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This thesis is a study of G.W. Leibniz’s views on compossibility. Leibniz calls substances that can be brought into existence together “compossible,” and he says that substances that cannot be brought into existence together are “incompossible.” Incompossibility and compossibility together divide substances into sets of individual substances that make up possible worlds. God then chooses from these possible worlds the best one to bring into existence. Thus without compossibility, the contingency of the world, and even God’s choice could have no rational basis. It is on these grounds that Leibniz thought compossibility was the most powerful—and perhaps, only—defense against the position that the actual world is the only possible world. This is a position that was powerfully argued for by Benedict de Spinoza. For largely theological reasons Spinoza’s position was unacceptable to Leibniz. Since Leibniz’s own time thinkers have found it difficult to see why all the substances are not compossible with one another given certain other philosophical and theological claims Leibniz is committed to. This state of affairs has been exacerbated by the fact that Leibniz himself seems not to have been concerned with providing a clear answer to this conundrum. In an attempt to fill in this omission, and to justify Leibniz’s intuition philosophers have proposed varying accounts of compossibility. Unfortunately, all of these accounts fall short of upholding a comprehensive rational explanation of the world’s contingency based on the objective rational choice of God. My dissertation presents a picture that is multi-faceted in its sensitivity to Leibniz’s theological, physical and logical concerns while nevertheless harmonizing with other tenets of Leibniz’s overall philosophy. I seek to achieve this end by defending the view that compossibility is based on the logical properties of the complete concepts of substances understood as embedded within networks of mutual intelligibility.