APHI 221 Different Forms of Inductive Reasoning - Generalisations, Analogies and Reasoning from General Principles

APHI 221 – Mrs AC Austin

Different forms of Inductive Reasoning – Generalisations, Analogies and Reasoning from General Principles

Let’s begin by reviewing what we have covered in the last couple of lectures

What is an argument? 

We know that an argument is made to address a specific problem, by offering a position and providing reasons for that position.  By definition an argument requires reasoning.

If someone makes an argument they are making an appeal to REASON. To make an argument you must be able to say – to support my conclusion I offer you reasons to support my conclusion.

Your reasons can be evaluated for their TRUTH or ACCEPTABILITY.

Your reasons can also be evaluated based on the RELEVANCE to the issue and whether they are SUFFICIENT.

So in order to make an argument:

1.  Your reasons should support a conclusion

2.  There should be a relationship between reasons and a conclusion

3.  There must be a connection between reasons and a conclusion

We have also learned that there are two common ways of making arguments – You can make a DEDUCTIVE ARGUMENT or you can make an INDUCTIVE ARGUMENT

A Deductive Argument is a type of argument where if the premises are true and acceptable then the conclusion must be a true conclusion.  Thus in a deductive argument the conclusion follows necessarily from the premises and inferences.

Deductive arguments can take the form of categorical syllogisms like the example below:

Ayanda is girl.  All girls are females.  Therefore Ayanda is a female.

A syllogism is a type of logical reasoning where the conclusion is deduced or derived from two linked premises.

Here’s another example: An apple is a fruit. All fruit is good. Therefore apples are good.

An Inductive argument is a type of argument where the strength or weakness of the conclusion is dependent on the strength of the premises. An Inductive argument works by gathering support in its premises leading to a probabilistic conclusion.  Thus in an inductive argument in an inductive, the premises are intended only to be so strong that, if they are true, then it is unlikely that the conclusion is false.

Inductive Arguments usually take the form of conditional or causal reasoning.  For example here below:

A pink flamingo was observed at the Small Craft Harbour, a pink flamingo was observed at the Durban Harbour,  pink flamingo was observed at Walvis Bay in Namibia,  a pink flamingo was observed at Fish Hoek in the Cape.  If all flamingos observed are pink then we can say with a degree of high probability that all flamingos are pink.

Causal Reasoning is a form of Inductive argument reasoning that allow us to determine which causes are most likely to be the reason behind an effect. A cause is something that brings an effect into existence. An effect is the result of something.

Today we will be looking into more detail at three forms of Inductive arguments – Genrealisations, Analogies, and Reasonging from General Principles. In these 3 types of Inductive arguments, we are asked to accept a conclusion because the situation, problem or issue is similar to another situation, problem or issue that we already know something about.

The first of these 3 forms of Inductive Argument is Generalisations.

GENERALISATION- is where we draw conclusions from a whole category based on specific cases or examples that we have from that category.  We take something we know in a specific instance and apply it, generalising it to a larger group.

Keep in mind though that generalisations do have the positive feature of helping us to form reasonable expectations about how people will react in certain situations, or what will happen in a certain situation.  

For instance – surveys and experiments are practical types of generalisations.  If we poll 600 people about whether we should stop selling guns on websites like Amazon or Ebay, and 90% of those polled say that we should stop selling guns on Amazon or Ebay, then we can extend that to statistic out of 6000 and 60 000 etc and say something like in a town of 60 000 people 54 000 would be opposed to guns being sold openly on Amazon or Ebay.  

Generalisations are often employed in scientific research.  For example a scientist may study a specific troupe of monkeys and their habits and social dynamics and generalise it to all  monkeys.

Even though generalisation typically tell us what is likely to happen in general – there is still room for exception.  

The extent to which we can apply generalisations ranges from “all the time” to “most of the time” or “often” all the way down to “sometimes.  This is when we call the form of inductive generalisation weak.  The argument suffers from Overgeneralisation.

