Here's what I'm going to do today. Inductive reasoning. I'm going to get the students to make generalizations about me and then about each other. Then I'm going to trap them into talking about generalizations about Japanese and Americans and then talk about how hasty generalizations and stereotypes are fallacies that could ultimately hurt their writing.
I think this'll be fun^^
Here are some notes:
Inductive Reasoning
According to Answers:
Adjusting a course of action based upon a limited amount of information gathered. It is a process where one starts from a specific experience and draws inferences (generalizations) from it. For example, a salesperson, by observing a potential customer's reaction to the sales presentation, may induce what the customer's needs and personality are and what should be said to obtain the sale.
According to Wikipedia:
Inductive reasoning is the complement of deductive reasoning. For other article subjects named induction, see Induction (disambiguation).
Induction or inductive reasoning, sometimes called inductive logic, is the process of reasoning in which the premises of an argument are believed to support the conclusion but do not ensure it. It is used to ascribe properties or relations to types based on tokens (i.e., on one or a small number of observations or experiences); or to formulate laws based on limited observations of recurring phenomenal patterns. Induction is used, for example, in using specific propositions such as:
This ice is cold.
A billiard ball moves when struck with a cue.
...to infer general propositions such as:
All ice is cold.
All billiard balls struck with a cue move.
Strong and weak induction
Strong induction
All observed crows are black.
therefore
All crows are black.
This exemplifies the nature of induction: inducing the universal from the particular. However, the conclusion is not certain.
...
Weak induction
I always hang pictures on nails.
therefore
All pictures hang from nails.
Assuming the first statement to be true, this example is built on the certainty that "I always hang pictures on nails" leading to the generalization that "All pictures hang from nails". However, the link between the premise and the inductive conclusion is weak. No reason exists to believe that just because one person hangs pictures on nails that there are no other ways for pictures to be, or that other people cannot do other things with pictures. Indeed, not all pictures are hung from nails; moreover, not all pictures are hung. The conclusion cannot be strongly inductively made from the premise. Using other knowledge we can easily see that this example of induction would lead us to a clearly false conclusion. Conclusions drawn in this manner are usually over generalizations.
Teenagers are given many speeding tickets.
therefore
All teenagers speed.
In this example, the premise is built upon a certainty; however, it is not one that leads to the conclusion. Not every teenager observed has been given a speeding ticket. In other words, unlike "The sun rises every morning", there are already plenty of examples of teenagers not being given speeding tickets. Therefore the conclusion drawn can easily be true or false (perhaps more easily false than true in this case), and the inductive logic does not give us a strong conclusion. In both of these examples of weak induction, the logical means of connecting the premise and conclusion (with the word "therefore") are faulty, and do not give us a strong inductively reasoned statement.
Validity
Formal logic as most people learn it is deductive rather than inductive. Some philosophers claim to have created systems of inductive logic, but it is controversial whether a logic of induction is even possible. In contrast to deductive reasoning, conclusions arrived at by inductive reasoning do not necessarily have the same degree of certainty as the initial premises. For example, a conclusion that all swans are white is false, but may have been thought true in Europe until the settlement of Australia, when Black Swans were discovered. Inductive arguments are never binding but they may be cogent. Inductive reasoning is deductively invalid. (An argument in formal logic is valid if and only if it is not possible for the premises of the argument to be true whilst the conclusion is false.) In induction there are always many conclusions that can reasonably be related to certain premises. Inductions are open; deductions are closed. It is however possible to derive a true statement using inductive reasoning if you know the conclusion. The only way to have an efficient argument by induction is for the known conclusion to be able to be true only if an unstated external conclusion is true, from which the initial conclusion was built and has certain criteria to be met in order to be true (separate from the stated conclusion). By substitution of one conclusion for the other, you can inductively find out what evidence you need in order for your induction to be true. For example, if you have a window that opens only one way, but not the other. Assuming that you know that the only way for that to happen is that the hinges are faulty, inductively you can postulate that the only way for that window to be fixed would be to apply oil (whatever will fix the unstated conclusion). From there on you can successfully build your case. However, if your unstated conclusion is false, which can only be proven by deductive reasoning, then your whole argument by induction collapses. Thus ultimately, pure inductive reasoning does not exist.
