Strong uncogent inductive argument examples

Unit 2 Assignment Philosophy

The following assignment tests the student’s ability to discriminate real arguments from mere opinions, recommendations, or mere statements.

1. Read the 10 passages (see attachment) and decide whether they are arguments.

2. Explain why you think they are/are not arguments.

3. If you think a passage is an argument, write it in argument form numbering the premise(s) and labeling each premise using the capital letter P, and the conclusion using the capital letter C.

4. If the argument is an enthymeme, supply the missing premise or conclusion. 5. Upload as Word document.

LOGIC

Logic can be a challenging subject; it takes hard work and patience to master the skills necessary to excel at logic. Students often question the value of studying logic. They often fail to see how studying logic can be useful in "real life."

Consider an analogy: many people go to the gym and walk or run on the treadmill, lift weights, and more. Why? After all, with a few exceptions, "real life" is not about treadmills, barbells, and elliptical machines. However, working out helps building and maintaining the muscles necessary to perform many other activities and staying in good health.

Studying logic is in many ways the same. It keeps the brain healthy and sharp. As a result, it enables good thinking and good writing—two of the most important skills for a college student.

LOGIC – DEFINITION, AND MORE

Logic is a science, the science that studies the principles and concepts of good reasoning.

This implies that there is a distinction between good and bad reasoning.

LOGIC THE SCIENCE OF ARGUMENTS

Different sciences, biology, mathematics, geology, and more, study their respective subject matters. Logic studies arguments. Arguments are the subject matter of logic.

An argument is an oral or written presentation of reasoning used to show or prove a point.

For example:

1. US presidents always have been men. 2. Men by nature are competitive and belligerent, women compassionate and caring. 3. But competition and war have led us to many issues—to mention a few examples, to social and economic

inequality, the neglect of public schools, and a disastrous health system. 4. If we want to make "America great again", we should allow a woman to become president. 5. Therefore, in the next elections you should vote for a woman.

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In the above example, a point is expressed—namely, "5. In the next elections, you should vote for a woman." This statement is called conclusion. Statements 1-4 support the conclusion.

ARGUMENT DEFINITION:

An argument is a group of premises (at least one premise) in support of a conclusion.

PREMISE DEFINITION:

A premise is a statement capable of being true or false.

"Fetch me a bagel!" is neither true nor false, and thus it cannot be a premise.

"Joe is my dog." is either true or false, and thus it is a premise.

"Chocolate truffles are high in calories." is a premise.

"Let's go to a movie tonight." is not a premise.

"Politicians always tell the truth." is a premise.

"Where is Paducah?" is not a premise.

CONCLUSION DEFINITION:

A conclusion is also a statement capable of being true or false, but a special statement. It is the main point of the argument, that is, the statement that is claimed to follow from other premises (statements).

HOW TO UNDERSTAND/RECOGNIZE AN ARGUMENT

When you read a passage or hear someone give a speech, to determine whether that person is formulating an argument ask yourself, "What's the point? What does the speaker want to persuade me to believe?" If you can identify a specific point in a speech or written passage, such a speech or passage is an argument.

Also you can spot the conclusion as it is often preceded by certain clue words, such as Therefore, Thus, It must be deduced that, So, Consequently…

On the other hand, premises often begin with these words: Since, Because, For, Given that…

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ARGUMENT FORM

People give arguments in the forms of a speeches, essays, books, and articles. Furthermore, they do not necessarily start with premises and end with a conclusion. Often people start with a conclusion or even omit the conclusion or omit the premises. It is, therefore, your job to sort out an argument and write it in argument form: number the premises and the conclusion and place the conclusion at the end as such:

1. All flowers are plants. (Premise 1) 2. All Roses are flowers. (Premise 2) 3. Therefore, all roses are plants. (Conclusion)

SUPPLYING MISSING PARTS – ENTHYMEMES

As I stated above, often arguers omit parts of an argument, premises or the conclusion. An argument that is missing parts is known as an enthymeme:

1. All chemists are scientists. 2. So Joe is a scientist.

Clearly, one of the premises is missing: "Joe is a chemist."

