True and False seem to be such clear and simple terms, opposites and mutually exclusive. In reality, however we may inhabit, in much or even most of our knowledge the fuzzy area in between the two. Discuss the difficulties of attempts to draw a clear line between the two categories in at least two areas of knowledge.

The question of the definition of true and false has for centuries of western civilization baffled the greatest of philosophers. The question being not just simply the definition of True and false, but rather where one can draw the line which delineates/segregates the two. In order to extrapolate an answer for this question an investigation into at least two areas of knowledge must be conducted for contrasting purposes. For this particular essay these areas are Mathematics and Psychology. The difference in relation to the above question between the two areas of knowledge is that they are nearly exact opposites. There exists an intrinsic truth to proper mathematics (proper mathematics example 7+5=12) because it is based upon and interconnected with Kant's synthetic judgments and a priori knowledge, whilst Psychology claims its base with a posteriori knowledge and analytic judgments. In addition Plato contends in direct contrast to Protagoras that truth isn't relative and is objective and absolute. Hence proper mathematics with its basis in a priori knowledge (universally and necessarily True) is the essence of "unfuzziness," whilst Psychology is because of its basis/support of a posteriori/experience knowledge is the opposite, the epitome of "fuzziness."
Immanuel Kant contends that inside of our mind exists what he calls a priori, or before experience knowledge, which is universally and necessarily True. Kant states that this a priori knowledge, of which time and space is an integral part, is the basis for our edifice of knowledge which we strive to build higher and higher, larger and larger metaphorically. In order to justify the existence of a priori take for example the human form. If one was to make void the human form of all perceptual characteristics (a posteriori) the only thing left is the space which it occupies, therefore the space must exist else the object does not exist. This is also true of time, causality, and other a priori, which lie outside the realm phenomena or experience. So these a priori are universally and necessarily True, and all knowledge adheres to these the inborn constructs of the mind.
Plato made a statement about the nature of truth, a rational view that truth is not relative, but rather objective and absolute. This view upon the nature of truth is displayed through the following composed dialogue created by Dr. Sahakian between Plato and Protagoras.
Protagoras: Plato, what is true for you, is true for you, and what is true for me, is true for
Plato: Do you mean to say that my personal opinion is true?
Protagoras: Indeed, that is precisely what I mean.
Plato: But my dear Protagoras, my opinion is that truth is not relative; truth is not a
matter of opinion, but objective and absolute. Furthermore, my opinion is that
you belief in the relativity of true is absolutely false and should be abandoned.
Do you still hold that my opinion is true?
Protagoras: Yes, you are quite right.
By stating that truth is not relative, Plato is essentially alluding to its' objective and absolute characteristics. These characteristics in turn lend that there exists within the frame work of the human mind all truth which is solely objective, limited, and unchanging.
How then are these perspectives applicable to the areas of Mathematics and Psychology? Let us take for example mathematics, which is part of the "exact sciences," coupled with geometry and logic. Take for example the proper Mathematics statement "7+5=12", called a synthetic judgment by Kant. This statement/synthetic judgment although symbols are used to identify the number is universally true because its basis/support lies in a priori knowledge. If someone was however to state that "7+5=12", then we would declare the statement to be false, because it contradicts the proper Mathematics statement of "7+5=12." According to Plato truth is absolute and unchanging as is the statement "7+5=12." Also as a general rule proper Mathematics works in perfect harmony with nature, and can accurately describe it in many ways (Physics), once again hinting to its inherent truth.