Theory of Knowledge. 5. That which can be asserted without evidence can be dismissed without evidence. (Christopher Hitchens). Do you agree?

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1 Theory of Knowledge 5. That which can be asserted without evidence can be dismissed without evidence. (Christopher Hitchens). Do you agree? Candidate Name: Syed Tousif Ahmed Candidate Number: School Code: School: Oaktree International School Word Count: 1597 words

2 Kitty Fane: Kitty Fane: Walter Fane: Kitty Fane: Walter Fane: Kitty Fane: It's raining cats and dogs. I said it's raining cats and dogs. Yes, I heard you. You might have answered. I suppose I'm not used to speaking unless I've something to say. If people only spoke when they had something to say, the human race would soon lose the power of speech. - (The Painted Veil, 2006) Asserting is an integral part of our communication with people. We assert when we describe something to someone over telephone, when we make a comment about the weather, or even when we gossip over a controversial event. In other words, we assert when we make a statement or a proposition where the proposition claims to hold but its certainty is not necessarily assessed at that point of time. However, the quote by Christopher Hitchens seems to be implying that one can be certain of an assertion to hold when evidence supports it, but should be rejected if no evidence is associated with it and also suggests that it can be rejected without any justification. This implication raises the knowledge issues that, is it necessary for an assertion to be supported with an evidence for it to hold and if it is, does the evidence need to be justified and do reason, perception and intuition play any role in its justification? It is also to be noted that, to hold denotes that the assertion in question can be true or false and therefore, the nature of the evidence does not necessarily need to justify if an assertion is true or not. Hence, in this essay, I would explore these knowledge issues over different areas of knowledge and would also support the position that all assertions are based on evidence and hence they cannot be rejected, as Kitty in the above conversation suggests that rejection would only lead to loss of power of speech. To begin with, assertion in mathematics is synonymous to conjecture and the evidence for that conjecture to hold is the proof derived from the formal system, which is a chain of reasoning set by Euclid, a Greek Mathematician who lived in Alexandria at around 300 B.C. This chain of reasoning consists of axioms which are statements assumed to be true without any proof, deductive reasoning and theorems (Lagemaat, 2010). For instance, Euclid in his book called Page 2 of 6

3 Elements, uses the axiom of adding and multiplying numbers to derive to the theorem that, when the sum of powers of two is a prime and is multiplied by the last term of the progression 1 2 of powers of two, the result is a perfect number, for instance: , 7 is a prime and hence 7 4 is 28 which is a perfect number (O'Connor & Robertson, 2011). Moreover, this theorem is also backed up by a rigorous proof by induction which serves to be its evidence, provided that the axioms hold true. Hence the assertion or the conjecture turns into a theorem, which is not refuted. However, a contradiction arises when Nicomachus forms the following assertions based on pure observations on the first four perfect numbers only: 1. The nth perfect number has n digits. 2. All perfect numbers are even. 3. All perfect numbers end in 6 and 8 alternately. 4. Euclid's algorithm to generate perfect numbers will give all perfect numbers. 5. There are infinitely many perfect numbers. (O'Connor & Robertson, 2011) Of these, some were proved to be true, some were proved to be false and some are still unproven, but all these assertions still hold as they have evidence based on perception. However, to a conventional mathematician, evidence based on perception is not sufficient for it to hold, for instance, the third assertion on the list is valid till the fifth perfect number (O'Connor & Robertson, 2011) and hence, the assertion cannot be generalised based on the first five perfect numbers only. Then why were these assertions considered as axioms for many years by mathematicians and were not refuted? The answer is that, although the assertions required rigorous proofs to hold true or false, only evidence based on perception were enough to put them into hold. For instance, the fifth assertion on the list is yet to be proven, but it still stands as one can continue to find perfect numbers along the infinite number line. Had it been rejected for the sake of lack of a proof, the search for perfect numbers would not have continued. In formal terms, for a mathematical assertion to hold, it does not always have to be an analytic priori assertion, which is an assertion that is true by definition and can be known to be true of experience (Lagemaat, 2010); because a synthetic posteriori assertion, which is an assertion that is not true by definition and cannot be known to be true independent of experience (Lagemaat, 2010), leaves space for empirical evidence, which can support the foothold of an assertion. Hence, it is seen from the above argument that the nature of evidence is vital for an assertion to hold. Page 3 of 6