1. Aliens built all bridges in NY State. 2. Brooklyn is in the State of NY. 3. The Brooklyn Bridge is in Brooklyn!

Here the conclusion is missing: Aliens built the Brooklyn Bridge

TEST YOUR KNOWLEDGE: WHAT'S MISSING IN THE FOLLOWING?

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- The use of condoms is completely unnatural. They have been manufactured for the explicit purpose of interfering in the natural process of procreation. Therefore, the use of condoms should be banned.

- God created the world. The world is good.

- You're not 21, and you must be 21 to drink in this state.

- You should vote for Congressman Smith. He's the kind of representative who cares about people.

- You can't vote; you haven't registered.

- Most major religions include a belief in a god. So, Confucianism must include a belief in a god.

- People enjoy imitations. Thus, they enjoy looking at photographs.

IN SEARCH FOR A GOOD ARGUMENT

What's a good argument? A good argument has 2 components:

1. True premises. 2. A conclusion that follows from the premises in either of these two ways:

a. Necessarily (deductively).

b. Very likely (inductively).

Since the conclusion of an argument can follow from the premises necessarily or very likely, there are two different kinds of arguments: deductive and inductive.

DEDUCTION VS. INDUCTION

As we have learned an argument is defined as a group of statements (premises) given in support of a conclusion.

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Thus, the premises may support the conclusion either necessarily or probably, or fail to support the conclusion.

Example:

1. If you are in Brooklyn, you are in the USA. 2. You are in Brooklyn. 3. Therefore, you are in the USA.

In the above argument, the conclusion is logically necessary. Given the premises, it is not merely probable that you are in the USA, but rather necessary.

So, the premises of the above argument support the conclusion by logical necessity. We call this type of argument DEDUCTIVE.

DEFINITION: An argument is deductive when the premises are intended to support the conclusion necessarily.

Thus if the premises succeed in supporting the conclusion necessarily, a deductive argument is called a valid argument.

If the premises of a valid argument are true, the argument is called a sound argument. Sound arguments are good arguments because they have true premises and a conclusion that follows necessarily.

If the premises of a valid argument are false, but they support the conclusion necessarily, we call that argument unsound. Here is an example:

1. Clouds are made of cheese. 2. Cheese can be eaten. 3. Therefore, clouds can be eaten.

The above argument is extravagant. However, its logical structure is valid irrespective of the falsity of its premises. Thus, it is a valid argument, but unsound.

Next, consider this argument:

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1. If you are in Brooklyn, you are in the USA. 2. You are in the USA. 3. Therefore, you are in Brooklyn.

In the above example, the premises claim to support the conclusion, but they fail! Even if the premises are true, the conclusion can still be false. Just because you are in the USA does not mean you are in Brooklyn. So the conclusion that you are in Brooklyn does not follow at al!

When the conclusion does not follow at all, we call such argument INVALID.

Premises are not always intended to support the conclusion by logical necessity. Consider this argument:

1. For the past 10 years it has snowed in January. 2. This January it has snowed. 3. Therefore, it will snow next January.

In the above example, the premises are not meant to support the conclusion by logical necessity. Rather, the arguer intends to offer strong reasons to believe that snowing will occur next January.

Thus, when the premises do not imply the conclusion, when the conclusion is not necessary but rather possible, an argument is referred to as inductive.

If the conclusion is very likely to be the case given false premises, such an argument is referred to as inductively strong and uncogent (This is not a good argument).

If the conclusion is very likely to be the case given true premises, such an argument is referred to as cogent (this is a good argument).

If the conclusion is not likely to be the case given false premises, such an argument is referred to as weak and uncogent. (This is not a good argument).

If the conclusion is not likely to be the case given true premises, such an argument is weak and uncogent. (This is not a good argument).

A strong argument that has true premises is a cogent argument. This is a good argument.

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REVIEW:

Deduction:

Conclusion follows necessarily + true premises = Deductively valid and sound (Good argument).

Conclusion follows necessarily + at least 1 false premise = Deductively valid and unsound.

Conclusion does not follow at all (even with true premises) = Deductively invalid.

Induction:

Conclusion follows very likely + true premises = inductively strong and cogent. (Good argument).

Conclusion follows very likely + at least 1 false premise = inductively strong and uncogent.

Conclusion does not follow likely + true premises = inductively weak and uncogent.

Conclusion does not follow likely + false premises = inductively weak and uncogent.

