One problem with having objectivity as a scientific goal is that it may be humanly impossible.
One area where this comes up is in the reading of a text. To read is to interpret, and it is impossible to interpret without bringing ones own concepts and experience to bear on the interpretation. This introduces partiality.
This is one reason why Digital Humanities are interesting. In Digital Humanities, one is using only the objective properties of the text–its data as a string of characters and its metadata. Semantic analysis is reduced to a study of a statistical distribution over words.
An odd conclusion: the objective scientific subject won’t be a human intelligence at all. It will need to be a robot. Its concepts may never be interpretable by humans because any individual human is too small-minded or restricted in their point of view to understand the whole.
Looking at the history of cybernetics, artificial intelligence, and machine learning, we can see the progression of a science dedicated to understanding the abstract properties of an idealized, objective learner. That systems such as these underly the infrastructure we depend on for the organization of society is a testament to their success.