Good Pdf of inductive and deductive reasoning
I think this'll be fun^^
Here are some notes:
Inductive Reasoning
According to Answers:
Adjusting a course of action based upon a limited amount of information gathered. It is a process where one starts from a specific experience and draws inferences (generalizations) from it. For example, a salesperson, by observing a potential customer's reaction to the sales presentation, may induce what the customer's needs and personality are and what should be said to obtain the sale.
According to Wikipedia:
Inductive reasoning is the complement of deductive reasoning. For other article subjects named induction, see Induction (disambiguation).
Induction or inductive reasoning, sometimes called inductive logic, is the process of reasoning in which the premises of an argument are believed to support the conclusion but do not ensure it. It is used to ascribe properties or relations to types based on tokens (i.e., on one or a small number of observations or experiences); or to formulate laws based on limited observations of recurring phenomenal patterns. Induction is used, for example, in using specific propositions such as:
This ice is cold.
A billiard ball moves when struck with a cue.
...to infer general propositions such as:
All ice is cold.
All billiard balls struck with a cue move.
Strong and weak induction
Strong induction
All observed crows are black.
therefore
All crows are black.
This exemplifies the nature of induction: inducing the universal from the particular. However, the conclusion is not certain.
...
Weak induction
I always hang pictures on nails.
therefore
All pictures hang from nails.
Assuming the first statement to be true, this example is built on the certainty that "I always hang pictures on nails" leading to the generalization that "All pictures hang from nails". However, the link between the premise and the inductive conclusion is weak. No reason exists to believe that just because one person hangs pictures on nails that there are no other ways for pictures to be, or that other people cannot do other things with pictures. Indeed, not all pictures are hung from nails; moreover, not all pictures are hung. The conclusion cannot be strongly inductively made from the premise. Using other knowledge we can easily see that this example of induction would lead us to a clearly false conclusion. Conclusions drawn in this manner are usually over generalizations.
Teenagers are given many speeding tickets.
therefore
All teenagers speed.
In this example, the premise is built upon a certainty; however, it is not one that leads to the conclusion. Not every teenager observed has been given a speeding ticket. In other words, unlike "The sun rises every morning", there are already plenty of examples of teenagers not being given speeding tickets. Therefore the conclusion drawn can easily be true or false (perhaps more easily false than true in this case), and the inductive logic does not give us a strong conclusion. In both of these examples of weak induction, the logical means of connecting the premise and conclusion (with the word "therefore") are faulty, and do not give us a strong inductively reasoned statement.
Validity
Formal logic as most people learn it is deductive rather than inductive. Some philosophers claim to have created systems of inductive logic, but it is controversial whether a logic of induction is even possible. In contrast to deductive reasoning, conclusions arrived at by inductive reasoning do not necessarily have the same degree of certainty as the initial premises. For example, a conclusion that all swans are white is false, but may have been thought true in Europe until the settlement of Australia, when Black Swans were discovered. Inductive arguments are never binding but they may be cogent. Inductive reasoning is deductively invalid. (An argument in formal logic is valid if and only if it is not possible for the premises of the argument to be true whilst the conclusion is false.) In induction there are always many conclusions that can reasonably be related to certain premises. Inductions are open; deductions are closed. It is however possible to derive a true statement using inductive reasoning if you know the conclusion. The only way to have an efficient argument by induction is for the known conclusion to be able to be true only if an unstated external conclusion is true, from which the initial conclusion was built and has certain criteria to be met in order to be true (separate from the stated conclusion). By substitution of one conclusion for the other, you can inductively find out what evidence you need in order for your induction to be true. For example, if you have a window that opens only one way, but not the other. Assuming that you know that the only way for that to happen is that the hinges are faulty, inductively you can postulate that the only way for that window to be fixed would be to apply oil (whatever will fix the unstated conclusion). From there on you can successfully build your case. However, if your unstated conclusion is false, which can only be proven by deductive reasoning, then your whole argument by induction collapses. Thus ultimately, pure inductive reasoning does not exist.
Good Pdf of inductive and deductive reasoning
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