Thus a good deductive argument is a sound argument.

A good inductive argument is a cogent argument.

DEDUCTIVELY VALID

DEDUCTION: An argument is deductive when it is presented in a form that claims the conclusion to be deduced from the premises. Like in math if I say that 2+2=4, I mean that 4 must be the only possibility when I add 2 + 2.

If I say 2+2=5 obviously 5 is not deduced from 2+2. However, in making the claim '2+2=5' I do not mean that 5 is probable. I make a categorical statement that 5 is deduced from 2+2.

Thus, in logic, an argument is deductive when the conclusion is claimed to be the natural outcome of the premises; an argument is inductive just if the premises establish a probability that the conclusion is the case (the conclusion follows probably).

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VALIDITY:

Validity is a property of only deductive arguments. An argument is valid when and only when it is presented in a form that claims the conclusion to be deduced from the premise—and in fact, the conclusion does follow from the premises.

SOUND = DEDUCTIVE + VALID + TRUE PREMISES

When an argument is deductively valid (the conclusion follows necessarily from the premises) and the premises are true, we call it a Sound argument:

1. All humans are mortal. 2. Nancy is human. 3. Therefore, Nancy is mortal.

1. All US presidents are politicians 2. Trump is our current US president. 3. Therefore Trump is a politician.

1. All physical objects occupy space. 2. My book is a physical object. 3. Therefore, my book occupies space.

1. Citytech is either in China or In Brooklyn. 2. Citytech is not in China. 3. Therefore, Citytech is in Brooklyn.

A deductive argument is INVALID when its conclusion does not follow at all.

1. If it rains my car is wet. 2. My car is wet. 3. It follows that it rains.

1. My uncle is 85 years old. 2. My uncle likes spaghetti. 3. Therefore, NYC College of Technology is in Brooklyn.

1. If you are eating you have food. 2. You have food. 3. Therefore you are eating!

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1. All bachelors are males 2. Joe is a male. 3. It follows that Joe is a bachelor.

1. All politicians are liars. 2. All used car salesmen are liars. 3. Therefore all politicians are used car salesmen.

1. All ants are insects. 2. All mosquitoes are insects. 3. Therefore, all ants are mosquitoes.

The above arguments are INVALID because their conclusions are not granted by the premises; or, they neither follow necessarily nor probably—they just don't follow! Any argument with the same form is invalid.

INDUCTION

On the other hand, INDUCTIVE arguments have a different nature. The conclusion of an inductive argument is never deduced from the premises, but rather inferred from the premises. Here is what I mean: if I tell you that in my pocket I have a triangle, knowing that all triangles have three sides, you deduce that the triangle in my pocket has three sides. Imagine each one of us has a triangle in his or her pocket; I ask you to take it out and look at its color and it turns out that most of them, or all of them, are red. Now based on this information, you could never know with absolute certainty that the triangle in my pocket is red too. But considering that most or all triangles are red, you may infer that my triangle is red. That is to say, there is a good chance that it is red.

Inductive arguments have the following characteristics:

1. The premises and the conclusion are all empirical propositions (observations/experiences). 2. The conclusion is not claimed to follow by logical necessity, but probably. 3. The premises do not imply the conclusion. (The conclusion does not follow by logical necessity). 4. The conclusion is inferred from the premises based on the assumption that the regularities described in the

premises will persist. 5. Terms such as probably, in all likelihood, and most likely are often used in inductive arguments.

There are 3 kinds of inductive arguments:

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1. Inductive Generalizations. 2. Arguments from Analogy. 3. Causal Arguments.

1. INDUCTIVE GENERALIZATION

To move from a sample to a general conclusion about a population.

An argument of this type involves a certain number of observations of an object or event.

I may observe that a desk is brown.

The desk is my sample.

The population is what I decide: All the desks in my office, in my building, in north America…

For example:

1. This desk is brown. 2. That desk is brown. 3. Therefore, all desks are brown.

1. All the teachers we interviewed at St. Francis College are underpaid. 2. Therefore, all teachers at St. Francis College are underpaid.

1. All the teachers we interviewed at St. Francis College are underpaid. 2. Out of 550 teachers, 450 teachers were interviewed. 3. Therefore, all teachers at St. Francis College are underpaid.

