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Formal Sciences

Abstract structures underlying reality

The formal sciences—mathematics, logic, information theory—deal with abstract structures that transcend physical instantiation. These disciplines reveal necessary truths and patterns that any possible world must exhibit, pointing toward a rational ground of reality.

Mathematics

The Existence of Mathematical Objects

Mathematical truths appear to be discovered rather than invented. The number π, prime numbers, and geometric relationships exist independently of human minds. Where do these abstract objects "live"?

  • Platonism: Mathematical objects exist in an abstract realm—but how do physical minds access them?
  • Nominalism: Mathematics is merely useful fiction—but why does fiction describe reality so precisely?
  • Theistic solution: Mathematical truths exist in the mind of God, explaining both their objectivity and accessibility

The Applicability of Mathematics

Eugene Wigner's "unreasonable effectiveness of mathematics" poses a puzzle: why should abstract mathematical structures, developed without reference to the physical world, turn out to describe it so precisely? On theism, both mathematics and physics flow from the same rational source.

Logic

The Laws of Logic

The laws of logic (identity, non-contradiction, excluded middle) are necessary truths that govern all possible worlds. They cannot be derived from physical processes, yet they constrain physical reality.

If logic is grounded in a necessary, rational mind, this explains both its necessity and its applicability. The alternative—that logic is a brute fact—leaves its existence unexplained.

Information Theory

Information as Fundamental

Modern physics increasingly recognizes information as fundamental to reality. John Wheeler's "it from bit" suggests that physical existence derives from information. But information requires a mind to generate and interpret it.

  • Specified complexity in biological systems indicates intelligent origin
  • The laws of physics can be viewed as information constraining matter
  • Consciousness may be the fundamental substrate from which information and matter emerge