4 Similarly, assertion in natural sciences is synonymous to hypothesis and the evidence for a hypothesis to hold usually comes from observation. However, assertions in natural sciences are governed by intuition as well, just like in the case of the atomic theory proposed by Democritus and Leucippus. They proposed that atoms are the smallest, indivisible particles (Wikipedia, 2013). It is inevitably just to say that Democritus and Leucippus could not have the empirical evidence that the modern scientists have today, to support their assertions. In complying with Hitchens, should not the assertion be rejected? Perhaps, that was the case with Copernicus as well. In 1543, Copernicus suggested that the Sun was at the centre of the solar system and at that time he didn t have empirical evidence to support his assertions (Hamper, 2009). However, it was only later proved to be true when Galileo and later Newton provided evidence to that assertion. Hence, what justifies Democritus, Leucippus and Copernicus s speech act of making those assertions? Perhaps, empirical evidence does not only provide base for an assertion, but also intuition, which served as the evidence for the former assertions. In the words of Bertrand Russell, Democritus and Leucippus s synthesis of intuition can be explained as that they just hit on a lucky hypothesis, only recently confirmed by evidence (Wikipedia, 2013). Moreover, the case of fabrication in Milikan s oil drop experiment strongly supports the above argument. The historian Gerald Holton stated that Milikan dropped off a large proportion of his experimental data which were not complying with his assertion and hence, although his result of the charge of an electron is true, it was fabricated to be true (Wikipedia, 2013). However, the philosopher Allan Franklin showed that the exclusion did not affect the resulting value of the charge of an electron greatly and thus rationalised Milikan s purpose of excluding the data as, just an act of avoiding disagreement within the scientific community at that time (Wikipedia, 2013). Therefore, as much as it suggests that the scientific community is biased towards rejecting an assertion on the basis of the degree of its certainty, it also suggests that empirical evidence does not necessarily support the validity of an assertion all the time. Hence, assertions cannot be rejected on the basis of their closeness to truth. In contrary to the above arguments, the case of Carlos De Luna who was executed in 1989 can provide us with an interesting scenario for assertions based on evidence. In 1983, Carlos De Luna was arrested for the murder of Wanda Lopez (Pilkington, 2013). In this case, the accusation can be defined as the assertion and the evidence underlying that accusation would decide whether the assertion holds or not. There were no direct evidence found, which is evidence of a fact based on a witness's personal knowledge or observation of that fact (nycourts, 2008), such as the blood stains found in the crime scene were not found on De Luna Page 4 of 6

5 at the time when he was arrested. However, he was sentenced to death based on circumstantial evidence, which is direct evidence of a fact from which a person may reasonably infer the existence or nonexistence of another fact (nycourts, 2008), that is the real murderer and De Luna had the same namesake, Carlos; they were the same height and weight, and looked alike as well (Pilkington, 2013) and hence, it was inferred that De Luna was the murderer, but his innocence was proved only after his execution. This case suggests that evidence derived from reason and perception can be deceiving in justifying an assertion and hence, an assertion should only be rejected, if and only if one cannot be absolutely certain of the relevance of the evidence to the assertion. However, the above argument fails as the relevance of evidence can only be determined by further evidence and this process results into the problem of infinite regress in which the relevance of evidence would require further evidence and the subsequent evidence would require even further evidence and this would continue to infinity. Hence, the logical fallacy, Argumentum ad lapidem suggests that, if the rejection of an assertion cannot be justified, then the assertion still holds as it cannot be disproved to hold and hence an assertion cannot be rejected at all. Overall, it should also be noted that Hitchens s quote need not to be explicated further as it is itself an assertion, which had no evidence at the beginning of this essay and could have been rejected. However, since his statement contradicts itself, it is plausible to say that it is false and can be disregarded. Hence, in my opinion, an assertion can never be rejected and the degree of its closeness to truth cannot be a criterion for its dismissal. Page 5 of 6

6 Bibliography Hamper, C., Higher Level Physics. In M. Rumble, ed. Higher Level Physics. 1st ed. Edinburgh: Pearson Education Limited. p.553. Lagemaat, R.v.d., Theory of Knowledge for the IB Diploma. In Lagemaat, R.v.d. Theory of Knowledge for the IB Diploma. Cambridge University Press. pp nycourts, Untitled Page. [Online] Available at: General/CJI2d.Circumstantial_Evidence.pdf [Accessed Monday January 2013]. O'Connor, J.J. & Robertson, E.F., Perfect numbers. [Online] Available at: [Accessed Monday January 2013]. Pagin, P., Assertion (Stanford Encyclopedia of Philosophy). [Online] Available at: [Accessed Thursday January 2013]. The Painted Veil [Film] Directed by John Curran. Pilkington, E., The wrong Carlos: how Texas sent an innocent man to his death World news The Guardian. [Online] Available at: [Accessed Monda January 2013]. Wikipedia, Democritus - Wikipedia, the free encyclopedia. [Online] Available at: en.wikipedia.org/wiki/democritus [Accessed Monday January 2013]. Wikipedia, Oil drop experiment - Wikipedia, the free encyclopedia. [Online] Available at: [Accessed Monday January 2013]. Page 6 of 6