<p>In this investigation, we attempt to establish a mathematical formulation for teleological explanation, based on path integral interference and information modulation mechanisms. A central hypothesis proposed is the mechanism-intent duality, which posits that a complete description of a physical system must involve both its structural mechanism and intrinsic purpose. Using the interference mechanism of the probability amplitude path integral as the mathematical foundation, the selection of actual paths is viewed as the result of information modulation by both purpose and natural laws. From the perspective of phase modulation, purpose and natural law are demonstrably equivalent in effect, and natural laws are interpreted as various objectively existing combinatorial forms of intrinsic purposes. Finally, we propose and analyze a thought experiment called the “drop arrow”, and examine classical cases such as free particle motion and the harmonic oscillator. This theoretical framework attempts to offer a possible approach to unifying matter, consciousness, and natural law.</p>