The title suggeststhat as we gain more knowledge through experience or study, doubt increases. Thisclaims that our confidence and faith in knowledge is inhibited which hinderscertainty as well as we learn more. For example, when I was studying IGCSE physics,I was highly confident and certain about what I was studying but as I progressedto IBDP standard level physics, as concepts became more complicated, my doubtincreased and my confidence of the subject decreased. In a broader sense, thisphenomenon can be recognized across a range of disciplines, academic fields andfrom the perspective of experts and non-experts alike.
To analyze this claim, Iwill respond to the following two knowledge questions. Firstly, to whatextent does gaining knowledge of the natural sciences limit our confidence inits understanding? Secondly, how far can knowledge gained within themathematics provide us with certainty? In this essay, I am going to illustrate andevaluate the central claim, with a balanced approach using supporting evidence.To answer these questions, I will explore the role ofdoubt in furthering the development of the Natural Sciences and how far theapplication of Mathematical concepts in other areas of knowledge limits thecertainty and therefore confidence of the knowledge produced.
In the NaturalSciences, it can be suggested that increased knowledge limits our confidence inits understanding. The nature of science is a constant development. Forexample, if a new hypothesis comes up, it will drag new questions, and proofsare required if the new hypothesis is to be appreciated as science. Accordingto Karl Popper, he claimed that scientists don’t use inductive reasoning but use deductive reasoning.By having more experiment about the theory, new observations that contradictthe conclusion can come out. Scientists then prove that the hypothesis is wrongand this is called falsification.
Therefore, falsifying the theory with newobservation suggests that any current established knowledge can be disregarded.And since we disregard current established knowledges, our confidence starts todecrease. For example, Stuart Firestein, a teacher and neuroscientist suggestedthat knowledge generates ignorance.
He illustrates that James Clerk Maxwellsaid that “Thoroughly conscious ignorance is the prelude to everyreal advance in science”1. It means in some point of science we have to neglectwhat we know. Because the nature of natural science is constant development,scientists keep research for new knowledge. Thus, knowing a lot of more dataleads to more ignorance.
And we use our knowledge to create a higher qualityand better ignorance. According to a graph of what people know about something andhow much do they actually know about it, undergraduate students have a highinterest on everything but they have a shallow knowledge about them. Master’s degree students know more than undergraduates buttheir interest has been decreased and PhD students know a lot about nearly nothing.Therefore, what do students know and how much do they know had indirectproportional relationship.
It shows that as students get higher education,their certainty on the subject decreases and their confidence might alsodecrease as well. However, there isalso an evidence to suggest that through gaining knowledge in science, ourconfidence increases. Scientific method is a rigorous process which provides ahigh degree of certainty and reason which increases confidence about developingnew knowledge. Not only reason and confidence, but scientific method providesus reliability and certainty. Therefore, confidence can increase fromreliability and certainty because scientific method has provided sufficient reasons.
Scientific method includes testing process, analysis of results, comparisonwith other similar studies and peer review from other scientists. One example isthe development of vaccination of Ebola. Ebola Virus Disease outburst inDecember 2013 and left 27,000 cases and 11,000 deaths in West Africa.2Due to the problem, an experiment involving 4,000 people has been undertaken byscientists, doctors and drug companies. When Ebola occurred, lots of researchersvaccinated every contact of sick people who are willing.
To see how well thevaccine protected people, the group of people were randomly assigned into twogroups. One group received vaccine as Ebola confirmed and another groupreceived after three weeks. The group which received a vaccine immediately hadno cases of Ebola for 10 days after vaccination but another group had severalcases. This proved to the scientists that receiving vaccination as soon aspossible reduces the risk of getting infected to Ebola from experimenting twodifferent sample groups. Using an empirical methodology, it allowed thescientists to generate new knowledge about the Ebola vaccination usage when theEbola occurs in a country and this showed scientists how to use the cure in thefuture.
