This book was written to serve as an introduction to logic, with in
each chapter - if applicable - special emphasis on the interplay
between logic and philosophy, mathematics, language and
(theoretical) computer science. The reader will not only be
provided with an introduction to classical logic, but to
philosophical (modal, epistemic, deontic, temporal) and
intuitionistic logic as well. The first chapter is an easy to read
non-technical Introduction to the topics in the book. The next
chapters are consecutively about Propositional Logic, Sets (finite
and infinite), Predicate Logic, Arithmetic and Goedel's
Incompleteness Theorems, Modal Logic, Philosophy of Language,
Intuitionism and Intuitionistic Logic, Applications (Prolog;
Relational Databases and SQL; Social Choice Theory, in particular
Majority Judgment) and finally, Fallacies and Unfair Discussion
Methods. Throughout the text, the author provides some impressions
of the historical development of logic: Stoic and Aristotelian
logic, logic in the Middle Ages and Frege's Begriffsschrift,
together with the works of George Boole (1815-1864) and August De
Morgan (1806-1871), the origin of modern logic. Since "if ..., then
..." can be considered to be the heart of logic, throughout this
book much attention is paid to conditionals: material, strict and
relevant implication, entailment, counterfactuals and
conversational implicature are treated and many references for
further reading are given. Each chapter is concluded with answers
to the exercises. Philosophical and Mathematical Logic is a very
recent book (2018), but with every aspect of a classic. What a
wonderful book! Work written with all the necessary rigor, with
immense depth, but without giving up clarity and good taste.
Philosophy and mathematics go hand in hand with the most diverse
themes of logic. An introductory text, but not only that. It goes
much further. It's worth diving into the pages of this book, dear
reader! Paulo Sergio Argolo
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