An excellent introduction to logic (in all possible worlds), September 24, 2002, by Dr. Lee D. Carlson (Baltimore, Maryland USA) [Amazon.com]

It is too bad this book is out of print, for the authors do a fine job of introducing the student of philosophy or mathematics to the essentials of modern logic. Their approach, as the title implies, is via the framework of possible worlds, a framework first proposed by the philosopher J. Hintikka. Their approach is unique at this level of textbook. "Possible worlds semantics", as it is now called, is a highly sophisticated and subtle branch of mathematical logic, but the authors give a very elementary introduction in this book, employing symbols very sparingly, and then only in the last two chapters. The goal, as stated by the authors, is to reach the reader who has difficulty with symbols. The book succeeds well in giving the reader an appreciation of logical reasoning and prepares well the reader for more advanced topics in symbolic and mathematical logic. Modal logic is also treated, and again, this is unique at this level. Useful exercises accompany the end of each section of the book.

One of the main virtues of the book is it distinguishes between conceivability (what we can imagine), and what is possible. The ability to conceive a state of affairs does not imply the possibility of that state of affairs, they argue (correctly). Conceivability is neither a necessary nor sufficient condition for possibility. Psychologism is to be avoided at all costs, along with collapsing into circularity, and the authors accomplish this by the use of examples, i.e. examples of possible worlds and examples of impossible worlds. These examples are generated using ostension, naming, description, etc.

Most interesting is the author's discussion on the properties of propositions. Propositions are classified as being possibly true or false, contingent, noncontingent, and necessarily true and false. Such distinctions are necessary given the framework in which the authors work, and its subsequent definition of truth and falsity. Objects and things, for the authors, are to be distinguished from properties and relations, and both of these concepts may be instanced in possible worlds other than the actual one. It is "true" that an object has an attribute if and only if the object has the attribute. It is "false" that the object has an attribute if and only if it is not the case that the object has the attribute. These considerations may at first seem trivial at first glance, but they are, again, a direct consequence of the "possible worlds", non-nominalist framework that the authors have chosen to work in. All of the discussions in the book are a fine example of the price that must always be paid in the selection of a particular framework in which to analyze or think philosophically.

There are many other interesting discussions in the book, such as the one of the product/process ambiguity and the paradox of analysis. Particularly interesting is the discussion on the counterexamples of the philosopher Edmund Gettier to the idea that a justified belief in a true proposition constitutes knowledge. The authors illuminate his arguments in their possible worlds context. The authors exhibit a clever example of a possible world in which a person justifiably believes a proposition which is true and yet does not know it.

Without a doubt the authors do hold that knowledge of the truth of some propositions really is possible. This leads them to address the question as to the limits of knowledge, and they conclude that there is a limit, a boundary between the class of humanly knowable true propositions and the class of (true) propostions which are not known to be true neither in the actual world or in any other possible worlds. Their justification for this leads to a consideration of "experiential" vs. "ratiocinative" knowledge and a fascinating discussion of the contributions of Immanuel Kant in this regard.

More than an introductory logic text, June 4, 2005, by D. Terry [Amazon.com]

This book is a fine introduction to logic and the philosophy of logic. The book provides a basic introduction to propositional logic, predicate logic, and modal logic, as well as a cursory description of Aristotelian syllogistics. It also provides an introduction to the theory of knowledge.

Throughout the book the authors define specific positions on issues of controversy or on issues where there is a lack of consensus among logicians and philosophers; they then justify their positions and provide arguments as to why their positions should be preferred.

For example, in a section of the book entitled "A Philosophical Perspective on Logic as a Whole", the authors introduce a threefold division of logic: propositional logic; predicate logic; and what the authors describe as concept logic, or the logic of analyzed concepts. They note that concept logic "is not well developed and is only rarely accorded recognition as a proper part of logic." They then state that one of their aims is to provide a philosophical defense of the inclusion of concept logic in the science of logic. As another example of the authors' defining a point of view over and against that of others, the authors go to great length to distinguish between sentences and propositions, and they then define propositions as the bearers of truth values. In doing so, they distinguish their position from that of W.V.O. Quine, who holds that sentences, not propositions, are the bearers of truth values. This characteristic of defining and justifying specific positions over and against the positions of others is quite unusual in an introductory textbook.

An important aspect of the authors' discussion of the philosophy of logic is their discussion of the relationship between semantics and syntactics. The authors open rich perspectives on the role that semantics plays in shaping contemporary philosophy of logic. The book provides a fine background for further study of semantics and the philosophy of language. The authors also provide a fine discussion of the de dicto/de re distinction. Finally, the Gettier counterexample to the tripartite theory of knowledge that the authors offer is the best such counterexample that I have read.

This is a fine book, and I recommend it heartily.

Book review – Possible Worlds: An Introduction to Logic and Its Philosophy, September 14, 2009, by Emil Kirkegaard.

I could write a long detailed review but it is entirely unneeded. This book is without doubt the most enlightening book that I have ever read about logic, and it doesn't even cover predicate logic! So that says a lot. It is recommended for anyone who wonders if talk of possible worlds is really worth it, who wants a systematic introduction to propositional logic and modal propositional logic, and who is not afraid of symbols.