Tuesday, June 26, 2007

Stool Pigeons and Quantum Logic

Claude brings us a nice ethical problem,

Many are brought up being told that you should never tell on someone. At the same time, whistle blowing can bring many benefits to society. When is it unethical not to tell? Where do you draw the line between answering the questions "Who threw that spitball?" and "Who dumped that toxic waste?"
Claude frames the issue perfectly in asking where the line is to be drawn. To think about it, let's see what is behind the line in the first place.

Ethical judgments are a combination of factors. When we approach a moral situation we need to be concerned with who did it, what s/he did, to whom s/he did it, the overall effects of having done it, and the effects on those to whom s/he has special moral obligations. The first factor is what Aristotle was playing with in his virtue system, the second is the sort of duty approach to ethics we see in Kant, the third is a rights-based approach, the fourth is the ends/means reasoning of utilitarianism, and the fifth is the sort of care-based approach that we find in second-wave feminist writers on ethics. Fortunately for us, in the vast majority of cases, these all line up and point towards the same choices. In almost every case, determining the morally right thing to do is trivially easy.

In the hard cases, we have conflicting intuitions because one or more of these factors conflict and we're not sure which to grant priority to. In the sort of case you bring up, look at the sort of words we use to describe the person -- on the one hand, snitch, stool pigeon, tattle tale; on the other, whistle blower. Clearly there is a conflict in here somewhere. Let's see if we can isolate it.

On the virtue line, someone who blows the whistle has been disloyal, a vice, but also concerned, a virtue. There is conflict inherent in the virtue approach from the start.

On the duty line, it seems fairly straight forward that the operative rule is always tell the truth. This one votes for snitching.

The rights-based concerns don't really enter in here since it clearly is not a violation of your own rights to speak what you know to be true, nor is it a violation of someone else's rights to tell what they have done. This one is on the sidelines (mostly).

Utilitarian concerns, as usual are entirely case dependent. Unabomber's brother, yeah, really intense ramifications of not calling the cops. Who threw the spitball, not so much. This one will be contextual.

Care-based is the one that says, "hey, you don't rat on a pal." When you have a personal relationship, it comes with certain obligations. Caring about someone often means doing things to pull their backsides out of the fire that may be a tad unseemly, hoping that they will have learned their lesson from it and will grow into more a responsible person who will not repeat that mistake.

So what we have here is an ethical tug-of-war between duty on one side and care on the other. The winner is often determined by utility. Sometimes the person needs to learn the hard way and take their lickins. In that case, you owe it to the person to tell. In other cases, you know that the offense was minor and that the fallout will way outweigh the misdeed. In that case, there's no problem not telling and protecting your friend, as long as you also shoot a disapproving look. Then there are the cases where there is serious peril to innocents if you don't let the cat out of the bag. In that case, utility clearly dictates coming clean. Will there be cases in which it isn't clear which way utility comes down? Of course, hard ethical problems are hard for a reason, namely they're hard. But where we draw the line is usually a matter of determining whether the world will be a better place in the end as a result of telling or not.

There are, however, some cases in which rights-based concerns pop into the equations. When someone cheats on a test that will be curved, for example. Now there are not only utility concerns, but also questions of whether the rights of other students in the class have been trampled upon. In those cases, rights will often side with duty and make the bar much higher for utility.

Justin asks,
What exactly is the contradiction between logic/mathematics and quantum mechanics? Will we ever know which one is right?
The first of several quantum questions this go round. First of all, there is absolutely no conflict between mathematics and quantum theory. Quantum theory is a set of state equations meant to model physical phenomena and so is mathematical by its very nature. Classical logic, on the other hand, is a more interesting story.

I used the phrase "state equation" above, let me explain what it means. The state equations of a system are the mathematical description of the state of that physical system. It sets out the relations among the state variables -- things like pressure and temperature (which we'll discuss tomorrow, I promise BB) or mass and velocity -- the basic properties of the things in the system.

The state equation of quantum mechanics is called Schrodinger's equation and it relates potential and kinetic energy, but it does so using the state variable psi or the wave-function. The question is what this psi is. We know, or at least think we do, what temperature, pressure, mass, and velocity are. We can sense them. We can measure them. But we can't measure psi. What we can do is express it in terms of other things we can measure. This is not that weird, we do something similar with energy, for example.

Where it gets weird is that when you look at the value that psi is supposed to be according to Schrodinger's equation, it turns out to be a combination of several, even an infinite number, of values for the observable quantities. Take position, for example. We think that everything is somewhere and it is exactly where it is. But you can set up quantum mechanical systems where a single indivisible thing, say a photon, an indivisible particle of light, is in a state where it is simultaneously going through one slit on the left and one slit on the right. It's not that half of it is going through one and half of it is going through the other because it is indivisible. no, the whole thing is half going left and half going right.

Super weirdness results when we try to observe this. the instant we start checking, it will go only through the left or only through the right. We never see the combination, or superposed, state. It knows when you are looking and randomly -- completely randomly -- goes all left or all right. But when you are not looking it will be in a superposed state of going left and right and we know this to be the case because it has observable physical ramifications (for example, light patterns that disappear when we turn on sensors to see which slit the light goes through and immediately reappear when we turn the sensors off).

Here is where traditional logic has been thought by some to be insufficient. The heart of classical logic is the law of the excluded middle, the rule that says what is not true is false and what is not false is true. There are two and only two truth values and all sentences possess one or the other. The sentence, "The photon went through the left slit," according to classical logic, is either true or false. Now one could try to marry quantum mechanics to classical logic and say that if it went right it was false and if it was in a superposed state then it is false since it didn't go completely and uniquely through the left slit. But this move clearly should not completely satisfy us since it did go through the left slit, meaning the sentence isn't exactly false. But if we restrict ourselves to exactly true and exactly false, we are stuck.

The thought is that we could have a three-valued logic, which allows sentences to be true, false or some other third truth value. How do we make sense of this third value? Is it indeterminate? Is it something else? This is something a lot of very smart folks have been playing with, but the idea is that the way the sub-atomic world works may be weird enough to warrant it's own formal structure for reasoning. That doesn't mean that traditional logic is false or useless or that I have a brother and don't have a brother and therefore am currently wearing a purple dress. It just means that if quantum theory is true, we may need a more intricate language for reasoning about some things.

Tomorrow, more physics...