Plato's Euthyphro is not the story of a battle between two intellectual heavyweights. Indeed, the reader is left with the impression that Socrates has manipulated and steered the dialog so that the ideas of the interlocutor Euthyphro are not given time to develop and mature. For it appears that Euthyphro's proposed definition for the holy is a defensible one, and if someone with the intelligence and perseverance of Socrates were arguing in its favor it would have passed muster.
The two Athenians are searching, at the request of Socrates, for the "eidos itself by which all pious things are pious" (6d). At this point the reasons for the quest are irrelevant, although one may surmise that Socrates hopes to either discover the truth or (more realistically?) demonstrate Euthyphro's ignorance while Euthyphro is only discussing the matter because Socrates is adamant in continuing the conversation.
Socrates dismisses Euthyphro's first attempt to answer the question about what is holy or pious on the grounds that the answer ("the pious is ... proceeding against whoever does injustice ..." (5e) ) is merely a listing of a few things that are holy and not an idea which can be used to identify the holy. What Socrates is after is the essential characteristic that makes something holy, a pattern to which things can be compared to assess their holiness or lack of holiness. Euthyphro seems very familiar with the concept of an idea, for at 6e he immediately proffers that "what is dear to the gods is pious, and what is not dear is impious."
Although judged a noble answer initially, this concept is then taken to task by Socrates. First, he obtains Euthyphro's approbation of a somewhat more formal version of the original statement: things dear-to-the-gods are pious and those hateful-to-the-gods are impious. Socrates then makes several assumptions, among them the assumption that the pious and impious are opposite and exclusive.
This is an idea that bears a bit of scrutiny. The statement is made that something is not both pious and impious. Modern society may be used to avoiding such pronouncements, preferring to examine the circumstance in which a thing exists before judging it. Socrates is not necessarily doing anything different. He is, however, asserting that if there is some ultimate concept of pious and impious (for the sake of this dialog it appears that is an essential axiom) then a particular things is not both. It may be neither, but it can not be both. This does not preclude looking at extenuating circumstances or mitigating factors. Indeed, such things may very well have to be considered. Regardless, there is only one correct assessment of a thing: that it is pious, that it is impious, or that it is neither.
The assumed absoluteness of piety is essential to the subsequent assault on Euthyphro's dear-to-the-gods answer. Equally important are several other assumptions that Socrates makes. The first of these is that the gods quarrel. Less of an assumption than a tacit acceptance of the poets' stories, this is a belief that few, if any, in Athens would publicly dispute. But in 7d Socrates says that gods and humans argue for the same reasons. Either caught off balance or unaware of the implication of such a statement, Euthyphro readily agrees to this second assumption. The third addition assumption is that gods "love whatever they believe noble and good and just, and hate the opposites of these" (7e). Euthyphro accepts this too, freeing Socrates to decimate the dear-to-the-gods answer.
Socrates essentially argues that when humans quarrel, they do so because they are unable to find an absolute measure of something of interest to them. That is, rarely are wars fought over disagreement about a length, weight, or calculation, because such a thing is easily ascertained. (If one wanted to know the length of a board, the board could be measured. Depending on the results, it might fit the idea of a seven foot long thing or a three inch long thing.) Instead, conflicts arise over good and bad, just and unjust, and noble and shameful because humans lack the knowledge of a standard by which such things can be ascertained. By assumption, gods also quarrel. Also by assumption, they quarrel for the same reasons as humans. This implies that gods differ in what they believe to be just, what they believe to be noble, and what they believe to be good. Since, again by assumption, gods love what they believe noble, good, and just, then different gods must love some things that other gods do not love and they must hate some things that other gods do not hate. Thus, some things may be both dear-to-the-gods and hateful-to-the-gods.
When presented with this implication, that some things are both pious and impious, which is a direct contradiction to the principle of mutual exclusion, Euthyphro grants a guarded approval of the logic, translated as "probably" in 8a. Perhaps he was covering a lack of understanding of the arguments Socrates made, but Euthyphro's hesitation to concur with the philosopher is warranted -- there are several nits that can be picked with what Socrates has done.
Foremost among the flaws in Socrates's argument is the assumption that gods and humans fight among themselves for the same reasons. Perhaps Socrates really is corrupting the gods of the poets, because he is saying that they are exceedingly human-like. If Socrates were willing to grant or Euthyphro willing to argue that gods may have had some higher motive or rational to their fighting then the entire argument might fall apart. For example, if the gods tussled with each other to demonstrate to humanity that recognizing the good and noble is not enough and one must also go to any lengths to inform others, then it could still be true that the gods all loved the same thing and it is our interpretation of what they love that is flawed. Or, to go to the extreme, knowing why the gods quarrel may simply be out of the human sphere and to project human traits onto godly behavior is in this case possibly deceptive and in know way a given.
