• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

If facts themselves never prove or disprove anything, what else is involved in the proof of a statement?"

Extracts from this document...

Introduction

"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. 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. ...read more.

Middle

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. ...read more.

Conclusion

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. ...read more.

The above preview is unformatted text

This student written piece of work is one of many that can be found in our International Baccalaureate Theory of Knowledge section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related International Baccalaureate Theory of Knowledge essays

  1. Albert Einstein. If we establish the fact that Einstein was not just a ...

    Einstein, being an ardent believer in the philosophy that the destiny of truth and knowledge come from God, would criticize the dystopian government of V for Vendetta as "playing God". Einstein encouraged searching for the truth-the "what is". But he did not support anyone dictating "what should be".

  2. TOk Discussion - Do we impose mathematics upon nature or is it naturally inherent ...

    Not only would that be visually awesome, it could provide an answer to using solar panels as a main source of energy. Mathematics and nature is all around us, so putting them together in design would make something incredible. A: Although we have discussed at length about mathematics, and how

  1. Science is built of facts the way a house is built of bricks: but ...

    to control such as people with different amounts of money might spend it differently but some people might not spend much at all and so on. The social sciences measure their results usually by trend because of the faculties in many results.

  2. Facts or feelings what is more important? We cant prove anything without ...

    the human kind has been bearing the brunt. The question raised is that was it right for them to eat the fruit and leave the rest of the human kind to put up with the consequences? Was it fair to us that till date men have to toil to fill

  1. Science is built up of facts, as a house is with stones. But a ...

    Other such incidents throughout United States history point to an inept government lieing and skewing real historical facts for political gain, "The U.S. government has a long history of lying in order to win public approval for its wars: On February 15, 1898, an explosion ripped through the USS Maine anchored off Spanish-controlled Cuba, killing 268.

  2. Salt, governments, beliefs, and celebrity couples are a few examples of things that can ...

    What is faith and how can it eliminate fear? Faith can be defined as a confident belief in the truth, value, or trustworthiness of a person, idea, or thing. Faith is the pressure of the Spirit on humanity, the force that urges humanity towards what is better, not only in the order of knowledge but in the whole order of spiritual life.

  1. TOK How do these considerations (of age, identity) play a role in convictions? Are ...

    arson and it was an accident fire caused by the heater or fault electrical wiring. In much the same way historians reconstruct the past using evidence such as relics and written documents. Compare and contrast Vasquez and Hurst's techniques, practices and processes.

  2. Justification, what distinguishes a good justification from a bad one?

    At the same time emotions can also provide us with energy to pursue to knowledge. Physiologist Antonio Damasio speculates that emotions are sources of knowledge and they help us make rational decisions about things. Some Areas of Knowledge like Ethics require emotions to give us a better understanding of the truth.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work