LESSON 6 – APHI 221 : Deductive and Inductive Reasoning – Class Handout - transcript of
Deductive and Inductive Arguments
0:00 Now that you’re familiar with the basic structure of arguments where there are always one or premises and a conclusion, Let’s look more closely at different types of arguments.
0:12 Remember—making an argument is all about staking out a position on a specific problem or issue. Now think about all the different types of problems one could confront. There are problems in everyday life: where should we eat dinner? Which house should we buy? Which school is better for my kids?
0:29 There are problems that college students like you deal with: how many classes should I take next semester? What should I major in? Should I get an internship or study abroad? There are problems in business: do we need to hire another employee? What database software should we use? How should we design this marketing campaign? There are political problems: what's the best income tax structure? What should our energy policy be?
0:55 As people make arguments to resolve these (and many more) issues, they may offer many different types of premises in defense of their position. We're going to dig deeper into two kinds of arguments:
1:07 DEDUCTIVE ARGUMENTS AND INDUCTIVE ARGUMENTS.
To get started consider the following two examples: n each case there's a question or problem to be resolved, and examples of possible premises that could be offered as part of an argument to address that question.
1:23 In the first example, the problem is that you and some friends are trying to decide where you should go for dinner the Red Iguana or Cafe Trang. There are two premises:
1)Red Iguana is open until 10 p.m.; Cafe Trang is only open 'til 9pm.
2) The Red Iguana has the best Mexican food in the area.
1:44 In another example, the problem is trying to answer the question,how many classes should I take next semester? Again there are two premises:
1) Tuition for 12 credit hours will cost $3,100; tuition for 15 credit hours will cost $3,700.
2) It's better to take more classes every semester so that you can get done faster.
In both examples, the first promise offered was a FACT that can be proven to be true or false. You can look up the hours for each restaurant or the tuition cost for different numbers of credit hours. However, the second premise offered was an OPINION that cannot be proven to be true or false. People may disagree on whether the Red Iguana has the best Mexican food or if it's the best idea to take a lot of classes to finish your degree more quickly.
2:36 Facts and opinions have different relationships with the conclusions that are drawn, and result in different types of arguments. For example let's say it's currently 9:05pm when your friend asks, "Should we eat at the Red iguana or Cafe Trang?". You reply, "Well Cafe Trang closed at 9pm but the Red Iguana is open until 10, so we need to go to the Red Iguana."
2:59 If you're correct - if the facts are true then your conclusion HAS to be TRUE. Your only option is Red Iguana. An argument in which the conclusion necessarily follows from the premises - if the premises are true then the conclusion is also true. This is a DEDUCTIVE argument.
On the other hand, what if it's only 8pm? Both restaurants are still open and available. When your friend asks which one you should choose, you reply, "Well Red Iguana has the best Mexican food in the area. Cafe Trang is okay, but it's not that great. We should go to the Red Iguana."
3:39 In this case the decision to go to the Red Iguana cannot be said to be "true." The conclusion does not logically follow from the premise. Just because you think the red iguana has better food does not mean you - or your friend - must choose it. You've simply tried to build a case for why it's the better option. An argument in which acceptance of the conclusion depends on the strength of the premises - in which the premises do not prove but merely support the conclusion - is an INDUCTIVE argument.
4:10 Deductive Arguments.
Remember, a deductive argument is one in which the conclusion necessarily follows from the premises if the premises are true the conclusion is true. What if you don't like the conclusion - if say you really wanted to go to Cafe Trang? Well, it's too bad the promises don't support that conclusion.
4:30 In our example, if the restaurant is indeed closed, you're outta luck. The conclusion that you should go to the Red Iguana, in some ways, states the obvious - if you only have two options and one of those options is closed (the premises of the argument), then it really goes without saying that you must go to the other one. It doesn't matter if you don't like the conclusion (say for example that you really wanted to go to Cafe Trang instead) - unless you can disprove one of the premises of the argument, you have no choice but to accept the conclusion. Anytime you're dealing with deductive arguments - whether you're evaluating an argument someone else has made or constructing your own argument, you shouldn't start with the conclusion.
5:13 When you evaluate someone else's argument, you must avoid “jumping to" the conclusion right away and deciding, without consideration of the argument as a whole, whether you agree with it or not. Similarly, when you make your own argument, you must avoid picking out your conclusion ahead of time and then finding ways to justify it. Instead, you need to start by examining or uncovering the premises (reasons and evidence), then follow where those premises lead - what logical conclusions can you draw from the evidence?
5:45 So, when you evaluate a deductive argument, you need to ask to questions:
1) are the premise is true? and
2) is the form of the argument valid?
If the answer to both questions is YES, then you have a sound argument. The first question is fairly simple, although it does not mean that it will always be easy to answer.
6:09 Premises in deductive arguments are facts that can, at least in theory, be proven true or false. They refer to condition or states of things - is the restaurant closed, for example. In this case it's pretty easy to find out if that premise is actually true or not - you could drive to the restaurant and find out. The second question - whether the argument is valid or not - refers to the logical structure.
