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Lewis Carroll explains the theory and applications of symbolic logic in a collection of entertaining problems
This carefully crafted ebook: “Selected Mathematical Works: Symbolic Logic + The Game of Logic + Feeding the Mind” is formatted for your eReader with a functional and detailed table of contents. Lewis Carroll wrote several mathematics books. He was mainly interested in using logic diagrams as a pedagogical tool. Symbolic Logic, first published in 1896, contains literally dozens of puzzles. He believed heartily that children would enjoy learning mathematics if they could be enticed by amusing stories and puzzles. The Game of Logic, published in 1897, was intended to teach logic to children. His "game" consisted of a card with two diagrams, together with a set of counters, five grey and four red. The two diagrams were Carroll's version of a two-set and a three-set Venn diagram. A manuscript of a brief lecture Lewis Carroll once gave, Feeding the Mind, discusses the importance of not only feeding the body, but also the mind. Carroll wittily puts forth connections between the diet of the body and mind, and gives helpful tips on how to best digest knowledge in the brain. This essay was originally printed in 1907. Lewis Carroll ((1832-1898) is best known as the author of Alice in Wonderland and Alice Through the Looking Glass. His real name was Charles Dodgson. His father, the Reverend Charles Dodgson, instilled in his son a love of mathematics from an early age. Lewis studied at Oxford, and later taught there as a Mathematics Lecturer.
This Game requires nine Counters--four of one colour and five of another: say four red and five grey. Besides the nine Counters, it also requires one Player, AT LEAST. I am not aware of any Game that can be played with LESS than this number: while there are several that require MORE: take Cricket, for instance, which requires twenty-two. How much easier it is, when you want to play a Game, to find ONE Player than twenty-two. At the same time, though one Player is enough, a good deal more amusement may be got by two working at it together, and correcting each other's mistakes. A second advantage, possessed by this Game, is that, besides being an endless source of amusement (the number of arguments, that may be worked by it, being infinite), it will give the Players a little instruction as well. But is there any great harm in THAT, so long as you get plenty of amusement
Since the first chapter of this book presents an intro duction to the present state of game-theoretical semantics (GTS), there is no point in giving a briefer survey here. Instead, it may be helpful to indicate what this volume attempts to do. The first chapter gives a short intro duction to GTS and a survey of what is has accomplished. Chapter 2 puts the enterprise of GTS into new philo sophical perspective by relating its basic ideas to Kant's phi losophy of mathematics, space, and time. Chapters 3-6 are samples of GTS's accomplishments in understanding different kinds of semantical phenomena, mostly in natural languages. Beyond presenting results, some of these chapters also have other aims. Chapter 3 relates GTS to an interesting line of logical and foundational studies - the so-called functional interpretations - while chapter 4 leads to certain important methodological theses. Chapter 7 marks an application of GTS in a more philo sophical direction by criticizing the Frege-Russell thesis that words like "is" are multiply ambiguous. This leads in turn to a criticism of recent logical languages (logical notation), which since Frege have been based on the ambi guity thesis, and also to certain methodological sug gestions. In chapter 8, GTS is shown to have important implications for our understanding of Aristotle's doctrine of categories, while chapter 9 continues my earlier criticism of Chomsky's generative approach to linguistic theorizing.
The fourth volume of the DIGAREC Series holds the proceedings to the conference Logic and Structure of the Computer Gameʺ, held at the House of Brandenburg- Prussian History in Potsdam on November 6 and 7, 2009. The conference was the first to explicitly address the medial logic and structure of the computer game. The contributions focus on the specific potential for mediation and on the unique form of mediation inherent in digital games. This includes existent, yet scattered approaches to develop a unique curriculum of game studies. In line with the concept of ‘mediality’, the notions of aesthetics, interactivity, software architecture, interface design, iconicity, spatiality, and rules are of special interest. Presentations were given by invited German scholars and were commented on by international respondents in a dialogical structure.
Our usual representations of the opposition between the "civilized" and the "primitive" derive from willfully ignoring the relationship of distance our social science sets up between the observer and the observed. In fact, the author argues, the relationship between the anthropologist and his object of study is a particular instance of the relationship between knowing and doing, interpreting and using, symbolic mastery and practical masteryor between logical logic, armed with all the accumulated instruments of objectification, and the universally pre-logical logic of practice. In this, his fullest statement of a theory of practice, Bourdieu both sets out what might be involved in incorporating one's own standpoint into an investigation and develops his understanding of the powers inherent in the second member of many oppositional pairsthat is, he explicates how the practical concerns of daily life condition the transmission and functioning of social or cultural forms. The first part of the book, "Critique of Theoretical Reason," covers more general questions, such as the objectivization of the generic relationship between social scientific observers and their objects of study, the need to overcome the gulf between subjectivism and objectivism, the interplay between structure and practice (a phenomenon Bourdieu describes via his concept of the habitus), the place of the body, the manipulation of time, varieties of symbolic capital, and modes of domination. The second part of the book, "Practical Logics," develops detailed case studies based on Bourdieu's ethnographic fieldwork in Algeria. These examples touch on kinship patterns, the social construction of domestic space, social categories of perception and classification, and ritualized actions and exchanges. This book develops in full detail the theoretical positions sketched in Bourdieu's Outline of a Theory of Practice. It will be especially useful to readers seeking to grasp the subtle concepts central to Bourdieu's theory, to theorists interested in his points of departure from structuralism (especially fom Lévi-Strauss), and to critics eager to understand what role his theory gives to human agency. It also reveals Bourdieu to be an anthropological theorist of considerable originality and power.