The range of significance in Type Theory

What exactly does "Types as ranges of significance of propositional functions. In modern 
terminology, types are domains of predicates" mean?

Update:
I found in this paper (Pag 14 or 234) by Russell, where he defines what is ranges of significance, not exactly including types else propositions.


A function is said to be significant for the argument $x$ if it has a value for this argument. Thus we may say shortly $\phi x$ is significant,
meaning the function $\phi$ has a value for the argument $x$. The range of significance of a function consists of all the arguments for which the
function is true, together with all the arguments for which it is
false.

Comes from Russell, and it's actually about the domain, not the codomain, if I understand ol' Bertie correctly. A propositional function like "x>3" only has significance if we limit the possible values of x to numbers. Today we would call that the domain, but his choice of words is defensible: the range of significance of a propositional fn is the set of values that make it meaningful - i.e. true or false - as opposed to meaningless nonsense, like "Pegasus>3". The range of significance of a numeric fn is the set of values for which it yields a value, rather than crashing, so to speak.

The relation to types is fairly obvious: the range of significance of a fn $f: A\rightarrow B$ is just the "values" of type $A$ to which $f$ can be meaningfully applied. The concept and term "type" is just a more commodious way of expressing the same basic concept. Google "propositional function range of significance" and you'll get links to his original paper and lots more.

StackExchange Computer Science Q#56795, answer score: 2