I hate nothing more than feeling uncertain about my views on an important topic. That’s why I cherish tools for thought that help me cut through the various confusions to which humans are prone. The sharpest tool we’ve got is modern symbolic logic, as it has been developed since the late 19th century. I’ve loved symbolic logic since I took my first logic class in college. I’ve been teaching Intro Logic for over twenty years at Princeton University, and I’ve published several papers and books that employ logic to try to gain clarity on philosophical issues.
This is a mathematics textbook unlike any other you have encountered before. Remarkably, there are no numbers—only structures, patterns, and arrows.
However, this book is not designed to teach you how to construct proofs. Instead, it offers a fascinating introduction to a new way of thinking mathematically.
In the last 60 years, the use of the notion of category has led to a remarkable unification and simplification of mathematics. Conceptual Mathematics introduces this tool for the learning, development, and use of mathematics, to beginning students and also to practising mathematical scientists. This book provides a skeleton key that makes explicit some concepts and procedures that are common to all branches of pure and applied mathematics. The treatment does not presuppose knowledge of specific fields, but rather develops, from basic definitions, such elementary categories as discrete dynamical systems and directed graphs; the fundamental ideas are then illuminated by…
A true gem in the realm of symbolic logic textbooks, this book stands out for its crystal-clear explanations and elegant English prose. It’s my top recommendation for anyone coming from a humanities background or returning to academia after a break.
Tomassi’s writing makes symbolic logic both accessible and engaging.
Bringing elementary logic out of the academic darkness into the light of day, Paul Tomassi makes logic fully accessible for anyone attempting to come to grips with the complexities of this challenging subject. Including student-friendly exercises, illustrations, summaries and a glossary of terms, Logic introduces and explains:
* The Theory of Validity * The Language of Propositional Logic * Proof-Theory for Propositional Logic * Formal Semantics for Propositional Logic including the Truth-Tree Method * The Language of Quantificational Logic including the Theory of Descriptions.
Logic is an ideal textbook for any logic student: perfect for revision, staying on top of…
One of my teachers once described this as "the best book with the most misleading title." Despite the title, it’s not about physics—it’s about the symbolic reasoning that underpins theoretical physics.
If you’re looking for a fast-paced overview of the mathematical tools used in cutting-edge physics, this book is unparalleled.
Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminating intuitive discussion of the "whys" of proofs and of axioms and definitions. This book, based on Geroch's University of Chicago course, will be especially helpful to those working in theoretical physics, including such areas as relativity, particle physics, and astrophysics.
Although I’m not a programmer, I couldn’t leave programming—a quintessential example of symbolic reasoning—off this list. For someone like me, with a background in mathematics and philosophy, this book provides a concrete look at how abstract reasoning can be applied in programming.
For programmers, it’s an engaging introduction to category theory. This is a brilliant example of interdisciplinary thinking at its best.
My favorite kind of book (about logically rigorous reasoning) is one in which you spend about half the time learning principles and the other half reasoning for yourself. Metaphorically speaking, such a book teaches you how to fish instead of feeding you processed fish paste.
I tried to write an introduction to symbolic logic of this kind. It’s not the only such book on the market, but it’s one of the only such to appear in recent years, and it goes against the current trend of spoon-feeding the reader. I also tried to write a book that is a stepping stone for the super-interesting advanced topics in logic, math, computer science, and philosophy.
