"open sentence" is not a part of a sentence.
It is an expression used in mathematics and logic to describe a sentence that contains a variable, which can be true for any value of the variable. For example, "X is greater than 0" is an open sentence because it is true for any value of X.
What is asserted is simply an open sentence!
Quine thought that this leads to contradiction when the open sentence contains an opacity-inducing verb like 'believes'believes
Similarly, 'φ(x)' will be used to indicate an open sentence in which the variable x may or may not be free, not a function of x.
Thus, '∃x Elephant(x)' is committed to ("presupposes") elephants because the open sentence 'Elephant(x)' applies to all and only elephants, and there are some.
(3) When replace one of the complete names in a sentence by a variable, the resulting expression will be called an open sentence or an open formula.
(Or, on the Tarskian account of satisfaction, if and only if the open sentence Fx is satisfied by every object in the domain of the model).
Such accounts analyze truthbearers, e.g., sentences, into their subsentential constituents and dissolve the relation of correspondence into appropriate semantic subrelations: names refer to, or denote, objects; predicates (open sentences) apply to, or are satisfied by objects.
In this semantics, co-referential open sentences are exchangeable not salve veritate, but (as he puts it) salve extensione; that is, the exchange does not alter the state of affairs designated by the statement in which it occurs.
Somewhat similarly, Russellian contents may be modified in order to reflect first-personal indexical contents by introducing contents that are akin to open sentences, with a gap in place of a component corresponding to the subject.
The Greek letters $\phi ,\psi, \theta, \ldots$ are variables for propositional functions, and, with individual variables $x, y, z, \ldots$ go together to form open sentences $\phi(x), \psi x,y $, etc.
Thus, accounting for the set-theoretic notions by open sentences accordingly, the calculus of SA is equivalent to the Leonard and Goodman calculus (Simons 1987: §2.4; Ridder 2002: 98), and hence to the other systems too.
