Tigtog is quite taken by the idea that humans -- at least in affluent Western societies -- are no longer undergoing natural selection. Instead, to the extent that we're evolving, we're undergoing artificial selection.
The distinction between natural and artificial selection appears to be a matter of the origin of the conditions that do the selection -- if it's something in nature that makes certain individuals unfit, it's natural selection, but if it's an aspect of culture, it's artificial selection.
The problem with making much of this natural/artificial selection distinction is that it breaks down in the real world. As long as humans have had culture, all of the conditions we face -- thus a fortiori all the conditions that could cause differential reproductive success and hence evolution -- are hybrid natural-cultural conditions. There was no time or place where Homo sapiens bopped along in a state of nature, subject only to natural impacts, and then later/elsewhere we were lifted into a cultural realm. The impacts of nature are always culturally mediated. This is why, for example, environmental studies researchers have long said "there's no such thing as a natural disaster."
(One could argue that all selection, even on non-human organisms, is hybrid natural-cultural in this sense, in that what natural conditions impact an organism is always in some degree shaped by the organism's habits. This may be a stretch of the word "culture," but the principle is the same.)
To focus on the specific examples in tigtog's post, why should we consider war and high infant mortality (or more precisely, the diseases like cholera that cause high infant mortality) to be "natural" conditions? War is a thing humans do, and do in different ways and to different degrees in different times and places. If you get killed in a war, your death (and your subsequent inability to pass your genes on to offspring) is a product of culture -- indeed, perhaps the purest type of artificial selection I can imagine. Even if the first Homo sapiens society on the east African plains was a warlike one, that doesn't make war "natural." Cholera etc. are also as much artificial causes of death among humans as they are natural -- while many societies lack the ability to eliminate cholera entirely (at a reasonable or unreasonable cost), social arrangements still shape which people get it and how deadly it is.
I'm tempted to point out here that many of the "natural" ills of the pre-industrial world are actually ills of the interregnum between the adoption of agriculture and the maturation of the industrial revolution, but I don't want to be taken as making the point "no, it's
health that's really natural!" I think it's important to get away from the underlying dualism that posits that humanity (and individual people) has a natural state which is then reined in and redirected by culture or consciousness.
None of this is to say that it's not a very interesting question to explore changes in what kind of selective forces people are subject to in different times and places, and hence what type of person is being selected for. But I don't see the distinction between natural and artificial selection as a particularly interesting, helpful, or even necessarily workable theoretical tool for this project.
Of more significance is the distinction between purposive and non-purposive selection. Purposive selection is that selection done deliberately by the selector in order to achieve some change in the creature -- a la horse breeders matching studs and mares to produce the next Kentucky Derby winner. Non-purposive selection is selection caused by some condition that systematically reduces the reproductive success of a certain type of organism, but without any conscious eugenic design. Outside of certain theistic evolution scenarios, all natural selection is non-purposive. But very little artificial selection is purposive -- even in the heyday of eugenics, eugenic manipulation was only a part of the social factors that affected reproductive success. Certainly the examples used in the post of artificial selection are non-purposive -- that is, nobody is creating those conditions with the goal of altering the genetic makeup of the human population. So by this distinction, there is no major qualitative difference between human evolution on the primal savannas and the streets of Sydney today. Unfortunately, the discussion in tigtog's comments tends to conflate the natural/artificial and non-purposive/purposive distinctions.
A final conflation that crops up in the discussion at tigtog's blog is between the naturalness of selection and the strength of selective pressure. That is, natural selection is seen as harshly weeding out all but the very fittest, while artificial selection is more gentle. This easily leads to the conclusion that if (some groups of) humans are less subject to natural selection, they are not evolving as much. But there's no reason to think that relationship is a necessary one, even if it happens to be empirically true for the modern West -- there are plenty of aspects of the natural world that exercise very little selective pressure, at least in certain times and places, and artificial selection can easily be so harsh as to wipe out whole groups of people (e.g. genocides).