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The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us
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The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us

4.02  ·  Rating details ·  725 ratings  ·  72 reviews
An exploration of the scientific limits of knowledge that challenges our deep-seated beliefs about our universe, our rationality, and ourselves.

Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, ma
Hardcover, 403 pages
Published August 23rd 2013 by MIT Press (first published January 1st 2013)
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Feb 18, 2014 rated it it was amazing
excellent drive through the paradoxes and limits of science - thankfully free of useless speculations and very moderate in the authorial bias towards this or that position, I would say that this book is a great example of how natural philosophy books should be written.

Very clear presentation - I knew most of the stuff there and read and thought about lots of it across time, but I still immensely enjoyed the book and there was new thing for me too, the Goodestein sequence example (of a more natur
Emre Sevinç
Nov 14, 2017 rated it really liked it
Back in the day, sometime in 1930, David Hilbert, a very smart mathematician said

"Wir müssen wissen. Wir werden wissen" (We must know. We will know. (It sounds way more authoritative in German, try it.))

to which another smart guy, Mr. Gödel had already replied:

"Hold my beer..."

The rest is history. And what a history it's been. Among the stellar achievements of humankind are the ones that sound like "oops, seems like there's no way we can solve this, here's the proof. Sorry." Because, we wouldn'
Muhammad Arqum
Jan 20, 2014 rated it it was amazing
What a book! What a gem of a book!
Initially I was a tad disappointed because I thought this would be a debate on metaphysics and most probably on existence of God or case of religion and that was the reason why I picked it up in the first place. It did not start that way, it did not even give an impression that it would eventually lead to that. The first few chapters introduce what logic is, how can we define reason and so fourth. It had plenty of problems that I had studied in my Programming a
يوسف صامت بوحايك
Oh I finished this awesome book !
The first time I read the book’s title, I thought it's gonna be a boring deep philosophical book fulling of complex philosophers’ discussions, but instead I found a simple book discussing the different limitations and contradictions that our thinking might lead us to, the book raised these limitations by presenting several paradoxes and its explication using proof by contradiction, to clear its impossibility as a limitation to our logic.
In other chapters, the boo
Mar 12, 2014 rated it really liked it
From its suggestive title, many might expect this to be a book (by a scientist, nonetheless) arguing for the relevancy of religious faith as an explanation for reality when science itself is unable to do so. Well, sorry to disappoint, but the book, thankfully, has nothing to do with religion vs. science. Rather, it's about the structure of reason itself and is an intellectual tour of paradoxes, limits to observation in physics, computing impossibilities, and the incompleteness of mathematical lo ...more
Bjørnar Tuftin
Who would I recommend this book too ... On the one hand it would be someone who knew less about the many topics in this book, as I found a lot of it tedious and overly detailed. But at the same time some of it went over my head. I definitely know the second to last chapter did. It was like revisiting a class I almost failed in university, and it was still incomprehensible. So perhaps someone who doesn't mind only enjoying part of a book?

Then again I also have issues with some of the contents, wh
Oct 23, 2014 rated it liked it
Shelves: mathematics, science
An interesting overview of the practical and theoretical limits of logic, mathematics and science. Deals with the limits of knowability, determinism, computation and predictability in science and mathematics. This is a clear and concise study of various topics from classical logic to modern physics, but lacks a quest for deeper understanding.
Vasil Kolev
Aug 04, 2015 rated it did not like it
This was horrible. Even the things I knew were explained so bad that I was unable to understand them, and as a whole the book tries to dazzle idiots instead of explaining the (actually pretty interesting) problems.
Harold Struik
Jul 08, 2019 rated it really liked it
Brilliant, in depth but not exhausting.
Mar 25, 2018 rated it really liked it
And here I thought quantum computing would be kind of a revolution...
Apr 11, 2020 rated it really liked it
This is such a thought provoking and beautiful book, it’s really made me wonder why there are so few poetic evocative works of popular science to combat the one reason religion always beats rational thought, the romance and the emotional content. Maybe I just haven’t read enough. Alan Lightman and Carl Sagan come to mind, and sure there are beautiful passages in many of the really serious books, but the popular science overviews made for filthy casuals like me are usually so prosaic. Passages of ...more
Sam Eccleston
Nov 04, 2016 rated it really liked it
This is a pretty interesting read- it covers a lot of information while managing to keep the discussion concise and to the point. The author tries, and mostly manages, to be fair to the different positions he outlines, even those he disagrees with, and is refreshingly honest about the difficulty of finding certain answers to difficult questions.