6:35 An argument is valid if it's not possible for the premise to be true AND the conclusion to be false. In our example, the premise tells us that there are two restaurants to choose from and one of them is closed. The conclusion, then, is that we must go to the other - open - restaurant. If that premise is true, then it is not possible for the conclusion to be wrong - it MUST be true as well.
7:03 Inductive arguments.
As you heard, an inductive argument is one in which the conclusion is supported (but not proven), to a greater or lesser degree, by the premises. The conclusion goes beyond the premises - the conclusion that you should go to Red Iguana is not logically implied by the statement - that it has the best Mexican food. Maybe your friend doesn't really feel like eating Mexican food; in that case, he could offer a counter-argument with reasons why you should go to Cafe Trang instead.
7:31 In the case of inductive arguments, the evaluation process has to be different than deductive arguments. You cannot necessarily "prove" or "disprove" the premises, nor can you determine if the premises lead inevitably to the conclusion or not.
7:47 Instead you must ask the following questions:
1) are the premises true or at least acceptable?
2) are they relevant to the issue at hand?
3) are the premises compelling enough
to justify the conclusion?
8:08 Your answers to these three questions will help you evaluate how STRONG or WEAK the argument is. So let's take a closer look at these questions.
8:17 First, with inductive arguments you may find premises that are not easily assessed as true or false; rather than facts, you will often have matters of opinion. The assertion that the Red Iguana has the best Mexican food is a matter of opinion over which people may disagree. In evaluating this argument, you need to consider whether this premise is ACCEPTABLE - can you accept it as reasonable? In this case, you might look at restaurant reviews or publish lists of the "Best of Salt Lake City." You might poll your friends to see how many people agree with this opinion. Second, you need to decide whether that premise - in this case the opinion that the Red Iguana has the best Mexican food - is relevant that is is the premise related to the issue at hand?
9:07 Here, it does seem relevant to consider the reputation of a restaurant when deciding where to eat. However if it's said that we should go to the Red Iguana because it has the nicest parking lot, you might question whether that reason is really relevant to deciding where to eat.
9:23 Finally, you need to consider whether the premise is sufficient to justify the conclusion - is the opinion that the Red Iguana has the best Mexican food really enough to base a decision on? Are there other things you might want to consider - for example, how long is the wait for a table? 1How good is the service? Evaluation of inductive arguments falls into a range from weak(er) to strong(er). If you determine that the premise is highly acceptable, is relevant to the issue at hand, and is enough of a reason to base your decision on, then you would conclude that the argument is fairly strong.
10:01 If you find that the promise is highly acceptable and it is relevant, but it's not really sufficient enough to make a decision based on that premise alone, then you might say the argument is "so-so" - not weak, 4but not strong enough. You can improve the argument by offering more promises 9to support it - "Yeah, the food’s great, and so is the service. Plus I just called and they said we could get a table in 10 minutes."
10:27 Or alternatively, you might offer a counter-argument = "Sure, the food is good, but their service is awful and there's always a really long wait." As you may have figured out, inductive argument can take on many different forms.
There are: Generalizations are where arguments involve making a general claim based on limited or specific evidence (for example drawing conclusions about the opinion of the nation as a whole based on public opinion polls of some smaller number of people.)
10:55 Analogies are similar to generalizations and that they involve proposed similarities; when making an analogy, you draw conclusions about one situation based on what you know about another - allegedly similar - situation.
General principles are the opposite of generalizations. These arguments involve applying general principles (for example, qualities a group of people are assumed to have) to a specific case (individual member of that group.)
Causal Reasoning arguments offer what is determined to be the best possible explanation for why something has happened; they offer an argument that one thing necessarily lead to another happening.
11:36 Now you should have some idea what deductive and inductive arguments are, and how they differ. Many of the topics introduced here will be discussed in more detail later. You will learn more about how to evaluate the truth and acceptability of premises, as well as how to assess the relevance and sufficiency of those premises. You will also learn how to use causal reasoning to both develop and assess arguments.
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Examples of Inductive Reasoning.
There are varying degrees of strength and weakness in inductive reasoning, and various types including statistical syllogism, arguments from example, causal inferences, simple inductions, and inductive generalizations. They can have part to whole relations, extrapolations, or predictions.
Some examples of inductive reasoning include:
-Jennifer leaves for school at 7:00 a.m.
Jennifer is always on time.
Jennifer assumes, then, that she will always be on time if she leaves at 7:00 a.m.
-The cost of goods was $1.00.
The cost of labor to manufacture the time was $.50.
The sales price of the item was $5.00;
so, the item always provides a good profit.
-Every windstorm in this area comes from the north.
I can see a big cloud of dust caused by a windstorm in the distance;
so, a new windstorm is coming from the north.
-Bob is showing a big diamond ring to his friend Larry.
Bob has told Larry that he is going to marry Joan.
Bob has bought the diamond ring to give to Joan.
-The chair in the living room is red.
The chair in the dining room is red.
The chair in the bedrrom is red.
All chairs in the house are red.
-Every time you eat peanuts, your throat swells up and you can't breath.
So, you are allergic to peanuts.
-All cats that you have observed purr.
Therefore, every cat must purr.
-Two-thirds of the students at this college receive student aid.
