The Foundations of Geometry Inductive and Deductive Reasoning Discussion

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This week we learn about the foundations of geometry. Geometry uses various modes of thinking. Describe inductive and deductive reasoning. Provide some examples from everyday life that compare and contrast these two ways of thinking?
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Inductive vs. Deductive Reasoning In deductive reasoning, one begins from the general and moves to the specific, that is, from few general ideas or premises to specific conclusions about a situation (Wilson, 2016). Expressed conceptually, deductive reasoning takes the shape of a funnel and a basic deductive syllogism is as follows; If A=B and C=A, then B=C (Wilson, 2016). In inductive reasoning, one uses a set of specific observations to reach an overarching conclusion. In essence, it is the opposite of deductive reasoning and in its conclusion, only a broad idea that is likely true is illustrated (Llevada, 2013). It takes the shape of an inverted funnel where one moves from specific to general statements. An example of an inductive syllogism is; my neighbor's cat hisses at me daily, at the pet store, all the cats hiss at me, therefore, all cats probably hate me (wilson, 2016). According to Llevada (2013) inductive reasoning can be used in geometry for example, where one can observe that in a few given rectangles, the diagonals are congruent, inductively it would mean that in all rectangles, the diagonals are congruent. Although in this instance, the answer is actually true, inductive statements are not always accurate and reliable in providing proofs (Llevada, 2013). The key difference between deductive and inductive reasoning is that, while deductive arguments are meant to prove a conclusion, inductive arguments are meant to predict a conclusion. Inductive statements try to show the most probable conclusion given their premises. Further, whereas inductive reasoning is used in Geometry to largely form hypotheses, deductive reasoning is applied more extensively in to prove ideas. In Deductive reasoning researchers test a theory by collecting and examining evidence to see if the theory is true. In inductive reasoning researchers first will gather and analyze the data, the researcher then will construct a theory to explain the findings. Inductive reasoning is very much the opposite of deductive reasoning. Inductive reasoning is used commonly in research, it is not without its weakness. Deductive reasoning in the other hand is known as the gold standard for scientific research. Examples of both theories are as such; Inductive reasoning: A person falls from a skyscraper, therefore all skyscrapers are dangerous. Deductive reasoning: My parents serve together in the Army. My Dad is going to the base to work. My dad is a Soldier. I look at deductive reasoning as a theory that uses a more logical process in order to get a better statement more specific. inductive reasoning is a more open-ended and exploratory. The theories are both needed in different cases and can be used to draw conclusions but one is more logical than the other. Rosie Reply | Hide Replies (2) NEW I appreciate this breakdown and the analyzing of testing theories by collecting and examining evidence to determine if a theory is presented in a different light, data must always be researched and constructed, so logically it would make sense to collect all aspects of a theory and present the evidence in a manner in which reasoning will be effective or non-effective. In order to fully draw conclusions, one must look at every aspect of a reason and then decide which is more logical, and applicable to every situation. Reply . 5/2/19, 9:15 PM You comments about deductive reasoning being more logical are quite accurate. I have considered both of them to be like statements or arguments in a court room. Deductive reasoning is more logical and accurate because it's based upon facts where as inductive reasoning is based on trends or a generalization. As a judge or jury, I'd much rather side with the argument based on facts than trends. Well done! Reply.. 3 hours ago, at 12:06 AM 5/2/19, 9:52 AM With inductive reasoning, data is presented and a general conclusion can be drawn from the observations but there is no guarantee that the conclusion is correct, or if there is only one conclusion. For example, my son picked his best friend first when choosing players to be on his team. The next day he chose his best friend first again. Inductive reasoning would conclude that the next time he needs to choose a player, his best friend would be picked first. Deductive reasoning results in a specific logical conclusion based on one or more premises that are assumed to be true. For example, my son needs to choose the best player to be on his team. His best friend is the best player. Deductive reasoning would conclude that my son would chose his best friend to be on his team. Both situations resulted in his best friend being chosen but inductive reasoning leaves the possibility for alternate outcomes. He may or may not choose his best friend the next go round even though there is a pattern of him previously doing so. Alternatively, his best friend must be chosen using deductive reasoning because of the assumed true statements. Reply. I Hide Replies (2) I found this a insightful. The one thing you said that stuck with me the most is that with inductive reasoning it leaves the possibility for alternate outcomes other than the one that was stated in the conclusion. This gave me another way of looking at what the difference is between inductive and deductive reasoning. Reply . 