Deductive+Reasoning

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Table of Contents
1. Overview 2. Validity 3. Soundness 4. Inductive Reasoning 5. The Problem Of Induction 6. Deductive reasoning over time 7. Citations

Overview
Deductive reasoning refers to the processes the brain goes through in order to reach conclusions about presented sets of evidence. A normal path of deductive reasoning will be something like this: "I bought a jar of peanut butter. Now there is no peanut butter. It must have gotten eaten by someone else."

You know that peanut butter cannot simply disappear, so you search for a more plausible solution to the issue. If you live in a house with other people who like to eat peanut butter, then it is very probable that one of the people you live with ate it before you got the chance to. You use knowledge you already have to come to conclusions about things, and to avoid coming to conclusions that simply cannot be. For example, your knowledge of humans and aging allows you to avoid coming to a conclusion like this: "Humans are born with the ability to grow hair. Mr. Schmidt cannot grow all of his hair. Mr. Schmidt must not be a human. Non-humans include robots, martians, and cats. Cats have hair, Mr. Schmidt must not be a cat. Cats are adorable, Mr. Schmidt is not a cat and therefore is not adorable. = = Robots can also be adorable, and if Mr. Schmidt is not adorable, he is not an adorable robot, and therefore is not a robot A martian is the only remaining option. Mr. Schmidt is a martian." You know that, though humans ARE born with the ability to grow hair, some humans have the genetic build that prevents hair growth later in life. Mr. Schmidt is obviously a human, so he must have simply lost his ability to grow hair as he grew up. The logic behind this conclusion is both valid and sound, which are the two main factors in determining whether deductive reasoning is working properly.

Validity
Validity examines the conclusion of an argument based on its' premise. A premise is the original set of information that conclusions are drawn from. The premise in the line of logic about Mr. Schmidt is "Humans are born with the ability to grow hair," and the conclusion is "Mr. Schmidt is a martian." An argument can be valid even if the premise is completely untrue, because validity is solely concerned with the connection between start and end and whether the conclusion makes sense based on the beginning information.

Soundness
All arguments that are sound are valid, but not all arguments that are valid are also sound. Validity, as you know, does not take into account whether the premise is true or not. Soundness looks for an argument to be valid, but it also takes into consideration whether the original argument is true or not. An argument can only be sound if the premise is true and the logic is valid.

Inductive Reasoning
Inductive reasoning is a form of deductive reasoning in which generalizations are made based on a widely accepted and universally agreed upon set of observations. For example, all the beagles ever seen have been smaller than a car. Therefore we can assume that all beagles are smaller than cars, even though we technically have no concrete evidence to disprove that statement. It is probable that if we've never seen a 2-ton beagle by now, 2-ton beagles simple do not exist. A strong induction indicates that the conclusion that has been reached is very probable, and a weak induction indicates that it is very improbable. An example of a strong induction would be the beagles example, because nobody has ever seen a 2-ton beagle so we can assume that all beagles are the small and adorable creatures we know and love. A weak induction would be: "The psychology teacher at SHS is named Mr. Schmidt. Therefore all psychology teachers are named Mr. Schmidt." Even though there is no evidence at SHS to disprove this, we know that there must be at least one psychology teacher who is not named Mr. Schmidt.

Backward induction is similar to inductive reasoning, but it works backward from an answer to determine what is the best decision to make for the outcome that most benefits the decision maker. For example, we can look at the example of being presented with the option of getting $1,000,000 every day for the rest of your life, or getting a penny on day one, then having that amount double every day for the rest of your life. At first glace, the decision may be made that $1,000,000 per day is the better choice to make. However using inductive reasoning we can see that the end result will be much more valuable if you go with the second option. Only about 28 days later, you'll be receiving about $1.3 million, which will be doubled each day after as well. Through inductive reasoning, you can determine that the $1,000,000 per day is not the best option.

The Problem Of Induction
The problem of induction is the set of arguments usually associated with critics of induction. Essentially, the arguments question whether knowledge results from induction. Induction, as we know, is simply a series of observations that support one hypothesis. Technically there is no way to prove any conclusion that is reached through induction, however we accept most of these conclusions as being true if there has never been any evidence to the contrary. A man named David Hume was skeptical about the effectiveness of using induction, because there is nothing final about induction. There is simply a set of observations which some people use as a means to predict what will happen in future situations involving similar circumstances. For example, if you say something that offends one member of a group of people (a Christian, a teacher, a black male, etc.) you may think twice about saying something similar to another person in that group in the future because it may offend them as well. Hume would argue that even if you made the mistake of saying something offensive ten times, you still technically have no grounds upon which to decide all members of that group will be offended by the same type of comment.

Supposing you have two observations. For example, those observations are: "I have found that if I do not do my math homework on Wednesday night, I always seem to be lucky because my math teacher never checks the homework for Wednesday night during thursday's class." and then "I can assume that my math teacher will never check my homework on a Thursday." Hume says that you connect those two statements not through deductive reasoning, but through induction. Therefore, the two inductive statements are connected through induction. As you know already, there is nothing conclusive about induction, merely speculation. Hume argues that since you are proving inductive statements to be supposedly true by using more induction, there is nothing actually conclusive or reliable about your argument. You are starting out with two uncertain principles that have simply never been proven false, although there is nothing saying they cannot be proven false. You are then proving the already uncertain ideas through uncertain and completely speculated logic. Hume argues that there is nothing to be gained through all this speculation, and that induction is simply not something that is useful for coming to conclusions.

Deductive Reasoning Over Time
As the video below shows, the abilities and processes that make deductive reasoning work change significantly over time. As you grow, you become more able to expand your thinking and accept new ideas that come to you. As the video below shows, the older subject is able to put aside what she already knows of the physical world and the limits it places on certain object, like a feather and glass.

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The boy is right. He knows that a hammer will break glass and a feather will not, even though the rules say that both a hammer and a feather will break the glass. He cannot expand what he already knows to say "even though I know one thing will really happen, I can humor the idea the second rule poses just to consider the possibilities." The older girl however, can put aside the fact that a feather could never break a glass just to consider the implications the rule places on already established psychological rules. The girl looks at the problem from a perspective of validity and knows that the end result makes sense in reference to the premise, but the argument is not sound because though the argument is valid, the premise is not true. This divide between validity and soundness becomes more apparent and easy to deal with as you grow older. The boy in the video is obviously not old enough to have gone through all of Piaget's developmental stages, which end around 12 years of age. The boy in the video is obviously closer to 7 or 8, which puts him in the concrete operational stage of thinking.

In the concrete operational stage of thinking, children can first think logically. Though their thinking is not extremely strong, they have the ability to relate ideas together and come up with some sort of answer. However they need aids to help them. When the boy reaches about age 12, his mind will be able to entertain the possibility of a feather breaking a glass just like the girl does. By this point, the ability to think about abstract things becomes much easier. Also, by the concrete operational stage, a child will begin to understand that others will not be able to interpret things in the exact same way as themselves because they do not share the same experiences and so on. This helps the child in their logical thinking because they can know when others will understand things and when they will not, which will most likely increase the level of explanation in their train of logical thought.