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Abstract: This paper argues that scientism—the view that science is the only source of factual knowledge—is both false and self-defeating. Drawing on counterexamples from literary theory, history, and the axioms of mathematics and logic, the paper demonstrates that non-scientific knowledge exists. A formal logical proof shows that scientism is inconsistent with this fact. Furthermore, scientism fails its own criterion: the thesis that all knowledge must be scientifically justified cannot itself be scientifically justified, rendering it self-referentially incoherent and rationally unacceptable.
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Abstract: Popular cosmology often claims that quantum physics explains how the universe arose from “nothing.” This essay examines that claim in the work of Alexander Vilenkin and Lawrence Krauss, showing that the “nothing” invoked is not absolute nonbeing but a physically and mathematically specified state—governed by quantum laws, configuration spaces, and boundary conditions. The Borde–Guth–Vilenkin theorem further complicates matters by implying past-incompleteness for inflationary spacetimes. Physics can describe state transitions within a law-like framework; it cannot derive existence from genuine nothingness.
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This short and informal essay briefly traces my journey from atheism, back to Christian theism. Central to this reconsideration are four interconnected problems: the irreducibility of consciousness, the difficulty of grounding rationality within a purely evolutionary framework, the persistent appearance of objective moral facts, and the question of ultimate meaning.
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Abstract: This essay discusses Gerhard Gentzen’s 1936 consistency proof for Peano Arithmetic, which reveals a profound epistemological paradox: securing finitary arithmetic requires transfinite induction up to ε₀, an apparently infinitary principle. This result challenges Hilbert’s Program and raises fundamental questions about mathematical justification. Rather than undermining confidence in arithmetic, Gentzen’s proof illuminates the interconnected nature of mathematical knowledge, demonstrating that PA cannot justify itself in isolation. I argue that mathematical certainty emerges not from reduction to indubitable foundations but from the coherent unity of mathematical practice, where finitary and infinitary methods…
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Abstract: This paper gives a simple argument that if God is perfect love, then God cannot be a single, isolated person. Real love is directed to someone, not just a potential that only appears once other people exist. And since God did not have to create anything, God cannot depend on creation in order to be fully loving. So if God’s love is perfect and essential to who God is, there must always have been someone for God to love within God’s own life. This conclusion does not, by itself, prove…
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Abstract: This paper replies to three common objections to the perfect-love argument. First, it explains why self-love is not the fullest kind of love the argument is about: a real relationship with someone distinct. Second, it argues that being “ready to love” is less than actually loving, so perfect love cannot be merely a disposition. Third, it clarifies that the argument does not by itself prove the Trinity; it only requires at least two divine persons. It concludes that God’s beloved must be eternal and uncreated within God’s own life.
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Abstract: This paper formalises a modal argument from perfect-being theology to intra-divine personal plurality. If God exists, perfect love is an essential great-making perfection; if perfect love is irreducibly interpersonal, then necessarily, if God exists God stands in a lover–beloved relation to a distinct personal other. Since creation is contingent, there is a possible world in which God exists and no creatures exist. A unipersonal God would then lack any distinct beloved in that world, yielding a contradiction. The conclusion is that God is not unipersonal.
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Abstract: This paper examines a tension within perfect-being theology: if God is essentially perfect love, and love is irreducibly relational, can God be solitary apart from creation? Using modal possible-worlds reasoning and the doctrine of aseity, it argues that contingent creation cannot supply the beloved required for essential interpersonal love. The paper presents a formal argument concluding that an essentially perfectly loving God must include eternal intra-divine personal plurality (at least Lover and Beloved), and previews how Parts II and III will formalise and defend the claim.
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Abstract: How do we measure the “strength” of a formal mathematical system—not by elegance, but by what it can prove about itself and other theories? Ordinal analysis answers by assigning each theory a proof-theoretic ordinal that tracks the reach of its induction and proof complexity. Starting with Primitive Recursive Arithmetic and moving to Peano Arithmetic, we see a sharp rise from ω^ω to ε₀. The pattern extends into second-order systems such as ACA₀ and ATR₀, where larger ordinals map the landscape of provable consistency and mathematical power.
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Abstract: The Banach-Tarski paradox—rigorously proved yet physically impossible—reveals fundamental tensions between mathematical abstraction and physical intuition. This essay explores how the Axiom of Choice generates counterintuitive results, beginning with Vitali’s non-measurable sets before presenting the formal construction that decomposes a sphere into finitely many pieces reassemblable into two identical spheres. Rather than mere curiosity, the paradox illuminates the relationship between mathematical truth and physical reality, forcing us to confront what it means for logical systems to produce results that radically violate our spatial intuitions while remaining mathematically valid.
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