Logic For Mathematicians

This book deals with models and model-building in classical and quantum physics; it relies on logic and the philosophy of science as well as on modern mathematics. The reader will also find vistas into the history of ideas. The philosophical analysis is based on the separation of syntax and semantics which is at the root of Kolmogorov's theory of probability; recursive functions and algorithmic complexity are used to discuss entropy and randomness.

Written for mathematicians, logicians, historians, and philosophers–especially those interested in the historical interaction between these disciplines–this authoritative account tells an important story from its most neglected point of view.

One can distinguish, roughly speaking, two different approaches to the philosophy of mathematics. On the one hand, some philosophers (and some mathematicians) take the nature and the results of mathematicians' activities as given, and go on to ask what philosophical morals one might perhaps find in their story. On the other hand, some philosophers, logicians and mathematicians have tried or are trying to subject the very concepts which mathematicians are using in their work to critical scrutiny. In practice this usually means scrutinizing the logical and linguistic tools mathematicians wield. Such scrutiny can scarcely help relying on philosophical ideas and principles. In other words it can scarcely help being literally a study of language, truth and logic in mathematics, albeit not necessarily in the spirit of AJ. Ayer.

Editors: Abramsky, S., Kontinen, J., Väänänen, J., Vollmer, H. (Eds.)
Covers a relatively new area of logic, introduced by Väänänen, that has seen rapid development
Dependence logic has applications in numerous, seemingly unrelated subjects, including causality, random variables in statistics, database theory, Mendelian genetics, and quantum physics
Will be of interest to a broad group of logicians, mathematicians, statisticians, philosophers, and scientists

There are many kinds of books on formal logic. Some have philosophers as their intended audience, some mathematicians, some computer scien­ tists. Although there is a common core to all such books, they will be very different in emphasis, methods, and even appearance.