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The moral core of an individual, also called moral fiber or moral instinct, is described in some theories of ethics as the limits to the rationality of ethics itself, i.e. those which hold that morals are primarily aesthetic, and not directly sharable between living beings.
A moral core is presumed to be formed by epigenetics, including especially parental moral examples, and the slow growth via cognition of a set of conditionings, inhibitions, and concepts of beauty through his or her entire lifetime. Although it may be demonstrated to train or inspire others, it cannot be shared in any way, and is constantly changing.
Some theories of morality, notably moral relativism, but also branches of theology, e.g. Gnostic Christianity, hold that there is little value in attempting to share moral cores or even to align moral choices except to the bare minimum, e.g. to prevent serious bodily harm due to direct conflict.
The opposite belief, imposing various degrees of standardization via a moral code and its enforcement, usually in a legal system, is that such cores either can be shared or are irrelevant to the process of social control and learning proper conduct, e.g. mandatory labelling guiding a philosophy of moral purchasing.