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).

It is common to interpret Kant as insisting that the objects we observe in space and time exist independently of any particular observation we make of them,but also insisting that space and time are forms that we impose on our experience rather than characteristics of reality as it exists in itself. Likewise, it is common to read Kant as insisting that causal relations exist independently of any particular observation we may make, but also insisting that causal ordering is something that we impose on our experience rather than something that is present in reality in itself. These contrasting claims are reflected in Kant's famous distinction between the phenomenal and the noumenal, and in his endorsement of empirical realism and transcendental idealism.

Whether Kant's position is a consistent position is a topic of much dispute. It is common to invoke the image of colored glasses to explain how he can insist that what we see is independent of ourselves but how we see it depends on our own activities and capacities (our glasses). The problem with this image of colored glasses is that the objects viewed through glasses are still in space and time, and still causally related to one another; if you strip these features from the objects in front of the glasses, it seems impossible to understand what is left. Kant himself emphasizes the impossibility of understanding reality as it exists in itself (the noumenal world) but he thinks that we have good reason to think that such a world exists.

There is nothing inconsistent about believing in a world that is independent of our representations and believing that we require certain sorts of representations in order to have knowledge of the world. It would be inconsistent, though, to think that we can know anything about the world apart from our representations -- including knowledge of whether it is or is not in space and time, or whether it is or is not governed by causality.

It's the difference between thinking that everything is, ultimately, made out of ideas (what we think of as the physical world is somehow a mental construction) and having ideals (and optimistically thinking that people can and should live up to them).

As a Hobbesian might say about sovereigns, "absolutely" not.

The "justice" of sovereigns is, more seriously, a curious issue in Hobbes and more complicated than it may at first appear. One might be tempted to say that because the Hobbesian sovereign is an "absolute" sovereign, that anything he or she does is "just." In other words, one might say that whatever the sovereign commands is for Hobbes by definition "just."

But justice in Hobbes might be thought of in two ways: "civil" and "natural." In terms of civil justice (the justice defined by actual laws and dictates made by governments), one question concerning Hitler's conduct would be whether or not it was unjust of him to violate the terms of international law and the various treaties his government negotiated--for example, the Non-Aggression Pact with the Soviets and the peace treaty Hitler's representatives negotiated in bad faith with Neville Chamberlain. Arguably, however, for Hobbes, the sovereign is not bound by civil law in his or her dealings with foreign sovereigns. That's because with regard to other sovereigns the sovereign remains in the "state of nature" and at war. For Hobbes there is no true international civil order and no civil obligation for sovereigns to obey "civil laws" they have negotiated among absolute sovereigns.

Even, for the most part, with regard to his or her own subjects, the Hobbesian sovereign is above the particularities of civil law that subjects are obliged to obey. So, were George W. Bush a Hobbesian sovereign, there would have been no injustice in his violating the FISA laws (though subordinate government agents would have been unjust in violating those laws, unless specifically ordered by the sovereign to do so). There is, however, one very big condition a sovereign must meet in dealing with his or her subjects; and thinking about this overriding condition draws our consideration of Hitler as a just or unjust sovereign beyond the simple dictates of positive civil law into the realm of natural law and natural justice.

Hitler can, I think, be thought of as unjust in Hobbesian terms, if not for violating civil law, then for violating the terms of natural justice. Keep in mind that Hobbes's overriding concern is that the sovereign provide for the security of his or her subjects. That is, the objective of making a social contract and setting up a sovereign is to end the ''war of all against all' and secure a lasting peace. In undermining the peace and security of German citizens by rounding them up, imprisoning them, and putting them to death, Hitler then obviously violated the the social contract and the most basic objective of Hobbes's political thought. Indeed, Hobbes maintains that as a matter of natural law one ought to honor the contracts one makes. (In this sense, Hitler's violation of treaties might in a natural sense--though again not a truly civil sense--be thought of as unjust).

Hitler's actually promoting war and advancing wars against foreign powers that subjected Germans to violence at the hands of the Allies can also, I think, be thought of as a violation of the objective of securing peace. It's just this difference on the issue of war, in fact, that most starkly marks the difference between Hobbesian philosophy from the thought of Nazi theorists like, for example, Carl Schmitt. For Hobbes war is an evil to be overcome, but for National Socialists, war (or, anyway, the struggle against national enemies) is not only an inevitable but also a beneficial dimension of political life. Hobbes in contrast to the Nazis writes, for example, that "every man ought to endeavour peace, as far as he has hope of obtaining it." On the basis of his making war on his subjects and actually promoting war with other nations, then, Hitler was decidedly unjust to his own subjects and to others. (Hitler was not bound by a social contract to protect the lives of the non-Germans he killed, but his conduct towards foreigners can still be thought of as unjust according to natural principles of justice.)

Hitler's racist ideology of Aryan supremacy also violated the principles of natural equality Hobbes recognized. Hobbes maintained and Hitler did not that every human (every "man," at least) is "equal by nature." And according to Hobbes, as a matter of natural justice, when civil society is established, subjects ought to be treated equally before the law--no one should, Hobbes writes, "reserve to himself any right, which he is not content should be reserved to every one of the rest."

Among the Hobbesian provisions of natural justice Hitler violated, then, we may count (1) violating the social contract by attacking members of the German social contract; (2) violating all kinds of people's natural right to self-preservation; (3) promoting war; and (4) failing to recognize people's natural equality.

For all these reasons, then, Hitler was in Hobbesian terms an "unjust" sovereign.

Let me add a short note to Andrew's fine answer. Imagine the following reasoning:

The mind 'imposes' space and time upon the empirical world. The concepts 'at the moment of' and 'before' have meaning only because of that imposing. Therefore, it makes no sense to ask what empirical reality was before or at the moment of the mind's act. It makes no sense not because we cannot get back to that prior reality, but rather the question itself is meaningless.

Now, I agree with Andrew's assessment that Kant did not in fact agree with the first statement above. Nevertheless, the conclusion to the above bit of reasoning is still salient. Kant was interested in discovering the transcendental conditions of any experience of a shared empirical reality. He was not interested in the empirical or psychological 'mechanics' of the human mind such that it arrives as perceptions (as were, arguably at least, his great predecessors Hobbes, Locke and Hume).

I think the short answer is that Kant's transcendental idealism and empirical realism does not imply the each of us "structures reality" at the very moment we perceive objects and events in the world because one part of what it means to assert the empirical reality of the spatial and temporal world we experience and within is that all of us live together in a single world whose existence and structure is not dependent on acts of our minds. This is part of what Kant has in mind when he argues that his transcendental idealism should not be interpreted as empirical idealism – he accepts empirical realism and argues that transcendental idealism is needed to explain how it is possible for us to experience the empirically real world.

To be sure, each of the Kantian claims and assertions that you discuss raises exegetical and philosophical puzzles and there are also interesting puzzles about how these various strands of Kant's thought fit together and about how Kant's thought on these topics changes over the course of his philosophical career. So, there are any number of good questions and concerns that you could raise either about what Kant really had in mind or about whether his views are correct. To my mind, however, none of those issues lead us toward the thesis about “structuring reality” that you describe in your question – although I would be able to say more if you had said more about why you think that Kant is committed to that view.

Finally, Kant does address one interesting question about “chaotic” nature, although his thought here is also notoriously hard to understand and assess. In the First Introduction to the Critique of Judgment Kant addresses the importance of the assumption that nature is uniform, and he discusses why we are justified to assume that this is the case. I think that one of the things Kant was concerned about nature becoming “chaotic” at a moment’s notice, and so this might be a good text for you to study. Alas, however, it is unclear exactly what Kant takes himself to justify, an in particular it is unclear whether he is attempting to defend the uniformity of nature as a regulative principle (for example, one that we need to make to provide us with motivation to continue scientific investigations of the world) or a constitutive one about the nature of the world.

Finally, I think your question rightly identifies a lacunae in Kant’s discussion of empirical reality in the Critique of Pure Reason: he doesn’t address issues related to the uniformity of nature there, and I believe that his account of the twinned doctrine of transcendental idealism and empirical realism isn’t complete until he does. So, I congratulate you for picking up on an issue that Kant came to appreciate as he continued to develop his critical system of philosophy!

First, it should be noted that not all astrophysicists agree that time and space began with the Big Bang. There may be no meaningful way to measure or study space and time before the Big Bang, but that does not necessarily mean that there is no such thing. Scientists can agree on empirical findings and on the theories that best predict further findings without agreeing about the nature of the reality that underlies those findings. (This is especially clear in the case of Quantum Mechanics, where several competing interpretations have scientific adherents.)

Kant claimed that an entirely empty space, and an entirely empty time, are perfectly conceivable. So if the reason behind believing that space and time began with the Big Bang is the belief that the intelligibility of space and time depend on the presence of objects in space and time, he would disagree. Indeed, this view is the explicit target of several of his arguments in the Transcendental Aesthetic of the Critique of Pure Reason.

