Propositional attitude verbs like 'believes' are intensional operators requiring fine-grained objects of belief that sentence types, lacking intensional identity conditions, cannot supply.

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Fine-grained objects of belief(as used in philosophy of mind): The detailed, specific contents of what someone believes—distinguishing between beliefs that seem similar but are actually different. For instance, believing 'water is wet' is different from believing 'H₂O is wet,' even though water is H₂O.
Intensional identity conditions(as used in metaphysics and philosophy of mind): Rules that determine when two different ways of describing something should count as the same or different from the perspective of someone's beliefs or thoughts. It's about how fine-grained our descriptions need to be to capture what someone actually believes.
Intensional operator(as used in logic and philosophy of language): A word or phrase that changes meaning based on how we describe the object of someone's thought, rather than just what the object actually is. For example, 'believes that Superman is strong' is different from 'believes that Clark Kent is strong' even though they're the same person.
Propositional attitude verbs

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