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Laws Of Form
''Laws of Form'' (hereinafter ''LoF'') is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy. ''LoF'' describes three distinct logical systems: * The "primary arithmetic" (described in Chapter 4 of ''LoF''), whose models include Boolean arithmetic; * The "primary algebra" (Chapter 6 of ''LoF''), whose models include the two-element Boolean algebra (hereinafter abbreviated 2), Boolean logic, and the classical propositional calculus; * "Equations of the second degree" (Chapter 11), whose interpretations include finite automata and Alonzo Church's Restricted Recursive Arithmetic (RRA). "Boundary algebra" is Meguire's (2011) term for the union of the primary algebra and the primary arithmetic. ''Laws of Form'' sometimes loosely refers to the "primary algebra" as well as to ''LoF''. The book The preface states that the work was first explored in 1959, and Spencer Brown cites Bertrand Russell as being supportive of his endea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wittgenstein
Ludwig Josef Johann Wittgenstein ( ; ; 26 April 1889 – 29 April 1951) was an Austrians, Austrian-British people, British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He is considered by some to be the greatest philosopher of the 20th century. From 1929 to 1947, Wittgenstein taught at the University of Cambridge. In spite of his position, during his entire life only one book of #Legacy, his philosophy was published, the 75-page ''Logisch-Philosophische Abhandlung'' (''Logical-Philosophical Treatise'', 1921), which appeared, together with an English translation, in 1922 under the Latin title ''Tractatus Logico-Philosophicus''. His only other published works were an article, "Some Remarks on Logical Form" (1929); a book review; and a children's dictionary. #Works, His voluminous manuscripts were edited and published posthumously. The first and best-known of this posthumous series is the 1953 b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Duality (mathematics)
In mathematics, a duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of is , then the dual of is . Such involutions sometimes have fixed points, so that the dual of is itself. For example, Desargues' theorem is self-dual in this sense under the ''standard duality in projective geometry''. In mathematical contexts, ''duality'' has numerous meanings. It has been described as "a very pervasive and important concept in (modern) mathematics" and "an important general theme that has manifestations in almost every area of mathematics". Many mathematical dualities between objects of two types correspond to pairings, bilinear functions from an object of one type and another object of the second type to some family of scalars. For instance, ''linear algebra duality'' corresponds in this way to bilinear maps from pairs of ve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy Of Mind
Philosophy of mind is a branch of philosophy that studies the ontology and nature of the mind and its relationship with the body. The mind–body problem is a paradigmatic issue in philosophy of mind, although a number of other issues are addressed, such as the hard problem of consciousness and the nature of particular mental states.Siegel, S.: ''The Contents of Visual Experience''. New York: Oxford University Press. 2010.Macpherson, F. & Haddock, A., editors, ''Disjunctivism: Perception, Action, Knowledge'', Oxford: Oxford University Press, 2008. Aspects of the mind that are studied include mental events, mental functions, mental properties, consciousness and its neural correlates, the ontology of the mind, the nature of cognition and of thought, and the relationship of the mind to the body. Dualism and monism are the two central schools of thought on the mind–body problem, although nuanced views have arisen that do not fit one or the other category neatly. * Duali ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy Of Language
In analytic philosophy, philosophy of language investigates the nature of language and the relations between language, language users, and the world. Investigations may include inquiry into the nature of meaning, intentionality, reference, the constitution of sentences, concepts, learning, and thought. Gottlob Frege and Bertrand Russell were pivotal figures in analytic philosophy's "linguistic turn". These writers were followed by Ludwig Wittgenstein ('' Tractatus Logico-Philosophicus''), the Vienna Circle, logical positivists, and Willard Van Orman Quine. In continental philosophy, language is not studied as a separate discipline. Rather, it is an inextricable part of many other areas of thought, such as phenomenology, structural semiotics, language of mathematics, hermeneutics, existentialism, deconstruction and critical theory. History Ancient philosophy In the West, inquiry into language stretches back to the 5th century BC with Socrates, Plato, Aristotl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Algebra (logic)
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (''and'') denoted as ∧, disjunction (''or'') denoted as ∨, and the negation (''not'') denoted as ¬. Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction and division. So Boolean algebra is a formal way of describing logical operations, in the same way that elementary algebra describes numerical operations. Boolean algebra was introduced by George Boole in his first book ''The Mathematical Analysis of Logic'' (1847), and set forth more fully in his '' An Investigation of the Laws of Thought'' (1854). According to Huntington, the term "Boolean algebr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Formal logic contrasts with informal logic, which is associated with informal fallacies, critical thinking, and argumentation theory. While there is no general agreement on how formal and informal logic are to be distinguished, one prominent approach associates their difference with whether the studied arguments are expressed in formal or informal languages. Logic plays a central role in multiple fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises together with a conclusion. Premises and conclusions are usua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cognition
