Yes, it is possible to know something you've never been explicitly taught or formally studied. There are a few ways this can happen:
Intuition: Sometimes, people have a natural intuition or instinct about certain things. This could be based on their inherent cognitive abilities, past experiences, or exposure to related concepts.
Observation and Deduction: Observing the world around you and making deductions based on those observations can lead to acquiring knowledge without formal teaching. By connecting dots and drawing conclusions, people can learn new things.
Innate Knowledge: Some philosophers and psychologists have proposed the idea of innate knowledge—knowledge that is inherent in humans or present from birth. However, this concept is debated, and specific examples of true innate knowledge are scarce.
Unconscious Learning: The brain is remarkably adept at processing information on both conscious and unconscious levels. People can learn and store information unconsciously through various experiences, even without actively trying to do so.
Collective Knowledge: Living in a society means you are surrounded by the knowledge and experiences of others. Through cultural transmission, societal norms, and interactions with others, you can pick up knowledge that you've never been explicitly taught.
Epiphanies and Insights: Sometimes, people have sudden realizations or insights, often referred to as "aha moments," where they come to understand something without direct instruction.
It's important to note that while people can acquire knowledge through these means, the depth and accuracy of that knowledge might not be as extensive as what can be gained through formal education and study. Nevertheless, the human mind is capable of continuously learning and adapting to its environment in various ways.