Final answer:
In epistemology, knowing what is not already in one's collection of known propositions, or collection C, is limited because one cannot know propositions outside of it without further inquiry.
Step-by-step explanation:
To address the question of whether it is possible to know what one doesn’t know within the context of a logical system, we need to delve into the realms of epistemology and logic. At its foundation, epistemology is the study of knowledge—its nature, scope, and limits. The idea espoused by Socrates to 'know what you do not know' reflects the acknowledgement of human limitations in knowledge acquisition. The logical structure of knowledge dictates that you cannot know propositions that are not in your current collection C because knowledge is split into two types: a priori and a posteriori.A priori knowledge is gained through reason alone, such as mathematical truths, which may first be memorized and then understood logically. Conversely, a posteriori knowledge is gained through experience, like knowing the shortest route to the nearest restroom.
When considering whether we can know things not in collection C, this aligns with the scope of propositional knowledge, which consists of declarative sentences with truth values. Within collection C, if you 'know' a proposition, it must be true per its definition in traditional epistemology. However, the conception of knowledge as justified true belief (JTB) implies that simply having a collection of propositions does not necessarily constitute complete knowledge. One also needs justification and belief in the truth of these propositions. Furthermore, encountering skeptical arguments raises questions about certainty, as doubt precludes the certainty required for true knowledge, according to skeptics.
Lastly, understanding the limitation of our knowledge is crucial. If we are not conscious of our ignorance, we won’t strive to learn. Thus, acknowledging the boundaries of our knowledge, including what lies outside of collection C, becomes a vital part of philosophical inquiry and the pursuit of knowledge.