Final answer:
The question likely refers to a historical or scientific proposal by individuals named Singer and Nicholson, but the provided background texts do not address such a proposal. Without more context, it is not possible to give a specific answer regarding what Singer and Nicholson proposed.
Step-by-step explanation:
What Singer and Nicholson proposed refers to various historical figures and contexts that are unrelated to one another. Singer could refer to individuals in different disciplines, and Nicholson could refer to historical figures. However, none of the provided texts mention Singer and Nicholson making a joint proposal. One extract discusses the music career transition of Leonard Cohen; another extract is a story about an individual's contemplation of an artist's sincerity; the third extract details the historical account of Jacob Leisler and the rule of Lieutenant Governor Nicholson; and the final one talks about the ongoing discourse over women's role in music.
For educational purposes, if the question pertains to the Fluid Mosaic Model in biology, it would be referencing Singer and Nicholson’s scientific proposal in the 1970s about the structure of cell membranes. However, since no context is given for 'Singer and Nicholson' in the question and the provided information does not address any proposals made by any Singers or Nicholsons, it is not possible to give a precise answer without additional information.