A Priori and A Posteriori Definition, Knowledge And Meaning
(law) Known ahead of time.
(logic) Based on hypothesis rather than experiment.
In his opening argument, the student mentioned nothing beyond his a priori knowledge.
Self-evident, intuitively obvious
Presumed without analysis
(linguistics, of a constructed language) Developed entirely from scratch, without deriving it from existing languages.
Adj.1.a posteriori - involving reasoning from facts or particulars to general principles or from effects to causes; "a posteriori demonstration"
synthetical, synthetic - of a proposition whose truth value is determined by observation or facts; "`most men are arrogant' is a synthetic proposition"
inductive - of reasoning; proceeding from particular facts to a general conclusion; "inductive reasoning"
a priori - involving deductive reasoning from a general principle to a necessary effect; not supported by fact; "an a priori judgment"
2.a posteriori - requiring evidence for validation or support
empirical, empiric - derived from experiment and observation rather than theory; "an empirical basis for an ethical theory"; "empirical laws"; "empirical data"; "an empirical treatment of a disease about which little is known"
Adv.1.a posteriori - derived from observed facts
a priori - derived by logic, without observed facts
A Priori vs. A Posteriori Knowlege
A Priori Knowledge:
A priori knowledge is knowledge that we can have "prior to experience". We don’t need to observe how the world is to have such knowledge. We can arrive at such knowledge through reason alone (sitting in our armchairs by the fire, as it were, and simply using our powers of reasoning).
Examples: "All bachelors are unmarried", "All triangles have three sides."
A Posteriori Knowledge:
A posteriori knowledge is knowledge that we can have only after we have certain experiences. We have to make some observations to gain such knowledge. (We can’t just reflect from the armchair, we have to go out in the world and see how things actually are.)
Examples: "There is a cup on this table", "Smoking causes cancer."
Meaning of Priori knowledge
A Priori is a philosophical term that is used in several different ways. The term is suppose to mean knowledge that is gained through deduction, and not through empirical evidence. For instance, if I have two apples now, and I plan to add three apples, I will have five apples. This is knowledge gained deductively. I did not actually need to get the three other apples and place them with the first two to see that I have five. To this extent, the term A Priori is valid.
The problem, though, is that the word is used to describe something entirely different. It is used to describe knowledge that exists without reference to reality. One example is inborn knowledge. Another example often used is mathematics. To understand why this second definition, which is how the term is really used, is flawed, we have to look at exactly what is being said and meant.
Let's look at mathematics. It's easy to see, in the apple example above, that mathematics fits under first, valid meaning of the term. If this were all that was meant by saying that mathematics is a priori, there would be no problem. However, this isn't it. Philosophers then go on to say that mathematics is true without reference to reality. The knowledge of mathematics (as opposed to the knowledge created by mathematics) is a priori. It is known without reference to reality. It is claimed that mathematics is a higher form of knowledge. That even if the world around us doesn't exist, mathematics is still true. That it is a form of knowledge that we can be certain of, even if we deny reality.
How do they make such a statement? First, they see that mathematics is the science of units, and any units are acceptable. I could have said trucks instead of apples above. The validity would be the same. It is true without reference to any unit.
This sounds okay at first. The problem stems from the method of deriving the mathematical abstractions. Teach a child to do simple arithmetic, and you'll recognize that to gain the knowledge of math, one must use some units. Maybe apples. Maybe oranges. It doesn't matter which units. It does matter, though, that some unit is picked. To grasp math, one needs a foundation. Particulars from which an abstraction can be made.
Calling mathematics a priori, or knowledge independent of reality, is to undercut its base. This is the essence of the second meaning of a priori. The meaning that is actually used. An abstraction is made from particulars. Once the abstraction is made, the process from which it was derived is then ignored. The base on which it was built is denied. The abstract knowledge is then said to exist without reference to reality, since the reference is ignored.
In this way, certain kinds of knowledge are said to exist without being dependent on reality.
A posteriori knowledge, on the other hand, is knowledge that comes directly from observation of the physical world. The term a posteriori means “from what comes later” and, thus, refers to knowledge that comes as a result of experiencing the physical world.