Final answer:
In formal logic, 'Neither' is used to state that out of two elements, neither is involved in the action or possesses the attribute in question. It is linked to logical principles like the law of excluded middle and the law of noncontradiction, which together imply that statements are either true or their negation is true, without any middle option.
Step-by-step explanation:
In formal logic, "Neither" identifies that out of two elements, none is participating or having the characteristic mentioned. This is closely related to logical laws such as the law of excluded middle and the law of noncontradiction. The law of excluded middle posits that for any statement, either the statement is true, or its negation is true. This means that there is no middle ground or third option. An example of its application in a sentence could be, "Neither the students nor the teachers have proposed a field trip," which clearly indicates that neither group is in favor of proposing a field trip.
Logic is often considered normative, which implies that there are standards for reasoning that ought to be followed. Logical principles such as noncontradiction suggest that one should not hold contradictory beliefs, such as asserting that one is both 5 feet tall and not 5 feet tall simultaneously. In essence, logical rules form the bedrock of coherent reasoning. Without such norms, reasoning would collapse into a cacophony of unrelated ideas.