Areas of Knowledge

“If facts themselves never prove or disprove anything, what else is involved in the proof of a statement? ” Answer with reference to at least two Areas of Knowledge.

The title assumes facts themselves never prove or disprove anything. I will show that this two-part assumption is incorrect. I believe facts can disprove incorrect propositions, but that they can not, by themselves, prove anything. I contend that proof is no more than adequate grounds for the acceptance of the proposition; admittedly, what counts as adequate and acceptable changes from one area of knowledge to another.Further, my position is that facts add to only one aspect of what we will consider as “proof”, namely providing evidence for justifying ones knowledge. To prove a statement, in its purest sense, means to provide unshakable, undeniable and irrefutable grounds for the acceptance of the claim.

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Proof of a proposition, to this standard, is unobtainable in all areas of knowledge except mathematics (Bostock et al, 1982). If we stick literally to this meaning of proof we would need to restrict our discussions to mathematics alone.This would be impossible as the title requires investigation into at least two areas of knowledge.

I am therefore forced into pulling back from the rigorous, demanding requirements of proof in the mathematical sense, and instead adopt, for the purpose of this essay, a less exacting definition. In this essay I will consider proof to mean the accepted standards required by an Area of Knowledge that need to be attained for a proposition to be considered as knowledge. These standards vary from one Area of Knowledge to another.A fact lives independent of observers, or of other conditions. A fact is true, and not something open to debate. A fact just is, it’s, “an indisputable truth” (Slick, 2006). These are sweeping statements, but necessary for us to understand how facts influence knowledge.

A few examples of facts might help. I am hungry. No one other than me can test this statement. It is either true or false and assuming it is true, then it is a fact.

A true statement is a fact. This example requires an observer, admittedly only one, namely me. Now consider this fact.A tree falling in an empty forest makes a noise. I believe this to be a fact as I believe it is a true statement, but I am unable to prove it. This is an important point, and one that distinguishes fact from knowledge. Facts do not require proof or even evidence or justification, they do not even need us to believe in them; they just are.

Knowledge, at least knowledge of a propositional nature, requires us to satisfy the criteria of justified, true belief (Abel, 1976). Consider one further example. The world is flat.This was believed by many (all) people hundreds of years ago. Sailors refused to sail beyond the sight of land “because they were fearful of sailing over the edge of the world” (Flat Earth, 2006). Their beliefs were strong. They had some evidence for this belief. Water on the surface of a ball falls off, sailors who were foolish enough to explore beyond the horizon never returned, how could the world be round – people at the bottom would fall off! Their justifications, by modern standards, do not hold up to scrutiny, but to them their logic must have seemed impeccable.

Was the world flat? Was it true, or a fact, to them? My contention would be no. Their beliefs and their justifications were false. The world was always round, regardless of who thinks so, and regardless of whatever evidence has been gathered for or against the statement. The world is round is a fact (assuming we ignore semantic problems such as the world is approximately ellipsoidal with local variations — mountains and oceans). There may be facts that we, like our seafaring fathers, think are false, but will in the future turn out true.

I can not, for obvious reasons, give definitive examples, but I can propose some possible “facts” that we (not necessarily all of us) have got wrong. There is no life on the Moon. Nothing travels faster than light.

Ghosts do not exist. The reason for pointing out these examples is that “facts” can only be reliably used to investigate a statement if they are actually facts. Wrong facts do not exist, but things we think are facts, but turn out to be false certainly can exist, and have done so in the past. What can and can not be proved with facts, and if facts by themselves are inadequate, what else is involved?A fact is simply a true statement. If presented with a fact I would know no more than, “this statement is true”. For example, the fact that Washington is the capital of the USA is simply a true statement.

