface to support this experience, and then focus on the enabling technologies. Intelligent aids should be considered for enhancing human performance; the extent of success will depend on the domain of application and the potential performance of the aid. Intelligent aids are inherently model based, drawing upon symbolic logic, mathematical paradigms, and/or statistical models; understanding the underlying modeling assumptions is key to establishing confidence in and trust of such aids. Intelligent systems technology has much promise but also many perils that warrant attention; its prospects depend on well-reasoned strategies for development and adoption.Less

Introduction

Brendan Dooley (ed.)

in The Continued Exercise of Reason: Public Addresses by George Boole

This introductory chapter provides an overview of the life and work of George Boole. Boole is known for developing the system of algebraic logic, which eventually found an unexpected engineering ... More

This introductory chapter provides an overview of the life and work of George Boole. Boole is known for developing the system of algebraic logic, which eventually found an unexpected engineering application in the design of switching circuits. He was also an early advocate of the mass distribution of knowledge, using the methods at his disposal in early Victorian times. In the classroom and lecture hall, he interpreted the results of recent discoveries and debates originating among specialists in numerous fields—history, psychology, ethnography, and much else—and communicated them to a broad audience. Less known and therefore less appreciated is Boole's role in the history of the making and organization of knowledge. A better understanding of this feature, may eventually provoke a more thoroughgoing reappraisal of the whole figure.Less

The Peculiar Codex Jerusalem 22

in All the Names of the Lord: Lists, Mysticism, and Magic

This chapter explores Horus Apollo's Book on the Hieroglyphics. The subject is the symbolic logic behind the Egyptian script. The passage itself introduces the peculiar cultural association between ... More

This chapter explores Horus Apollo's Book on the Hieroglyphics. The subject is the symbolic logic behind the Egyptian script. The passage itself introduces the peculiar cultural association between the world in its entirety and the sacred Cynocephalus Hamadryas, the dog-headed baboon whom the Egyptians associated with the underworld, the spirits of the dead, and Thoth, the patron god of wisdom, magic, and writing. The common ground on which this unexpected association rests, is—yet again—the number seventy two. Moreover, the analogy does not immediately lend itself to perfect homology: seventy two is a measure of time in the cynocephalus myth, while it serves clearly as a spatial matrix for the division of the world. This correspondence was essential to the Egyptians, so much so that they based on it one of their central hieroglyphs for writing the cosmos.Less