If 'S knows that p' were context-sensitive, then two speakers using it in different contexts to describe the same epistemic situation could both speak truly while contradicting each other, which is semantically incoherent.

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Epistemic situation(epistemology): The facts about what someone knows or believes, and the circumstances around that knowledge—basically, everything relevant to whether a person actually knows something.
Knowledge (in philosophy)(epistemology): More than just true belief—philosophers define it as justified true belief, meaning you need evidence or good reasons to back up what you claim to know.
Semantically incoherent(philosophy of language): When something doesn't make logical sense in terms of meaning—it violates basic rules about how language and truth work together.
context-sensitive(Used to describe terms like 'I' and 'left' whose reference shifts with the context of use.): A term whose semantic value or referent varies depending on features of the context of utterance, such as the identity or orientation of the speaker.

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