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The positivist believed in empiricism -- the idea that observation and measurement was the core of the scientific endeavor.

post-positivism is a wholesale rejection of the central tenets of positivism

One of the most common forms of post-positivism is a philosophy called critical realism.

Positivists were also realists. The difference is that the post-positivist critical realist recognizes that all observation is fallible and has error and that all theory is revisable.

the critical realist is critical of our ability to know reality with certainty

Because all measurement is fallible, the post-positivist emphasizes the importance of multiple measures and observations, each of which may possess different types of error, and the need to use triangulation across these multiple errorful sources to try to get a better bead on what's happening in reality.

The post-positivist also believes that all observations are theory-laden and that scientists (and everyone else, for that matter) are inherently biased by their cultural experiences, world views, and so on.

post-positivism rejects the relativist idea of the incommensurability of different perspectives, the idea that we can never understand each other because we come from different experiences and cultures.

Most post-positivists are constructivists who believe that we each construct our view of the world based on our perceptions of it. Because perception and observation is fallible, our constructions must be imperfect.

Post-positivists reject the idea that any individual can see the world perfectly as it really is. We are all biased and all of our observations are affected (theory-laden). Our best hope for achieving objectivity is to triangulate across multiple fallible perspectives!