Defenders Podcast Defenders: Excursus on Natural Theology (Part 9): 1st Philosophical Argument for the Beginning of the Universe
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Jun 8, 2022 Delve into the Kalam Cosmological Argument and unveil the mysteries surrounding the universe's inception. Discover the distinction between potential and actual infinities, examining what it means for our cosmos. Venture into the intriguing realm of Hilbert's Hotel, where absurdities of infinity are laid bare, challenging the notion of an eternal universe. The conversation highlights the philosophical implications of these ideas, pointing towards a universe that must have a definitive beginning.
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Mathematical Actual Infinity And Transfinite Arithmetic
- In set theory an actual infinite is a completed set like the natural numbers with aleph-null members, manipulable by transfinite arithmetic.
- Transfinite arithmetic allows addition and multiplication of aleph numbers but forbids inverse operations to avoid contradictions.
Math Coherence Is Not Proof Of Real Infinites
- Mathematical coherence of infinite set theory doesn't prove actual infinites exist in reality; it merely creates a consistent universe of discourse.
- Craig: set theory could be a useful fiction like Sherlock Holmes rather than evidence of metaphysical reality.
Divine Infinity Is Qualitative Not Numerical
- God's infinity is qualitative, not quantitative; theologians mean omniscience, omnipotence, eternity, etc., not an actually infinite number of parts.
- Craig warns against conflating divine 'infinity' with mathematical actual infinities.