Let me ask this. If I am wrong and Socrates did not ground objective morality in the transcendent where did he ground it. Without something that transcends humanity you are left with no possible way to arrive at or discover objective moral facts because there is no source for them.
Something one must always keep in mind when talking about the Greeks is that they were very concerned with "sophia" or "wisdom". They believed, especially the Athenians, that true knowledge was out there. That we could find and reason the knowledge that exists without a shadow of a doubt. Its a very different approach to the scientific way we deal with things today where nothing is 100% certain.
Also with the history of the Socratics starts with Socrates but only through the lens of Plato. Plato very specifically believed that all knowledge that could be considered "true knowledge", "sophia" or "wisdom" could be derived from logic and reason within one's own intellect. Socrates in Plato's writings sought knowledge through endless questioning till one would get to the essence of what it was. The Socratic method as it was called was in some ways a precursor to the scientific approach we have today though still fundamentally different in practical applications.
But we can assume that since Socrates as Plato describes insinuates that there is "true knowledge" and that "morality" can be found in true knowledge, as in discerned from the pure logic and reason of the mind, and yet at the same time there was no god that could dictate it, we are left with the assumption that it is simply a truth. Just as no god could ever produce a square circle no god could change the truth of what is moral and what is not.
Since haggling over what specific Greeks said would be a sidebar here lets use another source. Jefferson said when asked what foundation for human rights and duties exists. He (and he was certainly no Christian) replied that nature and nature's God was the only possible source for them.
Actually he said
"We hold these truths to be self-evident, that all men are created equal; that they are endowed by their Creator with inherent and inalienable rights; that among these, are life, liberty, and the pursuit of happiness; that to secure these rights, governments are instituted among men, deriving their just powers from the consent of the governed; that whenever any form of government becomes destructive of these ends, it is the right of the people to alter or abolish it, and to institute new government, laying its foundation on such principles, and organizing its powers in such form, as to them shall seem most likely to effect their safety and happiness." --Declaration of Independence as originally written by Thomas Jefferson, 1776. ME 1:29, Papers 1:315
He didn't say god. He said "creator". At this time it is well understood that it is mostly a political verbiage but not necessarily out of line. As a deist he would have assumed that by whatever means that something was created, it is not of this substance. Jefferson, a well known Aristotelian, would have taken the idea and the concepts and this didn't necessary require anything else. However to say that we are simply innate among ourselves without saying we are "endowed" would not have come off as great.
Though again we fall into the same ontological situation where it does not matter if he said "god", "creator", "evolution" ect. The meaning was the same. That by whatever means that we were created we have now been endowed with equality (though that really only applied to White men who were land-owners so I don't know how accurate we want to say this very specific quote is to his views but none-the less).
In other words not explained by nature but by something beyond nature or the supernatural.
In a way yes. But typically it was not to god but to himself in who he is. The mystery of life and all that. Though again I would like to stress that he has not appealed to a god at this point.
Of course I was not suggesting Socrates had any Christian type of world view. Just that morality having two definitions (one objective and the other subjective) is a well established historical understanding. It is not Christianity which grounds morality. It is the presence of a transcendent, personal, moral God. Christianity happens to posit such a God but other types of theism and deism do as well at times. I am not arguing for the biblical God but for objective moralities necessary foundation.
I understand your point. If there is a deeply person moral god that created the very fabric of morality then it would be hard pressed to argue against that. However there is no reason to assume that it is logically impossible to have an objective morality in the absence of such a being.
For example what if there is no single creator but there are natural laws of spirituality? Certain things such as the Brahman or "the all" which would be pantheistic in nature so it is no longer deeply personal or innately moral but there could be objective moral truth's. Such as Buddhism and Hinduism takes Karma without deeply personal morally dictating gods. It simply is part of the universe despite there not being a being such as you described.
I would love to investigate Socrates a bit further, however that would be an off ramp from what I am primarily stating, there is so little known about him that getting any certainty about him is unlikely, I am swamped with posts that I need to reply to, and my lab is having testing problems that require my time. For now I will defer to your knowledge of him since it does not affect my argument. One last note. IMO the Greeks were the first to ask the right questions but they seldom got the right answers. I think the Romans began to answer the Greeks questions. Did you see the Roman definitions of Mallum in se and Mallum prohibitum I posted?
Yes. The Greeks I think had the best answers for interpersonal moral questions in some cases (especially Aristotle) but the Romans were very practical in the way that they systematically defined and conceptualized ethics rather than morality. In truth the only difference is that morality is dependent upon the personal while Ethics is from the perspective of the community. And which would be considered the better or greater cause for "goodness"? Personal moral capability or ethical responsibilities as realized from the whole group?
Though this is also what I was getting into earlier about different levels of subjectivity to moral truths. Not all morality and moral opinion is objective no matter which way we talk about god or not god. But there are things that do seem to be universally applicable.
The Romans realized this but they took it in function. Mallum Prohibitum deals with things that are not innately wrong in and of themselves but are prohibited due to law for usually side effects of those actions. For example running a stop sign is not innately evil in any way. It is not an immoral action. But it is an unethical action due to the saftey of others and the dedicated guidelines that hopefully have had full thought and reason put into it all for the greater good of the community or humanity in general.
Then there are things that are Malleum Se which would mean evil "cuz man its just evil". It hits our natural sense of morality and we have that gut wrenching feeling that it is wrong. We know this is innate. We know that it is more or less universal. But is it objective? All three of those things, innate, universal and objective are different in fundamental ways to this argument. One does not necessary mean the other.