Since the process of thinking if different for each person, doesn't that imply that morality is subjective?
No. A person is either correctly assessing a situation or they are not (thus why I used the specific term critical thinking)
. Different people doing an algebra equation may come up with different answers. But that doesn't mean that algebra is subjective. Only that some people aren't good at mathematics.The same is true with morality. Lots of people don't know how to best promote well being. But that doesn't mean morality is subjective. Only that some people aren't good at assessing the outcomes of complex situations.
However, different reactions to the same situation can both be viewed as moral or immoral, depending on your viewpoint.
Just because different people have different viewpoints doesn't mean that morality is subjective. Because morality is not measured by sincerity. It's measured by effect. Hitler was sincere in his belief that Jews should be exterminated. But his actions were nonetheless in direct conflict with the well being of sentient creatures.
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In regards to your question of whether or not to steal life saving drugs - the "correct" action to take is the one that maximizes well being while causing the least amount of unnecessary harm and suffering. The well being of sentient creatures covers a lot of ground. But we start with some basic precepts - life is generally preferable to death, pleasure/happiness is generally preferable to pain/suffering, fairness is generally preferable to bias, etc - and we work from there.
Weather or not it's moral to steal is entirely dependent upon the actions that theft would have. If there is a finite amount of medicine and stealing would mean someone else dying - then due to unfairness it may not be moral to steal. Or if stealing caused everyone else to start stealing all the time - then it may cause more harm than good. However, if the theft causes very little or no harm to anyone else and it saves a life - then the action would be moral. And, just because we may not know the outcome of a particular situation - doesn't mean there's not a correct answer.
I should also point out - morality is almost never binary. That is to say, there may be actions that would cause the most unnecessary harm and actions that would cause the most well being - but there are very often actions that lay somewhere in between. Maybe bribing the pharmacist is better than outright stealing. Or breaking in and stealing ALL the drugs would be worse than just taking what you need. etc.