Understanding logic - the First Order of Reasoning

To the uninitiated, logic may appear a contrived formal approach to reasoning. Far from it, we need only scratch the surface of any human endeavour and logic is present. It cuts across every gender, racial and cultural boundary forming the core of all systematic inquiry, not least mathematics, and seems to be an unavoidable intellectual manifestation of the order in our universe. Were we one day to meet with alien civilisations, it seems impossible to imagine that they could be without logic.

Purpose:
This book is written for everybody who would like to penetrate that realm of human cognition that most differentiates us from all other creatures we know of in the universe. It is written to present this faculty as the ultimate embodiment of thought in an age when the superficial and irrational is not only rife, but has become a dominating cultural expression of intellectual laziness. The danger of this culture forwarns the degeneration of civilisation into a society where unschooled minds appreciate the opinion of celebrity ignorants, military bullies, and the values of pop-up religions more than academia’s systematically scrutinised wisdom. Such a culture stimulates the emergence of narrow mindedness, prejudice, and foolishness, feeding totalitarianism and oppression.

We hereby join the battle that may ensure a tolerable existence for future generations, by expounding the virtues of critical thinking in its purest embodiment. We hope that this book will show how deeper meaning lurks beneath the skin of every man and woman. Anyone can harness the tools that can empower us to escape the relentless sea of puerile mass-culture. Allow us to persuade you with the allure of truth and the means to discover it.

Audience:
The book is for anybody who would wish to strive to learn more of our innate faculty of reason. In practice the book can be used not only for basic, but also for fairly advanced undergraduate studies in logic with a special focus on applications in systems science, while still observing both a formal as well as a philosophical perspective. Read as intellectual ‘entertainment’ with a view to glimpsing the power and beauty of thought or simply to understand the formal culmination of centuries of cultural history.

The book thoroughly covers propositional and predicate logic, set theory and functions, complexity theory and algorithm analysis as well as modal logic and model theory. It can be used for basic and also for more advanced studies in logic with a special focus on applications in systems science. The material there is sufficient for 2-3 courses in logic and can be divided in two basic parts and a more advanced part.