Number Systems: A Path into Rigorous Mathematics aims to introduce number systems to an undergraduate audience in a way that emphasises the importance of rigour, and with a focus on providing detailed but accessible explanations of theorems and their proofs.
The book treats two approaches to decision theory: (1) the normative, purporting to determine how a 'perfectly rational' actor ought to choose among available alternatives; (2) the descriptive, based on observations of how people actually choose in real life and in laboratory experiments.
This study looks to the work of Tarski's mentors Stanislaw Lesniewski and Tadeusz Kotarbinski, and reconsiders all of the major issues in Tarski scholarship in light of the conception of Intuitionistic Formalism developed: semantics, truth, paradox, logical consequence.
Thirteen promising young researchers write on what they take to be the right philosophical account of mathematics and discuss where the philosophy of mathematics ought to be going.
Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science.
In recent years there have been a number of books-both anthologies and monographs-that have focused on the Liar Paradox and, more generally, on the semantic paradoxes, either offering proposed treatments to those paradoxes or critically evaluating ones that occupy logical space.
This is a charming and insightful contribution to an understanding of the "e;Science Wars"e; between postmodernist humanism and science, driving toward a resolution of the mutual misunderstanding that has driven the controversy.
Our understanding of how the human brain performs mathematical calculations is far from complete, but in recent years there have been many exciting breakthroughs by scientists all over the world.
This volume brings together many of Terence Horgan's essays on paradoxes: Newcomb's problem, the Monty Hall problem, the two-envelope paradox, the sorites paradox, and the Sleeping Beauty problem.
Attempts to understand various aspects of the empirical world often rely on modelling processes that involve a reconstruction of systems under investigation.
The biological and social sciences often generalize causal conclusions from one context or location to others that may differ in some relevant respects, as is illustrated by inferences from animal models to humans or from a pilot study to a broader population.
If we must take mathematical statements to be true, must we also believe in the existence of abstracta eternal invisible mathematical objects accessible only by the power of pure thought?
McCarthy develops a theory of radical interpretation--the project of characterizing from scratch the language and attitudes of an agent or population--and applies it to the problems of indeterminacy of interpretation first described by Quine.
Some combinations of attitudes--of beliefs, credences, intentions, preferences, hopes, fears, and so on--do not fit together right: they are incoherent.
Some combinations of attitudes--of beliefs, credences, intentions, preferences, hopes, fears, and so on--do not fit together right: they are incoherent.
The past few decades have seen an explosion of research on causal reasoning in philosophy, computer science, and statistics, as well as descriptive work in psychology.
The past few decades have seen an explosion of research on causal reasoning in philosophy, computer science, and statistics, as well as descriptive work in psychology.
Our words and ideas refer to objects and properties in the external world; this phenomenon is central to thought, language, communication, and science.
Our words and ideas refer to objects and properties in the external world; this phenomenon is central to thought, language, communication, and science.
In this collection of essays written over a period of twenty years, Solomon Feferman explains advanced results in modern logic and employs them to cast light on significant problems in the foundations of mathematics.
This book explores an important central thread that unifies Russell's thoughts on logic in two works previously considered at odds with each other, the Principles of Mathematics and the later Principia Mathematica.
This is a charming and insightful contribution to an understanding of the "e;Science Wars"e; between postmodernist humanism and science, driving toward a resolution of the mutual misunderstanding that has driven the controversy.
With a never-before published paper by Lord Henry Cavendish, as well as a biography on him, this book offers a fascinating discourse on the rise of scientific attitudes and ways of knowing.
Very Short Introductions: Brilliant, Sharp, Inspiring Kurt Godel first published his celebrated theorem, showing that no axiomatization can determine the whole truth and nothing but the truth concerning arithmetic, nearly a century ago.
Very Short Introductions: Brilliant, Sharp, Inspiring Kurt Godel first published his celebrated theorem, showing that no axiomatization can determine the whole truth and nothing but the truth concerning arithmetic, nearly a century ago.
Essays on Existence and Essence presents a series of writings--including several previously unpublished--by Bob Hale on the topics of ontology and modality.
