thinking

This article caught my eye today:

http://www.newsweek.com/2010/08/05/the-limits-of-reason.html

It’s interesting for a number of reasons.  First, the content itself is kind of cool – why are humans irrational?  It’s a good question.  Second, they mention specific examples – including some actual logic analysis – of things people get wrong, and maybe why they get it wrong.  Finally, and perhaps most importantly, it’s interesting for what it doesn’t do.  It doesn’t do a good job of analyzing how the conclusion was reached.

1. Why are humans irrational?

This is a great question, because it is a major contradiction in our day-to-day lives that has a huge impact on how we live and our success as individuals and societies.  And looking at it from the evolutionary perspective is insightful, because it strikes at the core of the contradiction — if our reasoning is flawed, wouldn’t it follow that our faulty conclusions would diminish our survival?

For these reasons, I feel the work being discussed is very relevant and worthwhile.  It is a great question, and a good context within which to ask that question.

The article claims (or rather, cites other work which claims) that we tend to make reasoning mistakes which can help us win arguments.

I’m not sure I really agree with this conclusion.  The main problem is: Wouldn’t it just be better for humans if we were swayed by more logically-correct arguments?

In other words, the article’s conclusion seems to simply defer the contradiction of bad human reasoning to a new problem of bad human argument-listening.  This is still a huge, looming problem that hasn’t even been attempted here.

Here’s another approach we could take to tackling this problem: categorize the types of mistakes humans most often make (I think this has already been worked on), and then look for situations in which the mechanism behind the “faulty” reasoning is actually helpful.  This method – finding good properties of evolved traits – makes much more sense to me.

If you want to understand why something evolved, you must understand how it helps survival.

2. Logic analysis

As a mathematician, I can’t avoid commenting on the logic analysis of the article.  Specifically, the article says:

Consider the syllogism “No C are B; all B are A; therefore some A are not C.” Is it true? Fewer than 10 percent of us figure out that it is, says [Hugo] Mercier.

Actually, this line of reasoning is not generally correct.  To be more precise, if any B exist, it is correct, but if no B exist, then the conclusion may or may not be correct.  If you know what a Venn diagram is, then that’s probably the simplest way to visualize the problem:

The first statement omits anything from being in C ∩ B.  The second omits anything in B outside of A.  The result is the Venn diagram on the right.  Clearly, anything in B must be in A but not C, which would verify the conclusion.  The possible mistake is that B and A outside of C could be empty!

Let me illustrate with an example.  Fermat’s Last Theorem states that there is no integer solution to the equation x^n + y^n = z^n with x,y,z,n > 0 and n > 2.

Let’s plug in some values to the above argument.

Let A = (quadruples (x,y,z,n) of positive integers with n > 2).

Let B = (quadruples (x,y,z,n) of positive integers with n > 2 and x^n + y^n = z^n).

Let C = (quadruples (x,y,z,n) of positive integers with n > 2 and x^n + y^n ≠ z^n).

We can apply the above argument:

First, No C are B.  Yes, that’s true.

Second, all B are A.  Yes, that’s also obviously true.

Therefore, some A are not C.  But anything in A and not C is a counterexample to Fermat’s Last Theorem!  According to the article, I’ve just proven the theorem false.  But of couse I haven’t.  I’ve just pointed out that this line of reasoning can fail.  So the 90% of humans who “fail” to confirm the syllogism aren’t so stupid, after all.

3. The missing analysis

I’m about to criticize this article, but I want to preface the criticism by saying that I’m glad the article exists.  There is a gaping hole in journalism around science.  We need more science journalism because we need a culture that celebrates research and progress.

The best kind of scientific journalism is both appreciative and critical at once – this article is not critical enough.  It doesn’t sufficiently explore the key question of any good investigation: why do the researchers think the new claim is true?  Sadly, this is the norm in mainstream so-called scientific journalism.  The articles are so caught up in trying to decipher the complexities of the new ideas that they forget to ask why we need the complexities in the first place.  Why don’t the simpler answers suffice?

It is a bit ironic that an article decrying the carelessness of human reasoning fails to reason carefully.