There is the fact that it is possible to treat something badly or to damage it, whether or not it is sentient. A pair of shoes can be badly or well looked after, and it is wrong not to look after a good pair of shoes properly. A living thing like a hedge can be properly maintained or attended to, but something more is involved. Sometimes, it seems to me, the aesthetics of the "art object" (horrible phrase) can reflect what it actually is. So it is natural to trim a box hedge in one way, and a mixed hedge in another way, perhaps a less formal and more undulating, the shapes reflecting the different kinds of growth - hawthorn, or privet or beech. (A hedge that is full of straggly and unwanted sycamore looks awful, and the holes soon begin to show.) Pugs and poodles may be perfectly happy qua sentient beings, though often there are specific health problems with specific breeds, but it is perfectly coherent to object to the whole process of breeding and thinking of living things as being objects for our use - manipulation - and enjoyment only. Much the same comments can be made about the wilderness, and your question and suggestion raise profound and important questions of ecological ethics and aesthetics. For some, the ethics of GM foods has a spiritual dimension too.

You are quite right that Gödel's (first) incompleteness theorem attracts all kinds of bizarre "interpretations". Various examples are discussed and dissected in Torkel Franzen's very nice short book, Gödel's Theorem: An Incomplete Guide to its Use and Abuse, which I warmly recommend.

My guess is that a main source for the whacky interpretations is the claim that has repeatedly been made that the theorem shows that we can't be "machines", and so -- supposedly -- we must be something more than complex biological mechanisms. You can see why that conclusion might in some quarters be found welcome (and other technical results in logic generally don't seem to have such an implication). But as Franzen explains very clearly, it doesn't follow from the theorem.

"Fulfill" is a bit of a weasel word, isn't it? Suppose one partner would like to make love every night. The other, less libidinous spouse is more a two-or-three time a week type. We might say that the first spouse is "unfulfilled," but that sounds like a really poor excuse for adultery.

If the lack of "fulfillment" amount to some deep incompatibility, a good question to ask first might be: have the partners in the marriage talked about what's not working? Can it be fixed? If the answer really seems to be no, then the next obvious question is whether the marriage is worth saving.

Life is complicated, of course and blanket generalizations don't do justice to the complexity of people's relationships. But the old question: "How would I feel if the tables were turned?" is always a good one to ask when we're trying to decide if we're acting rightly. It's not just an old bromide; it gets at something pretty deep in our notions of right and wrong.

I'm not as confident as Peter Fosl about the testability issue: perhaps we need to know a bit more about what counts as "the theistic hypothesis".

After all, a lot of theistic hypotheses look perfectly testable by ordinary scientific standards. Take, for example, the claim that Zeus exists. I take it that no one now reading this site believes that that claim is literally true! But why? Well the existence claim, taken literally, is bound up with a range of stories about how the world works; and we now know the world just doesn't work that way. Mount Olympus is not populated with gods; bolts of lightning are naturally caused discharges of electricity; clouds and rain are not gathered by supernatural agency; burnt sacrifices to Zeus do not increase the chances of better crops or victory in battle; and so it goes. Science -- in the broadest sense of our empirically disciplined enquiries into how things work -- has shown we have no need of the Olympian gods to explain anything. Of course, that doesn't mean that the Greek myths aren't full of insights into the secrets of the human heart! But in so far as they essentially embody creation stories and stories about the origin of natural phenomena like storms and tempests, science -- in the broad sense -- uncontroversially shows that they are literally false.

So if someone claims that the empirical testing methods characteristic of science can't in general impact on the questions about the existence of various gods, then that's surely wrong. Which raises a nice question: why should the question of the existence of the Judeo-Christian God (the theistic hypothesis, perhaps) be different in this respect from the question of the existence of Zeus?

Well, the questions won't have a different status if we take the God-story also to be essentially bound up with e.g. certain biblical creation stories. Science has more than adequately shown that those stories aren't literally true. And again, petitionary prayer to God is no more effective in bringing about worldly goods than sacrifice to Zeus (it does no better in helping you recover from illness, say, than can be explained as a placebo effect). In so far as claims about the existence of God are bound up with specific such claims about how the world works, science can impact. And indeed, does impact strongly negatively.

But of course, sophisticated, scientifically knowledgeable, believers can and do react to that point in (at least) two different ways. One way is to disentangle the theistic hypothesis from the creation myths, and other stories about how the world works: though you might well begin to wonder, as God becomes more and more abstract, more remote from the quotidian world in which we live our lives, why we should care. Another way (characteristic I think of one strand of English Anglicanism) is to agree that in so far as talk of God is bound up with stories about how the world works, it is encroaching on the province of science, and is mostly literally false. However, that doesn't mean that the Christian myths, say, aren't very good myths to live ones life by, or that sharing Christian ritual practice isn't a sustaining prop to living a good life in a community.

