What are the semantic differences between “white swan” and “swans are white”? (a) One of the semantic differences is that “white swan” is non-propositional and “swans are white” is propositional. That is, “white swan” is neither true nor false but “swans are white” is the opposite: It’s either true or false. (b) The other semantic difference is that “white swan” asks you to imagine something that’s both white and a swan and “swans are white” tells you that if you see a white, then you’ll see something white: the swan. “White swan,” being non-propositional, doesn’t tell you anything about, say, “black swan,” but “swans are white,” being propositional, tells you that “swans aren’t black.”
That is:
- “White swan” brings together in your imagination whiteness and swanness.
- “Swans are white” not only brings together in your imagination whiteness and swanness but also proposes that whiteness and swanness go together.
(It’s important to point out that “swans are white” tells you that with swanness comes whiteness, not the opposite: that with whiteness comes swanness. That is, s < w, not w < s.)
With the double labels ab, ~ab, a~b, and ~a~b:
- It’s possible to bring together in your imagination ab, ~ab, a~b, or ~a~b.
- It’s also possible to propose that ab, ~ab, a~b, or ~a~b go together. (That’s what the copula does.)