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It is not the case that It would be incoherent for a person who believes a deductive cosmological argument for God's existence is sound to then deny that God exists.
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Reasons For
2 perspectives
Reason for 1 of 2
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1.
A person can believe an argument is valid and its premises true while remaining agnostic about whether the conclusion-term refers to anything real.
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2.
The concept 'God' in a cosmological argument's conclusion may not map onto the theistic God of worship, leaving existential commitment coherently suspended.
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Reason for 2 of 2
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1.
Hinge propositions, as Wittgenstein argued in 'On Certainty', function as framework commitments that resist revision by argument alone, even sound argument.
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2.
An atheist's denial of God's existence may operate as a hinge proposition immune to doxastic revision through logical inference, not as a logical inconsistency.
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Reasons Against
1 perspective
Reason against
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If someone believes that a deductive cosmological argument (proof) for God's existence is sound, then accepting the soundness of the argument logically commits them to accepting the conclusion that God exists.
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