“Deductive reasoning is any form of reasoning that moves from the general to the particular” (R. Lagemaat, 2005, p. 114). A syllogism is a form of deductive reasoning which consists of the following elements: two premises and a conclusion; three terms, each of which occurs twice and; quantifiers, such as ‘all’ or ‘some’ or ‘no’, which signifies a quantity that is being referred to. Referring back, an example of a syllogism would be, ‘All Cambridge University graduates are intelligent’, ‘My brother is a Cambridge University graduate’, and ‘Therefore, my brother is intelligent’. However, to be sure that the conclusion of an argument is true, the following statements must be correct in order to ‘preserve’ the truth – ‘Are the premises true?’ and ‘Is the argument valid?’ Even if these statements prove to be true, deductive reasoning still relies on inductive reasoning to begin with, thus showing the weaknesses of it as it is now primarily functioned as a way of knowing to preserve the truth and used as a tool in order to justify results.
However, the counter-claim for this argument would be that, even to this date, deductive reasoning still plays a huge role in the area of knowledge of mathematics. René Descartes once said, “To speak freely, I am convinced that it [mathematics] is a more powerful instrument of knowledge than any other…”(R. Lagemaat, 2005, p. 187) and because the foundation of mathematics is primarily built from deductive reasoning, it shows the significance of reason in modern mathematics. Although in mathematics the names are altered (premises are called axioms and conclusions are called theorems), the theory and basis of certain claims such as Riemannian geometry originates from deductive reasoning.
That said, many would still remember and argue that deductive reasoning came from inductive reasoning – surely this idea or concept must apply again in mathematics? That is correct; once again, inductive reasoning must occur first before deductive reasoning could then occur. In order to explain what I mean, consider the following situation: the Euro-millions, where there are fifty-numbers to choose from ranging from one-to-fifty and you are required to choose five numbers. To add to the difficulty, another two ‘star’ numbers must be chosen with a range from one-to-eleven. Through inductive reasoning where we move from the particular to the general, we are able to find the probability of winning the Euro-millions when buying a single ticket which is one-in-three hundred and twelve million, five hundred thousand, one hundred and twenty one. As in a normal ‘experiment’ in mathematics, this is to be repeated again before a conclusion or theorem is made. In Hong Kong’s Mark Six lottery, six numbers ranging from one-to-fourty nine has to be chosen with an additional bonus number ranging from one-to-fourty nine as well. Therefore, the probability of winning the Hong Kong Mark Six is one-to-one-point-three eight four one two eight seven two five to the power of ten, and through ‘experience’ and inductive reasoning, the general formula could be deduced. As a conclusion, the probability of winning is shown through the equation: “P = R1N1 + R2N2”, where ‘R1’ is the first set range of numbers, ‘R2’ is the second set range of numbers, ‘N1’ is the number of answers required for the first set of numbers, ‘N2’ is the number of answers required for the second set of numbers and ‘P’ is the probability of winning and only now could we consider deductive reasoning significant as a generalised statement is made which is valid.
Referring back to inductive reasoning, it is basically reasoning from the particular to the general. As mentioned above, we rely mainly on inductive reasoning whether or not we know this – even through deduction, the basis of it came from inductive reasoning first. Therefore, the real important question is not how significant this form of reasoning is, but more on how reliable induction actually is. The problem with induction is that we tend to make ‘hasty generalisations’ and jump to conclusions without a significant amount of data collected. As a result, problems arise as shown through this real-life situation – by boiling water at home or being even more precise in a laboratory, it is noted that pure water boils at 100C. Now, imagine you are to climb Mount. Everest and obviously the first stop would be at the Base Camp of Mount. Everest. Hot water and food is essential at such harsh climates; so imagine the inductive knowledge you’ve learnt before and now try to boil the water for drinking and cleaning – what is the problem? We’ve repeated the experiment many times before on Earth where the pressure was 1atm and we know that pure water would boil at 100C. However, because of this change in atmospheric pressure, the temperature in which water would boil at would alter – if you had only brought a heater up to a certain temperature and not pass the boiling point of water when at a different pressure, you could potentially die as a result from your previous ‘hasty generalisation’ whereby pure water must boil at 100C. Not enough data had been collected to prove this generalisation.
Additionally, reason does not only rely on inductive or deductive reasoning but also in a third form called informal reasoning. There are different fallacies that help us reason – the first; circular reasoning is a form of reasoning in which we assume the truth of something that we are supposed to be proving and a good example of this would be when a Catholic states “I know that Jesus was the Son of God because he said he was, and the Son of God would not lie.” (R. Lagemaat, 2005, p. 125) Through the area of knowledge of Religion, this individual believes that the Son of God would not lie but the question still remains relatively unanswered, as the individual had just simply assumed the very thing they were supposed to have proven. By assuming one factor after another, this creates a cycle of assumptions, which exposes the weakness in this argument, as there is no evidence to prove their claims. Another form of informal reasoning include ‘False dilemma’ whereby you assume there would only be a black or white alternative that exists. For example, if you are not dead, then the assumption would have to be that you’re alive. Although this proved to be useful in history whereby their survival was mainly based on this sort of reasoning, the modern world proves to be more problematic with various factors included in the problem thus reducing the reliability when using ‘False dilemma’ to reason an answer.
When evaluating the strengths and weaknesses of reason as a way of knowing, it seems that the strengths outweigh that of the weaknesses. Even though there are doubts concerning the reliability of both induction and deduction, it is difficult to see how we could do without these two ways of reasoning in practice. Another significant point is seeing how well deductive and inductive reasoning complement one another – although there are other ways of knowing through language, emotion and perception, reason is still considered the most significant way of knowing as it takes into account of the environment and other factors as well which may affect the ‘truth’. Finally, even though we’ve examined the three forms of reasoning, the overall effect it has on a person’s way of knowing is still unknown due to the other three factors – to find the ‘truth’, we must then examine all the ways of knowing to fully evaluate the effect of reason as a way of knowing.
WORD COUNT: 1599
- Lagemaat, Richard van de.. Theory of knowledge for the IB Diploma. Cambridge: Cambridge University Press, 2005. Print.
- "Hong Kong Mark 6 Lottery | Mark Six Results | theLotter." Lottery Online - Lottery Ticket Results | theLotter. N.p., n.d. Web. 14 June 2012.
- "Euro Millions Results | EuroMillions Results | Results of Euromillions." EuroMillions | Euro Millions | EuroMillions Lottery Draw. N.p., n.d. Web. 14 June 2012.