It tells me nothing other than Washington is the capital of the USA. No further knowledge can be gleaned from the fact. I do not even have to alter my beliefs based on the statement, but to do so on no evidence, save perhaps the claim of the person presenting me with the fact, is to take a tremendous leap of faith.We all know Washington is the capital of the USA, but what if I presented you with the “fact” that I share my birthday with Jill, a girl I went to school with. Do you now have any knowledge? Do you believe it to be true? Do you have evidence that supports the claim? Is it a fact, i. e. is it actually true? Well, it is true, but you still have only my word for it (hopefully that is enough), but as an objective observer my word might not satisfy the demands of accepted standards of justification. Consider now a fact from History.

Julius Caesar died in 44 BCE (Lendering, 2006).If this is a fact, and for arguments sake, let us assume it is, then this fact alone (perhaps together with a little logical reasoning) is sufficient to disprove the claim, Julius Caesar brought Christianity to Rome. The logic works like this.

Caesar died in 44 BCE (before Christ), Christianity did not exist before Christ, so Caesar could not have brought Christianity to Rome. Here, one fact is sufficient, provided you allow some logical reasoning, to disprove a claim. What is important is that no further justification (evidence, artifacts, documents, etc.) are needed, nor do we have to believe the claim, we only have to accept the fact, plus the logical argument.From the Natural Sciences, Michelson and Morley’s experiment (Fowler, 2006) “returned the famous null result” (Timeline of Luminiferous Aether, 2006) that there was no such thing as aether, a result that set the whole of science onto a new path, a paradigm shift, leading ultimately to Einstein’s theory of relativity. As Einstein himself said, “No amount of experimentation can ever prove me right; a single experiment can prove me wrong. ” (Albert Einstein Quotes, 2006).

In mathematics too, one counter-example is sufficient to disprove a conjecture. In 1732, one of the all-time great mathematicians, Euler, proved that an earlier conjecture of Fermat’s, that all numbers of the form are prime, was false by showing . Fermat’s conjecture was thus put to rest, permanently (Hollingdale, 1991). So a fact can disprove a statement. Can a fact, on its own, prove a statement? My conviction is no, it can not.

Proving something is knowledge requires that the accepted standards of the Area of Knowledge be attained. No self-respecting historian would put forward a claim based on one piece of unsubstantiated evidence.One fact, in isolation, without supporting frameworks such as socio-political context, military activities, national and international relations, etc.

would be barren, incapable of spawning a theory. The historian needs to triangulate his/her information, set it into context so that is agrees with other established (or believed) conditions, interpret and extrapolate from the known into the unknown, before he/she can present a fresh view of history. One fact, by itself, is insufficient. A scientist would be ridiculed for proposing a new theory in science based on one fact, however strong that fact might be.This differs from getting rid of an old theory (as Michelson and Morley did). A new view of science would require multiple examinations of the “facts”, as many experiments and observations as can be found, repetition of the results that propose a new theory under as many circumstances as possible, and the agreement of a significant proportion of the scientific community. In mathematics, a new theorem is not based on a fact. I would even say that there are no facts in mathematics.

Facts are always true. Mathematical statements are 100% certain, true if you wish, provided you accept the axioms.There is no such proviso for facts in other disciplines.

A scientific fact does not require the pre-acceptance of gravitation. An historical fact does not require the assumption France and Prussia were at war. So, in mathematics, the 100% certainty in facts, e. g. 1+1=2, depends upon a more fundamental supposition: the acceptance, without question, of the axioms of arithmetic. If such a pre-requisite exists in all of mathematics, and all of modern mathematics is axiomatic, then how can mathematical facts exist independently of other conditions? Facts are just true; they do not require other assumptions.As such, mathematics contains no facts.

In mathematics all true statements ultimately depend upon an acceptance of unprovable axioms. With the inclusion of deductive reasoning, new theorems arise from previously proved statements or from the axioms. In conclusion, knowledge is justified, true belief. Facts, which are true statements, can only help in justifying a knowledge claim; they are insufficient to establish the claim as knowledge. However, a single fact, along with a certain amount of logical reasoning, can disprove an incorrect statement.