There is no such thing as a priori knowledge.
The term, "a priori," supposedly refers to knowledge that can be derived by reason alone without reference to any evidence. It is used in contrast to, "a posteriori," which is knowledge derived by reason from actual evidence. It is usually assumed that, "a priori," is inborn, either explicitly or latently.
Human beings are not born with any kind of knowledge. At birth they have the capacity to discover and learn. That capacity is called the mind. (See the article, "Mind.")
A newborn child knows nothing and must learn everything. Certain reflexes (like sucking and other biological functions) are sometime mistaken for, "Instinct," which would not be knowledge even if true—which it isn't.
One of the things every child must learn is a language. Since human intellectual knowledge is only possible by means of language, and no human being is born knowing a language, the very idea of a priori knowledge is impossible.
A Priorism, A Form of Mystic Knowledge
The concept of a priori knowledge is one of several wrong ideas about how knowledge is acquired, and includes, "revelation," "intuition," "instinct," and "a priori" knowledge. No rational explanation is ever provided to explain how any these kinds of knowledge are acquired or how they can be distinguished from delusions or hallucinations. In most cases they are neither of those but simply ideas that have actually been learned, though usually wrong, because they are simply accepted based on the teachings of some authority or, "expert," without evidence or rational explanation.
What "A Priori Knowledge" Is, Never Explained
Those who believe in "a priori knowledge," do not explain how one has such knowledge, how it works, or even exactly what it is. Since it cannot be based on the rational identification of existence or reasoning from evidence and since it is not learned, where it resides, since memory only stores learned knowledge, is also never explained.
Instead of an explanation, those who believe in, "a priori knowledge," only provide examples. For example, I was asked, "How do we know two things cannot occupy the same space, or that one thing cannot be in more than one place at a time, or that a thing cannot be both black and white at the same time? Isn't that a priori knowledge?"
Of course none of these are examples of, "a priori," knowledge. They are examples of things learned. Very young children do not know any of these things, and often attempt to do things they would know were impossible if they did know them.
No one can know, "two things cannot occupy the same space," until they know what a "thing," is, what a "space," is, what the word, "same," means, and what, "two," means, and the example leaves out, "at the same time," which also must be known.
Only after one understands all of these concepts is it possible to discover two things cannot occupy the same space. Since most of these discoveries were made long ago, most people today do not discover them for themselves, they are taught them, but they cannot be taught them until they understand all the concepts required to state them.
So just how does one know two things cannot occupy the same space at the same time? The answer is an ontological one. Ontologically a thing's attributes are what it is including it's positional attributes. If two things have precisely the same positional attributes they would not be two things, but the same thing. (Ontology is the philosophical study of the nature of material existence.)
The truth is most people do not know why two things cannot logically occupy the same space at the same time, and simply assume it is true, which is safe enough because it is true, though none could tell you why it is true.
The other wrong example of a priori knowledge, "a thing cannot be both black and white at the same time," is simpler. The source of this knowledge is both ontological and determined by the nature of perception. Ontologically no existent can have attributes which are contradictory; an existent that has the attribute white cannot be the same existent if it has the attribute black since a thing is whatever its attributes are. Perceptually, colors, like many other percepts, are mutually exclusive, and we learn this from our experience of colors. If I am seeing red, I'm seeing red, not green, black, or white. If I'm seeing any other color, I'm not seeing red. That is the experience and anyone can test it. Therefore if what I'm seeing is red, it is red, and not any other color, because if it were some other color that is the color I would see, not red.
I was given another list of examples by another individual which included the one's already discussed with the following added: "A straight line is the shortest line between two points. No two straight lines can enclose a space. Whatever object is colored is also extended. Whatever object has shape has also size. If A is a part of B and B is a part of C, then A is a part of C. 4=3 +1. 6=2(33–30)."
I'll start with, "whatever object is colored is also extended," because most people will not know what it means. In fact, what it means is a bit obscure. The term, "extended," was used in philosophy to mean substantive or having three dimensions, but has pretty much been dropped from all modern philosophy. In the field of topology it is also not true. A Möbius strip has only two dimensions and has only one side and one edge, but certainly can be colored. [See illustration at the beginning of this article.]
