By Dr. James A. Lindsay
Infinity and God have been close bedfellows over the recent millennia of human thought. But this is James A. Lindsay’s point. These two ideas are thought, mere concepts. Lindsay shows in a concise and readable manner that infinity is an abstraction, and shows that, in all likelihood, so is God, particularly if he has infinite properties.
This book is about math. It is about God. It is about stressing the importance of not confusing these two ideas with reality. Never the twain shall meet.
“A short and engaging read on the meeting of two huge ideas, infinity and God, that leaves us seeing both as abstract ideas that may have nothing to do with reality. Honest and accessible, Dot, Dot, Dot is a great little book to stretch your thinking.” – Peter Boghossian, author of A Manual for Creating Atheists
“Timely, important and very readable, this book pulls the rug from under theists’ feet.” – Jonathan MS Pearce, The Little Book of Unholy Questions
“Read this to avoid making any more cardinal sins and learn how much math is an amazing human endeavor.” – Aaron Adair, PhD, The Star of Bethlehem: A Skeptical View
Here are some Amazon reviews of the book:
This book has the most stunning and insightful powerful arguments against putting infinity with God I have ever read. He single handedly dismantles the idiocy of trying to make God infinite. The best explanation anywhere in print, and one of the most important books written on this topic. This is a MUST read for everyone who thinks God is infinite. It can’t work, and with minimal math, he demonstrates with simple logic why it is folly. A devastating destruction of William Lane Craig’s Kalam argument as well. Craig simply has no clue what he is talking about. Go with Lindsay.
Infinity is a really, really weird concept. It takes any intuitions we have and makes us say apparently silly things. But there are rigorous ways of dealing with infinity, but there are also limitations, even for the most brilliant mathematicians.
One of the points is that you never really reach infinity. No matter where you start on a number line or how long you count forward, you never even get closer to infinity. This means that it is not possible to use something finite to create an infinite set. That is, you cannot construct infinity from finite sets and operations. Hence we get lazy when writing a set that is supposed to go on forever with … (hence the title of the book). And yet we can talk about infinite sets. In fact, we can talk about different sized infinities. If that didn’t make sense to you, then you are getting the point about how weird infinity is.
In this book, mathematician James Lindsay shows many important points about how infinity is used and understood by mathematicians and how the terminology is poorly used in other contexts, especially when applied to God. In many ways the book is focused on problems with the infinite god concept, but what I found as one of the more interesting threads running through the book is the problem with mathematical Platonism. What Lindsay shows very well is how much math is a human project. We chose the various axioms and definitions, and those different choices can lead to all sorts of amazing conclusions. But showing how much math is a human invention, it shows that there isn’t really a “true form” of the set of all rational numbers and the like. We chose the rules. Historically, there have been arguments about whether negative numbers are really numbers, or if i is a number or not. Or even if zero is a number! Why do most people consider these objects numbers in the end? Because of what we can do with them. They are practical, even imaginary numbers (I couldn’t do the physics I learned in grad school without them).
Seeing the human side of math (rather than the human side of certain mathematicians) was excellent, especially when it comes to the sorts of concepts that bugger human comprehension. I value the volume for doing more than just showing what makes an infinite God incoherent, but it shows how much math is truly a human adventure and not simply that boring stuff forces on you in school.
It is not often that one comes across an atheist text with such superlative content. Lindsay is no charlatan. This is not a book of making guesses; this is a book of putting things in context, most specifically the idea of God, Infinity and the “existence” of abstract concepts. One could say, “Plato is dead,” and from this event naturally follows the death of God. It gives me great pleasure to know that theists will struggle immensely with the clear contents of this book (not because it is in any way hard to understand but because the arguments are so basic and complete).
There are two contemporary atheist books that stand out in my mind as being exceptional (and God knows I have read lots of atheist books!): one is the The Atheist Primer by Malcolm Murray, and now added to the list is Infinity Plus God by James Lindsay. These books both have the same quality; they cover tons of ground in a short space; both authors are exceedingly clear and have an authoritative command of their subject.
This book is not only applicable to atheists and theists; it is relevant to anyone who wants to think clearly in the realm of ideas; to anyone interested in the nature and function of logic; to anyone who has ever been burdened by the thought of infinity.
Lindsay’s dialectical power, which is a power of logical clarity and concision, is quite exceptional. I hope to see him debate William Lane Craig (as he forever destroys the cosmological argument in this book) as well as the hot-headed, over-exaggerated, preying on ignorance, John Lennox. [My advice to Lindsay is to have a written exchange, as these sophists use the imprecise format of a verbal debate to push their loaded questions.]
The value this book has in the realm of education, for the purpose of promoting clear thinking, is hard to estimate.
Just buy a copy and read it. Even if you disagree with his conclusions your thinking will be sharpened and refined. You have nothing to lose!
“…as weird as it is, a philosopher could prove “logical necessity” for the existence of some entity, say a deity, and yet no such entity must actually exist in reality. This claim sounds preposterous, but if the logical framework the philosopher is using doesn’t match reality, we can prove all sorts of things are logically necessary and yet physically meaningless.” pg.30