Here are a few examples of arguments that lean on generalisation (take note that these may not be true or good inductive arguments from generalisation – but they are nonetheless examples of generalisations

• ·        Last week 4 of the accused standing trial for crimes related to violent hijackings told the judge that they were unable to pay for private lawyers as they could not afford it.  From this we can infer that people who violently hijack other people are very poor.
• ·        According to the statistics on crime in South Africa – in most instances where white farmers and families were murdered on their farms, the perpetrators were black young men.  From this we can infer that all black young men in South Africa want to murder white farmers and their families.
• ·        Of the 19 hijackers on Sept 11, 2001, 15 were Saudi Arabian Nationals.  I think we can safely conclude that Saudi Arabians are terrorists.
• ·        I have 4 Indian male friends ranging from 20 to 30 years old.  All of them have Golf GTI’s.  Don’t even bother trying to sell your Subaru to Priyesh, Indian men only buy Golf GTI’s.
• ·        I knew this guy who was a beggar.  He was capable of doing work and getting paid for it just like me, but he was irresponsible and lazy and spent all his time drunk. Don’t give your hard earned money to any beggars on the street. They will spend all your heard earned money on alcohol.
• In South Africa, many government officials have been exposed as corrupt officials who have used public money to enrich themselves personally.  From that we can say that all South African politicians are corrupt crooks, thieves and liars.

ANALOGIES

Analogies are good ways for us to think about what might happen in a new situation based on what happened in a similar one that we have some knowledge about.

So an analogy is when you make an example of something that is similar enough to something to make a comparison.  You are able to see the similarities between the two and then transfer your understanding of the earlier thing that you know something about to the new similar thing that is new.

John is like a rock.  - the comparison here is between a rock (something we have some understading about - the properties of rocks are that they strong, solid, steadfast) and John so(Something/somecsomen we dont know about He is strong, solid and steadfast. 

Arguing by analogy means that if you say “A is similar to B, then if  X is true for A, then X is also true for B.  For example – A cricket ball is round and it rolls, a soccer ball is also round so it should also roll.

Another example of an analogy would be something like:

·        Drug use is a matter of addiction and a breakdown in the impulse control mechanism in the brain. It's like overeating or alcoholism. It would be ridiculous to declare war on food or alcohol, so it's ridiculous to declare war on drugs.

Here is another famous analogy that Karl Marx wrote:  “Religion is the opiate of masses.”

 A Drug is something that makes people unmotivated, takes away their personal power and freedom and may ultimately kill them.   Religion is analogous to a drug so the conclusion we draw (by similarity) is that Religion makes people apathetic and unmotivated and stops them from coming into their full power as themselves.

An Analogy’s strength is judged by how similar the examples being compared are.  When you are presented with an argument by analogy you must closely examine the two situations being presented.

These are the questions you ask yourself to evaluate an analogical argument (inductive argument by analogy)

·        

How are they similar?

·        How are they not similar?

·        How important are these differences?

An important thing to note is that all analogies are imperfect.  The whole idea is that you are comparing two situations are not identical but fairly similar. Your job is to figure out whether they are sufficiently similar.

It is an error in reasoning when a person relies on a weak or false analogy.  An analogy where the two cases are similar only in a few ways is a weak one.  It may not be strictly speaking wrong but it is not strong enough support for the conclusion

·        Maria does not enjoy the taste of lettuce.  So Maria thinks she will not enjoy the taste of spinach either because they are both healthy and both are used to make a salad.

A false analogy is one which none of the important or relevant features are similar.  Although the two cases may be similar in other ways that aren’t relevant to the issue.  For example:

·        Soccer and Cricket are both played with balls – so if you’re good at soccer you would be good at cricket.

Note here that that being good at a sport has nothing to do with the tools or equipment needed to play that sport.

