Link to his Nagel's argument here;
Nagel claims that the basis of morality is a concern for other people. He argues that morality is based on a natural empathy for others, and does not believe that ethical obligations can be reduced to religious or legal ones. He believes that moral decisions are made when people empathize with other people. This is not due to someone’s natural compassion for other people but mainly due to the idea that if you would not wish the action unto yourself, you would not do it unto anyone else. Nagel also argues that everyone should care about their actions, others and the repercussions of their actions on others. The basis of morality is “objective” as the belief that good and bad to particular people/animals are not just good and bad in your perspective, but also from a general point of view which every thinking person can understand.
Nagel argues for his idea of the Objectivity of Morality by exploring the analogy of stealing an umbrella. Imagine you were attempting to steal an umbrella but some passerby sees you and asks “How would you like it if someone did that to you?”. This would result in you realising that you would resent it if someone stole your umbrella so you have a reason why someone should not do it to you. From this notion, you then can understand that there must be a reason to not do it to anyone as if it’s a reason anyone would have not to hurt anyone else in this way, then it’s a reason you have not to hurt someone else in this way. This establishes that stealing someone else’s umbrella is wrong – Nagel’s analogy of the umbrella can then be extended to other actions as we can deem actions good/bad through logical reasoning.
Nagel stated that they would then have to face the question of “how would you feel if someone did (insert the person’s action) to you?”. The majority of people, when faced with this question, would realise that they wouldn’t like the action done unto them as there is some reason that someone shouldn’t do the (insert the person’s action) to them. But then, it’s simply a matter of logic: if there is a reason not to do an action to you, then there’s a reason for you to not do the same action to anyone else. And, if you do the action, you should feel guilty about it even if you don’t care about other people. Essentially, when one suffers, it is not just bad for them but bad, period.
The definition of Objective is when someone is “not influenced by personal feelings or opinions in considering and representing facts.”; I believe that Nagel successfully demonstrated that morality is not a subjective idea as he has shown the moral laws of the universe to be: “don’t do unto others what you don’t want done unto you” – Confucius. People wouldn’t want bad things done to themselves (as I believe our Human Nature is inherently selfish) so they wouldn’t do things that would conversely result in harm to themselves. But would I say that he has proven morality to be objective? No. With every philosophical argument, there are always some outliers and exceptions to the theory but for this theory, I believe that the number of anomalies is far too many: although if someone were to be asked the question “how would you feel if someone did that to you”, they would realise that their action was bad and not do it; but, how many people actually experience this? Many people act quickly in self-interest, through aggressive emotions and don’t even go through the experience of thinking through their actions and weighing out the morality behind it. This is why I believe morality, theoretically (if everyone was to ask themselves “would I like this if it were done to me?”), could be objective but practically, it is completely up to the person to express and is subject to feelings and emotions.