One of the greatest challenges with attempting to discuss post-modernism is figuring out exactly what claims are being made. For a start, many of the figures typically associated with post-modernism didn't label themselves as post-modernist, so it isn't as unified as it might have been if it had been an explicit movement, rather than just people who wrote about similar things. Secondly, the roots of post-modernism are in continental philosophy, which has much less of a focus on clearly defining terminology and logic flow than analytical philosophy and so is often harder on the reader. Thirdly, post-modernism tends to be popular among a certain crowd and many in that crowd tend to be less interested in rigour than I would like (think artists, literature majors, sociology students). Due to these factors, it is particularly important to clarify exactly what is being said when talking about post-modernism or otherwise reduce how often people end up talking past each other.

Post-Modernism is usually contrasted with modernism. Modernism isn’t any one thing, but a collection of related beliefs such as a progression of history, optimism about the power of science to answer our questions, a belief in an objective reality that we can know or at least progress towards knowing. It is also associated with certain movements in art, film or architecture, but these are outside the scope of this article. Post-Modernism is posited as a rejection of these assumptions. It may argue that grand narratives a merely a fallacy, that science isn’t truly objective, that our interpretations of the world are unavoidably a product of our culture and perhaps even that there is no objective truth or reality.

Scott Alexander wrote an article that attempted to put post-modernism in terms that rationalists could understand. He later retracted the article based on feedback from people who told him that it wasn’t a good explanation of Post-Modernism. I actually think that the content was good, but that he should have framed it differently. While he did a great job of defending a Modernist (or Rationalist) position that made significant concessions towards post-modernism, the beliefs conveyed in the article weren’t really post-modernism. Nonetheless, this is a useful perspective which deserves its own name, so I will henceforth refer to this as Skeptical Modernism.

More precisely, Skeptical Modernism tries to acknowledge just how limited our knowledge of the world is, whilst still defending science, logic and the progress of society as better than the alternatives. It makes as many concessions to post-modernism as it can, while still remaining a modernist philosophy. This allows it to provide an effective challenge against overconfident Modernism, whilst also allowing Post-Modernists to clarify their position by explaining how it differs from skeptical modernism. Expanding on the later, one of the most common complaints about post-modernism is that it involves Mott and Baileys. Defining Skeptical Modernism greatly reduces the scope for this to occur and helps clarify what a post-modernist is claiming that cannot fit within a modernist world-view.

So what exactly is Skeptical Modernism? Perhaps the best place to start is the summary by no_bear_so_low:

1) Theories have strategic uses

2) Words have strategic definitions

3) Ideology formation is often done in shockingly cynical ways.

4) Even when it's not intended cynically it ends up being used that way.

5) The answers to popular debates are often less interesting than the question 'why are we having these debates at all?'

After that, I’d read the SlateStarCodex article, but two key points it mentions are:

1. Seemingly objective facts are often actually subjective (the date when Rome fell depends on how you define “falling” and perhaps the date we use is affected by incentives)
2. Objective criteria of what counts as what are generally dependent on subjective opinions about what should count as important

I’ll also list a bunch of additional arguments or points that characterise Skeptical Modernism:

1. Science is not quite as objective as it appears, as while there are certain standards or rules as to how various pieces of conflicting evidence should be compared, there isn’t a comprehensive, universally agreed upon standard for this
2. Our culture raises us from birth to think a certain way and it is impossible for us to completely escape this influence
3. Most people have a tendency to generalise their beliefs of how society should work to other societies with a very limited understanding of the cultural context. Even people who are well educated generally don’t have the same experience that people in that culture have.
4. The language that we have access to makes some ideas easier or harder for us form and communicate
5. That moral intuitions differ widely between societies so we should strongly question whether our moral beliefs are well justified
6. Society seems to have been progressing over the last few hundred years, but not in all ways and this progress is far from guaranteed
7. Democracy is generally good, but it requires a specific type of cultural context to work

We can seperate the first five (statements about epistemology) from the last two (statements about grand narratives). It is possible to take a Skeptical Modernism approach to epistemology, but not grand narratives, or vice versa.