When you are trying to evaluate strong or weak Analogous arguments, you can ask yourself the following questions:

·        are the similarities relevant to the conclusion being made

·        are the differences significant enough to undermine the analogy

EXERCISE:

Here are some more examples of analogous Inductive Arguments – evaluate them to be strong or weak arguments from an Analogy – if you think they are weak – explain why with reference to similarity and relevance of premises and conclusions. (take note that the inductive arguments made here do not necessarily reflect the opinion of the compiler of these common analogies)

·        Since the world is similar to a clock in respect to its orderly design, and a clock has a maer, the world must also have a maker

·        In the natural word, in order for a species to survive, its members have to reproduce.  In most species there is a male and female and their coupling leads to reproduction.  We are natural too – therefore homosexuality is ethically and morally wrong.

·        Europa is a moon of Planet Jupiter. Europa has an atmosphere.  The earth has an atmosphere.  There is biological life forms on earth.  Since there is life on earth there must be life on Europa.

·        We should not blame the media for deteriorating moral standards. Newspapers and TV are like weather reporters who report the facts. We do not blame weather reports for telling us that the weather is bad.

REASONING FROM GENERAL PRINCIPLES

An Argument made when you are reasoning from general principles is the opposite of generalisations. In generalisations – you move from knowing things about a specific or few specific cases to a larger or general unspecific group.

Reasoning from general principles however, involves applying general principles to a specific case.

An argument from general principle takes something that is true or held to be true about the whole and applies it to a specific case that is determined to fall within the category of the whole.

For example:  Most Conservative Christian folk in South Africa have indicated support a legislation that would criminalise abortion.  Therefore if one had to run a poll asking people whether we should criminalise abortion, in typically Christian provinces like the Western Cape - where Sibongile a strong Christian lives, will vote to imprison women who choose to have abortions.

The strength of an argument based on the application of a general principle depends on how acceptable the principle is.  In addition – the strength of the argument is also based on the degree to which the specific case fits into the category, covered by the principle. 

For example:

Many people hold the general view that taxi drivers disregard traffic regulations. 

That in itself should be fine, but see what happens if you make the following argument. 

Since it is generally observed that all taxi drivers disregard traffic regulations, then Mbuyiseni who is a taxi-driver, must be a reckless, traffic law violating driver.

When a general principle is applied to a specific case that does not fit then the author has made an error in incorrectly applying the argument from general principles.

APHI 221 - Evaluating Premises and Conclusions - Validity, Truth/Acceptability, Relevance and Sufficiency

Transcript of Ep 1.4 - Premises and Conclusions - courtesy of  Center for Innovation in Legal Education (https://www.youtube.com/watch?v=OpNoCmNtP5c) and short class exercise.

MODULE LESSON 7 - APHI 221 – Philosophical Perspectives on Communication – Mrs AC Austin

Ep 1.4 Transcript (Center for Innovation in Legal Education)– Premises and Conclusions –

0:00            Evaluating Premises and Conclusions: An Overview.

0:03            So far ,you know that arguments are made up of a conclusion and the premises offered to defend or uphold it.  Some arguments are deductive, that is, if the premises are true and the former the argument is valid, then the conclusion has to be true and the argument is sound.

0:23            Other arguments are inductive. In an inductive argument if the premises are either true or at least acceptable, remember that means that their relevant to the issue at hand and provide sufficient justification, then the conclusion is likely to be true and we consider these inductive arguments to be strong

0:43            In questioning both types of arguments there are a number of evaluations you can make to determine the soundness or strength up the argument in this module you learn about two main ways to evaluate an argument first you'll hear about how to evaluate premises in and of themselves on their own merits then you learn how to evaluate the logical link that connects the premises to the conclusion

1:10            This module provides an overview of the key evaluation approaches you should use to assess

any argument you encounter later modules will dig deeper into each approach and explain how you can effectively use the techniques to evaluate different types of arguments

1:26            EVALUATING PREMISES TRUTH AND ACCEPTABILITY

Premises supply the evidence on which an argument is based and their strength can range from the strongest premises that are straightforward facts such as the Earth revolves around the Sun to weaker premises.

