If Ethics and Maths both employ logical thinking and argumentation to produce knowledge, can claims in Ethics be as well justified as those in Math?
Before discussing the prompt, it is necessary to address the vagueness of the terms “logical thinking” and “argumentation”, and distinguish them from the formal logic used in Mathematics. While the ethics use a form of logic, it is generally either dialectic or philosophical, seeking to establish well-founded arguments or looking at the behaviour of language in relation to logic. Another question that raised itself is that of whether all forms of ethics employ formal logic, and whether logical thinking is applicable to all areas of ethics. Keeping this in mind, two (overlapping) lines of argument were formulated: the character of premises in the two areas, and the truth values of claims in Mathematics and Ethics.
A key distinction between the two fields is that the premises upon which they are based, their axioms, are different in character. While axioms in Mathematics are internally referential and, if discussing external phenomena, quantitative, those in Ethics can be linked to the Human Sciences and thus — of a certain subjectivity. While in Mathematics, axioms may be invented in response to inadequacies in existing theory (for instance, the invention of the Zermelo-Fraenkel axioms in order to resolve Russell’s paradox), such inventions hold different significance in Ethics. Perhaps a key difference between the two Areas of Knowledge is their function: while Mathematics exists primarily in a theoretical realm (though it has significant practical applications), Ethics hold different connotations as they seek to essentialise truths related to the nature of human behaviour. The reconceptualisation of axioms or premises in Ethics is thus more linked to individual perception and can either represent or bring about significant shifts in societal consciousness. Ethics prior to and after the popularisation of humanism can be linked to shifts in major value systems, and the development of Ethics as a field must be considered in the context of to the ideas prominent at a given time. While in certain times (that of the Ancient Greeks first comes to mind) Mathematics might hold similar significance, the effects of changes in axioms are arguably less marked, and more restricted within the field itself.
Furthermore, the logic employed in Mathematics generally relies on universally accepted definitions (after a certain point) which have defined ‘truth values’. It is, however, less clear if ethical statements can have the same characteristics. While formal logic may be employed in the discussion of ethical statements, it does not apply to Ethics with the same rigidity. The primary benefit of logic is argumentative rigour—that if the premises of an argument is true, then the conclusion is true as well. Such a function has its roots in classical philosophers like Aristotle, who employed logic to ensure that his arguments were sound. That being said, logical methods do not discriminate between true and untrue premises, which are the true areas of contention in Ethics. Different approaches to implementing opposing premises could be employed to reach different conclusions in Ethics, and all would be internally sound but still untrue.
Engaging with the prompt, however, it must be reiterated that it looks for “justification” and not “truth”. Argumentative logic allows claims in Ethics to be proven as internally sound, thus making them justified to that extent. However, the premises used to arrive at said claims may not be justified through this logic. In making statements on the nature of human behaviour, Ethics are vulnerable to a subjectivity in the perception of human nature, and logical thinking is ill-equipped to resolve those shortfalls.