Analogy aids understanding, not justification

“The role of analogy is to aid understanding rather than to provide justification.” To what extent do you agree with this statement? Through analogies, monotonous, forthright statements and inordinately plain explanations can be brought to life and given color. However, others claim analogies are inherently reductive as they always search for similarities and simplify things so far that their essence is lost. Another puzzling characteristic associated with the analogy is whether it is able to provide evidence or proof that a belief is true and reasonable or that they aid the comprehension and interpretation of knowledge. For the purpose of this essay, I will give an initial definition of three key terms presented in the essay question. An analogy is a way by which similarities and differences between two comparable subjects are juxtaposed. It is asked whether it aids understanding, in this context, this can be perceived as the ability to interpret and comprehend a subject. On the other hand, can an analogy provide justification or does it have the ability to explain a subject with reason to back up a claim? After looking over each definition, I was confronted by a perplexing query. Are there any limits to what we can learn about the world through perception? This implies that both the justification and understanding of a topic can be generalized into perception. Yet different people perceive the same things differently and this could be because of different conditioning of their minds since their childhood. So how does analogy bring various and dissimilar perceptions to become almost analogous? Through the exploration of the areas of knowledge of mathematics and ethics at the hand of reason, I intend to construct a clear path of reflection and reasoning to answer the posed questions. From what I recount one of my maths teachers sayings, “good analogies can take an idea that is baffling and turn it into something simple and enjoyable, especially in math. Solving a mathematical problem or concept is like trying to cross a river and the way you approach it or solve it is with a raft.” I was unsure of what he meant as I was familiar with the analogy of counting with the help of apples, “numbers are apples”. I remember the confusion that I felt when I was presented with the number -1. How could you have a negative apple? This is when the analogy of using apples couldn’t stand anymore. “Then if numbers aren’t apples, they are lines”, my third-grade teacher said. I was introduced to a number line, and could easily visualize negative as being part of the picture. At this point, zero does not represent anything in fact, it represents the middle point. This image of a number line made things much easier to understand, whether a number was negative or positive depended on which side it was to zero. Despite this miraculous discovery, some of my friends still couldn’t perceive what was being told. The concept hadn’t ‘clicked’ in their minds, announcing a visible complication. Why do some analogies come easier to some than others? This develops toward the theory of nature versus nurture. Am I biologically better at mathematics than my peers or is it my early childhood experiences, my surrounding culture, or the manner that I was raised that makes me more prone to understanding this mathematical analogy? Nonetheless, as my knowledge of mathematics developed, I was again faced with something incomprehensible, i2 = -1. When you square a number it never turns negative. 12 = 1, -22 = 4, 02 = 0. Once again, we change our analogy to aid our understanding of a mathematical concept. This time, I was told to add a number line, but this one would go down and up, contrary to left and right. In this instance, when you say i2 = -1, you are multiplying the number 1 by me and then by i. In the new analogy we created, this shows a 90° rotation and since we get 2 x 90° rotations, this equals -1. How did my maths teacher know that analogies could be so good at explaining perplexing concepts? Using my reasoning, why should I not use analogies to help understand all mathematical concepts? I chose to approach one of the equations considered “absolutely paradoxical” Benjamin Pierce 1759. It’s bewildering to think that e (irrational) to the power of I (weird dimensions) times by pi (also irrational) could so perfectly equal -1. However, using proofs, this could perturbing and complex equations could be made to look so simple and easy. This time, I colored each different symbol and I knew that each symbol meant something different. I know that e represents growth, I represent a sideways push and pi represents half a circle. With this image in mind, I without a doubt land backward, on a negative one. This brought up the question, does math need a language to be understood, or is math a language in itself? If so, an analogy can be described as a form of language to convey mathematical understanding in a more familiar manner. You can also think of this manner of solving as deductive reasoning. The process of forming a conclusion is based on the concordance of multiple premises, theories, or premises (assumed to be true). On the other hand, there are instances in which analogies provide justifications rather than an aid to understanding. Using the concept of analogical arguments, analogies can arguably provide an explanation to a subject with reason to back up a claim. To argue by analogy it is necessary to argue that because two things are similar, what is true of one must be true of the other. When making analogical arguments, it is necessary to make clear what are the similarities between the two different subjects. Once again my train of thought was put to stop. If justification is the act of showing something to be reasonable, is it not subjective? If so, to what degree of subjectiveness can an analogy no longer work effectively to justify? This could imply that a justified ‘true belief’ may not be accurate and valid but that at least the person trying to convey and justify their belief through analogy is attempting to understand and make others believe it and understand it. A clear-cut way of presenting an analogical argument is to take the following structure. ● ● ● Premise 1: Object A and B are similar because they both share aspects g, z, r, s. Premise 2: Object A has a property t. Conclusion: Therefore, object B also has the property t. This is something I have retained from my ethics class. In moral reasoning, we tend to often use analogical arguments which help to think of the consistency of our moral outlook. Mrs. Amy (my ethics teacher) asked us, “Is it morally wrong for me to hit a human baby, and laugh?”. We all quickly answered yes in shock at what our teacher had so blatantly told us. She then said, “It’s similar to beating a dog for fun right?” It took us a little longer to answer, but we all concluded that it was. She then told us that both actions (X and Y) are morally wrong because in each you are intentionally inflicting pain on an innocent being for ‘fun’. Therefore, for consistency, action Y is, to an extent, as morally wrong as action X. Our Ethics teacher showed us that because actions X and Y are comparable in certain aspects, and that she has listed some of the similarities for consistency, then the controversial action Y should justifiably get the same verdict as the action X. Through reason of comparisons, she has justified the moral outlook on these situations. However, once again this would imply that it is universally recognized that actions Y and X are the same. But this is not fully true as some people will argue that beating a dog for fun is completely different from beating a baby for fun. Culture and belief play a significant role in ethics and therefore, when conveying an analogy to justify a belief, it may be recognized by some but also dismayed by others. Nonetheless, an analogy can still, to a certain degree, provide justification for Ethics. In conclusion, I can only agree to a certain extent with the statement, “the role of analogy is to aid understanding rather than to provide justification”. It is clearly demonstrated that analogy plays a significant role in understanding mathematics. Nevertheless, the ability to understand the comparison between one thing and another may depend on the person. It can be compared to learning a new language. Analogies also have a notable role in justification for Ethics. However, as justification is subjective, this can be problematic because, from the knower’s perspective, there is not much to distinguish belief from knowledge. Arguing to the contrary takes the appearance of a circular argument. This means that instead of providing proof, it asserts the conclusion in an alternate form, hence persuading the listener to accept the fallacy. Yet in both areas of knowledge, aid in understanding and justification through analogies can vary among different people. With this thought in mind, to which degree is a knower’s perspective essential in the pursuit of knowledge? I could have furthered this essay by exploring the role of nature vs nurture more in-depth. In addition, while writing about the role of analogies in mathematics and ethics, my mind quickly became preoccupied with these arising questions, “To what extent can an analogy find similarities between different topics and effectively communicate these similarities to two different people?”. This question that was brought up during my essay captivated my attention and nudged me to further explore the mystery of analogies.