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What exactly is the meaning of the term 'being that exists' which is associated with the argument from contingency. Can I equate this term with an abstract object (SEP) such as 'element' in the mathematical definition of a set so that I can make a set of the elements of 'being that exists'? Does this break some sort of philosophical principle?

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    It sounds like you are using the high school definition of a set as a "collection of objects." This definition is not used in formal set theory. A set is simply anything that obeys the axioms of whatever flavor of set theory you are working in. There is no definition of a set. Sets are characterized by their behavior under the axioms. And you can't just form sets out of "everything that exists" or "being that exists" as you put it, due to Russell's paradox. en.wikipedia.org/wiki/Russell%27s_paradox
    – user4894
    Dec 16, 2021 at 4:24
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    Maybe we can consider "imaginary beings": a unicorn is one example and it does not exist. Thus the issue boils down to: is God an imaginary being or he is a "real" one i.e. a "being that exists"? Dec 16, 2021 at 8:36
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    Clarify and linked language to stave off closure.
    – J D
    Dec 16, 2021 at 8:50
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    Modern authors, like Rowe, interpret infinite regress of causes in exactly this vein, form a set of contingent beings in a causal chain, see Existence of infinite causal chains. As long as one does not try to form the set of all 'beings that exist', which might be paradoxical, it does not violate any "principles".
    – Conifold
    Dec 17, 2021 at 19:18

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The argument of the first mover was developed in Aristotle and subsequently identified in Islamic and Christian philosophy with an act of God and hence a reasoned argument for the existence of God from rational grounds.

This argument has nothing to do with the ontological status of sets or of the elements of sets. You can take a mathematical realist position here, as the mathematician Connes does, and say that such things exist in an world intelligible to the mind. Or you can take a more agnostic view, as David Hilbert did, and merely take this to mean that the axioms are self-consistent.

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  • Sir, This can be also seen in the 'law of identity' in logic, which classically says: 'Every thing that exists' has a specific nature, Abstractly, For all x, x=x. In a mathematical perspective, "For all x" is sensible to me when x is contained in a universal set U which is already been defined in a 'context'. Mar 9 at 4:58

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