Axioms

Mathematics deals with deducing conclusions from mathematical axioms.

Interestingly, the axioms themselves cannot be proved. Axioms are usually assumed to be self-evident.

Axiom of extensionality: Sets A and B are equal if they contain the same elements

However, some axioms are debated. One famous example is the Axiom of Choice. Some people thought it was obvious. Others were not so certain. It was later proved that you can safely assume it to be either true or false (but not both at the same time).

Different sets of axioms will result in a different systems of mathematical logic. This is okay, so long each system is consistent with itself.

Some cultures shake their head to mean 'yes'

Kurt Gödel proved that there will always be questions we cannot answer without accepting new axioms. But we must be very careful about which axioms we accept.

One mistake, and the mathematical universe explodes.

Similarly, the field of Ethics deals with deducing conclusions from moral axioms.

Interestingly, the moral axioms themselves cannot be proved. Morals axioms are usually assumed to be self-evident to the individuals who hold them.

The Golden Rule is accepted by nearly everyone

However, some moral axioms are debated. For example, who does the Golden Rule apply to? Sentient beings? Unborn babies? Animals? Plants? Depending on your answer, you may arrive at a radically different conclusion to me on issues such as abortion and diet.

Compared to the rigor of the Mathematical universe, the field of Ethics is a house of cards. The problem is that our morals are rarely consistent. We let our emotions rule rather than rationality.

But perhaps that is for the better; those who feel most certain of their moral codes have turned out to be some of the most ruthless people in history (think witch-hunts, Hitler, and the recently self-declared 'Islamic State')