Consider the following statements:^{[139]}

`x`

`is a star`

`x`

`has two moons`

`x`

`has`

`m`

`moons`

`x`

`is between Earth and`

`y`

`x`

`is between`

`y`

`and`

`z`

Here *x, y, z*, and *m* are *parameters* or *placeholders*. As a consequence, the statements aren’t propositions (i.e., they aren’t unequivocally either true or false), precisely because they do involve such parameters. For example, the statement “*x* is a star” involves the parameter *x*, and we can’t say whether it’s true or false unless and until we’re told what that *x* stands for—at which point we’re no longer dealing with the given statement anyway but a different one instead, as the paragraph immediately following makes clear.

Now, we can substitute *arguments* for the parameters and thereby obtain propositions from those parameterized statements. For example, if we substitute the argument *the sun* for the parameter *x* in “*x* is a star,” we obtain “the sun is a star.” And this statement is indeed a proposition, because it’s unequivocally either true or false (in fact, of course, it’s true). But the original statement as such (“*x* is a star”) is, to say it again, not itself a proposition. Rather, it’s a *predicate*, which—as you’ll recall from Chapter 5—is a truth valued function; that is to say, it’s a function that, when invoked, returns a truth value. Like all functions, a predicate has a set of parameters; when it’s invoked, arguments are substituted for the parameters; substituting arguments for the parameters effectively converts the predicate ...

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