What you are citing is not the principle Rawls is actually defending as his second principle of justice, it is merely a principle he considers along the way. In its canonical formulation, the second principle reads: "Social and economic inequalities are to satisfy two conditions: first, they are to be attached to positions and offices open to all under conditions of fair equality of opportunity [the opportunity principle]; and second, they are to be to the greatest benefit of the least advantaged members of society [the difference principle]."

With the correct text substituted, your point about the least advantaged makes more sense. Still, what Rawls is demanding for the least advantaged is really in one sense more than a safety net. The word "safety net" suggests a certain minimum, perhaps some amount sufficient to meet one's basic needs. But Rawls is demanding the highest feasible bottom position, even if this turns out to be well above the level needed for economic security. So, even if there is a nice safety net for the least advantaged, the society still falls short of justice if it is possible to raise the lowest income even higher. And this makes your questions -- what do the rich get out of it? -- even more acute.

To answer your question: Rawls is theorizing so-to-speak before there are rich and poor, before society is built, before its basic rules are formulated. We can make this more vivid by imagining a few adults stranded together on an island and deliberating about how to set up the economy of their new society. How much economic inequality should the rules of their society allow? To this question, one natural answer is: no inequality at all. Let everyone be entitled to a share of the joint product that corresponds to his or her share of the labor contributed. So, if you did 20 percent of the work in a given year, say, then you should get 20 percent of the social product that year.

Rawls assumes that it may be possible to do better than this, better for everyone, by raising average productivity (output per hour worked). One obvious way to do this is to agree to prizes for the most productive workers. This gives everyone an incentive to try hard to be productive and, with most people working harder (than would be the case without prizes), the average output per hour is higher. We use some of the extra product to pay out the prizes and then distribute the remainder at an equal hourly rate -- and we find that even those who do not win a prize get more than they would have received without prizes.

To give a concrete example, suppose that, if the islanders organized their economy on a principle of equal hourly pay, then their total product would be 24,000 units of food and their labor time 12,000 hours -- so everyone would get paid two units per hour (= average productivity). Now suppose instead a prize were offered promising double pay to the most productive worker, and suppose this would result in a social product of 30,000 units and a total labor time of 10,000 (average productivity 3 units per hour). Since you are the most productive worker this year, you get paid as if you had contributed twice as many hours as you actually did contribute -- you get credited with 4000 hours, say, rather than the 2000 you actually worked. With 30,000 units available to pay for 10,000 hours of work plus your 2000 additional credited hours, each hour would fetch 2.5 units. You get paid 10,000 units, effectively giving you 5 units per hour. The others get 2.5 units per hour, which is still more than everyone would get if there were no prizes at all.

There are of course infinitely many ways of setting up such a prize system that, by rewarding the more productive, raises average productivity. Which of the many institutional design options should be chosen? Rawls answers this questions in two steps. In the first step, he argues that we should consider only those rule systems that raise everyone's hourly pay above what it would be under the equal-pay system (what you are quoting reflects this step). In the second step he then argues that we should choose that rule system under which the lowest raise (over the equal-pay system) is as high as possible -- or, in terms of prizes, Rawls argues in the second step that one should design the prize system in such a way that the hourly pay of those who win no prize is as high as possible.

We can now adjust your question in two ways. First, you can ask whether Rawls's proposal may not still be shortchanging the most productive (the richest under his scheme). Perhaps they get paid twice as much as the least productive even while they are really four times as productive. If this is so, do the more productive not deserve to be paid four times as much? Rawls's answer is that the capacity for greater productivity typically depends on factors (such a natural talents, good parents) for which the more productive can claim no credit, and that the more productive therefore should receive greater rewards only insofar as this also benefits the less productive. (But is there not, you may ask back, such as thing as culpable laziness?)

Second, you can ask why, in our society, where the rich have very much more than they would have in a Rawlsian society, the rich should accept the transition to a Rawlsian society. They have no prudential reason to accept this transition (no more than slaveholders did to accept the abolition of slavery). But if the existing rewards are unjustly excessive, then they do have a moral reason to help scale them back (just as slaveholders had a moral reason to support abolition).

