Final answer:
The sentence in question is a statement because it can be evaluated as true or false. It is actually a false statement since positive integers cannot have negative squares, and their primality is irrelevant in this context.
Step-by-step explanation:
The given sentence in question is "All positive integers with negative squares are prime." This sentence is a statement. According to logic and philosophy, a statement is any declarative sentence that has a truth value, meaning it can be declared true or false. In this case, the sentence is false because there are no positive integers with negative squares (as the square of a positive integer is always positive), and thus the part about them being prime is not applicable.
The correct answer, referring to the options provided, would therefore be statement. The sentence is false; however, this does not nullify its status as a statement. The truthfulness of a sentence does not affect its classification as a statement; rather, the ability to determine its truth value does. The sentence can be assessed for correctness and is either true or false, which satisfies the requirements for being a statement.