It seems to me that one of the most fundamental concepts in philosophy is "objectivity" since trying to find an answer for a question of any sort would ultimately depend upon the answer of the particular question of "Is there an objective thing?", and naturally/logically then "Is there an objective truth?"
There are some philosophical/psychological viewpoints basing themselves on statements like "There is no objective thing at all". It seems that the following arguments show that such statements are intrinsically self-refuting or contradictory:
1- If there were only subjective things and henceforth only subjective minds and ideas, how is it possible for someone to imagine the notion of objectiveness? In fact, during the course of such an imagination he could only conceive a relativized version of "objectivity" which, by definition, is ultimately forced to be subjective! However, our intuition suggests and actually supports the idea that we all can understand what objectivity means (something whose existence/being is independent from any specific subject). In the same line of ideas, when we are able to imagine the notion of independence, this conception cannot be dependent!
2- If there were nothing objective independent of our minds, how is it possible for us to understand each other's speech? The situation becomes more difficult if we consider people from different cultures and histories, with different languages that are still able to understand each other. (For example, an archaeologist speaks about concepts that people of ancient times were thinking about).
Are there some arguments that can satisfactorily answer the above objections against the hypothesis of non-existence of an objective thing/truth?