It is of value for someone to be free of suffering or disease. But in order for this to be valuable period, the being in question must have a certain intrinsic value. And this intrinsic value of persons, in virtue of which it is valuable that they be free of suffering or disease, is a value that they have independently of whether they are healthy or disabled. This intrinsic value of persons is presupposed as what gives value to what they value and also gives value to their developing their moral and other capacities along with a stable disposition to add value to the lives of others. This disposition to be productive, again, is valuable in virtue of the intrinsic value of the people whose lives are enriched by this productivity. In short, the word "value" is a bit tricky here as it's used both for the intrinsic value of persons and for the contingent and variable value that their health, feelings, capacities, and conduct may have in enriching (adding value to) their own lives and the lives of others.

Perhaps there is really nothing wrong with a theft that does no harm -- stealing an apple from a privately own tree that is never picked, for example. But your case is not like this. If the dead man has no heirs, as you say, then his winnings will typically fall to the state. So the question here really is whether is is permissible to steal in a way that diminishes state revenues. And this is rather close to the question whether it is permissible to steal from the state or to cheat on one's taxes. To this latter question, asked in regard to a reasonably just state, you would probably answer "no". If so, I don't see why the answer should be different for the case you describe. Now in some jurisdictions unclaimed winnings would go to the lottery operator. This would increase its profits and thereby augment the taxes it pays. But the thief would also pay taxes on her winnings, so the state might be equally well off either way (or better off, even, if the thief pays taxes at a higher rate). Still, the...

There are several classical attempts to do just that. The two most influential, perhaps, are those Plato makes in his Republic and Jean-Jacques Rousseau's in Of the Social Contract . I have tried a somewhat different tack in regard to international politics in T. Pogge World Poverty and Human Rights (Polity 2008), ch. 5: "The Bounds of Nationalism," esp. pp. 126-30.

I understand well what you're saying. Points have zero extension, and lining up a bunch of them won't get you beyond zero extension. It's like adding up zeros: 0+0=0 0+0+0=0 and so on. There's no reason to think that adding infinitely many zeros together would get you anything other than zero. And likewise with the lining up of points. But when we are dealing with infinities, things are often tricky and counter-intuitive. So let's see whether we can construct an argument for your teacher's conclusion. Consider this. We begin with a line -- let's say it is 32 inches long -- and we divide it into two equal segments, these again into two equal segments, and so on. Dropping the inches, we can write this as follows: 1*32 = 2*16 = 4*8 = 8*4 = 16*2 = 32*1 = 64*1/2 = .... Here the number before the "*" signifies the number of segments and the number after the "*" signifies the length of each segment. Now the question is this. If we keep dividing an infinite number of times, then what...

In a finite lifetime, you won't be able fully to inspect an object with parts that are infinitely far from you, at least if we assume that you are limited by the speed of light. But there's other evidence. For example, you may be able to measure the gravitational pull of the ladder. If this pull turns out to be exactly what our theory would predict for a ladder that's like the piece of it we have before us (same material, thickness, density, etc.) and infinitely long, then this would be evidence for infinite length. (Note here that the gravitational pull exerted by any one inch of ladder declines with the square of its distance from you. So no matter how long the ladder its, its gravitational pull will not be infinite.) It's also possible that the ladder is expanding (as our universe is), or perhaps contracting. In that case you get a nice Doppler effect: a transformation of light reaching you from distant parts of the ladder -- the farther the light has traveled, the more strongly transformed it...

In relation to my earlier answer, the following article from the Economist may be of interest. It's advertised as follows: "Can the laws of physics change? Curious results from the outer reaches of the universe." The link is www.economist.com/node/16941123?story_id=16941123&fsrc=nlw|hig|09-02-2010|editors_highlights This is not exactly what I had in mind, but relevant nonetheless. BTW, this question is probably best classified under "physics" rather than "mathematics."

In terms of income, the panelists on this site by and large belong to humanity's top ventile (5%) -- where the average income is 9 times the global average. This is roughly 300 times more than what is available to people in the bottom quarter, where average income is about 1/32 of the global average. (The difference is still about 100:1 if one adjusts for purchasing power parities.) Moreover, people in the bottom quarter typically work longer hours in more exhausting jobs, and have about 20 to 30 fewer years of life. So, yes, those among whom you live do not enjoy anything like our opportunities to live a full human life, anything like our freedom to learn, think, enjoy, and be creative. These huge discrepancies are profoundly unjust, and it would be good if many people in the more affluent countries used their much greater powers to change the world toward overcoming such injustice. Unfortunately, this is not happening, though some are trying. Those who have most power to contribute to change also...

I think part of the answer is that education can be well targeted on the children in need. By contrast, it's hard to provide food and shelter to children in ways that are not exploitable by their caretakers. So the worry is, for example, that, if we institute the mandatory provision of shelter for children, then adults who want a decent apartment will have children in order to be provided with one. In my view, this problem is often overstated. A decent health-care minimum can be targeted (and in any case adults should enjoy it as well regardless of income), and targeting for food could also be improved (e.g. by providing good food in schools and kindergartens rather than food stamps that can often be traded in for cash or commodities from which children do not benefit). So my answer to your "why" is meant as an explanation, not a justification. The shortfalls in food, shelter and health care that children suffer, in the US and in the world at large, are horrific. They should be much reduced -- and...

I believe editors have no such responsibility to print known falsehoods that some want to see in print. In fact, I believe editors have a responsibility not to print such letters. If editors practiced such misconceived "even-handedness," then this would provide a powerful incentive to determined groups to use such letters to create uncertainty in a public that often isn't very capable of discerning what's true and what is not. Reading many letters to the effect that Obama is foreign-born and hence ineligible for the Presidency may persuade a sizable minority of US citizens that their country has been hijacked by foreign agents. And groups could then abuse the letters-to-the-editors facility to inspire this persuasion, perhaps in preparation for terrorist activities such as the Oklahoma City bombing. Companies could also abuse this sort of false even-handedness. Thus, imagine a company A that sells an expensive drug which reduces the symptoms of some dreadful disease. And imagine that a competing...

How about sending them Jostein Gaarder's Sophie's World ? It's been very popular and very effective in the sense you intend.

I agree that Kant's Critique of Pure Reason is as much a critique of empiricism as it is of rationalism. But the title still makes sense if you understand two things about it. First, the word "Critique" here means not merely criticism but, more broadly, critical examination. The book draws limits to reason in some respects but also vindicates our reason in others. Second, the word "of" here means not only that reason is the object of critical examination, but also that reason is conducting this critical examination. So, in a nutshell, Kant promises in his title a critical self-examination of reason: an examination undertaken by reason of what reason can and cannot do.