Archive for the ‘Logic’ Category

Incompleteness: The Proof and Paradox of Kurt Godel

Monday, March 10th, 2008

I’ve just finished reading this book and despite some bad reviews on Amazon I wasn’t disappointed. The author’s writing style is a bit unusual with some unknown words that you need a dictionary but after a chapter I became used to it and it wasn’t a problem anymore. If you heard about Gödel theorems before but cannot repeat precisely what they are about then this book is for you and you will find detail-free sketch of the proof very clear. I really liked the author’s attack on positivism and postmodernism especially in the light of previously read Fashionable Nonsense. I also liked the conclusion at the end of the book that the life of Gödel was “incomplete” too. The book discusses Vienna Circle and Wittgenstein, relationship between Einstein and Gödel and even some political issues in the Institute for Advanced Study related to Gödel’s life (this is why I included this book under Politics category too). One remark about bad review from the professor who participated in publishing edited works of Kurt Gödel: I can publish works of Aristotle nowadays without much efforts. Will it give me the right to judge other works and proclaim without sound justification that they don’t know philosophy?

Incompleteness: The Proof and Paradox of Kurt Godel (Great Discoveries)

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- Dmitry Vostokov @ LiterateScientist.com -

Discrete Thoughts

Tuesday, February 12th, 2008

This one I discovered last year and just finished reading. Interesting collection of articles written in the late 70’s and early 80’s about application of mathematics. My favourite were two articles about statistics and two articles about Husserl. The article about Kant biography was nice as well.

Discrete Thoughts

- Dmitry Vostokov @ LiterateScientist.com -

Classical and Nonclassical Logics

Tuesday, February 5th, 2008

Very good book to learn about mathematical logic, distinction between syntax and semantics, different interpretations of formal languages and how this leads to various different non-classical logics. It will deepen your understanding of mathematics if you studied or encountered only classical propositional and predicate logic and want to learn more about fuzzy logic, for example, among many others. All necessary prerequisites are covered in the first 230 pages of this 500 page book including informal set theory and topology. I read most of this book couple of years ago and want to re-read it soon.

Classical and Nonclassical Logics: An Introduction to the Mathematics of Propositions

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- Dmitry Vostokov @ LiterateScientist.com -

Causal Models

Tuesday, January 15th, 2008

Just finished reading this book written by Steven Sloman. Very readable explanation about a causal modeling framework involving probability distributions and causal graphs, explanation of counterfactuals, logic of intervention, Markov equivalence, explanation discounting, causal structures and language, reasoning and decision making, the difference between observation and action. I became interested in causality from software troubleshooting and debugging perspective where we need to diagnose causes (defects) from symptoms (failures) and this book was a good introduction to me.

Causal Models: How People Think about the World and Its Alternatives

- Dmitry Vostokov @ LiterateScientist.com -