What a fun group.
Some things that I would like to observe:
Mathematics and Logic are simply analytic tools to insure the consistency of any conclusions.
They do not form an ethical system.
Self referential statements should be avoided, and comments about ethical statements should reference that fact. This is important for clarity and not simply a trick. As example, mathematicians have known for a long time to reference a group of Sets by the term “Class”. Using this fact have provided many useful theorems where the use of classes are required.
Assuming that we could establish an ethical system then we can establish a class of ethical systems by simply establishing an equivalency relationship. As example, Let Ai be a collection of statements ending with “is right” in the ethical system A then let B be another ethical system where each statement in B is defined so that Bi is equivalent to Ai if and only if Bi has the same beginning as Ai but ends with “is wrong” These are two ethical systems which are related to each other. We can most likely create an entire universe of ethical systems. Many of the systems may form equivalency classes. How do you know what is right? You might argue that if two classes are isomorphic then they are the same. Kind of like Plato’s Ideals but from the above example if you believe A is the absolute correct Ethical system how can you exclude B? Somehow you are going to divine some measure call it m. If this is analogous to a mathematical measure then you will find that there are many different measures that can be devised from m and others that are completely unrelated. How do you know which is right?
Some of the paradoxical statements should be corrected for the sake of clarity.
Fredrick wrote:
"They want to insist, on the one hand, that no one should presume to dictate a single point of view to others because this is wrong. Meanwhile they also insist that nothing is really right or wrong. They claim, on the other hand, that no one really knows what is morally correct – except that they really know this.
There are no true ethical values, they say, but everyone is entitled to his or her point of view and no point of view is better than any other – except for the point of view that no point of view is better than any other and that everyone is entitled to his or her point of view. Amazing."
“THEY” should restate their comments as follows:
If Ai be a collection of ethical systems and m be a measure of Ai then m(Ai) = m(Aj)
for all i and j.
The Nazis had Friedrich Nietzsche and Social Darwinism - I think Friedrich should be very careful.