Paradox

The MIT Press Essential Knowledge

by Margaret Cuonzo

Thinkers have been fascinated by paradox since long before Aristotle grappled with Zeno's. In this volume in The MIT Press Essential Knowledge series, Margaret Cuonzo explores paradoxes and the strategies used to solve them. She finds that paradoxes are more than mere puzzles but can prompt new ways of thinking.

A paradox can be defined as a set of mutually inconsistent claims, each of which seems true. Paradoxes emerge not just in salons and ivory towers but in everyday life. (An Internet search for "paradox" brings forth a picture of an ashtray with a "no smoking" symbol inscribed on it.) Proposing solutions, Cuonzo writes, is a natural response to paradoxes. She invites us to rethink paradoxes by focusing on strategies for solving them, arguing that there is much to be learned from this, regardless of whether any of the more powerful paradoxes is even capable of solution.

Cuonzo offers a catalog of paradox-solving strategies -- including the Preemptive-Strike (questioning the paradox itself), the Odd-Guy-Out (calling one of the assumptions into question), and the You-Can't-Get-There-from-Here (denying the validity of the reasoning). She argues that certain types of solutions work better in some contexts than others, and that as paradoxicality increases, the success of certain strategies grows more unlikely. Cuonzo shows that the processes of paradox generation and solution proposal are interesting and important ones. Discovering a paradox leads to advances in knowledge: new science often stems from attempts to solve paradoxes, and the concepts used in the new sciences lead to new paradoxes. As Niels Bohr wrote, "How wonderful that we have met with a paradox. Now we have some hope of making progress."

Genres: Philosophy, Nonfiction, Logic

240 pages, Kindle Edition

First published February 14, 2014

About the author

Margaret Cuonzo is Associate Professor of Philosophy and Coordinator of Humanities at Long Island University, Brooklyn.

Reviews

[Andrea C. Briceño · Rating 4 out of 5]

Where there is progress, there is paradox. Each fuels the other.
Great read

[David Dinaburg · Rating 2 out of 5]

I’m not sure what led me to the MIT Press Essential Knowledge Series, but I know I wanted Self-Tracking. The library didn’t have it, however, so I took what I could get: Paradox. And, well, it was a pretty good book that devolved into a collegiate homework assignment somewhere past the halfway mark.

Note, though, that expectations color my world; I called it a “pretty good book” because I approached it as a cohesive narrative, not as a reference guide. The text itself began with interesting stories:

Intuitively, one would think that a population of predators would tend to do better if the amount of food available to its prey were to increase. More food for the prey means that more prey is available to the predator, and hence the predators’ population should expand as well. Yet, in fact, sometimes the opposite happens [citation omitted]. An increase in the food available to rabbits, for example, in a given area might lead to an overabundance of rabbits, and increase the population of its predator—say, wolves—until the population of wolves becomes unsustainably large and is destabilized. So more food for the rabbits can actually pose a threat to the population of wolves. This example shows our ordinary intuition—that more food and hence more prey is always good for a predatory group—is flawed.

The paradox of enrichment is a good example that will likely stick with me. The general thesis of Paradox—and I should mention that the book closes with a reminder of this, so it is not guilty of wandering—is that when paradoxes arise, they require people to actually examine the things they think they know. I learned something! Mission complete.

But there is much more text in the book, and a large portion of it just bounced off my brain:

The Pythagoreans argued along the following lines: assume that the square root of 2 is rational. That is, assume that there are two mutually prime integers, n and m, such that n/m = the square root of two. Put another way, n² =2m². If this is so, then because a square number cannot have any prime factor that is also a factor of the number of which it is the square, n² and n must be even. But according to our initial assumption, n and m are mutually prime, so if n is even, then m must be odd. Assuming that n =2k, we get 2m²= 4k², or m² = 2k²; then, by repeating the same reasoning, we can show that m is even. Thus, n must be both odd and even.

Yikes. This is not subway reading. This is not...well, this is not reading. At least not for me. Apologies to Paradox for being the book to reset my expectations for the MIT Press Essential Knowledge Series; as a basic primer or sporadic reference source, it does what it needs to do to promulgate knowledge on paradoxes. But it has none of the non-fiction storytelling conventions that I am starting to realize I actually require to approach dense texts. Your mileage may vary, but if you’re like me and are better at intuiting word problems then in manipulating formulae, this might not be the book for you.

