Readers' Reviews of
Possible Worlds: An Introduction to
and Its Philosophy
by Raymond Bradley and Norman Swartz
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,
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
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
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.