Volker Peckhaus
- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780195137316
- eISBN:
- 9780199867912
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195137316.003.0018
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
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
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).
Leila Haaparanta (ed.)
- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780195137316
- eISBN:
- 9780199867912
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195137316.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
This book presents a history of modern logic from the Middle Ages through the end of the 20th century. In addition to a history of symbolic logic, the book also examines developments in the ...
More
This book presents a history of modern logic from the Middle Ages through the end of the 20th century. In addition to a history of symbolic logic, the book also examines developments in the philosophy of logic and philosophical logic in modern times. The book begins with chapters on late medieval developments and logic and philosophy of logic from Humanism to Kant. The following chapters focus on the emergence of symbolic logic with special emphasis on the relations between logic and mathematics, on the one hand, and on logic and philosophy, on the other. This discussion is completed by a chapter on the themes of judgment and inference from 1837–1936. The book contains a section on the development of mathematical logic from 1900–1935, followed by a section on main trends in mathematical logic after the 1930s. The book goes on to discuss modal logic from Kant till the late 20th century, and logic and semantics in the 20th century; the philosophy of alternative logics; the philosophical aspects of inductive logic; the relations between logic and linguistics in the 20th century; the relationship between logic and artificial intelligence; and ends with a presentation of the main schools of Indian logic.Less
This book presents a history of modern logic from the Middle Ages through the end of the 20th century. In addition to a history of symbolic logic, the book also examines developments in the philosophy of logic and philosophical logic in modern times. The book begins with chapters on late medieval developments and logic and philosophy of logic from Humanism to Kant. The following chapters focus on the emergence of symbolic logic with special emphasis on the relations between logic and mathematics, on the one hand, and on logic and philosophy, on the other. This discussion is completed by a chapter on the themes of judgment and inference from 1837–1936. The book contains a section on the development of mathematical logic from 1900–1935, followed by a section on main trends in mathematical logic after the 1930s. The book goes on to discuss modal logic from Kant till the late 20th century, and logic and semantics in the 20th century; the philosophy of alternative logics; the philosophical aspects of inductive logic; the relations between logic and linguistics in the 20th century; the relationship between logic and artificial intelligence; and ends with a presentation of the main schools of Indian logic.
Leila Haaparanta
- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780195137316
- eISBN:
- 9780199867912
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195137316.003.0009
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
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
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.”.
Daniel J. Cohen
- Published in print:
- 2005
- Published Online:
- January 2012
- ISBN:
- 9780197263266
- eISBN:
- 9780191734854
- Item type:
- chapter
- Publisher:
- British Academy
- DOI:
- 10.5871/bacad/9780197263266.003.0006
- Subject:
- History, British and Irish Modern History
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
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.
Michael Heim
- Published in print:
- 1994
- Published Online:
- October 2011
- ISBN:
- 9780195092585
- eISBN:
- 9780199852987
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195092585.003.0002
- Subject:
- Philosophy, Metaphysics/Epistemology
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
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.
Amirouche Moktefi
- Published in print:
- 2019
- Published Online:
- April 2019
- ISBN:
- 9780198817000
- eISBN:
- 9780191858697
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198817000.003.0004
- Subject:
- Mathematics, History of Mathematics
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
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.
Nino B. Cocchiarella and Max A. Freund
- Published in print:
- 2008
- Published Online:
- October 2011
- ISBN:
- 9780195366587
- eISBN:
- 9780199851898
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195366587.003.0002
- Subject:
- Philosophy, Philosophy of Language
The authors construct different modal calculi in this chapter. These cover all the well-known systems, S1–S5, of Lewis and Langford's 1932 classic Symbolic Logic. These systems are constructed first ...
More
The authors construct different modal calculi in this chapter. These cover all the well-known systems, S1–S5, of Lewis and Langford's 1932 classic Symbolic Logic. These systems are constructed first on the level of sentential (or propositional) logic. Every sentential modal logic that they consider is also closed under tautologous transformations, in addition to be being based on the same formal language. These systems are called modal CN-calculi and are classified in terms of an order of increasing specificity as (quasi-)classical, (quasi-)regular, and (quasi-)normal modal CN-calculi.Less
The authors construct different modal calculi in this chapter. These cover all the well-known systems, S1–S5, of Lewis and Langford's 1932 classic Symbolic Logic. These systems are constructed first on the level of sentential (or propositional) logic. Every sentential modal logic that they consider is also closed under tautologous transformations, in addition to be being based on the same formal language. These systems are called modal CN-calculi and are classified in terms of an order of increasing specificity as (quasi-)classical, (quasi-)regular, and (quasi-)normal modal CN-calculi.