To answer this question, it may be helpful to say something about the mathematical formalism usually used in probability theory. The first step in applying probability theory to study some random process is to identify the set of all possible outcomes of the process, which is called the sample space. For example, in the case of an infinite sequence of coin flips, the sample space is the set of all infinite sequences of H's and T's (representing heads and tails). Probabilities are assigned to events, which are represented by subsets of the sample space. For example, in the case of an infinite sequence of coin flips, the set of all HT-sequences that start with H represents the event that the first coin flip was a heads, and (assuming the coin is fair) this event would have probability 1/2. The set of sequences that start with HT is a subset of the first one, and it represents the event that the first flip was heads and the second tails; it has probability 1/4.

Now, consider some infinite HT-sequence s. For any positive integer n, we can consider the set of all sequences that agree with s for the first n terms. This set contains s, and imitating the reasoning in the last paragraph we see that it represents the event that the first n coin flips come out as specified by s, which has probability 1/2ⁿ. Since {s} is a subset of every one of these sets, the event that the entire infinite sequence is exactly s must have probability less than 1/2ⁿ for every n. But that means that the event must have probability 0. So you are absolutely right that the reasoning here involves a limiting process: the probability is 0 because 1/2ⁿ approaches 0 as n approaches infinity.

With this background, it is also now easy to see the distinction between zero-probability events that are possible and those that are impossible. The event that the entire infinite sequence is s is represented by the set {s}. It has probability 0, but is possible. The event that the first flip is both a heads and also a tails is represented by the empty set (since there are no elements of the sample space that fit this description); it has probability 0 and is impossible.

There's a lot of subtext in your question--you seem to be suggesting that if there are genes that influence whether one is homosexual or heterosexual, that indicates that being gay is a mental illness. That would be a very strange argument, since the fact that there are genes that influence traits or behaviors says nothing about whether that trait or behavior is good or bad in either the biological or ethical sense.

Perhaps you are thinking that because homosexuals do not have the desire to mate with the opposite sex, any genes that may underlie homosexuality are "maladaptive" in the way some mental illnesses are caused by maladaptive genes. But that is also a mistake, since (a) in humans' past evolutionary environments homosexuals may have reproduced (they wouldn't be the only humans who have had sex for procreation without being particularly attracted to their mates!), (b) there are interesting data suggesting that homosexuality in some animal species (perhaps including humans and their ancestors) is a biological adaptation (the short story is that homosexuality might be associated with increased altruism towards relatives and hence cause a net increase in related genes), and (c) any genes related to homosexuality may have been selected for because they "code for" other traits that are adaptive, while homosexual feelings or behaviors are simply byproducts of those traits (this would not mean homosexuality was "maladaptive" any more than our ability to do calculus or dance the tango is maladaptive--the useful desires and abilities to do calculus and to dance are byproducts of other traits that were selected for).

So, all of this is to say that even IF there are genes that influence humans' sexual preferences (and that has not been demonstrated yet), then that does not suggest that homosexuality is biologically "unfit" or maladaptive in any way (as mental illnesses generally are). But whether there are such genes also says nothing about whether a pill could be created to suppress homosexual desires (or to suppress sexual desires in general, which may be useful for some politicians to have!). Such pills seem feasible as long as these desires and behaviors are influenced by the sorts of things pills influence (e.g., our brain states), as they surely are.

This brings us to another problematic implication of your question--that the lack of a desire to procreate (or lack of procreating behavior) is a bad thing that should be suppressed. In our current environment, it might be a good thing for humans to procreate less (and for some politicians to procreate less "diversely"). Of course, if no (or too few) humans wanted to have sex with the opposite sex, well, we might need to do something, but in that case I doubt it would take a pill to get people to either have heterosexual sex or to use the artificial means we have to reproduce.

I should add that if it turns out that homosexuality is shown to be more a matter of genes than upbringing or choice, then it seems like that would help people arrive at the ethical conclusion that there is no reason to discriminate against homosexuals (as we have, too slowly, arrived at that conclusion about race, gender, and indeed, some mental disorders). But the worry is that, using the weak arguments I discussed above, people may instead think that homosexuality is unnatural or maladaptive or an illness that needs to be cured (or worse, eliminated). So, if you did not mean anything like this by your question, I apologize that my answer sounds a little grumpy!

No.

But that's no limitation on such a god's power. We're not saying that there is some possible task that this god fails to be able to pull off. We're saying that there isn't any task that is coherently describable as "making a square triangle".