Socrates and Euthyphro also ignore or gloss over certain contingencies. Assuming the gods love what they believe to be noble, good, and just and hate the opposite, seems to limit as dear-to-the-gods and hateful-to-the-gods things which either have or lack all three qualities. If something is believed to be noble and good, but not just, then it is neither dear-to-the-gods or hateful-to-the-gods.
So it is apparent that there are at least two ways for Euthyphro to defend his characterization of the idea of the holy as that which is dear-to-the-gods. First, he could exploit the difficulty in the Socratic assumption of similarities between gods and humans. Although this does not provide Socrates with a way to discern what is dear-to-the-gods and what is not, is does prevent him from saying that their fighting is necessarily an indication that they differ over what is good, noble, and just. So while this does not prove that dear-to-the-gods and hateful-to-the-gods are exclusive, it does invalidate the conclusion Socrates would like to arrive at -- that from Euthyphro's proposed idea of the holy it can be shown that some things are definitely both pious and impious.
Another alternative open to Euthyphro is to take issue with one of the other underlying assumptions that Socrates makes. Euthyphro was asked to teach Socrates the nature of the holy. Euthyphro answered that the holy is that which is dear-to-the-gods. But in his attempt to show that leads to a contradiction, Socrates questions the idea of dear-to-the-gods. Why does he do this? Most likely it is because he wants (either for himself or for Euthyphro) a way to discern what is pious and what is not. However, the definition of holy that Euthyphro proposes is not suited for that. Euthyphro did not answer the question "how can I determine what is holy." Instead, he answered the question "what characterizes something that is holy." Socrates does not seem to be able to use Euthyphro's answer directly, because things are not labeled dear-to-the-gods (at least with labels visible to humans), so he takes an indirect route and characterizes the dear-to-the-gods as things which are believed by gods to be all of noble, good, and just. It is this assumption, Euthyphro could point out, that leads to the contradiction because it does seem that different gods find different things noble and good and just. But, due to a lack of knowledge, humans do not appear to have the means to determine that this definition of dear-to-the-gods is correct. Merely stating that the pious is that which is dear-to-the-gods does not, by itself, lead to a contradiction -- if one is careful in defining dear-to-the-gods or if one accepts it as a fundamentally consistent and basic idea that has no further definition.
In any case, such solutions were not presented by Euthyphro, and he accepts the presentation of Socrates. It becomes apparent to him that what Socrates is driving at is something must be loved by all the gods to be holy. Euthyphro does not states this immediately, but instead points out that all the gods do agree that "whoever kills someone unjustly must pay the penalty" (8b).
Socrates and Euthyphro toss this point around, and eventually two key issues emerge. One is the restatement of the idea of the pious as whatever is dear-to-all-the-gods and the impious as whatever is hateful-to-all-the-gods. This is not explicitly put forth; instead, Socrates and Euthyphro use the phrase "what the gods love." The difference between this statement and "dear-to-the-gods" is important to Socrates and forms the crux of a later argument, but Euthyphro does not seem to readily grasp the difference.
The other issue that emerges is the distinction between a concept and reality. Socrates convinces Euthyphro that both gods and people all believe certain things, for example, that injustice merits a penalty. However, different gods and appeal seem to have different concepts of what things are unjust.
Although the two continue to discuss various aspects of piety and holiness, this represents a fundamental turning point in the dialog. Euthyphro continues on almost sullenly, because he feels that he has answered the question Socrates posed -- what is the eidos of the holy. Socrates disagrees and presses on, because he is unable to utilize the definition Euthyphro provides.
The criteria Euthyphro was originally asked to meet included developing an idea that maintained the exclusivity of the pious and impious and would provide a pattern by which all things could be judged as pious, impious, or neither. Although the original answer fell short, there are several rectifications that could be made to address the original shortcoming, which was that exclusivity was not preserved.
The amendment that Socrates is most willing to grant and that Euthyphro accepts is that the pious is that which is dear-to-all-the-gods. Logically, several other changes were possible, but one involves redefining what dear-to-the-gods is and the others involve contradicting certain fundamental Athenian or Socratic assumptions (i.e., the replacement of a plurality of gods by a single god).
What results is a seemingly valid and defensible (noble to the Athenians) idea of the pious. That Socrates chooses to cast it aside reflects his desire to have a different type of definition and his desire to avoid the nondeterminism of exactly what is 'dear-to-the-gods' and 'hateful-to-the-gods'. Euthyphro is either unable or unwilling to point out that it may very well be beyond the sphere of human understanding to delve any deeper into the nature of why something is 'dear-to-the-gods' -- that it may be an end unto itself. Due to the perseverance of Socrates and the lack of ability of Euthyphro, the dialog moves on, discarding a definition of the holy.