Kripke's semantics for S5 shows that necessary existence requires truth across all possible worlds, but S3 is a strictly weaker system that cannot license such strong modal closure.

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Kripke: Kripke refers to Saul Kripke, an influential American philosopher and logician known for revolutionizing how we think about names, meaning, and possibility. He argued that names like "Albert Einstein" refer directly to the actual person rather than through descriptions of their properties, which changed philosophy fundamentally. His work also introduced "possible worlds" as a way to understand concepts like necessity and possibility, making him one of the most important philosophers of the 20th century.
Modal closure(as what S3 cannot support as strongly as S5): A logical rule that says if something is true, then it's necessarily true (or follows some other pattern of necessity); a 'strong' closure means this rule applies very broadly.
Necessary existence(Contrasted with contingent existence in discussion of God's mode of being): Existence that is not contingent; the being does not just happen to exist or not exist.
S3 (modal logic system)(as a comparison system that is weaker than S5)

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