Having said this, he sometimes does not express positions he disagrees with in quite the detail or forcefulness that they deserve; on occasion he skirts
Doctor Moss
May 31, 2020 rated it really liked it
Shelves: philosophy
I was hoping for two major discussions in Yanofsky’s book.

First, a survey of paradoxes and other conundrums, frustrations, etc. having to do with the limits of “reason” as a tool for understanding the world. And then a probably very speculative analysis to find themes and maybe some theoretical conjectures about how we might tie together and understand those limits.

We get much more of the first than the second. Yanofsky takes us through a fascinating survey of paradoxes and other types of limit
Jan 20, 2014 rated it liked it
I wanted some unique insight into reason but did not find it. I was happy that Douglas Adams and Yogi Berra were each quoted once, though. The one insightful take-away was from the Norwegian Boy Scout Handbook: "If the terrain differs from the map, believe the terrain." Are you listening GPS users!!! ...more
Nov 06, 2013 rated it really liked it
Quite interesting, covers a pretty broad range of topics in terms of their limitations. The book is largely equation free, but I'd recommend learning a bit about logic and its notation if you want to get the most out of it. ...more
Tim Sharp
Mar 04, 2016 rated it liked it
A grand tour of various fallacies, logic problems, linguistic contradictions and mathematical/philosophical issues with reason. Very tied down to rationality, as one would expect. This wasn't quite the grandslam against reason I expected, but a generally entertaining read nonetheless. ...more
Mills College Library
001.01 Y24 2013
Giacomo Mantani
Oct 01, 2017 rated it really liked it

The Outer Limits of Reason is as far as I remember one of the best research essay that I have read so far. I definitely recommend the book to all inquiring minds around and to anyone who is too much confident about him/her-self knowledge.

Noson S. Yanofsky confirmed his knowledge page by page and with astonishing clarity explain hard topic such as Chaos, Relativity Theory and Quantum Mechanics. As a graduate student of Computer Science and Engineering I have found really well written explanations

Gary Schroeder
Mar 15, 2021 rated it liked it
This is an entertaining review of the concept of knowability. Some authors out there (Like David Deutch, for instance) have written books that attempt to prove that there are no limits to knowledge, that all problems are solvable. Noson Yanofsky takes a different approach: he tries to show all of the problems for which a solution does not exist and all of the aspects of the universe which may be forever unknowable.

Some unknowbale things are so because of the limitations of language. Some things
Sep 20, 2020 rated it really liked it  ·  review of another edition
Very interesting read, although it was quite the effort (a lot of re-reading of explanations and passages) to even get a basic grasp of a lot of the concepts that were being discussed (that being said, the models and diagrams really helped).

My biggest gripe with the book is the interpretation of quantum mechanics that the author describes in a few passages. I'm an absolute layman, but as Mr. Yanofsky stated that consciousness causes wave function collapse (during the exploration of the Schröding
Jan 31, 2016 rated it really liked it
What can we know and what can we not know? This is the subject of Noson S. Yanofsky’s thought-provoking book “The Outer Limits of Reason: What Science, Mathematics, and Logic Cannot Tell Us.”
The branch of philosophy that deals with what we can know is called epistemology. Although this area of thought may seem far removed from our everyday lives and hopelessly intellectual, it is, in fact, of fundamental importance to understanding what it means to be a human being.
This 2013 book enumerates,
Sayed H Fatimi
Sep 02, 2020 rated it really liked it  ·  review of another edition
An absolute must read for all those with an insatiable appetite for knowledge and understanding. Without delving too deep into each topic, this book does well to introduce the reader to a diverse, but well connected, web of information and problems that face human beings; our existence and the universe, not being the least. From elementary logical formalism, to introductory physics spanning a couple centuries, paradoxes that boggle the greatest minds, mathematics underpinning our very reality, p ...more
Marcus Chee
Dec 05, 2017 rated it really liked it
This review has been hidden because it contains spoilers. To view it, click here.
Mar 20, 2020 rated it really liked it
The author explains how although we consider science and reason to be infallible and beyond doubts, in a lot of ways, these also have their own limitations. The very basis of science - induction, which is the ability to predict something based on few sample studies, is flawed. He doesn't downplay the importance of science though, simply opens our eyes to that fact that like everything, this too is not without its share of drawbacks and science can certainly not answer everything.

