One definition of knowledge is true belief based on strong evidence. What makes evidence ‘strong’ enough and how can this limit be established? There are many types of evidence such as empirical evidence, logic and the use of authority but they can only be strong enough if the propositional knowledge it supports cannot be disproved. Strong evidence has to be sustainable, valid, accurate, reliable, consistent and satisfactory through experience. The limit is naturally established at the point in time when a group of experts agree upon that propositional knowledge in its own specific field.
In this essay, I will be looking at three Areas of Knowledge: Mathematics, Natural Sciences and History, which use logic, empirical justification-the perceptual or sensory experience-and Authority to succor a propositional knowledge. When an authority, or a community of experts shares knowledge, we have to accept them as how strong they can be. Logic in mathematics is sustainable, valid, accurate, reliable, consistent and satisfactory. In other words, it is concrete and the strongest.
One can’t change the fact that in an equilateral triangle all sides are equal or the formation of equilateral triangles could form a circular shape: It is absurd if this knowledge could be changed. When we compare two number sequences “1,3,5,7,9” and “2,4,6,8” we see a consistent pattern. Look at sigma notation, a mathematical formula, below: This is a summation of a sequence of numbers using addition, which, in this case, is from 1 to 100. You can represent “i” as K or Z or even an image of my teddybear and the results will still be the same: 2050.
In mathematics, every formula such as algebraic formulas could be proved and gives the same results: they are sustainable, valid , accurate, reliable, consistent and satisfactory. Deductive logic is always used in mathematics: because the information the mathematician deduces is always right, the conclusion deduced is definitely right and the outcome is consistent. On the other hand, for inductive logic, which reasons from general principles to general, the outcome is not consistent.
For example, when we throw a dice five times consecutively and the result is 1 throughout, it still does that mean at the 6th throw might not yield the same results. Thus, deductive logic is strongest in mathematics as the results are sustainable, valid, accurate, reliable, consistent and satisfactory. Referencing the sigma notation example again where instead of adding 1,2,3,4,5 all the way to 100, we could rely on the formula we deducted (n^2 + n)/2 from the sequence to work out the results quickly.
All mathematicians would agree on mathematical knowledge and mathematics is quickly finding its way into other Areas of Knowledge due to its reliability. In natural sciences however, things are different. The laws in natural sciences are not as certain as mathematics, where proof is concrete, rationalized, unchangeable and are based are on axioms-obvious and definite truths. In natural sciences, you need empirical evidence to back your claims up. We use the scientific method in natural sciences to gain knowledge through observation, reason and experiment.
Observations are made through our sensory perceptions, which we prove using reason and experiments. In natural sciences, unlike mathematics, nature assists us in our discoveries and understanding of the physical reliability. If the outcome could be consistent, valid, accurate, reliable, and satisfactory, then the evidence could be considered strong enough for the propositional knowledge and finally be used in our society where the community of experts agree on it.