Sunday, April 03, 2005

All the Fallacies, Baby

People make all kinds of mistakes. One of the more popular songs the kids are listening to is “Rich Girl” by Gwen Stefani. Its refrain goes like this:

If I was a rich girl (Na, na, na, na, na, na, na, na, na, na, na, na)
See, I'd have all the money in the world, if I was a wealthy girl
No man could test me, impress me, my cash flow would never ever end
Cause I'd have all the money in the world, if I was a wealthy girl


On two accounts Gwen mixes up her cause and effect, committing the Casual Fallacy of Wrong Direction.

-Just because you are rich does not imply that you have all the money in the world. I can think of lots of rich people that do not fulfill the criteria (like, all of them).

-Just because you have all the money in the world does not imply that quantity is infinite. In fact, the amount of money is a set comprised of a limited number of elements, thus it is actually finite.

Most people would agree that it’s simply a matter of direction and the reverse (if I had all the money in the world, I would be a wealthy girl) is logically valid—assuming "I" is a young female). Casually speaking, I would agree with them.

But let’s be anal retentive economists and see if there’s a way to make it invalid. Money is often quantified into four broad categories: M0, M1, M2 and M3 (economists aren’t very creative). Each one of these definitions can be applied to different currencies. Suppose Gwen is talking about M0—all cash and coin in circulation—of, say, the Soviet ruble. Since the Soviet ruble is no longer in circulation, that total is zero. Having all the money in the world can result in no change to your bank account. If you have no other holdings, then you certainly are not rich even with the inclusion of these rubles.

She also made the Inductive Fallacy of Hasty Generalization when she said “No man could test me, impress me” as a result of her theoretical limitless funds. Perhaps in her experience all the men she’s encounter have been intimidated by wealth but I doubt she’s been tested by a large enough portion of the population to logically make that conclusion (especially since all we need is one case that makes the assertion invalid). However, it’s reasonable to conclude a proportion of men could not test nor impress her if she was wealthy, which I think she is.

To make her song logically valid to our anal retentive selves, it would have to go a little something like this:

Suppose I was a rich girl (Na, na, na, na, na, na, na, na, na, na, na, na)
Now suppose I have all the legal tender in the world (assuming that quantity of legal tender represents a significant proportion of economic activity and the economy in question is widely defined), thus I would be a wealthy girl
A larger portion of men couldn’t test me, nor could they impress me, my cash flow would be larger than possibly most
Because I'd have all the legal tender in the world (assuming that quantity of legal tender represents a significant proportion of economic activity and the economy in question is widely defined), I would be a wealthy girl


Logical errors may make result in poor understanding, but they are certainly useful in music.

Note: I'm aware that "widely defined" and "a significant proportion" are not terms appropriate to logical agruments but the vagueness of the word "wealthy" barred me from constructing a more precise logical statement.

Bonus Question: There is an economic argument that questions the validity of my claim that even after correcting for Wrong Direction and Hasty Generalization, the lyrics still don't logically hold. What's the argument?

4 comments:

Mike said...

Of what value, Mr. Youngberg, is "all the legal tender" held by one person? Holding all the legal tender is equivalent to holding none of the legal tender. I offer, then:

Suppose I was a rich girl (Na, na, na, na, na, na, na, na, na, na, na, na)
Now suppose I have a vastly large amount, (but still not a majority) of the legal tender in the world (assuming that quantity of legal tender represents a significant proportion of economic activity and the economy in question is widely defined), thus I would be a wealthy girl
A larger portion of men couldn’t test me, nor could they impress me, my cash flow would be larger than possibly most. Even though the holding of currency in and of itself is not necessarily a cash flow.
Because I'd have a vastly large amount, (but still not a majority) of the legal tender in the world (assuming that quantity of legal tender represents a significant proportion of economic activity and the economy in question is widely defined), I would be a wealthy girl

Lisa said...

This is one of the funniest things I've read in a long time. Way to hold pop music accountable to reason.

David said...

Your concern, Mr. Mills, that having all the legal tender in the world must then mean that legal tender becomes useless is well-recieved, but be careful. Legal tender does not always include checks, credit cards and debit cards. Thus cash would still be useful even if all the physical cash was concentrated with one person.

So the lyrics would go like this:

Suppose I was a rich girl (Na, na, na, na, na, na, na, na, na, na, na, na)
Now suppose I had all the legal tender in the world (assuming that quantity of legal tender represents a significant proportion of economic activity and the economy in question is widely defined and the legal tender is restricted to cash units of a certain country), thus I would be a wealthy girl
A larger portion of men couldn’t test me, nor could they impress me, my cash flow would be larger than possibly most. Even though the holding of currency in and of itself is not necessarily a cash flow.
Because I'd have a vastly large amount of the legal tender in the world (again assuming that quantity of legal tender represents a significant proportion of economic activity and the economy in question is widely defined and the legal tender is restricted to cash units of a certain country), I would be a wealthy girl

Anonymous said...

After talking to Mike today about this blog I decided to log and and see what was going on. This post caught my eye, seeing how I both enjoy money theory and pop music.
I raise contention with the third and fourth line. Now, lets imagine that someone really did hold an incredibly large amount of money compared to everyone else. First, if it was legal tender, therefore being given value by leglislation, then I could see a government being like "Well Shit, this sucker has all of our damn money, lets just print some other type of money so our economy can function." Second, if a person held a rediculous amount of privately issued currency this would cause a distortion in the value of that currency and therefore the price level. Therefore, some entrepreurial soul would come along and create a new currency that wasnt so "busted" to use a term from pop music. So, to change the lyrics some more...

Suppose I was a rich girl (Na, na, na, na, na, na, na, na, na, na, na, na)
I would have to base all of my wealth on something else than money, say pork bellies, or something people really really want, like my sexy body.
A larger portion of men couldn’t test me, nor could they impress me, my cash flow would be larger than possibly most. Even though the holding of currency in and of itself is not necessarily a cash flow.

Kyle M.