For consider: what could possibly count as making a square triangle? To be a square requires having four sides. To be a triangle requires not having four sides but only three. So nothing can possibly count as being both a square and a triangle. Hence whatever the god (or anyone else) does, it couldn't correctly be described as "making a square triangle" for that isn't a coherent description of anything.

Take a mundane case. I pass you the cookies. You can take one. Or you can take none. Both are within your power. But you can't simultaneously both take one and not take one. But saying that plainly isn't to say that there is some limitation on your powers of choice vis-a-vis cookies! The point is that nothing could count as simultaneously both taking one and not taking one -- it's just not a coherent description of a possible action. Likewise to say that some god can't make a square triangle isn't to limit his creative powers: the point is that nothing could count as succeeding at that.

Such work is surely often unethical or downright wrong -- for the reasons you suggest and also for the additional reason that such work may well be used by others to commit great crimes (e.g., to single out for torturous interrogation French citizens suspected of having ties to the Résistance). But your question, I think, is whether such work is unethical, or wrong in itself. To this my answer is no, for two separate reasons.

One reason derives from what I call the "sucker exemption": in some cases, ordinary moral constraints on one's conduct toward others are weakened or canceled by how these others are behaving or have behaved. If you have various agreements with another person, for instance, and he turns out routinely to violate these agreements whenever it suits him, then you are not morally required to honour your agreements with him when it does not suit you. Similarly here, it may not be wrong to spy on spies or, more generally on people who themselves flout serious moral constraints.

I hasten to add that this cannot be a blanket permission to treat suspected transgressors in any way we please. First, we need a high degree of confidence that the other is indeed a constraint violator. Second, our constraint-violation must be proportionate and related to the other's constraint violation (so the other's violating his agreements with you does not justify your beating him up, for example). Third, our constraint violation may not be permissible when it would adversely affect third parties (e.g., by spying on a spy we will often also spy on his innocent contacts -- but see next paragraph). Fourth, our constraint violation must not be fortuitous: there should be a plausible reason for it (as when by spying on a group of people we may be able to prevent or solve or punish a serious crime, something that we could not accomplish otherwise). -- I add these cautions because we have in recent years massively violated these four provisos in our treatment of suspected terrorists and suspected resisters to our occupations of Afghanistan and Iraq.

Another reason derives from the harm that spying might prevent (or the good it might accomplish). To be sure, this is implicit in the fourth proviso to the sucker exemption above. But it has force also outside the sucker exemption, that is, it can justify spying on perfectly innocent people. Thus, to give an obvious example, it would have been alright surreptitiously to tap the phones of French citizens in occupied France in order to learn something about German troop movements in their local area and thereby to hasten the defeat of the Germans. More controversially, it would be permissible to spy on an innocent secretary in order to obtain access to his boss's life-saving pharmaceutical invention, which this boss wants to hold back in order to obtain a higher price later when the pandemic disease will have become much more widespread.

Now, "working in intelligence" raises yet further issues because the hired spy may not be given full information about her assignments ("need to know") and may not have the freedom to turn down assignments on a case-by-case basis. Taking on such a job requires a high degree of confidence that one's prospective superiors have carefully thought about, and are committed to observe, the limits on spying as sketched above. From what I know, I would place such a high degree of confidence in only a handful of national intelligence services. Shrouded in a cloak of secrecy, the operations of an intelligence service are fully understood only by a few top officials who may not have much of a prudential incentive to keep these operations morally decent. They get rewarded for results and very rarely punished for abuses. Putting oneself at the service of such people, one is likely to become involved in wrongdoing.

Given the way many in the wealthy parts of the world live, this is a compelling question. I think, however, that as posed the answer must be "no." For one thing, the best paying jobs may sometimes contribute more bads than goods to the world. For example, in some circumstances criminal activity or highly polluting industry may offer the best paying job. Also, it is not morally obligatory to live off as little as one can manage, giving away the rest to charity. People have obligations to themselves as well as to others, and one must balance what one owes to others against what one owes oneself. Finally, it's important to understand that some acts are morally admirable without being morally obligatory; and from where I sit extraordinary self-sacrifice for the sake of charity to others counts as just such an act. Having said that, it remains true, I think, as a matter of judgment, that many people in wealthier parts of the world live in ways that have tipped the balance excessively in the direction of self over others--becoming, in short, selfish and gluttonous. Given the serious environmental consequences of our excessive population and excessive consumption patterns, it has become morally obligatory for many of us to live off significantly less than we have been, whether we donate the remainder to charity or not. Living in less consumptive ways may, in fact, require not acquiring the best paying job possible, as many of the best paying jobs are part of highly consumptive enterprises.