I'll address the basic arguments in Euthyphro concerning the failure of "loved by the gods" to be an adequate definition of piety.
The first, and somewhat weaker, argument against the adequacy of this definition is that the gods disagree about many things. For example, Artemis approves of celibacy and Aphrodite abhors it. The gods supported opposite sides in the Trojan war. The gods are often portrayed as squabbling among themselves. Thus piety cannot be defined as what the gods love; they love many different things.
This argument is countered by the modified assertion that that piety has to do with what is beloved universally by all the gods. This is countered in turn by a more philosophically complex argument, namely one of causation, that leads us to an aporia. This complex argument is based on the problem of whether the gods love things because they are pious or whether divine love imbues things with piety. The former, however, means that we still have not located a definition of piety, because we have not yet listed a set of criteria defining the essence of piety, but have only described the way the gods react to it.
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