Cognition refers to "the mental action or process of acquiring knowledge and understanding through thought, experience, and the senses". It encompasses all aspects of intellectual functions and processes such as: perception, attention, thought, intelligence, the formation of knowledge, memory and working memory, judgment and evaluation, reasoning and computation, problem solving and decision making, comprehension and production of language. Imagination is also a cognitive process, it is considered as such because it involves thinking about possibilities. Cognitive processes use existing knowledge and discover new knowledge. Cognitive processes are analyzed from different perspectives within different contexts, notably in the fields of linguistics, musicology, anesthesia, neuroscience, psychiatry, psychology, education, philosophy, anthropology, biology, systemics, logic, and computer science. These and other approaches to the analysis of cognition (such as embodied ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Consciousness
Consciousness, at its simplest, is sentience and awareness of internal and external existence. However, the lack of definitions has led to millennia of analyses, explanations and debates by philosophers, theologians, linguisticians, and scientists. Opinions differ about what exactly needs to be studied or even considered consciousness. In some explanations, it is synonymous with the mind, and at other times, an aspect of mind. In the past, it was one's "inner life", the world of introspection, of private thought, imagination and volition. Today, it often includes any kind of cognition, experience, feeling or perception. It may be awareness, awareness of awareness, or self-awareness either continuously changing or not. The disparate range of research, notions and speculations raises a curiosity about whether the right questions are being asked. Examples of the range of descriptions, definitions or explanations are: simple wakefulness, one's sense of selfhood or sou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Whole Earth Catalog
The ''Whole Earth Catalog'' (WEC) was an American counterculture magazine and product catalog published by Stewart Brand several times a year between 1968 and 1972, and occasionally thereafter, until 1998. The magazine featured essays and articles, but was primarily focused on product reviews. The editorial focus was on self-sufficiency, ecology, alternative education, "do it yourself" (DIY), and holism, and featured the slogan "access to tools". While WEC listed and reviewed a wide range of products (clothing, books, tools, machines, seeds, etc.), it did not sell any of the products directly. Instead, the vendor's contact information was listed alongside the item and its review. This is why, while not a regularly published periodical, numerous editions and updates were required to keep price and availability information up to date. Steve Jobs compared ''The Whole Earth Catalog'' to Internet search engine Google in his June 2005 Stanford University commencement speech. When I wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heinz Von Foerster
Heinz von Foerster (German spelling: Heinz von Förster; November 13, 1911 – October 2, 2002) was an Austrian American scientist combining physics and philosophy, and widely attributed as the originator of Second-order cybernetics. He was twice a Guggenheim fellow (1956–57 and 1963–64) and also was a fellow of the American Association for the Advancement of Science, 1980. He is well known for his 1960 Doomsday equation formula published in ''Science'' predicting future population growth. As a polymath, he wrote nearly two hundred professional papers, gaining renown in fields from computer science and artificial intelligence to epistemology, and researched high-speed electronics and electro-optics switching devices as a physicist, and in biophysics, the study of memory and knowledge. He worked on cognition based on neurophysiology, mathematics, and philosophy and was called "one of the most consequential thinkers in the history of cybernetics". He came to the United States, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cult Classic
A cult following refers to a group of fans who are highly dedicated to some person, idea, object, movement, or work, often an artist, in particular a performing artist, or an artwork in some medium. The lattermost is often called a cult classic. A film, book, musical artist, television series, or video game, among other things, is said to have a cult following when it has a small but very passionate fanbase. A common component of cult followings is the emotional attachment the fans have to the object of the cult following, often identifying themselves and other fans as members of a community. Cult followings are also commonly associated with niche markets. Cult media are often associated with underground culture, and are considered too eccentric or anti-establishment to be appreciated by the general public or to be widely commercially successful. Many cult fans express their devotion with a level of irony when describing entertainment that falls under this realm, in that somethi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