Andrea Henderson
- Published in print:
- 2018
- Published Online:
- May 2018
- ISBN:
- 9780198809982
- eISBN:
- 9780191860140
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198809982.003.0003
- Subject:
- Literature, 19th-century Literature and Romanticism
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 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.
Michael Heim
- Published in print:
- 1994
- Published Online:
- October 2011
- ISBN:
- 9780195092585
- eISBN:
- 9780199852987
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195092585.003.0007
- Subject:
- Philosophy, Metaphysics/Epistemology
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
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.
Andrea Henderson
- Published in print:
- 2018
- Published Online:
- May 2018
- ISBN:
- 9780198809982
- eISBN:
- 9780191860140
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198809982.001.0001
- Subject:
- Literature, 19th-century Literature and Romanticism
Algebraic Art explores the invention of a peculiarly Victorian account of the nature and value of aesthetic form, and it traces that account to a surprising source: mathematics. The nineteenth ...
More
Algebraic Art explores the invention of a peculiarly Victorian account of the nature and value of aesthetic form, and it traces that account to a surprising source: mathematics. The nineteenth century was a moment of extraordinary mathematical innovation, witnessing the development of non-Euclidean geometry, the revaluation of symbolic algebra, and the importation of mathematical language into philosophy. All these innovations sprang from a reconception of mathematics as a formal rather than a referential practice—as a means for describing relationships rather than quantities. For Victorian mathematicians, the value of a claim lay not in its capacity to describe the world but its internal coherence. This concern with formal structure produced a striking convergence between mathematics and aesthetics: geometers wrote fables, logicians reconceived symbolism, and physicists described reality as consisting of beautiful patterns. Artists, meanwhile, drawing upon the cultural prestige of mathematics, conceived their work as a “science” of form, whether as lines in a painting, twinned characters in a novel, or wave-like stress patterns in a poem. Avant-garde photographs and paintings, fantastical novels like Flatland and Lewis Carroll’s children’s books, and experimental poetry by Swinburne, Rossetti, and Patmore created worlds governed by a rigorous internal logic even as they were pointedly unconcerned with reference or realist protocols. Algebraic Art shows that works we tend to regard as outliers to mainstream Victorian culture were expressions of a mathematical formalism that was central to Victorian knowledge production and that continues to shape our understanding of the significance of form.Less
Algebraic Art explores the invention of a peculiarly Victorian account of the nature and value of aesthetic form, and it traces that account to a surprising source: mathematics. The nineteenth century was a moment of extraordinary mathematical innovation, witnessing the development of non-Euclidean geometry, the revaluation of symbolic algebra, and the importation of mathematical language into philosophy. All these innovations sprang from a reconception of mathematics as a formal rather than a referential practice—as a means for describing relationships rather than quantities. For Victorian mathematicians, the value of a claim lay not in its capacity to describe the world but its internal coherence. This concern with formal structure produced a striking convergence between mathematics and aesthetics: geometers wrote fables, logicians reconceived symbolism, and physicists described reality as consisting of beautiful patterns. Artists, meanwhile, drawing upon the cultural prestige of mathematics, conceived their work as a “science” of form, whether as lines in a painting, twinned characters in a novel, or wave-like stress patterns in a poem. Avant-garde photographs and paintings, fantastical novels like Flatland and Lewis Carroll’s children’s books, and experimental poetry by Swinburne, Rossetti, and Patmore created worlds governed by a rigorous internal logic even as they were pointedly unconcerned with reference or realist protocols. Algebraic Art shows that works we tend to regard as outliers to mainstream Victorian culture were expressions of a mathematical formalism that was central to Victorian knowledge production and that continues to shape our understanding of the significance of form.
- Published in print:
- 2008
- Published Online:
- March 2013
- ISBN:
- 9780226388700
- eISBN:
- 9780226388724
- Item type:
- chapter
- Publisher:
- University of Chicago Press
- DOI:
- 10.7208/chicago/9780226388724.003.0009
- Subject:
- Religion, History of Christianity
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
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.