[Frobisher Smith · Rating 4 out of 5]

It's pretty good, and I definitely enjoy the MIT Essential Knowledge series and will pick up more of them. Felt a little rushed near the end, Cuonzo takes us from Pythagoras to Kant to current philosophy of science with Popper/Kuhn/etc. in about 50 pages. Also, it surprised me that a book so heavy on discussion of the Liar's Paradox ("This sentence is false.") and recent developments in Logic as a field of study did not mention Gödel's incompleteness theorem at all. That very paradox lies at its heart and was an important (and explosive!) piece of modern formal logic.

Still, it is very good for what it is meant to be -- a thought-provoking introduction for the average reader. It's exploration of Bayesian analysis was especially informative to me, as I was pretty unfamiliar with that.

[Dominick Cancilla · Rating 5 out of 5]

I very much enjoyed this book, and its mathematical approach to classifying paradoxes is something I hadn't encountered before. My only disappointment is that there was not a comprehensive overview or list of famous paradoxes.

[Joel · Rating 4 out of 5]

Heavy reading. I'm not sure I absorbed the full implications of the different ways of solving/excusing paradoxes, but it was a geeky introduction to a field with no practical relevance to my life.

[Sarah · Rating 5 out of 5]

Smart book. Clarifies much. Not that I'm not still confused.

[Chris Esposo · Rating 4 out of 5]

This is a very excellent book outlining the analytic philosophical approach towards dealing with paradoxes. Unlike say a mathematical logic approach to this problem, which would probably define paradox strictly as a contradiction in a formal system, the author's scope includes paradoxes which may arise through natural language, and sleight of hands (like Monty Hall - otherwise wouldn't be viewed as a paradox), which includes paradoxes that occur in word puzzle settings.

The author introduces several overall strategies to tackling paradoxes including: "Preemptive Strike", which would be called refinement in other settings (think naive set theory to Zermelo-Frankel set theory) , the "Bayesian Approach", using a naive Bayes to determine posterior probabilities of paradoxes, based on the likelihood of the predicates, "Odd guy out", basically questioning some hypothesis identified as possibly causing the paradox, "Its all Good", arguing that the paradox arises to a type of linguistic legerdemain, and "You can't get there from here" (A Michigan reference it seems), which questions the reasoning where the paradox arose.

Of these, only two "Odd man out" and "Preemptive Strike" would probably be classified as a legitimate approach by mathematicians, since the rest would have been removed by well-formedness arguments and the like. "Odd man out" leads to an interesting aside conversation the author makes on the Quine-Duhem thesis, which states that it is not possible to isolate and test an individual hypothesis from a set of hypothesis.

In the mathematical context, this seems silly, but this is probably a very relevant conversation for a scientist, including those in the social sciences, which utilize "partial" and "marginal" arguments all the time, mostly out of necessity, as opposed to a clear thought out program a priori.

Other topics covered include the various ideas of Zeno, the semantical truth mappings of Tarski, variations of the set of sets paradox, Monty Hall, and even a small conversation of EPR at the end.

I thought the book was really good at conveying challenging material verbally, I had to replay certain segments a few times, and the book did suffer from not including any pdfs of diagrams, but we'll worth the listen. Highly recommend

[Anthony O'Connor · Rating 4 out of 5]

Solid

A good basic look at paradoxes - apparent inconsistencies or incoherencies which clash with our logic and/or our deepest intuitions. The author takes a look at some of the well known paradoxes. Zeno of course, time travel problems, the sorites problem, kantian antinomies, even the famous Monty Hall problem. And then looks at the ways we try to resolve them. Some are easily resolvable. For example the Monty Hall problem is just slightly non intuitive but is clearly understood with a little clear thinking. Others obviously come from mere ambiguity of words and expressions. But others are harder. The only clear resolution to the paradoxes of time travel is that time travel is impossible. But in current general relativity it isn’t. Closed time like curves and all that. So it remains puzzling.
Descriptions and explanations are thorough and readable. Even if the attempted Bayesian account of levels of paradoxicality is a bit lame. There is no great depth in any of this but it’s ok and worth a quick read.
The author concludes that paradoxes are great. They are opportunities. They reveal some limitation to our understanding begging for a deeper look and some eventual resolution. I couldn’t agree more.

[Steven Hart · Rating 2 out of 5]

I think this book possesses the same flaw as so many other academic books: it is unclear about what it is trying to accomplish. That is to say, it fails to present its information in a compelling way.

