Claims in maths and claims in ethics are inherently different, though they shared similarities. Some of the similarities that both share is the existence of assumptions; in mathematics it is axioms, and in ethics it is moral principles. The claims in ethics makes judgements to whether something is right or wrong from the assumption that moral principles are always established, and correct.
We never question axioms, or moral principles whether in maths or ethics. Axioms are established facts in maths. Moral principles are claims established by our society to what is right or wrong.
Some claims in maths are a priori, which means that they are independent from experience, something that hasn’t been necessarily “proven”. To prove something in math, one would have to provide an algebraic proof to a concept in order for it to be considered a truth in maths. Many “claims” in math are a priori, as they are not necessarily algebraically proven, but still regarded as true at some times, through the deductive reasoning, and proof of exhaustion. For example, the prime numbers.
Both claims in maths and claims in ethics have flaws in the assumption that what we base our knowledge off is somewhat unquestionable.
Claims in maths are usually driven by evidence and reason. Ethics can also be driven by evidence and reason, but Lewis also states the existence of the “law of nature”, where moral laws don’t need to be introduced to people as they naturally understand them. Can we necessarily back up something that is just supposed to be “natural” or do we ever need reason in order to justify truths. If we incorporate reason into ethics, it would make the moral principles inconsistent. Reason in ethics is not about the “facts”, and create logical inconsistencies. It creates logical inconsistencies because a anti-homosexuality activist would say it is unnatural for humans to engage in these actions. Would this reason mean that he also does the support the notion of abortion?
Therefore, reason in maths do not encounter these problems, therefore I believe that reasons in maths are more justified, though there are advantages and disadvantages.