If facts by themselves never prove or disprove anything, what else is involved in the proof of a statement?
Charlotte Nguyen
TOK
06-09-08
If facts by themselves never prove or disprove anything, what else is involved in the proof of a statement?
Throughout our lives we enter a journey in order to gain knowledge and, hence discover what justified true belief is. The word ‘fact’ is often defined as a piece of information presented as having objective reality. Furthermore, the word ‘fact’ often connotes that there is a substantial amount of truth, and some would even go as far as saying that facts are almost synonymous with truths. If facts by themselves never prove or disprove a statement, then we would be forced to engage and utilize other ways of knowing in order to determine the degree of truth and validity present within a given statement. However, without the ability to incorporate facts, which are one of the more objective and concrete ways of knowing, which ways of knowing could we utilize and still form valid and seamless proofs?
The elements of which a proof of a statement is comprised of vary generally from one area of knowledge to another. Therefore, we would consider the usage of different ways of knowing, differing from one area of knowledge to another. For example, mathematicians have strived to derive mathematical models that stimulate the world around us. The theorems that we now use in our everyday lives, once were only conjectures that needed to be proven. Mathematicians developed a plethora of proofs that now solidify and enable us to incorporate and learn from these theorems with an air of security. In mathematics, the use of inductive proofs is plentiful. From a specific example, we develop a conjecture, and then prove this conjecture within set limits and the aide of axioms, definitions, and other theorems, while using other examples in order to prove for all situations that the conjecture is true. However, would we not consider axioms, definitions, and theorems as facts? Even the resulting step that we arrived at with the use of inductive logic could be considered as a fact, so how could we successfully prove a conjecture without facts? There would be nowhere to start from as the very foundation of mathematics has come to be proven by pieces of information that we now consider as facts, as well as axioms, which we deem to be facts, without any proof. We could argue that we could come to the conclusion that the conjecture has been proven by the use of pure logic and inductive reasoning, although how could we rest assured that the conjecture indeed has been proven true? Although mathematics is an area of knowledge that is considered as much more objective in comparison to the other areas of knowledge, we could resort to the use of intuition. For example, in my recent mathematics exam, I had to solve an inequality and show that it was true for a range of x-values. However, when solving an inequality that involves absolute value, one must consider very carefully for which values the inequality would be greater than or equal to zero. As it is very difficult for me to visualize concepts, I merely resorted to using my intuition and considering if the answer I had arrived at felt ‘right’.