Final answer:
The usual notion of necessity in Kripke semantics differs from the theistic notion of a necessary being in that Kripke's system uses modal symbols to indicate logical necessity across possible worlds, while theistic necessity posits a metaphysical claim that certain divine beings inherently exist in all possible worlds due to their specific qualities.
Step-by-step explanation:
How the usual notion of necessity in Kripke semantics differs from the notion of necessity used by theists for necessary beings concerns a distinction between modal logic and philosophy/theology. In Kripke semantics, which is a formal system for representing modal logic, necessity is denoted by the symbol □ (box), whereas the diamond symbol ◇ (diamond) represents possibility. This formal system involves the evaluation of statements across possible worlds to determine if a statement is necessarily true, possibly true, or true only in some worlds.
Conversely, when theists, like Anselm in his ontological argument for God's existence, speak of a necessary being, they are referring to a being that cannot fail to exist in any possible world. Anselm posits that God is a being than which no greater can be conceived and, if such a being exists in the understanding, it must also exist in reality because existence in reality is greater than existence in the understanding alone. The theistic notion of necessary existence is not simply about truth across possible worlds but is tied to the existence of a deity with specific qualities, such as omnipotence and omniscience.
Kripke's logic does not inherently concern itself with the existential attributes of divine beings, while theistic arguments delve into metaphysical and existential claims about divine attributes. So, the crucial difference is that theistic necessity is not bound by the formalisms of modal logic but is steeped in theological and metaphysical commitments.