You make an interesting point when talking about Oppenheimer; I'd phrase the question as: Is it possible to be great, but not good? I think so, but it depends again on how you define greatness. If you define greatness in terms of impact on the world, then a person could be greatly good or greatly evil.

And if greatness is something we identify within ourselves, by what standards do we judge it?

“I met a traveler from an antique land
Who said: Two vast and trunkless legs of stone
Stand in the desert….”

(Trust an English major to relate this to a poem.)

Percy Bysshe Shelley's poem “Ozymandias” speaks of greatness – the Pharaoh's narcissistic vision of himself and his works (even though Shelley's history and description are, we'll say, liberal and slightly inaccurate). The idea behind the poem is that nothing lasts forever, not even the great works of great kings. The irony is that in writing the poem, Shelley contributes to the Pharaoh's greatness. It's all suddenly starting to get a little paradoxical.

A conundrum of sorts to consider: Robert Oppenheimer and his team at Los Alamos did some great work, they achieved their objectives and goals and did their work right. Their legacy lives on today and we remember them quite well. But was their achievement truly great? Were they fully aware and cognizant of what the outcomes of their work would be? Did anyone know what the result was going to be? Oppenheimer, at least, was to one extent: “Behold, I become death, the Destroyer of worlds.” And yet they carried on.

What then are we do with ourselves in achieving our greatness? Do we build great works to have them turn to dust before a Shelley of the future resurrects them? How do we know that what we're doing is great? I think, for me, greatness is something found inside, as you say, “something we identify in ourselves.” I find the notion of “done right” and “innocence of motive” appealing. And if others think it's great, that's alright, too.

I don't know if you've read Zen and the Art of Motorcycle Maintenance, but it goes down a similar path with regards to “quality.” Quality can't be defined, so how do we know it even exists. Maybe the same could be said of “greatness”?