Meaning: The quote "The ultimate reason of things must lie in a necessary substance, in which the differentiation of the changes only exists eminently as in their source; and this is what we call God." by Gottfried Leibniz, a German philosopher and mathematician, reflects his profound metaphysical and theological views. Leibniz is best known for his contributions to rationalism, metaphysics, and the philosophy of mind. His quote encapsulates his belief in the existence of a necessary and unchanging substance as the ultimate reason for all changes and differentiations in the world, which he identifies as God.

Leibniz's philosophy is deeply rooted in the concept of substance and the principle of sufficient reason. According to Leibniz, the world is composed of substances, which are independent entities that possess intrinsic properties and are the ultimate bearers of change. These substances are not passive entities but are characterized by an inherent force or active power that enables them to undergo changes. Leibniz's notion of substance is closely tied to his theory of monads, which are simple, indivisible, immaterial substances that constitute the basic building blocks of reality.

In the quote, Leibniz suggests that the ultimate reason or explanation for the existence and changes in the world must be grounded in a necessary substance. This necessary substance, according to Leibniz, is God – the perfect, infinite, and unchanging being. In Leibniz's metaphysical framework, God serves as the ultimate source of all differentiation and change in the world. As the necessary substance, God contains within Himself the eminent or perfect representation of all possible changes and differentiations, and thus, He is the source from which all contingent realities derive their existence and meaning.

Furthermore, Leibniz's concept of God as the necessary substance aligns with his idea of the best possible world. He argues that God, as the supreme being, has chosen to actualize the best of all possible worlds out of an infinite number of possible worlds. In this best possible world, every existing substance and every event is harmoniously arranged according to the principle of pre-established harmony, which is established by God. This pre-established harmony ensures that each substance unfolds in accordance with its own internal principle of activity, while also harmonizing with the activities of all other substances in the world.

Leibniz's quote also reflects his belief in the principle of continuity and the interconnectedness of all things in the universe. For Leibniz, the differentiation of changes in the world is not arbitrary or disconnected but is grounded in the unity and coherence of the underlying necessary substance, God. This view points to Leibniz's optimism about the rationality and orderliness of the world, as well as his conviction that the universe operates according to a grand metaphysical plan designed by God.

In conclusion, Gottfried Leibniz's quote encapsulates his fundamental metaphysical and theological beliefs, emphasizing the existence of a necessary substance, identified as God, as the ultimate reason for all changes and differentiations in the world. Leibniz's philosophy of substance, monads, and pre-established harmony underpins his view of God as the source and guarantor of the intelligibility and coherence of the universe. This quote provides insight into Leibniz's profound metaphysical system and his vision of a harmonious and purposeful cosmos governed by the necessary substance, God.