I have no idea what your metric for "strangeness" is. Using similar reasoning we can also assert that "The speed of light is objective" is not an objective cla

I have no idea what your metric for "strangeness" is. Using similar reasoning we can also assert that "The speed of light is objective" is not an objective claim. And we can further assert that both the inner and outer statements are true without arriving at a contradiction. It doesn't take a genius, merely a very thick skin and a grasp of contextuality, to hold this perfectly reasonable conclusion in a society dominated by naive understanding of non-contradiction. Objectivity, being an unattainable philosophical ideal, it doesn't prevent us from using the term in more pragmatic/cultural/inter-subjective sense. A white lie - if you will - that only a determined pedant would scrutinize to such philosophical extent. Just as well, such overt pedantry deserves mockery and contempt.