5/2/19, 12:42 PM I enjoyed reading your response. I agree with Stich, the way you defined inductive reasoning and gave the complementing example really helped me understand the difference between the two different types of reasoning. Great job! Reply . 5/2/19, 9:02 PM user Inductive reasoning is a way of understanding ideas through the aspect of many different components that are comprised of specific details. I like to think of it as you "introduce" all the tiny details and then move one to a derivative of a more general thought process. Deductive reasoning is a way is the opposite. You start with a general theory and then through a matter of course proceed to you get down to more specific details to held clarify what your reasoning may be at the time. I can see how these relate to Geometry. Sometimes you are given a formula and sometimes you must find the formula. Every weekly work meeting we have is boring. It could have been sent in an email. Therefore, the meeting next week, will be boring and probably about stuff I already know that could have been sent in an email. My coworker eats out every day for breakfast, lunch, and dinner. I work with this coworker at a certain place of business. Therefore, all of us must eat out three times a day as well. For the record, I do have a coworker that does that. I personally don't eat out that much. All I can usually think about is what her insides must look like and how much money she usually spends a week! Reply 5/2/19, 9:04 PM Inductive vs. Deductive Reasoning Inductive reasoning is reasoning where the premises support the conclusion. The conclusion is the hypothesis, and this means that inductive reasoning is often referred to cause and effect or bottom-up reasoning defining the conclusion first. Whereas; deductive reasoning is reasoning based on developing a true and valid conclusion. The conclusion must be true and not saturated with opinions like in the case of inductive reasoning. For example, if someone points out that in their personal experience all women are bad drivers, and they cause the majority of accidents this is referred to as inductive reasoning, the conclusion that all women aren't defensive drivers and cause the majority of accidents is an opinion of the person leading the argument. To counteract that statement with deductive reasoning one might suggest that the majority of accidents that occur anywhere in the world is contributed to speed and carelessness of the driver regardless of gender. This is deductive reasoning because it presents the argument with factual information and is not saturated with opinions. What other valid arguments can be given from this example? Thoughts?? Reply. Hide Replies (1) NEW Kim, Great post, but I am a little confused when you said that the conclusion is the hypothesis. Thank you for your insight on what inductive reasoning is. I have never heard it called cause and effect or bottom-up reasoning. Also, with deductive reasoning I do not think that the conclusion has to be true. The conclusion can be false but still be logically valid. One could argue that all mechanics likes burgers, John likes pizza, therefore John is not a mechanic. Even though the premises may be true, the conclusion makes an invalid assumption. ANA mi 5/3/19, 2:08 AM Hi Class, Inductive reasoning is the process of drawing a broad conclusion that is made from specific observations. For instance, let's say you looked at a list of salaries at a company from lowest to highest earnings. You find that the lowest four earners on the list are female. Using inductive reasoning you might draw the conclusion that all females in the company earn less than the males within the same company. Inductive reasoning allows the conclusion to be false even though the premises that led to that conclusion to be true. Conversely, deductive reasoning draws a conclusion by introducing a theory then confirming the theory through observations. One example of this might be the following: Guns shoot bullets. A Glock pistol shoots bullets. Therefore a Glock pistol is a gun. This is an example of syllogism. Syllogism is a form of deductive reasoning where two premises reach a logical conclusion. This can be expressed in the following way, A=B and B=C, therefore A=C. In deductive reasoning, the conclusion must be true as well as the premises that lead to that conclusion. Reply. Hide Replies (1) NEW Hi Joseph! I loved that you were able to introduce syllogism to help everyone understand how deductive and inductive works. I always did find it a little confusing that inductive reasoning allows the conclusion to also be false even though all the details before it led to create that reasoning a certain way. Reply 5/3/19, 11:57 PM NEW
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Good work! It is clear from your post that deductive reasoning is based on testing a theory and
proving whether it is true or not. On the other hand...


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