Broad on induction and probability

Abstract

Modern inductive logic rests upon a tradition that integrates confirmation theory with the structural analysis of nature. Induction is fundamentally inconclusive unless reformulated in terms of probability, a shift requiring specific material assumptions about the physical world. The Principle of Limited Independent Variety and the theory of natural kinds provide a necessary ontological basis for assigning finite initial probabilities to scientific laws, preventing them from vanishing under mathematical scrutiny. While the Laplacean doctrine of inverse probability faces significant limitations when applied to open natural classes, the hypothetical method allows for the incremental confirmation of laws through their logical consequences. Further refinement of inductive methods involves a formal “Logic of Conditions,” which systematizes the search for necessary and sufficient causes by refining traditional eliminative canons. Scientific advancement transitions from observing simple conjunctions of determinables to establishing complex laws of correlated variation among determinates. This conceptual framework reveals a deep interdependence between the notions of substance, kind, and causation. Ultimately, the justification of induction remains a central tension between necessitating principles and empirical regularities, though the formalization of these processes clarifies the logical grounds for rational belief in scientific generalizations. – AI-generated abstract.