Inductive cosmological arguments are prima facie more promising for the natural theologian than deductive arguments, such as the Kalam cosmological argument, which is not sound. In the cosmological scenario of an infinitely old universe, however, there is no valid explanandum for the hypothesis of theism. The claim that theism might explain the infinite series of time-slices of the universe ‘as a whole’ is based upon a fallacy of ambiguity. There is no valid explanandum either for a synchronic cosmological argument. Finally, the argument from the Big Bang to God is problematic for a multitude of reasons. It cannot avoid the risk of God-of-the-gaps. It cannot satisfy the relevance condition, because the likelihood of the Big Bang singularity given theism is negligible (if it can be determined at all). Also, the prior probability of the Big Bang singularity cannot be small compared to that of God, for example (if it can be determined at all).
Keywords: Classification of cosmological arguments, Principle of sufficient reason, Causal explanations, Infinite causal regress, Georg Cantor, Kalam cosmological argument, William Lane Craig, Actual infinity, Hilbert’s Grand Hotel, Three cosmological scenarios, Big Bang theory, Pope Pius XII, Idealization, Bayes’ theorem, An infinitely old universe, The universe as a diachronic whole, A first state of the universe, The synchronic cosmological argument, Planck time, The Big Bang singularity, Generatio spontanea mundi, Creatio ex nihilo, Principle of collective causality, Leibniz, The universe as a whole, David Hume, Quentin Smith, Bede Rundle, Counterfactuals, Prior probability of the singularity, Principle of indifference, Measures of simplicity, Infinite properties, Speed of light, Morally indifferent God, GIGO principle, Attributive adjectives, Predicative adjectives, God’s complexity
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