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Wikimedia Commons, Viet Hans Schnorr
What is a priori, a posteriori, analytic and synthetic? I have 4 definitions below:
A priori knowledge is acquired without experience
A posteriori knowledge is acquired through experience
Analytic knowledge is the meaning of a concept
Synthetic knowledge extends beyond the meaning of a concept
Using these four definitions, we can divide knowledge into four types: a priori analytic, a priori synthetic, a posteriori analytic and a posteriori synthetic.
Before describing each type of knowledge, I should mention that I believe all thoughts are experiences. This makes all thoughts a posteriori knowledge. For example, imagine that you're climbing a mountain and when you get to the top, you have the thought that you've accomplished a great feat and you're proud of yourself. I believe that this conscious awareness is an experience. The same goes for any emotion or idea you experience.
A priori analytic
A priori analytic is knowledge of the meaning of a concept without experience. I believe that a priori analytic knowledge doesn't exist, because all definition retrieval occurs within the bounds of experience. For example, imagine that you ask yourself the meaning of the word 'fence'. To answer this question, your mind needs to retrieve a mental representation of what 'fence' means. I believe this definition retrieval would be an experience, thereby making it a posteriori knowledge.
A priori synthetic
A priori synthetic is knowledge that extends beyond the meaning of a concept without experience. I believe that a priori synthetic knowledge doesn't exist, because I regard all mental activity as an experience. In this regard, every belief that I have about reality was initially based on a previous experience in my life.
I also believe that mathematical equations are known a posteriori. For example, take the equation 86 + 14 = __. To demonstrate this, imagine that you combine 86 apples with 14 apples and then count the total. Even if you count the same total a million times in a row, there is still a chance that you miscounted every time. Even if you do this exercise entirely in your mind, you could potentially make the same mistake. We need experience (physical or mental) to determine the answer. For this reason, I believe that all mathematical equations are known a posteriori.
A posteriori analytic
A posteriori analytic is knowledge of the meaning of a concept through experience. For example, imagine that you ask yourself the meaning of the word 'rock'. To answer this question, your mind needs to retrieve a mental representation of what 'rock' means. This inquiry would tap into your past experiences and look for instances when objects were labeled as a 'rock'. I believe this picture retrieval would be an experience, therefore making it a posteriori knowledge.
A posteriori synthetic
A posteriori synthetic is knowledge that extends beyond the meaning of concept through experience. For example, think about this proposition: There is a bowl in the kitchen. This proposition is synthetic because the definition of 'bowl' doesn't include 'in the kitchen'. This proposition is also a posteriori because it would be impossible to know whether it was true or false without first-hand experience or mental reasoning.