I am reading Classical Mathematical Logic by Epstein. I am a little bit unclear on some of his terminology:
No [abbreviated] wff such as $p_0 \wedge \neg p_1$ is true or false; that is the form of a proposition, not a proposition. (Page $11$)
A formal wff is true oe false in the model according to whether its realization is true or false. (Page $17$)
If we are given a certain realization and its valuation:
$p_0 =$ the sky is blue (True), $p_1 = $ iron is red (False)
Is $((p_0) \wedge (\neg (p_1)))$ a proposition? Or is it just a statement that happens to be false (as per the second quote) , but it is not a proposition?
Say, the variables are realized, but they are not valuated. Is $p_0 \wedge \neg p_1$ a proposition then?
Epstein defined as follows:
Proposition: "A Written or uttered declerative sentence used in such a way that it is true or false, but not both."
Realization: "A realization is an assignment of propositions to some or all of the propositional variables. The realization of a formal wff is the formula we get when we replace the propositional variables appearing in the formal wf with the propositions assigned to them; it is a semi-formal wff. The semi-formal language for that realization is the collection of realizations of formal wffs all of whose propositional variables are realized. "
Valuation: " We agree that sentences assigned to propositional variables...are propositions... But it is a further agreement to say which thruth-value it has. When we do that we call all the assignments of specific truth-values together a propositional valuation, $v$, and write $v(p) = T$ or $v(p) = F$ according to whether the atomic proposition $p$ is taken to be true or false.