This is an interesting question. Is morality objective?
I recently watched a video where Tovia Singer, an orthodox Jewish rabbi, claimed that he once debated with an atheist. The atheist apparently stated that he did not need God and he is aware by himself that murder, theft and other immoral actions are wrong. To this, the rabbi responded that humans were made in God's image, and that's why he has intrinsic awareness of morality - because God put it in him.
How would Buddhism respond?
OP: Does the Dhamma allow the philosophical establishment of an objective and/or universal morality without God?
Yes, of course.
According to the Kimattha Sutta:
"Skillful virtues have freedom from remorse as their purpose, Ananda,
and freedom from remorse as their reward."
You can read the whole sutta to see how skillful virtues lead to enlightenment. It starts from freedom from remorse, which leads to joy and so on.
So, if skillful virtues result in freedom from remorse, then immoral behavior lead to remorse. So, this means that virtue is universal or objective in Buddhism.
Well, some things are not universal or objective. For example, should you try to beat the lights when the traffic light is red? Now with the pandemic, many governments enforce social distancing rules - should you follow them? These are not universal or objective. These are learned.
But some things like taking a life, taking what belongs to others, speaking untruth and adultery are definitely universal or objective.
OP: If yes, how?
Where is this source of objective morality?
According to Udana 5.1:
I have heard that on one occasion the Blessed One was staying near
Sāvatthī at Jeta's Grove, Anāthapiṇḍika's monastery. And on that
occasion King Pasenadi Kosala had gone with Queen Mallikā to the upper
palace. Then he said to her, "Mallikā, is there anyone dearer to you
"No, great king. There is no one dearer to me than myself. And what
about you, great king? Is there anyone dearer to you than yourself?"
"No, Mallikā. There is no one dearer to me than myself."
Then the king, descending from the palace, went to the Blessed One
and, on arrival, having bowed down to him, sat to one side. As he was
sitting there, he said to the Blessed One, "Just now, when I had gone
with Queen Mallikā to the upper palace, I said to her, 'Mallikā, is
there anyone dearer to you than yourself?'
"When this was said, she said to me, 'No, great king. There is no one
dearer to me than myself. And what about you, great king? Is there
anyone dearer to you than yourself?'
"When this was said, I said to her, 'No, Mallikā. There is no one
dearer to me than myself.'"
Then, on realizing the significance of that, the Blessed One on that
Searching all directions
with your awareness,
you find no one dearer
In the same way, others
are thickly dear to themselves.
So you shouldn't hurt others
if you love yourself.
Also found in the Dhammapada 10:
All tremble at violence; all fear death. Putting oneself in the place of another, one should not kill nor cause another to kill.
All tremble at violence; life is dear to all. Putting oneself in the place of another, one should not kill nor cause another to kill.
One who, while himself seeking happiness, oppresses with violence other beings who also desire happiness, will not attain happiness
One who, while himself seeking happiness, does not oppress with violence other beings who also desire happiness, will find happiness
What does this show?
Morality is objective, not because it has a source like God.
Rather, it's because we know that nobody is dearer to us than ourselves (if we still have self view and conceit), and we recognize that this is also the case for other unenlightened sentient beings.
So, you would feel remorse when hurting others, because you know that if others did that to you, you would feel pain. The basis of morality is compassion towards the suffering of others, because we can relate to it due to our own suffering.
How do I know this to be true?
Simply list out every possible way you can hurt another person, and most likely, you would have derived the basic code of morality found in most religions by negating every item in your list.