First off, I don't think we necesarily need to determine a purpose for society or other individuals, I just think it's important that we accept that that objective purpose itself exists.
Secondly, it seems like there are two fundamental values you outlined in your message as being important:
1. The ability for us to progress in this discussion
2. The rules of logic itself
These are values. If they aren't objectively important, then you're right, we won't move forward in this discussion. There wouldn't even be a point to moving forward because "forward" wouldn't exist.
I value logic too, but I understand that logic serves a purpose. A purpose that is outside logic. Logic serves this purpose in it's proper context.
It sounds like you think value doesn't come into play in the sciences. How then, can you explain the fact that there's a functionally infinite amount of scientific data out there, but somehow we manage to only pay attention to the scientific data that matters? A scientist must select the data, they must design the correct experiments, and they must have the right orientation towards their work in order to arrive at the so called "objective truth."
Well, what makes that scientific truth objective?
(If you respond to nothing else in this message, please answer that last question)