'Hesperus' and 'Phosphorus' can be analyzed via distinct complex predicates ('E(x) ∧ S(x)' and 'M(x) ∧ S(x)') involving different functions specified in terms of evenings and mornings.
A logical formula where 'M' means 'morning,' 'S' means 'star-like,' 'x' is the object being described, and ∧ means 'and'—so this reads 'x is morning and star-like.'
Phosphorus(Standard example in philosophy of language)
A proper name used to designate the morning star (the planet Venus), functioning as a rigid designator
analyzed via(as used in philosophical explanation)
Broken down or explained in terms of; the statement is saying we can understand these names by looking at the characteristics they describe.
where ‘\(E(x)\)’ and ‘\(M(x)\)’ indicate different functions, specified (respectively) in terms of evenings and mornings. This leaves room for the discovery that the complex predicates ‘\(E(x) \land S(x)\)’ and ‘\(M(x) \land S(x)\)’ both indicate functions that map Venus and nothing else to the truth-value T. The hypothesis was that the propositions expressed with ‘Hesperus is bright’ and ‘Phosphorus is bright’ have different (fundamental) constituents, even though Hesperus is Phosphorus, but n