What Is Logic? A Reading of the Philosophy of Science from the Logic of Calculus

This preprint proposes a conceptual bridge between logic and differential and integral calculus, examining how the philosophy of science interprets knowledge development[cite: 3]. It maps the empirical verification of necessary and sufficient causal conditions to the derivative (instantaneous rate of change) and compares the historical accumulation of scientific paradigms to the integral[cite: 3]. Through Boolean formalization, Occam's razor, and epistemological models (such as Kuhn and Lakatos), the work illustrates how the mathematical behavior of calculus clarifies continuous versus revolutionary progress in science[cite: 1, 3].