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It is not the case that Swinburne's cosmological argument should be constructed inductively rather than deductively
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Reasons For
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Reason for 1 of 2
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1.
Leibniz and Clarke's deductive cosmological arguments succeed precisely because necessary existence is not a contingent empirical hypothesis subject to probabilistic confirmation.
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2.
Inductive inference to a personal God via Bayes' Theorem presupposes a well-defined reference class of universes, which does not exist and renders prior probability assignments arbitrary.
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Reason for 2 of 2
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1.
Aquinas's Third Way demonstrates that a deductive argument from contingency to necessary being avoids the regress problem without invoking probabilistic reasoning.
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2.
Swinburne's inductive framing reduces God's existence to a hypothesis that is in principle falsifiable, which conflicts with classical theism's commitment to divine necessity as a non-empirical truth.
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Reasons Against
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Reason against
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1.
The PSR, when used to construct a deductive cosmological argument, leads to a logically necessary being that cannot explain logically contingent existence
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2.
Bayes' Theorem provides a valid basis for inductive argumentation in confirmation theory
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