Never read the book but I heard an NPR interview with the author about the book (here). According to the book's descriptions, Landsburg claims that notions from math, economics and physics can effectively shed light if not solve some of life's most intractable problems. I was skeptical that this economist will shed any kind of new light on the truly deep questions of life that is also the traditional territory of philosophers.
His NPR interview sure as hell doesn't shed any light on any deep questions. Some of the topics are quite interesting and philosophically relevant but the conclusions he anounces basically would not be very surprising to most philosophers (or intelligent layman) such as Landsburg's claim that many of our most deeply held beliefs are likely wrong and that if we are rational, we'd come to consensus on much more of what we'd disagree on. No surprises there. This is what many of the most famous philosophers have been preaching for thousands of years. Granted he does use "formal" economic models to arrive at his conclusions but I don't know if that is all that necessary at least in this case. It would be like using a sledgehammer to open a can of soup when a can-opener was at hand and then proclaiming victory over the "intractable" can of soup.
But what got me was his seeming naivity and hubris in dealing with some other (non epistemic) issues. He claims that those who are against free trade are committing a greater slight against truth than those who deny the veracity of the theory of evolution. This is because the theory of evolution is an empirical theory (some philosophers of science actually think that the theory of evolution, is in some sense, not empirical!) while the argument for free trade can be made "on pure logic". Here's a direct quote from the interview:
When it comes, on the other hand, to the argument for free trade; [it] is based not on evidence,...not on looking at something in the laboratory or looking at something in the world, it's based on pure logic. There is a purely logical argument for why free trade has got to make people on both sides of the border richer.
First of all, even if there were a "purely logical" way of proving that free trade will make everyone richer, that still wouldn't show that we'd be better off with free trade. There are non monetary reasons why people might reject free trade (ethical, environmental, etc.). So Landsburg is probably at least guilty of a strawman here and he will likely have to argue further, using non "purely logical" means to do so. But it also seems extremely naive to think that one can prove using nothing but pure logic (I don't exactly know what he means by that) that free trade will make everyone richer. Is he saying that results from free trade as it is modeled in the formal mathematical models used in economic modeling will always apply to real life economic circumstances? That's seems preposterous and economically naive. If not then it's not a purely logical argument and the truth of free trade being economically good for all will not be necessarily true in real life.
In a section of his book's introductory chapter, he claims that the truths of mathematics are necessarily true ("eternal and immutable" in his words). But this is a very controversial philosophical question that has beset philosophers for a long time and there is no consensus on it.
Take for example, what by many mathematicians to be the most interesting unsolved question in all of mathematics: the continuum problem. Kurt Godel (1939) and Paul Cohen (1963) proved that the continuum hypothesis (CH) is independent of ZFC. There are some philosophers and logicians who happen to think that we can prove it (or its negation) if we add an additional axiom. Godel once proposed a possible axiom that might do the trick but the weird thing is that now some logicians think that its negation might be actually correct! Adding an axiom is an extra mathematical affair. The proposed axiom's truth and even coherence will have to be argued for using arguments outside of math itself. There are also formalists who think that CH is neither true nor false, simpliciter. We can add either as an axiom to our formal system and get a consistent system (so long as we don't add both). If this is true then that means that many of the most interesting truths of mathematics are not human independent; they are determined by the particular formal system chosen.
There is a bunch of work done on mathematical platonism/anti realism debate by many good philosophers. I am not an expert on this area but I do know that it would be a supreme act of hubris to ignore the wealth of philosophical debate here and simply either assume that the truths of mathematics are "eternal and immutable" or argue from within mathematics for their truth. Such issues can never be resolved from within mathematics because they are, by their very nature, metamathematical (hence very much philosophical).
So if what Landsburg is really saying is that he is not arguing for the total replacement of philosophical methodology in tackling these questions with mathematical, economic and physics methodology but simply that these other disciplines have much to enrich philosophy, then
1. that would also not be surprising at all for philosophers have always used ideas developed in other disciplines to analyse more traditional philosophical problems. The discipline of philosophy is famous for this and there is overwhelming amount of examples. More interestingly, many sciences were spawned from philosophy as a way to enrich philosophy by developing novel methodologies for understanding the world (such as modern economics!). Philosophy is a multi-disciplinary subject; it may be the multi-disciplinary subject par excellence and that is how most philosophers have always thought of it.
2. I'd like to see an example where Landsburg does illuminate one significant controversial philosophical problem using notions borrowed from these other disciplines (that hasn't already been done by a philosopher!) but none has been offered or even touched on. Surely he could have provided one good example in the interview? Why hasn't a single "deep question" been illuminated on or even dealt with during the interview or on the cover of the book? That's very odd and seems evasive.
In the end, we seem alway to come back to philosophy. These questions are difficult and require philosophical analysis. Landsburg comes off as having an extremely crude understanding of philosophical problems and the work that has been done.
So it seems to me from the interview and some of the book's descriptions that there is much hand-waving, arrogance and ignorance from a non-philosopher towards philosophy. I'll have to read the book to find out for sure (maybe he does do what he claims to) but after reading some of the reviews on Amazon.com, my initial skepticism has only deepened.