Objectivity is a fundamental concept in the Work, in that what we experience is subjective, originating from our inner world, whereas the world we participate in is objective—a common reality (at our level).
By declaring his criticism to be objective, Gurdjieff is indicating that what he describes is common to us all. We are left to determine whether his criticism is indeed impartial.
The etymology of the word is simple enough. Originally, in the philosophical sense it means “considered in relation to its object” from Medieval Latin objectivus, from objectum “object.” It implies impartiality.