Final answer:
It is true that the ways of knowing operate differently in personal compared to shared knowledge. While personal knowledge is subjective, shared knowledge is more objective and collectively accepted. This distinction is part of the broader philosophical discussion on the nature of knowledge after challenges posed by Gettier cases to the traditional definition of knowledge as justified true belief.
Step-by-step explanation:
The question you've asked relates to how Plato's traditional account of knowledge as justified true belief has been challenged over time, particularly by the introduction of Gettier cases. Knowledge has traditionally been understood as a belief that is true and for which we have justification. However, Gettier's cases have shown that this is not sufficient for true knowledge, as it is possible to have a belief that is both true and justified but still fails to be knowledge. Philosophers have proposed various solutions to this problem, either by strengthening the justification required or by adding a fourth condition to the definition of knowledge.
One important aspect to understand is that knowledge also comes in different forms, such as propositional knowledge and procedural knowledge. Propositional knowledge refers to knowledge of facts that can be expressed in true or false statements, and this can be further divided into a priori knowledge (gained through reason) and a posteriori knowledge (gained through experience). Procedural knowledge, on the other hand, involves the know-how or ability to perform tasks successfully which may not necessarily be captured by propositional knowledge.
In the context of your question, it is true that ways of knowing operate differently in personal and shared knowledge. Personal knowledge is subjective, and influenced by individual experiences and perspectives, while shared knowledge represents more objective information that is accepted collectively by a group or society.