What are positive sociology and sociological positivism?
The answers differ when you are asking about positive sociology (a fairly small subfield) or about positivism in sociology (also known as sociological positivism).
Positive sociology (as you can see from the stub of the article that can be read without paying in the sociologyencyclopedia.com link) is the sociological study of the good things in life. Most sociology focuses on the negatives--it tries to explain crime and poverty and things like that. Positive sociology, by contrast, seeks to understand how people arrange their lives so as to be happy.
Sociological positivism is a whole approach to sociology that can be traced back to Auguste Comte. Positivism in sociology is the idea that social scientists can truly be scientists. They can study societies in a scientific way. As the eNotes link below says, it is a method of study in which
metaphysical speculation is rejected in favour of ‘positive’ knowledge based on systematic observation and experiment.
The second definition, sociological positivism, is by far the more prominent in the field of sociology.