On the other hand, (in the Antinomies of the Critique of Pure Reason and elsewhere) Kant also warned against the attempt to decide whether space and time are finite or infinite. That is not a decidable question according to him. So I imagine that he would be sympathetic to those who simply refuse to speculate about space and time before the Big Bang.

Finally, the claim that space and time are transcendental conditions on the perception of objects does not by itself require a denial of their objectivity. We may need to experience objects in space and time in order to experience anything at all, but that leaves open the possibility that space and time also exist quite apart from our experience. Kant does sometimes assert that space and time are forms of experience that are imposed by us; but he also offers powerful arguments against the view that objects do not exist independently of us in space and time; how to reconcile these two claims is a disputed area of Kant scholarship.

Oh yes, lots disagree profoundly.

For a start, recall that around half of what Wittgenstein wrote after the Tractatus period was about the philosophy of mathematics (indeed, he wrote in 1944 that his “chief contribution has been in the philosophy of mathematics”). You can find a useful though rather charitable survey of his thinking on mathematics here. As you'll see, Wittgenstein's line is radical, to say the least, in its suspicions of standard infinitistic mathematics. Very few philosophers of mathematics agree with him at all. (Stewart Shapiro's excellent introductory book Thinking about Mathematics doesn't even mention Wittgenstein's view, he is so wildly outside the mainstream.)

Another point where (rightly or wrongly) very few philosophers agree with Wittgenstein is on the question of the nature of philosophy itself. Even if they find value in Wittgenstein observations about the mind, say, very many philosophers want to recruit the worthwhile insights into something like a high-level theory which at various points connects with, or even shades off into, more detailed psychological theories. True-believing Wittgensteinians think this is being "scientistic"; many others think it is just being sensibly naturalistic.

This doesn't seem at all clear. First of all, the argument assumes that, to know whether we know, on Nozick's account, we would have to know whether a certain counterfactual is true. But this isn't obvious. Water is H2O, but it doesn't follow that, to know whether something is water, you have to know whether it is H2O. Similarly, even if knowledge is (say) Nozick-style tracking, it does not follow that, to know whether you know, you have to know whether you track Nozick-style. That might follow if Nozick's account is construed as providing some kind of conceptual analysis, but even then there are issues that tend to go under the heading "The Paradox of Analysis".

Second, even if the foregoing is waived, I don't see why we can't know "whether the subjunctive condition Nozick deems necessary for knowledge is fulfilled". Surely we do have lots of knowledge about possibility, necessity, and counterfactuals. Of course, the epistemology of modal knowledge is a vexed issue, but so is the epistemology of everything else.

Well spotted! Nozick holds that, in order for you to know p, it must be the case that, if p were false, you wouldn't believe p. This condition is not fulfilled when p is "it is not the case that I am a brain in a vat on Alpha Centauri being stimulated to have my present experiences": if p were false (if I were a brain in a vat on Alpha Centuri being stimulated to have my present experiences), then I would nonetheless be believing p.

But this condition may well be fulfilled when p is "I am typing." It is fulfilled if, were I not typing, I wouldn't believe that I am.

With this move, Nozick takes himself to have shown at least how knowledge is possible: it's possible that I am really typing and that, if I weren't typing, I wouldn't believe that I am. But do I know that I am typing or do I not? Well, according to Nozick, this depends on what I would believe if I weren't typing now. Nozick assumes that there's a definite answer to this question, a fact of the matter. But, even if we grant this, how can we find out what the answer is? How can we examine the possible world in which I am not typing that is closest (whatever this means) to the actual world in order to ascertain whether, in that possible world, I (or "I") believe that I am typing? We cannot find out. More generally, though we may well know many things, in Nozick's sense, and even know that we know them, in his sense, we cannot find out for any belief we might hold whether it constitutes knowledge or not (because, even if we can find out that our belief is true, we cannot find out whether the subjunctive condition Nozick deems necessary for knowledge is fulfilled or not).

So Nozick's showing how knowledge is possible shows the possibility of knowledge in something other than the ordinary sense. We may have knowledge in Nozick's sense, but we can in principle never find out whether we know anything and, if so, what. As you suggest, this isn't much of a victory over scepticism.

(BTW, I wrote up this critique in a termpaper in my first semester at Harvard and got a B+ from Nozick. So there you go.)