What is the difference between asserting "$\phi(a)$" and asserting "$\phi(a)$ is true" in Whitehead and Russell's PM? The first edition of Principia Mathematica clearly distinguishes "Socrates is a man" and "'Socrates is a man' is true." Judging from the context, the distinction is neither a primitive idea nor a definition; it is something the reader is supposed to "see." For some reason I can't "see" it, although I can deliberately memorize the distinction the same way I memorize multiplication table. I have an inkling that this distinction should directly appeal to the sense, like the distinction between red and blue. If you can "see" this distinction, please kindly help me out.
The following passage is from page 41, Introduction, Chapter II, section II, The Nature of Propositional Functions.

http://i.stack.imgur.com/ejGD1.png
These symbols are for your convenience:
propositional function: $\phi(\hat{z})$
Ambiguous value: $   \phi(z) $
A function with itself as an argument: $\phi(\phi(\hat{z}))$

The only thing I can think of is that "Socrates is a man" is a sentence in the sense that it has a truth value, but we do not make any claim as to what that truth value may be. The claim that "Socrates is a man" is true, is asserting not only that the same sentence has a truth value, but also that that truth value is True. 
Just to round things off: "Socrates slept quickly" is not even a sentence since it has no truth value at all, it is simply nonsense written in a grammatically plausible fashion. However, "Socrates had exactly 100,000 hairs on his head by his 18th birthday" is a sentence. It may be true or false, but we'll never know.
I hope this is at all in the right direction to answer your question. 
