Strong objectivity is, supposedly, an alternative to the epistemological choice between objectivity and relativism.
Objectivity is basically the belief that in order for something to be 'true' it must be absolutely true (i.e: universally true).
Relativism is the traditional alternative to objectivity. It holds that truth is something relative (hence the name...) to a particular standpoint. That is, things are never absolutely true, but only contingently so.
Both of these views have serious problems, and this is what "Strong" Objectivity hopes to remedy. Rather than proposing a God's eye view (as regular, 'weak' objectivity does) it accepts that its own viewpoint is a historical, contingent and utterly socialized one. There is a trick that allows strong objectivity to avoid relativism however. Basically the argument runs like this:
We acknowledge our viewpoint as contingent.
By acknowledging this, we eliminate its 'tainting' effects from our knowledge claims.
This makes our viewpoint 'more true' than others, because we have eliminated a source of bias that they have not.
Thus, we are both contingently situated and objectively validated.
This notion of objectivity has (I think) a LOT of insurmountable problems(See my A Critique of Feminist Standpoint Epistemology for my arguments against strong objectivity)
, but it is nevertheless popular in some circles. It is particularly popular in: