
Approaching Infinity by Michael Huemer Publisher: Palgrave Macmillan, 2016. This is a page of information about my book, Approaching Infinity. Please consider buying it. 
The publisher has granted permission to post the excerpts linked below. Please do not reproduce without permission of the publisher.
List of Figures  xi 
Preface  xii 
PART I The Need for a Theory of Infinity  
1 The Prevalence of the Infinite  3 
2 Six Infinite Regresses  9 
3 Seventeen Paradoxes of the Infinite  17 
PART II Old Theories of Infinity  
4 Impossible Infinite Series: Two False Accounts  41 
5 Actual and Potential Infinities  49 
6 The Cantorian Orthodoxy  71 
PART III A New Theory of Infinity and Related Matters  
7 Philosophical Preliminaries  93 
8 Sets  108 
9 Numbers  119 
10 Infinity  143 
11 Space  162 
12 Some Paradoxes Mostly Resolved  176 
13 Assessing Infinite Regress Arguments  229 
14 Conclusion  247 
References  261 
Index  269 
From ancient times, infinity has been steeped in paradox. According to one famous argument, nothing can ever move, because to move from one point to another, one must first travel half the distance, then half the remaining distance, and so on. Another puzzle asks us to imagine that a lamp that starts out off, then is turned on after half a minute, off after a quarter minute, and so on; at the end of one minute, is it on or off? Most observers think that the first of these infinite series can be completed, but the second cannot. Why? This book addresses this and many other puzzles about infinity, most of which have no generally accepted solutions. A new theory of the infinite is advanced, on which an infinite series is uncompletable when it requires something to possess an infinite natural, intensive magnitude. Along the way, the author addresses the nature of numbers, sets, geometric points, and related matters.