D. Rationalism vs. Empiricism
Theories of knowledge divide naturally, theoretically and historically into the two rival schools of rationalism and empiricism. Neither rationalism nor empiricism disregards the primary tool of the other school entirely. The issue revolves on beliefs about necessary knowledge and empirical knowledge.
Rationalism believes that some ideas or concepts are independent of experience and that some truth is known by reason alone.
a. a priori
This is necessary knowledge not given in nor dependent upon experience; it is necessarily true by definition. For instance "black cats are black." This is an analytic statement, and broadly, it is a tautology; its denial would be self-contradictory.
Empiricism believes that some ideas or concepts are independent of experience and that truth must be established by reference to experience alone.
b. a posteriori
This is knowledge that comes after or is dependent upon experience. for instance "Desks are brown" is a synthetic statement. Unlike the analytic statement "Black cats are black", the synthetic statement "Desks are brown" is not necessarily true unless all desks are by definition brown, and to deny it would not be self-contradictory. We would probably refer the matter to experience.
Since knowledge depends primarily on synthetic statements -- statements that may be true or may be false -- their nature and status are crucial to theories of knowledge. The controvercial issue is the possibility of synthetic necessary knowledge -- that is, the possibility of having genuine knowledge of the world without the need to rely on experience. Consider these statements:
1) The sum of the angles of a triangle is 180 degrees.
2) Parallel lines never meet.
3) A whole is the sum of all its parts.
Rationalism may believe these to be synthetic necessary statements, universally treu, and genunie knowledge; i.e., they are not merely empty as the analytic or tautologous statemenst (Black cats are black) and are not dependent on experience for their truth value.
Empiricism denies that these statements are synthetic and necessary. Strict empriicism asserts that all such statements only appear to be necessary or a priori. Actually, they derive from experience.
Logical empiricism admits that these statements are ncessary but only because they are not really synthetic statements but analytic statements, which are true by definition alone and do not give us genuine knowledge of the world.
Rationalism includes in genuine knowledge synthetic necessary statements (or, if this term is rejected, then those analytic necessary statements that "reveal reality" in terms of universally necessary truth; e.g., "An entity is what it is and not something else.")
Empiricism limits genuine knowledge to empirical statements. Necessary statements are empty (that is, they tell us nothing of the world).
Logical empiricism admits as genuine knowledge only analytic necessary (Black cats are black) or synthetic empirical statements (desks are brown). But the anyalytic necessary statements or laws of logic and mathematics derive from arbitrary rules of usage, definitions, and the like, and therefore reveal nothing about reality. (This is the antimetaphysical point of view).
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