Final answer:
Aquinas's proof for God's existence based on observable purposes in nature is known as the teleological argument, which infers an intelligent designer from the complex design observed in the world.
Step-by-step explanation:
Thomas Aquinas formulated a teleological argument for the existence of God, which is based on the observation of purpose and design in nature. This argument proposes that the intricate detail and complex order observed in the world suggest the presence of an intelligent designer. Unlike the cosmological argument, which derives from the existence and order of the universe, or the ontological argument, which is a priori and does not consider the physical universe, the teleological argument is an a posteriori argument, meaning it is based on empirical evidence from observations in nature. Aquinas's argument is known for focusing on the evidence of intelligent design within reality, indicating the existence of a creator due to the presence of order, unity, and complexity in the world.