## Infinity: New Research FrontiersThis interdisciplinary study of infinity explores the concept through the prism of mathematics and then offers more expansive investigations in areas beyond mathematical boundaries to reflect the broader, deeper implications of infinity for human intellectual thought. More than a dozen world-renowned researchers in the fields of mathematics, physics, cosmology, philosophy and theology offer a rich intellectual exchange among various current viewpoints, rather than displaying a static picture of accepted views on infinity. The book starts with a historical examination of the transformation of infinity from a philosophical and theological study to one dominated by mathematics. It then offers technical discussions on the understanding of mathematical infinity. Following this, the book considers the perspectives of physics and cosmology: can infinity be found in the real universe? Finally, the book returns to questions of philosophical and theological aspects of infinity. |

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### Contents

1 | |

Inﬁnity as a Transformative Concept in Science and Theology | 19 |

The Mathematical Inﬁnity | 55 |

Warning Signs of a Possible Collapse of Contemporary Mathematics | 76 |

Technical Perspectives on Inﬁnity from Advanced | 87 |

A Potential Subtlety Concerning the Distinction between | 119 |

Much Better Than | 130 |

Some Considerations on Inﬁnity in Physics | 167 |

Inﬁnity and the Nostalgia of the Stars | 193 |

Inﬁnities in Cosmology | 218 |

Perspectives on Inﬁnity from Philosophy and Theology | 231 |

Notes on the Concept of the Inﬁnite in the History of Western | 255 |

Theological Insights from Cantors Mathematics | 275 |

A Partially Skeptical Response to Hart and Russell | 290 |

299 | |

Cosmological Intimations of Inﬁnity | 176 |

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### Common terms and phrases

Absolute Inﬁnity actual inﬁnity analogy apophatic argument Aristotle attributes Axiom of Choice Christian claim class of Woodin concept of inﬁnity Conjecture consistent cosmic cosmology counting number creatures deﬁned deﬁnition difﬁculties distinction divine inﬁnity element Ennead eternity existence extended ﬁeld ﬁnd ﬁnite ﬁrst ﬂat ﬂuctuations formal full code G¨odel Georg Cantor given God’s inﬁnity Gregory of Nyssa Hence inﬁnite inﬁnite number inﬁnite sets inﬂation Inner Model interpretation large cardinal axioms Lemma limit logical mathematical mathematicians metaphysical multiverse multiverse law negation Nicholas of Cusa Nikolaus von Kues notion of inﬁnity ordinal Pannenberg paradox peiron philosophical physical Plotinus possible predicates prewellorderings problem proof Let proper class properties quantum question reﬂection Reinhardt cardinal relation scientiﬁc sense set theory signiﬁcant space spacetime speciﬁc supercompact cardinal Suppose theology theorem things thought transcendent transﬁnite truth understanding universe of sets weak Reinhardt cardinal Woodin cardinals