Now the question is whether the meaning of (1) can be the same as the meaning of any other universal proposition such as ( 2) or (3). Russell says: Now when you come to ask what really is asserted in a general proposition, such as 'All Greeks are men' for instance, you find that what is asserted is the truth of all values of what I call a propositional function, l
From this remark it follows that what has been asserted in (1) is the truth of all values of the propositional function ~If x is a man, then x is mortal'. He also says that 'All men are mortal' means the same as "'x is a man' implies 'x is mortal'" whatever x may be, 2 and it also means the same as ~If anyone is a man, then he is mortal'? From some of his remarks about the ~is' of predication, 4 and the meaning of a predicate such as ~mortal' which means a certain quality, 5 it follows that ~All men are mortal' would mean the same as 'Wherever there is humanity, there is mortality'. Hence, according to Russell, the sentences from (1) to ( 5) would not differ in meaning. Now the question is whether (1) is equivalent to (6). In several passages he has said that a universal proposition (or a general proposition) cannot be made true by a set of particular facts. He says:
There are particular facts, such as 'This is white'; then there are generalfact~, such as 'All men are mortal'."
Moreover, according to Russell, we cannot describe the world completely in terms of particular facts or atomic facts. He says:
Suppose that you had succeeded Ln chronlchng every single pamcular fact throughout the universe, and that there &d not exist a single particular fact of any sort anywhere that you had not chronicled, you still would not have got a complete descripnon of the umverse unless you also added: 'These that I have chronicled are all the particular facts there are'.:
As regards the objectivity or the nature of a general fact Russell says:
It is perfectly clear, I think, that when you ha~e enumerated all the atomic facts m the world, it LS a further fact about the world that those are all the atomic facts there are about the ~orld, and that is just as much an objective fact about the world as any of them are. It ~s clear, I think, that you must admit general facts as d~stmct