Catalogue Search | MBRL
Are you sure you want to remove the book from the shelf?
{{itemTitle}}
146
result(s) for
"Metamathematics."
Sort by:
How to bake pi : an edible exploration of the mathematics of mathematics
\"In How to Bake Pi, math professor Eugenia Cheng provides an accessible introduction to the logic and beauty of mathematics, powered, unexpectedly, by insights from the kitchen: we learn, for example, how the béchamel in a lasagna can be a lot like the number 5, and why making a good custard proves that math is easy but life is hard.\"--Publisher description.
Book
Logic and Metalogic: a Historical Sketch
This paper briefly discusses the relations between logic and metalogic in history. Metalogic is understood as a reflection on logic in its various senses, particularly
(formal, mathematical) and
(formal logic plus semantic plus methodology of science). It is shown that metalogic in its contemporary understanding arose after mathematical logic had become a mature discipline. Special passage is devoted to metalogic in Poland. The last part of the paper discussed so-called logocentric predicament.
Journal Article
Fuzzy logic and mathematics : a historical perspective
The term “fuzzy logic” (FL) is a generic one, which stands for a broad variety of logical systems. Their common ground is the rejection of the most fundamental principle of classical logic—the principle of bivalence—according to which each declarative sentence has exactly two possible truth values—true and false. Each logical system subsumed under FL allows for additional, intermediary truth values, which are interpreted as degrees of truth. These systems are distinguished from one another by the set of truth degrees employed, its algebraic structure, truth functions chosen for logical connectives, and other properties. The book examines from the historical perspective two areas of research on fuzzy logic known as fuzzy logic in the narrow sense (FLN) and fuzzy logic in the broad sense (FLB), which have distinct research agendas. The agenda of FLN is the development of propositional, predicate, and other fuzzy logic calculi. The agenda of FLB is to emulate commonsense human reasoning in natural language and other unique capabilities of human beings. In addition to FL, the book also examines mathematics based on FL. One chapter in the book is devoted to overviewing successful applications of FL and the associated mathematics in various areas of human affairs. The principal aim of the book is to assess the significance of FL and especially its significance for mathematics. For this purpose, the notions of paradigms and paradigm shifts in science, mathematics, and other areas are introduced and employed as useful metaphors.
eBook
Logical Dynamics of Information and Interaction
This book develops a view of logic as a theory of information-driven agency and intelligent interaction between many agents - with conversation, argumentation and games as guiding examples. It provides one uniform account of dynamic logics for acts of inference, observation, questions and communication, that can handle both update of knowledge and revision of beliefs. It then extends the dynamic style of analysis to include changing preferences and goals, temporal processes, group action and strategic interaction in games. Throughout, the book develops a mathematical theory unifying all these systems, and positioning them at the interface of logic, philosophy, computer science and game theory. A series of further chapters explores repercussions of the 'dynamic stance' for these areas, as well as cognitive science.
eBook
The metamathematics of Stable Ramsey’s Theorem for Pairs
We show that, over the base theory RCA0\\textit {RCA}_0, Stable Ramsey’s Theorem for Pairs implies neither Ramsey’s Theorem for Pairs nor Σ20\\Sigma ^0_2-induction.
Journal Article
A way to see the interplay between theory and reality with a look at the quantum case
The purpose of this paper is to argue that neither mathematics nor logic can be applied ‘directly’ to reality, but to our rational representations (or reconstructions) of it, and this is extended to scientic theories in general. The difference to other approaches (e.g., Nancy Cartwright’s, Bueno & Colyvan’s or Hughes’) is that I call attention to something more than what is involved in such a process, namely, metamathematics. A general schema of ‘elaboration’ of theories, which I suppose cope with most of them, is presented and discussed. A case study is outlined, the quantum case, whose anchored description, in my opinion, demands a different metamathematics and a different logic.
El propósito de este artículo es argumentar que ni las matemáticas ni la lógica pueden aplicarse “directamente” a la realidad, sino a nuestras representaciones (o reconstrucciones) racionales de la realidad, y esto se extiende a las teorías científicas en general. La diferencia con otros enfoques (por ejemplo, el de Nancy Cartwright, el de Bueno & Colyvan o el de Hughes) es que llamo la atención sobre algo más de lo que está involucrado en tal proceso, a saber, la metamatemática. Un esquema general de “elaboración” de teorías, que supongo que se adaptan a la mayoría de ellas, se presenta y discute. Se esboza un estudio de caso, el caso cuántico, cuya descripción afianzada exige, en mi opinión, una metamatemática diferente y una lógica diferente de la clásica.
Journal Article
Quantifying Aristotle
This book offers an entirely new perspective on the alleged incompatibility between Aristotelian philosophy and the mathematical methods and principles that form the basis of modern science. It surveys the tradition of the Oxford Calculators from its beginnings in the fourteenth century until Leibniz and the philosophy of the seventeenth century and explores how their various techniques of quantification expanded the conceptual and methodological limits of Aristotelianism.
eBook