My personal opinions are value judgments – that can be like your friend saying “This music is awful”.  One standard for evaluating a premise is to determine whether it's true or false. 

1:54            We can use observed or empirical evidence, that is things we see touch hear smell taste and so on 1to figure out whether certain kinds of premises are true. Now it may not be easy to determine the truth of a premise. For a lot of early human history proving that the earth revolved around the son was quite difficult but we at least know how we're supposed to go determining its truth, which means proving or disproving the premise.  Sometimes while it may be possible in theory to actually observe the truth to the premise it may be, practically speaking, impossible to do so  - for example - take the claim that all swans are white.  In order to definitively prove this to be true we would be defined every single Swan on the planet to see what colour it is - a daunting task, especially considering more swans are being born all the time.  However we could rely on Swan experts conducting research involving as many Swan as is reasonable and investigating all aspects of swan biology to tell us an experts view on swan colour.  While we wouldn't prove that the premise was true,

we could judge it to be more or less acceptable.

 3:07           In addition to hard to prove empirical claims there are other premises that cannot be evaluated on whether they're true or not.  Premises that relate to aesthetic moral or ethical claims fall in that category.  Opinions in value judgments represent personal cultural communal social and religious perspectives and beliefs.  These by their very nature cannot be proven or disproven, however that does not mean that they cannot or should not be subjected to scrutiny and evaluation to determine whether they provide acceptable reasons for agreeing with the particular argument.

3:47            Throughout your personal academic and professional life you grapple with the number of arguments based on opinions or value judgments, you should resist the temptation to simply say “well everyone's entitled to their own opinions” and to accept all such argument is equally plausible.  There are many important issues and problems about which which you'll find serious disagreement.

4:09            Critical thinking is meant to arm  you with the tools and resources to carefully consider those arguments, assess the relative strengths and weaknesses and come to an informed and considered opinion of which one you believe to be true or reasonable.

4:25            RELATING PREMISES AND CONCLUSIONS – VALIDITY, RELEVANCE AND INSUFFICIENCY

4:29            It's not enough to simply evaluate individual premises to determine their truth or acceptability, consider the following argument: “The sky is blue, therefore I should wear sunglasses when I'm outside!”. Now it is true that the sky is blue, but a reasonable person might wonder what in the heck does the sky being blue

have to do with wearing sunglasses?   The truth of the premise does not necessarily guarantee that you're dealing with a valid argument.  Instead consider an argument that says: “the Sun is bright I should make sure to wear my sunglasses today”.  Now this argument seems much stronger and it is stronger because

1)  the premise is or can be determined to be upon visual examination true and

2)  there's a reasonable connection between brightness and the wearing of sunglasses. Remember that deductive arguments are those were the truth to the premise can lead to a valid conclusion so when evaluating deductive arguments you should look for whether the former the argument is valid.

5:36            A deductive argument has a valid form if it is impossible for the premises to be true and the conclusion to be false so to illustrate this, consider an example of an argument with an invalid form:  Your friend tells you the old business building is worn out and it's unsafe so we should tear it down for the safety of the students.

5:58            While the premise is that the building is old and unsafe are true they don't necessarily lead to the conclusion that the building has to be torn down.  One obvious alternative is that repairs could be made to make the building safe.  In this case even though the premise is true it's still possible for the conclusion to be false because it's not necessarily related to the premise.

6:22            Now think about this alternative example that has a valid form:  Your friend says the old business buildings are unsafe because it doesn't have a fire alarm system, which makes it unsafe so we should install a fire alarm system for the safety of the students.  Here clearly if the premise is true then the conclusion

must also be true.  For inductive arguments two separate standards must be used to evaluate arguments logical validity, relevance and sufficiency.  Instead of the true or not standard used for deductive arguments. Inductive arguments rely more or less on acceptable premises to make them stronger or weaker.  This makes the relationship between the premises and conclusions much more complicated.  It's not the case that a premise you judge to be true can serve on its own to defend a conclusion.  Instead you're dealing with premises that are often opinion rather than fact and these premises have a range in their acceptability.

