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    On the S5 axiom system of modal logic, all possible world... — Carmelics
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    Supports→It is impossible that nothing exists.

    On the S5 axiom system of modal logic, all possible worlds are connected, so if S is metaphysically possible in one world, S is metaphysically possible in all possible worlds—i.e., S is necessarily possible.

    Natural Theology
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    Topics

    Natural Theology

    Key Terms

    Modal logic(logic)
    A system of logic that deals with concepts like possibility, necessity, and what could or must be true.
    Necessarily possible(the conclusion drawn about how S5 treats possibility)
    Something that is not just possible in one situation, but *must* be possible in every conceivable situation—it's a guaranteed kind of possibility.
    S5 axiom system(the particular logical system being applied)
    A specific set of rules in modal logic (named S5) that philosophers use to determine which statements about possibility and necessity are valid; it's one of several competing rule systems.

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    Browse more in Natural Theology
    Related propositions within the same area of thought.
    metaphysically possible(as used in metaphysics)
    Something that could exist or happen in reality without violating the fundamental laws of nature — not logically contradictory.
    possible worlds(Leibniz's modal semantics, anticipating contemporary possible-worlds semantics)
    Worlds that have existence in a tenuous sense; fictional worlds used to characterize the nature of possibles that are never actualized

    Related

    But one can conceive of a possible world with at least one actual and hence poss...Hence, if nothing exists, there are no possible states of affairs at all.If no actual states of affairs exist, no merely possible states of affairs exist...It is impossible that nothing exists.
    +2 moreShow less
    Suppose nothing exists. Then no actual states of affairs exist.This contradicts the supposition that there are no possible states of affairs.

    Similar

    By modal Axiom S5, if it is possible that a necessary being exists, it...79%If it is possible that it is necessary that a supernatural being of so...77%Nothing can be simultaneously metaphysically, axiologically, and soter...76%Mathematical possibility does not entail metaphysical possibility75%

    Source

    AI-extracted
    SEP: cosmological-argument
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    In the first part of the 20th century, with the rise of Positivism, the argument was largely abandoned. C. ” But since existence claims cannot be logically necessary, the statement is absurd. However, he notes, within us lies a deep-seated question: why should anything exist at all? Smart does not know what sort of question this is for it fails to fit his conception of propositions as either necessary truths or empirical claims. However, he continues, this awe-inspiring theological question appeals to those with a religious attitude. In this, the cosmological argument is reduced to a mystical ...

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