Outside the philosophy of science, there are, as Alexander points out more than can be easily named.
In the philosophy of science, I would say the position farthest from Positivism is the strong Kuhnian position on incompatibility of paradigms. It maintains that during certain periods of science, when the community of practice in general is unhappy with their ability to make progress with the dominant paradigm, alternatives arise and one of those is selected as a basis for further progress.
In the strongest version of Kuhn's view, the new material in those alternative replacement paradigms is completely incomparable. There is no strictly logical basis for comparison between the alternatives. Each has a hard core that basically captures what it can from the existing system, and so can be comprehended in its terms. But beyond that, they inject vocabulary and concepts that are outside the system and cannot be clearly stated in its terms. (The primary progress the new paradigm is offering will be accomplished by nailing those down, reducing them from conceptual imagery to well-founded science.)
This means (to the degree it is true) that the choice of a new paradigm cannot be made in logical positivist terms, but must be made on the new paradigm's appeal to intuition or clarity.