After presenting Apostel’s views on scientific realism, I present definitions of the concepts of ontology and metaphysics. I then proceed to develop Apostel’s basic ontology and his metaphysics. Apostel proposed a particular understanding of existence based on his views on causation. He also developed a view of the universe as a causal self-explaining system. I discuss and illustrate three kinds of what he calls “metaphysical deductions” that aim to deliver such a view of the universe. The most important one is (...) the Leibnizian variational method, that should allow us to deduce the existing universe as the ‘best’ of all possible worlds. (shrink)