He does use a lo
Mario Krapp
Mar 28, 2020 rated it did not like it
Shelves: not-finished
I had to put this down after the first chapter. I do not remember how this book ended on my „to read“ list but usually those books are recommendations I pick up from anywhere else (and usually they are good). I also had to read a few review los of this very book, just to see if I’ve missed a point or something.

I haven’t.

This book is simply not for me. I don’t like the style. It’s overly detailed, repetitive, and boring. Again, I’ve just read the introduction and the first chapter. But skimming t
Nov 16, 2017 rated it liked it
explain advanced topics using simple term, yet somehow fails to clearly explain them.
what's the target reader of this book? somehow it fails to clearly define that.
too much tedious yet half-baked proof and statements provided.
non-stem readers will be overwhelmed by this book, yet more advanced reader will not be satisfied with its content as well (hello? can you please not say "it is too tedious to put the proof here" when you flashed the topic in early part of the book please?)
Ogi Ogas
Mar 16, 2019 rated it it was ok
My ratings of books on Goodreads are solely a crude ranking of their utility to me, and not an evaluation of literary merit, entertainment value, social importance, humor, insightfulness, scientific accuracy, creative vigor, suspensefulness of plot, depth of characters, vitality of theme, excitement of climax, satisfaction of ending, or any other combination of dimensions of value which we are expected to boil down through some fabulous alchemy into a single digit.
Jun 22, 2020 rated it really liked it
There's a lot of very interesting material in this book, and it's generally well presented. Less one star because there's also some surface skimming, under-explanation, and repetition. And because the author is not the most sparkling of prose stylists. A good read, not a great one, that covers a lot of the same ground as other books on the subject. Still, I profited from reading it. ...more
Howard H.  Stevenson
A great challenge to the accepted dominance of reason

The book shows the difference between unknowable and irrational. Often academics and scientists presume that something is knowable and deny the irrationality of that assumption. Thank you!
Tony Gualtieri
Oct 24, 2017 rated it really liked it
I read a lot of popular mathematics books, so there is little that is new here, but it's interesting to find all these paradoxes in a single place. A good synthesis of the limits of logic and the strangeness of contemporary physics. ...more
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26 likes · 4 comments
“Douglas R. Hofstadter, an American researcher, speculates that the human mind has consciousness because it has the capability of self-reference. Since we can think about ourselves and think about ourselves thinking about ourselves, etc., we are capable of feeling that we are an "I". Contrast that with what we have learned in this chapter. This chapter tries to show that the computer's ability to perform self-reference is the cause of its limitations. Can we say that self-reference in computers brings limitations while in humans it causes consciousness? Perhaps.” 2 likes
“One of the more interesting paradoxes about knowledge is called the surprise-test paradox. A teacher announces that there will be a surprise test in the forthcoming week. The last day of class is Friday of that week. What day can the surprise test happen on? If the test is going to be on Friday, then after school on Thursday night the students will already know that the test is on Friday and it will not be a surprise test. So the test cannot happen on Friday. Since this was purely logical reasoning, everyone knows this. Can the test be on Thursday? After class on Wednesday night the students can deduce that since the test has not happened already and it cannot be on Friday, it must be on Thursday. But again, since they know that it must be on Thursday, it will no longer be a surprise test. So the test cannot occur on Thursday or Friday. We can continue reasoning in the same way and conclude that the test cannot happen on Wednesday, Tuesday, or Monday. When exactly will this surprise test occur? Logic has shown us that a teacher cannot give a surprise test within a given time interval. This is a paradox because it goes against the obvious fact that teachers have been torturing students with surprise tests for millennia. It” 0 likes
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