All of the other statements are true, but not examples of "a priori" knowledge. Most of them would not be known at all if not identified by
objective empiricists who discovered them learning how to identify and understand the nature of material existence. If it weren't for Thales, Euclid, Pythagoras, Aristotle and others, most people would not have a clue about any of these so-called "a priori" ideas.
The last examples worse. "If A is a part of B and B is a part of C, then A is a part of C," is called a transitive relationship, which we supposedly just know, a priori. Here's a better example of a transitive relationships. If A is left of B, and B is left of C, A is left of C: unless they're in a circle, then A is left of B, and B is left of C, and C is left of A, so A is right of C. But you already knew that, a priori, right?
The very worst examples are the ones from mathematics, "4=3+1." and "6=2(33–30)." All of mathematics as based on the ability to use numbers to count. Addition is actually a shortcut method of counting, and multiplication is a shortcut method of addition. There are still tribes in this world that have not learned to count. If addition and multiplication are known a priori, how can there be tribes of human beings who don't know how to count, add, and multiply? Why does basic math have to be taught in school, since it is already known a priori?
Not A Priori At All
A careful examination of what is called a priori is not really a priori knowledge, but examples of another bad idea called "analytic" propositions which are contrasted with what are called "synthetic" propositions. An analytic proposition supposedly can be known to be true simply by knowing what the terms mean, because both sides of the proposition mean the same thing. For example, "ice is solid," and, "all bachelors are single," are true without needing any empirical observation. A synthetic proposition can supposedly only be known to be true by means of some empirical evidence. For example, "ice floats on water," can only be known by actually observing ice in water and "John is a bachelor," can only be known if one knows John and knows he is not married.
The argument is that since an analytic proposition can be known to be true simply by examining the proposition it is known a priori, that is, before or without examining any empirical evidence.
Of course this is not true. The words of a proposition are evidence, and no matter how abstract the origin of their meaning, they are always derived from evidence, usually physical evidence (but can be psychological evidence, i.e. evidence of one's own consciousness). The proposition, "ice is solid," cannot be known to be true if one does not know what ice is or what solid means, both of which identify aspects of the physical, ice a physical existent and solid a physical property.
The most common examples of so-called analytic propositions are mathematical equations, such as 2+3=5. The argument is such equations are necessarily true because of the meanings of the terms and do not depend on any evidence to be true. Actually the terms, 2, 3, 5, +. and =, are all derived from the nature of the physical world.
Numbers, for example, are only symbols whose basic function is derived from the method of counting. In reality, 2+3=5, is neither true or false. It is correct in the sense that it conforms to the principles of addition, but it can only be true if 2, 3, and 5 are 2, 3, and 5 somethings and those somethings are the same somethings for each of the symbols. (This simple truth is the reason for the trite expression, "mixing apples and oranges," because such mixing leads to error, not truth.) The point is that until the method of mathematics is actually applied to the metaphysical, there is no truth in it.
[NOTE: A full discussion of the origin of mathematics and the true nature of mathematics cannot be provided here. It has been fully addressed in the following two articles: Cause, Induction, and Mathematics, especially the sections—Mathematics is a Method, Limits of Mathematics, Objective Base of a Method, and Measurement; and Knowledge Methods, for any who would like to explore this question further.]
Why A Priori
Why do men so desperately desire for there to be some kind of mystic knowledge one just has without effort or study? Why do men despise or even dread the idea that there is no other means to knowledge except objective reason from real evidence?
I do not know the answer, at least for most men. I know why some promote the ideas of mystic knowledge, and why they want people to believe it; because once the gullible believe there is anything other than rational objective knowledge, almost anything can be put over as religion, philosophy, ideology, or politics.
Some like the idea that they can have knowledge without effort. Objective reason is not easy and takes time and tremendously ruthless attention to insure none of one's beliefs are contradictory and all conform to the nature of reality.
Reality is the final and only arbiter of truth and a life determined by anything other than truth is on track for disaster. In reality all truth must be learned by every individual using their own mind and reason, because there is no unearned a priori knowledge.