The paper argues for a novel method for understanding Greek gods, building on the approach of J.-P. Vernant, but adding a new dimension to it.
Vernant attempted to read the Greek pantheon as a system of classification and to see the multifarious attributes and functions of the gods as parts of a meaningful structure, in this way allowing modern readers to understand the gods instead of seeing them an incongruous assemblage of various historically contingent traits. While considering this type of approach as fruitful, I argue that Vernant has overstressed the systematic side of the gods, downplaying their anomalous and chaotic aspects - not in the sense of their heterogeneous qualities that arise as a result of contingent historical development (as runs the usual criticism by historians of Greek religion) but much more importantly in the sense of their transgressive and antistructural features which are an integral part of their personalities.
These result from the fact that while the gods help to establish and guard various ideal categories of the human world, they do so from without and are not constrained by them themselves. In this way the gods are able to support the system while balancing out some of its inevitable limitations, mediating its internal contradictions and introducing flexibility into its static categories.
I subsequently draw methodological consequences from this general conception. When studying a god I suggest to pay attention to the boundaries this god both protects and transcends, i.e. to focus on both the normative and the transgressive of the god in question, on the ability to unite various conflicting principles in the god's personality, and on the transitions the god allows his or her worshippers to make.
In this way I hope to convey to the modern reader not just the meaningfulness of the gods but also their indispensability for the correct functioning of the Greek cultural system.