With this new knowledge, scientist can have more confidence in futureuse of vaccination. However, the limitation of the experiment is there are onlythousands of volunteers who got tested for the experiment so experiment is yetperfect.3Although there is a limitation, because of this undergone process, people cantrust the vaccination and it will serve people a reliability. It can be arguedthat Mathematics provides us with a highly reliable and certain form ofknowledge which can be applied to a wide range of practical applications,giving us a confidence about it as an area of knowledge.
Mathematics is one ofthe most objective and logical areas of knowledge that requires the applicationof reason and rational thinking. And because mathematics relies on reason,answers should be drawn from valid mathematical theorem. For example, Pythagorean theorem is a representative theorem inmathematics.
It illustrates that the square of hypotenuse is equal to the sumof the square of adjacent and opposite. People can’t debate about this theorem since it has been alreadyproved by mathematicians. Moreover, I could apply Pythagorean theorem toconcepts I have learned in IB physics.
For example, I used Pythagorean theorem whenI tried to find a resultant force vector in a physics lesson. I didn’t have a right-angel triangle but because I had anobtuse-angle triangle, I extended a line and made a right-angle triangle andfound a resultant force by using Pythagorean theorem. By applying mathematicalknowledge to physics, I could reach a high reliability and certainty.
Not onlyreason but mathematics also relies on language because unique mathematicallanguage such as pi( or integral ( can transferinformation to anyone in the world which increases certainty and validity. However,Mathematical models don’t always providereliable results in their application.When Mathematics areapplied to a subject such as Economics, it reduces our certainty andreliability. When I tried to apply mathematical model into Economics, model thatrequires probability completely contradicted my mathematical knowledge and it servedme doubt in mathematics. For example, when I was studying microeconomics in year12, I came across with a concept called “Price Elasticity”.
In price elasticity, there is price elasticity ofdemand(PED). It shows the responsiveness ofdemand after a change in a price of goods. However, where Economic conceptcontradicted my mathematical knowledge is when I saw negative percentage sign.
Inorder to calculate PED, I should figure out the change in percentage ofQuantity demand and the price of goods. When the figure of a previous year isbigger than the year after, it gives negative percentage value which means thatthe amount of price or quantity demand has been decreased compare to theprevious year and in Economics, we express it as –X%. However, what confused mewas in mathematical knowledge, percentage cannot be negative since thepercentage is a certain amount in hundred. But negative percentage came up whencalculating PED (% Change inQuantity Demand / % Price change). This served me doubtabout my knowledge in mathematical model.
Therefore, when I saw negativepercentage, which contracts my existing concept, my certainty started to decrease. Thus, I realized that in a subject such as Economics,AOK such as Mathematics doesn’t always work. To conclude, I believethat the statement “With more knowledgedoubt increases” is fair to someextent in the areas of knowledge of Natural Science and Mathematics. In Naturalscience, because of the nature of Natural Science which constantly develops, ifa new hypothesis comes up, a new question will come up.
In order to beappreciated as a science and gain validity, it has to be proved but becausescientists use deductive reasoning, they always try to falsify their hypothesiswith new observation which disregards current knowledge. Therefore, increasedknowledge of natural science might limit our confidence in its understandingand more knowledge will enlarge doubt. And this has been experimented by StuartFirestein from a survey of how much do bachelor’s students to PhD students know.
The survey about howmuch they know and what they know showed inverse proportional because PhDstudents studies in-depth, which increases doubt. So although increasedknowledge might increase doubt, scientists will have to gain more evidence toprove their hypothesis and gain validity from other scientists. Mathematics, one ofthe areas of knowledges that relies on reason and language might limit ourconfidence when it is applied to certain subjects such as Economics.
AlthoughMathematics provides us with a reliable knowledge if applied to physics, with ahigh degree of certainty, when Mathematical knowledges are applied toEconomics, it contradicts current established mathematical knowledge such aspercentage with a negative sign in some content in Economics, and this willincrease our doubt and decrease our certainty.