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 Gödel'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 Sérgio Argolo