7:24            So one thing you must do in evaluating an inductive argument is to first figure out if the premises are relevant to the issue at hand and the conclusion that strong.  Imagine your professor asked the class:  “Should I hold a review session before the midterm exam?”  Your classmate responds by saying:  “No you shouldn't, the text book for this class was really expensive now the claim that the textbook was expensive may be a perfectly acceptable claim but it doesn't have anything to do with the conclusion that there should not be a review session!  Consider an alternative response:  “No you shouldn't, my friends are in the other section in this class and they aren't having a review session, I don't think it would be fair if we have one.

8:10            In this case you will still want to evaluate the acceptability of the premises about fairness but it is clear that there is a connection between the premises and the conclusion.  In addition to figuring out whether the premises are relevant you must also assess whether they are sufficient that means you must think about whether the claims made premises or enough to justify the conclusion.

8:34            Let's go back to the second response on the midterm review question -the one we're classmate says “ no we shouldn't my friends in the other section and they are not having a review session.”  Let's say you determine the following things

1) if it is true that the other section is not having a review?

2) is fairness between sections is a reasonable and acceptable thing to be concerned about ?

3) is what's happening in the other section is relevant for your class?

9:01            So is that it?  Do you accept your classmates argument is strong enough or might you instead say:   “well I see your point it is important to be fair and I feel bad that the other class won't get to have a review but why should we suffer too - that's not a good enough reason”.  Essentially you're saying that your classmates premises are not sufficient reasons to accept his conclusion that is it's not enough to justify the conclusion.

9:29            Now you should have some idea of how to go about evaluating deductive and inductive arguments - you should examine the premises themselves and try to determine whether they're true and acceptable then

you need to consider the connection between premises and conclusions are the premises relevant to the issue and the conclusion reached or the sufficient to justify that conclusion.  Knowing to ask these questions

9:53is an important step in critical thinking.  In later modules you learn more about how to answer these questions.

_____ End of Transcript________

Exercise:  Evaluate the following arguments, state whether they are deductive or inductive arguments, and if they are valid, sufficient and relevant.

• ·        The CEO of this company has taken money collected by the staff for improvements to the staff rest area, and used it build himself a big, fancy and luxurious office.  He has fired the staff who have questioned his misbehaviour. He has replaced the fired staff with his family members who stand to gain luxurious offices of their own.  The CEO will enrich and benefit himself now without any interference from the staff representatives.  Therefor we should stop him and vote to remove him from office.

• ·        It’s dangerous to walk alone at night.  Daytime social events are boring.  During the day you can really take a good look at the beautiful surroundings.

• ·        The streets are wet outside, if the streets are wet it probably indicates the possibility of rain.  I should take my raincoat and wear gumboots.

• ·        Bread causes cancer.  My aunt had cancer, she ate bread.  Therefore Bread causes cancer.

• ·        You say:  “You shouldn’t take the MMS Supplement, it asks you to mix chlorite with an acid solution such as citric acid – this produces a mixture called chloride dioxide.  Chloride Dioxide is the chemical name for bleach. You are literally and willingly drinking bleach when you take the MMS supplement.  Bleach is toxic and it will make you sick.”  Your friend answers you with this argument:  “Andrew the physiotherapist takes MMS, so do I and so does my friend Colleen”      

APHI 221 - Deductive and Inductive Reasoning

LESSON 6 – APHI 221 : Deductive and Inductive Reasoning  – Class Handout - transcript of https://www.youtube.com/watch?v=BwtCScUoL_w - courtesy of Center for Innovation in Legal Education

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