Therefore, two-thirds of all college students receive student aid.
-All of the girls in the class have naturally dark and curly hair,
therefore all girls in this neighborhood have dark and curly hair.
-Michael just moved here from Cape Town.
Michael has red hair, therefore people from Cape Town have red hair.
-Children in that house scream loudly when they play in their bedroom.
I can hear children screaming in that house,
therefore the children must be playing in their bedroom.
-All chickens that we have seen have been brown;
so, all chickens are brown.
-All cars in this town drive on the right side of the street.
Therefore, all cars in all towns drive on the right side of the street.
-John is an excellent swimmer.
John's family has a swimming pool.
John's sister Mary must also be an excellent swimmer.
-All basketball players in your school are tall,
so all basketball players must be tall.
-All brown dogs in the park are small dogs.
Therefore, all small dogs are brown.
- All children in the day care center like to play with Legos.
All children, therefore, enjoy playing with Legos.
-Ray is a sumo wrestler.
All sumo wrestlers weigh more than 170kgs.
Ray weighs more than 170kgs.
-All observed houses on the South Street are falling apart.
Sherry lives on South Street. Her house is falling apart.
Now you can see how inductive reasoning works and the types of things you can discern using inductive reasoning.
Deductive-reasoning can be described as
-Inference in which the conclusion cannot be false given that the premises are true.
-Inference in which the conclusion is of no greater generality than the premises.
Deductive reasoning involves drawing conclusions from specific statements called premises.
Suppose that you wanted to find a fruit to eat. You look through the refrigerator and find a celery stick, a Granny Smith, and a cup of beans. You know that neither celery nor beans are fruits. You also know that all apples are fruits, and a Granny Smith is an apple. Therefore, the Granny Smith has to be a fruit.
This is an example of a syllogism, a form of deductive reasoning.
Deductive reasoning is a type of logic where general statements, or premises, are used to form a specific conclusion. The other type of deductive reasoning is conditional reasoning.
Syllogisms
Syllogisms are deductive arguments that are written in the form:
A is B
C is A
Therefore, C is B
Let's take the example above. If we broke down the syllogism into premises and conclusions, we would get:
Premise: All apples are fruits.
Premise: A Granny Smith is an apple.
Conclusion: Therefore, a Granny Smith is a fruit.
According to the first premise, all items that are classified as apples are also classified as fruits. According to the second premise, Granny Smith is classified as an apple. The first premise is a general statement, while the second premise refers to a specific case. The conclusion says that a Granny Smith has to be a fruit because of its inherent properties as an apple. This deductive argument is also valid, which means that the conclusion necessarily follows from the premises. So, does a valid deductive argument mean that the premises and conclusions are true? Suppose I formed this deductive argument:
Premise: All dogs have long ears.
Premise: Puddles is a dog.
Conclusion: Therefore, Puddles has long ears.
Given the premises that all dogs have long ears and Puddles is a dog, it is logical to assume that Puddles has long ears. After all, in this example, long ears are an inherent quality of dogs. This argument is valid.
Does it mean it is also true?
Not all dogs have long ears. Certain breeds, like Yorkies or pugs, have small ears. Because the conclusions are based off the premises and one of the premises is not true, it follows that the conclusion is not true, even though it is valid. You can see from this example that if one of the premises is not true, the conclusion is also not true.
Some more examples of deductive reasoning are listed here below
-All men are mortal.
Joe is a man.
Therefore Joe is mortal.
-Bachelor's are unmarried men.
Bill is unmarried.
Therefore, Bill is a bachelor.
-To get a Bachelor's degree at Utah State University, a student must have 120 credits.
Sally has more than 130 credits.
Therefore, Sally has a bachelor's degree.
Conditional Reasoning
So what is conditional reasoning? If the first two statements are true, then the conclusion must be true. Conditional reasoning uses if-then statements that are true to form a true conclusion. The conclusion can be either valid or invalid, even though the premises are true.
- If it rains, then the streets will be wet.
- the streets are wet, therefore it must have rained.
EXERCISE
Read the following arguments and determine whether they use inductive or deductive reasoning:
1. Since today is Friday, tomorrow will be Saturday. _____
2. Since it snowed every New Year's Day for the past four years it will snow on New Year's Day this year. _____
3. A child examines ten tulips, all of which are red, and concludes that all tulips must be red.____
4. If an isosceles triangle has at least two sides congruent, then an equilateral triangle is also isosceles. _____
5. Sandy earned A's on her first six geometry tests so she concludes that she will always earn A's on geometry tests. _____
6. If 5x = 25, then x =5. _____ Choose the number that would be next in the pattern:
2,4,6,____,10,12 Choices: 7, 3, 14, 8
Answer Key
1. deductive reasoning
2. inductive reasoning
3. inductive reasoning
4. deductive reasoning
5. inductive reasoning
6. deductive reasoning
7. First notice that the numbers are getting bigger. That means that number 3 cannot be the right answer. Then notice that the numbers are even. So 7 cannot be the answer. Then notice that the number has to come between 6 and 10. That means 14 is not the answer. 8 is the answer – deductive reasoning
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