Final answer:
The correct option is Rationalism.
Rationalism is not a method of knowing reflected in the options provided as it is based on innate knowledge and logical reasoning, not empirical evidence or observation.
Step-by-step explanation:
The method of knowing that is NOT reflected in the options provided is rationalism. Rationalism asserts that knowledge is not possible through experience but through reason. It is a non-empirical process that emphasizes the role of innate knowledge grasped by reason, as discussed by philosophers such as Plato. This contrasts with the empirical way of knowing, which involves gaining knowledge through our senses and the systematic application of the scientific method, which includes observation, the development of a hypothesis, and rigorous testing.
Options such as a single case study, shared public experience, introspection, and systematic observation are methods that can potentially lead to new insights or knowledge and can be empirical in nature, except for introspection which is subjective. However, they all involve the gathering or processing of information, unlike rationalism, which does not rely on empirical evidence or observation but rather on logical reasoning and innate ideas.