Monday, March 16, 2009

School Vouchers

There is a very poorly written op-ed by Walt Gardner in the Christian Science Monitor about Vouchers, called School Vouchers Leave too Many Behind. The argument seems to commit the Nirvana Fallacy, aka the Perfect Solution Fallacy, since Gardner seems to be simply arguing that because school vouchers are imperfect, they should be abandoned. This argument only makes sense if we assume there is some perfect alternative, which of course there isn't, and Russel Roberts succinctly criticizes Gardner for it. Nonetheless, I think there are some implicit arguments behind this op-ed that deserve consideration, even though this poorly written op-ed fails to argue them.

For one, Gardner seems to be saying at the end of his op-ed that the students left behind by vouchers are actually worse off with vouchers than without, writing,
Without anyone in their corner, children who remain in regular high schools have a graduation rate well below that in voucher high schools
voucher supporters believe these children constitute the unavoidable price that must be paid in the service of the principle of choice
He cites their poor graduation rates, but this evidence doesn't prove that point, since these students would probably do poorly with or without vouchers. I would imagine that these students would be better off with vouchers, since they would be attending smaller public schools, which could thereby serve their smaller student pool better. Also, since vouchers are considerably cheaper (saving 10-15 thousand, and even higher in DCs school district, PER student) then that frees up more money for these students, though, of course, more money per se, is not the route to better education ( though it can potentially open up more possibility for better education).

Gardner is also implicitly arguing that the kids who take advantage of the vouchers are not better off, evidenced by lack of improvement in test scores. This is also a weak argument, since test scores are a weak indicator of good education. Long term success is a better indicator. This is a doggedly difficult thing to measure since its ultimately impossible to tell how successful they would have been without the vouchers. Thus, that parents of voucher kids are happier with the program is probably the best indicator available, and it shows that the vouchers are good.

Thus, if Gardner is making an argument that doesn't fall into the Nirvana fallacy, it seems to be that vouchers don't help those who do take advantage of them and do hurt those who don't take advantage of them. I think both of these arguments are weak and are poorly supported.

Of course, Gardners primary argument is that people are wrong who claim politicians are being hypocritical by sending their kids to good private schools, and then trying to deny the vouchers that are the means of the less privileged going to good private schools. But this argument depends on showing that vouchers actually hurt the poor, which he fails to do.

In the end, I think vouchers are a good idea, mostly just on the grounds that they save oodles of money. I think an even better solution would be to eliminate public schools and vouchers. Behind vouchers are the threat of creating arbitrary and ineffective standards for schools to be eligible to receive vouchers. Without vouchers and public schools, education could serve students instead of governments. Poor youngsters would be better served since most likely this situation would create the existence of free charitable schools for the poor, which could serve those who couldn't afford even the most inexpensive private schools. And I think most likely such schools would be guided by a mission to actually recruit underprivileged and neglected children and try to bring them to their school. The problem is that when the government swoops in and takes responsibility for something, like educating the young, it lifts the burden of people to take personal responsibility for themselves and their community. You remove government and people will be trying to assure that the kids in their community are educated.

Update: Mike Smith, senior advisor to the Secretary of Education made a statement about whenever a decision is made about education curricula or standards, at the federal level, it will be inevitably guided by politics. The Cato Institute responds that whenever a decision is made at any level of government (federal, state, local) on education standards and curricula, it will inevitably be guided by politics. And they link to a paper Neal McCluskey published for Cato two years ago called Why We Fight: How Public Schools Cause Social Conflict, that argues the only way to avoid conflict about curricula and standards is to let parents choose their schools.

Monday, March 2, 2009

Eubulides' Paradoxes

I love paradoxes, and have tried to collect a considerable number of them, in philosophy as well as in other intellectual disciplines. I define paradox rather broadly as any real or apparent contradiction or just something that seems to defy common sense. In many cases the paradoxes are in a sense superficial since the apparent contradiction can be resolved.

In the ancient world most of the interesting paradoxes are either from from Zeno of Elea or Eubulides of Miletus. I'll talk about Zeno later, but I want to talk about Eubulides right now.

He has seven paradoxes attributed to him, but many of them are redundant. Ultimately he really has four unique paradoxes: the Masked Man paradox, the Horn Paradox, the Liar paradox and the Sorites paradox

The Masked Man paradox basically goes: if there is a masked man who is your father then someone might ask you, "Do you know your father?" To which you say "yes." Then they ask: "Do you know that masked man over there?" To which you answer, "No." But since the masked man is your father, you seem to be saying that you both know and don't know your father. This is only an apparent contradiction resolved by either seeing it as an equivocation on the word "know" The first "know" means "is acquainted with," and the second "know" means "can identify." Or the apparent contradiction is resolved by recognizing that the second answer, "No, I don't know that masked man," was simply made in error. Namely, you could say, "I didn't realize that I knew the masked man, because I didn't realize he was my father."

Next there is the horn paradox, which basically goes: If we assume that you have whatever you haven't lost, then from the observation that you've never lost horns, you therefore must have horns, but of course you don't have horns. This is also an only apparent paradox. It is just the result of a bad initial premise. No, we can't say that you have whatever you haven't lost. We can say, you have whatever how previously had and haven't lost."

The next paradox is the liar paradox, which has a few variations. For example, if I were to say, "Everything I say is a lie," or "This statement is false." Both variations are probably best explained as arising from some of the artificialities of language. It does appear to present some problems for logic, so a number of attempts have been made to resolve it. I think I'll return to it in more detail later.

Finally, there is the Sorites paradox ("sorites" means "heap"), another difficult paradox and I think Eubulides' most interesting paradox. The idea here is that if I have a heap of grains of sand, and I take away one grain of sand then it is still a heap. And if I take away another grain, it is still heap. And if I extend this logic, then at some point it will be too small to be a heap. But I can't make a heap into a non-heap by simply taking away one grain of sand. So, how did it become too small to be a heap?

Mostly this paradox is built on the vagueness of language, since "heap" and "non-heap" are not concretely defined terms. But when used in logical argument they are treated as a precise bivalent, black and white distinction.

Another way to think of it: If a million grains of a sand is a heap then certainly 999,999 is a heap, so is 999,998 and 999,997, etc. From this we infer that if x number of grains is a heap, then x-1 grains is a heap. If we iterate this reasoning again and again, we eventually can conclude that 1 grain of sand is a heap, as is 0 grains of sand. I would classify this as a vertical argument: an argument where each new premise is dependent on a previous conclusion. Vertical arguments grow weaker as one increases the steps since one increases the likelihood that there is a weak or fallible argument somewhere along the chain. Vertical arguments depend on an unbroken chain of infallible arguments to work (doable in math, but less so in philosophy). To conclude that 1 grain of sand is a heap requires a vertical argument of many thousands of steps, Any fallibility in the assumption that "if x number of grains is a heap, then x-1 grains is a heap" is amplified by the number of steps. The argument becomes rephrased "if x number of grains is a heap, then x-1 grains is a heap, and if x-1 grains is a heap then x-2 grains is a heap, and x-3 grains is a heap, and x-4 grains is a heap ... and x-999,999 grains of sand is a heap." We get an argument that grows weaker each step, just as correlatively the heap of grains of sand grows less likely to be called a "heap" the more grains of sand are removed, until we are left with a remaining bunch of grains that no one would call a heap and a vertical argument that has been stacked so high that it topples over.