Okay. I am reading Russell's paper "On Propositions: What They are and How They Mean". Since the truth or falsehood of a belief depends upon a fact to which the belief "refers", and propositions are defined in terms of beliefs, Russell feels that an adequate treatment of propositions requires that we first inquire into the nature of facts. So in this first section he discusses facts; in particular, he discusses negative facts, whose existence his contemporaries evidently find repugnant. He discusses three different ways of escaping the existence of negative facts and then refutes them. I am having trouble seeing the difference between the first and third ways of escaping negative facts.
Regarding the first way, when we deny something, we are really asserting something incompatible with what we deny. Regarding the third way, which he attributes to a Mr. Demos, propositions are in a ultimate, indefinable relation of opposition such that two propositions which are opposites cannot both be true, though both may be false (obviously this definition is circular, which Demos admits). Thus, on the third view, when we deny a proposition, what we are really doing is asserting "Some opposite of this proposition is true."
I don't see how Mr. Demos' view is any different than the one first one Russell considered and refuted. In fact, couldn't he give the table example to refute Mr. Demos' position? I ask because I don't find Russell's infinite regress response to Demos' view particularly convincing in showing the absurdity of Demos' view; after all, Demos thinks this notion of 'opposition' is epistemologically primitive, so why should he have to answer the obstinate fellows questions? I am trying to put Russell's argument in a premise-conclusion form but I am having trouble doing so, perhaps because I don't find the argument particularly convincing. Does anyone know how to render it in this form? If I were Russell, I would just advance the table example against Mr. Demos and be done with it.
On a side note, why did Russell's contemporary's find negative facts so repugnant? What was their motivation from ridding them from their ontology?