Small Steps toward Hypercomputation via Infinitary Machine Proof Verification and Proof Generation

After setting a context based on two general points (that humans appear to reason in infinitary fashion, and two, that actual hypercomputers aren’t currently available to directly model and replicate such infinitary reasoning), we set a humble engineering goal of taking initial steps toward a computing machine that can reason in infinitary fashion. The initial steps consist in our outline of automated proof-verification and proof-discovery techniques for theorems independent of PA that seem to require an understanding and use of infinitary concepts (e.g., Goodstein’s Theorem). We specifically focus on proof-discovery techniques that make use of a marriage of analogical and deductive reasoning (which we call analogico-deductive reasoning).