Although it does provide the reader with a clearly defined structure, the sections feel seem very disjoint. I'm not sure whether this is the result of poor writing or bad choice of structure, but either way, the result is a book that feels much more like a jumbled collection of thoughts and observations about paradoxes rather than a united theory or narrative.

I imagine it was quite pleasurable to write, but despite the merits of many of the ideas it presents, these structural problems prevent it from being an enjoyable read.

[Pat · Rating 4 out of 5]

It was inspirational to see the separation of the ideal and reality as a paradox. I think it gave me a bit of a grapple on how to understand the messiness of what it is to be a person in the real world. And as someone who was a little familiar with Bayesian statistics, it was fun seeing how it was applied to the context of a paradox. And I really liked the slight detour on discussion on the different beliefs of the scientific method.

[Kieran Wood · Rating 3 out of 5]

This was a very interesting book, but towards the end it became inundated with jargon that made it very difficult to parse. Even being someone who has looked at proofs and their limitations in analytical phil before I found myself getting caught out.

It's very interesting food for thought, but very very dense.

[amirah · Rating 4 out of 5]

Technical read.

[Lauren · Rating 5 out of 5]

Awesome book!! I picked this up after reading way to many Wikipedia articles about paradoxes and it was fabulous!

[Eric · Rating 3 out of 5]

I love the Lets Make a Deal paradox. On the whole, a bit too heavy. It's like a thesis in philosophy.

[Malola · Rating 3 out of 5]

Well, I'm definitely going to further check some of the paradoxes the author mentions.
One can clearly tell she's very smart, yet she's not good with words. The book is dense (which is good), but, given the topics, it might have not been the best idea to listen to it.

[James Townsend · Rating 4 out of 5]

Pretty decent introductory text on the topic of paradoxes. A good balance of general introduction, classification of solutions, and this history and future of the study of paradoxes, their implications, etc.

All in all, a fun read and very informative. I feel like I took away several particularly salient points about the various nuances and pitfalls of attempting to solve paradoxes that might be useful in my own work.

What kept this from being a 5 star book for me is that for a general audience text, I thought there were too many places where there were big gaps in the discussion that could only be filled if you had some deeper idea of where Cuonzo was going with the thought, which I imagine might be confusing for many readers (and certainly gave me pause at some points).

But mostly, I think this book succeeds in its general mission of taking the storied philosophical sub-topic of paradoxes and condensing a lot of information about it into an easily digestible volume for the motivated layperson. Give it a shot!

[Jonathan Haber · Rating 4 out of 5]

When the MIT Essential series came out, it focused on contemporary technology issues such as Open Access, Crowdsourcing and Memes. Having written a book in this series, the opportunity to create a short title introducing a complex concept to non-experts offered the chance to shape the definition of that concept (in my case, about Massive Open Online Courses, or MOOCs).

As the series shifted to cover philosophy (another major MIT list), I was curious how the authors would treat subjects that, unlike new technology, had a history of dialog attached to them. In the case of Paradox, author Margaret Cuonzo (a Professor of Philosophy at Long Island University) helps non-philosophers understand the intellectual challenges paradoxes have presented throughout history. In addition to walking readers through well known (Liar, Sorites) and not-so-well-known paradoxes, she describes various strategies for solving them while making the compelling case that it is the hunt for solutions (not the actual solving of them) that make paradoxes so intellectually fruitful.

[Alex]

Paradoxes are present when we're trying to solve the toughest of problems and constraints that we consciously or unconsciously apply to our everyday lives. Margaret Cuonzo provides a way for non-experts to learn about how logicians, philosophers, and mathematicians have thought about paradoxes and resolving them. In this process, you learn how paradoxes are essential for progress, that are logic systems are not bulletproof as we might have assumed, and tactics for thinking about the paradoxes we encounter in our own lives.

As much as she tries to introduce and clarify domain specific concepts, unless you have studied philosophy, logic, or math at a relatively high level you will probably be overwhelmed by the amount of new knowledge packed in the book like I felt. Regardless, there's enough you can learn from the book without understanding all the specifics that I think it's still worth checking out.

[Mark Z · Rating 5 out of 5]

A fresh take on paradoxes! Highly recommended.

[A L e X a N D e R · Rating 5 out of 5]

Great introductory text to the issue of paradoxes and the implications for scientific inquiry as well as philosophy.