A significant amount of knowledge in this world is derived from how we experience it.
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For example, we are aware that there's a bird on a tree outside of the window because we can observe it. We know the bird requires food and water in order for it to survive, because scientists have in fact observed these facts. In context, we are aware of our environment by how we perceive it and we gain access to scientific knowledge about our environment by observation and being able to conduct experiments.
Yet, there's some of our knowledge that isn't dependent on experience in this way. For instance, we are aware that all unmarried men are bachelors. How do we justify for believing this? Well, just by understanding the actual meaning and definition of bachelor we understand that all bachelors are in fact unmarried men. (In order to understand this, we do need to gain experience about knowledge in order to be able to learn what terms mean).
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More understandingly, what experience can lead us to deny that all bachelors are unmarried men? Since there's no experience that is possible, then how we justify for understanding this seems independent of our experience.
All knowledge that isn't derived from experience is called a priori knowledge, since it is justified prior to experience.
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Mathematical expressions are also considered to be a priori knowledge. For example, we are aware that 2 + 2 = 4. Yet we don't know this through experience.
A way to be able to tell if a claim can be justified a priori is: Would we be able to give up on a claim in the face of experience it? To say that 2 + 2 = 4 is known a priori is to say we can't give up to that claim, no matter how our experience turns out to be.
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There's arguments between many philosophers in regards to claiming that we can have a priori knowledge of anything other than the meanings of words and logic.
On the other hand, some philosophers claim that there isn't a priori of knowledge. They argue that even our knowledge of logic and mathematics, are derived and dependent on experience.
Sources and further readings:
Stanford University
University of Tennessee
Michigan State University
University of Nebraska
Wikipedia
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