A Priori and the Limitation of Human Knowledge

The beginning of this blog post requires prefacing a few things, as I often do. My goal here is to get to the origin of certain aspects of knowledge, and much of this is based on a statement made to me in the past that “Mathematics is an example of a priori knowledge.” I’m here to state, for the record, that such notion is BS. The first order of business is to define these terms “A Priori” and “A Posteriori.” “A Priori” is used in this context to refer to knowledge we possess independent of experience. “A Posteriori” is used to refer to knowledge that requires justification through empirical evidence. So, my point here is to say, all knowledge is A Posteriori, outside raw perceptual data provided by our senses. All human knowledge begins at sensory perception. The senses take in data in the form of light, sound, texture, taste, smell. Once the data is received by the brain, we can consciously interpret what that data means. For example, the reading process equates to perceiving light as it reflects off of a page then interpreting the data. This raw data is the simplest form of knowledge we can obtain. In the absence of input through our senses, our brains create false signals. With only 15 minutes of sensory deprivation, people will begin to experience hallucinations as real as those seen by someone on LSD. (Source: Wikipedia - Sensory Deprivation If you want more reliable data, you can search for the huge Kenyon study on Sensory Deprivation in PDF format, it’s hundreds of pages of technical data.) Once we possess that raw data provided by our senses, we can begin to analyze and extrapolate on our perceptions. We see a wood object that has a flat top, and four legs extending down, one from each corner. Is it a Chair? Is it a table? Abstraction is a process of separating the idea from the object. What separates the terms “Chair” and “Table” is the idea of their individual applications. The separation there is not implicit based on the raw data we have perceived. It is an abstraction we have developed based on the knowledge we already possess. So, this brings me to Math. Mathematics, strictly speaking is a PROCESS of defining things like space, quantity, change and structure. It is by definition, a process of abstraction based on experience (Read: A Posteriori.) Simple numbers that relate to quantity have nothing to do with mathematical process. “1+1 = 2” defines the process of adding one and one. It does not specifically define the perception of two of the same object. My general proof that mathematics is not A Priori is this: “2 – 3 = -1” A simple equation that demonstrates a core concept which is dependent upon data that is wholly abstract in nature. Subtracting three from two is, in reality, impossible. We cannot even lose three objects if all we possess is two, nor can we even fathom the concept outside theoretical boundaries. Proving that 2 – 3 = -1 can ONLY be done with what we educate as mathematics (which is actually called “pure mathematics”) wherein we teach math for the sake of math – As an abstraction; An idea separated from the object, and not A Priori. Perhaps my bigger purpose in writing about all of this is to convey an important point about the limitations of our knowledge. All knowledge begins at perception and the only knowledge that we possess that is A Priori is that sense data. (The A Priori / A Posteriori question is an epistemological one, not a metaphysical question.) “The sky is blue” is A Priori because we can determine such exclusively from sensory data alone. “All entomologists study bugs” is not A Priori. Even though “entomologist” specifically is defined as a person who studies insects, this distinction is literary, not epistemological. Ergo, statements such as “we don’t know” indicating that we do not know if there is another world beyond this, or that there is some order of existence we lack the faculty to perceive, are moot. Even information that isn’t directly provided by our senses (such as a frequency too high or low for the human ear to detect) can be measured through tools which still require sensory perception. We’re simply augmenting the means through which we perceive such data. Since our knowledge is ultimately limited to perceptual data in every context, theories about things we cannot perceive are not relevant to human existence. – If they affected our lives, we would be able to perceive them.