1. Every swan I've seen was white. 2. Therefore, all swans are white.

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1. 90 % of Citytech students are females. 2. Therefore, the first person I'll run into in the hallway is a female.

1. There are 1000 marbles in a jar. 2. I take one and it's red. 3. Therefore they're all red.

In all the above examples, assuming that the premises are true, it is possible that the conclusion is true.

Inductive generalizations can become strong, thus even cogent, if the number of samples observed increases or the number of the population decreases.

1. There are 1000 marbles in a jar. 2. I take 980 and they're red. 3. Therefore they're all red.

1. There are 50 marbles in a jar. 2. I take 48 and they're red. 3. Therefore, they're all red.

1. I've seen things fall to the ground when dropped. 2. Therefore, upon release, all objects will fall to the ground.

2. ARGUMENTS FROM ANALOGY

Using an analogy between two or more things (also people, events, etc.) in order to support a conclusion about one of them.

An analogy is a comparison between two objects, people, events, etc.

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Analogies are used to explain or claim that two distinct things are similar in some respect.

For example:

1. Capitalists are like vampires. 2. Vampires are dangerous. 3. Therefore capitalists are dangerous.

1. Like the Earth, Europa has an atmosphere containing oxygen. 2. Planets that have an atmosphere that contains oxygen might have life. 3. Therefore, there might be life on Europa.

1. The novel Pass The Salt is very boring. 2. The novel Smell My Feet is supposed to have a similar plot to Pass The Salt. 3. So, probably Smell My Feet is also very boring.

1. Most philosophers are single, liberal, and untidy. 2. Robert is a philosopher who is single and is liberal. 3. Therefore Robert is probably untidy.

1. Any mechanism like a watch is the product of intelligence. 2. The universe is a complex mechanism. 3. Therefore, the universe is also the product of intelligence.

1. The state is like family. 2. You must respect your family. 3. Therefore, you must respect the state.

3. CAUSAL ARGUMENT

Arguments that rely on the concept of causality.

Causal Arguments contain causal statements as either a premise or the conclusion.

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Causal statements (typically) state that an event A is the cause of another event B

Or that B is caused by A.

But we mean different things by "cause": Sometimes we mean that one thing brings about another; sometimes that one thing is required for the other to occur; sometimes that one thing contributes to the occurrence of the other.

A precise way to characterize these different senses of cause is by considering Sufficient VS Necessary Condition.

Example 1

Power failure cause loss of data in a computer's memory.

In the above example, how does the effect come about? If power failure occurs while you're typing your essay, we know that loss of data will occur. We can say that power failure is a sufficient condition for the loss of data.

If there is power failure there is loss of data; but if there is loss of data, it is not necessary that there is power failure. Other causes might explain the loss of data. So power failure is not a necessary condition for the loss of data; it is sufficient.

Example 2

The presence of oxygen caused the combustion in an engine.

In the above example, the presence of oxygen causes combustion. Is it the only cause? No. You need other factors, gasoline, a battery, etc. So, we say that oxygen is a necessary condition —necessary but not sufficient.

Example 3

Smoking causes cancer.

How does smoking cause cancer? We know that smoking is not sufficient to get cancer, since many people smoke but never get cancer. Is smoking necessary to get cancer? No. You may get cancer for other reasons. Thus, we call smoking a contributing factor or partial cause of cancer.

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TYPES OF CAUSAL ARGUMENTS

Causal Prediction: An argument consisting of a causal generalization, an example of an effect, and concluding that a specific effect occurs.

Given a causal statement, we can predict what will happen:

1. Reduction in swelling causes relief of pain. (Causal generalization statement) 2. The swelling in my arm is diminishing. (Example) 3. Therefore, relief of pain will occur. (Prediction)

Causal Explanation: An argument consisting of a causal generalization, an example of an effect, and concluding that an example of a specific cause explains the occurrence of the effect.

Given a causal statement, we can explain how two events are related.

1. Reduction in swelling causes relief of pain. (Causal generalization statement) 2. There is relief of pain. (Example) 3. Therefore, the swelling in my arm has gone down. (Explanation)

Causal Prescription: An argument consisting of a causal generalization and concluding with a prescription for producing or preventing a certain effect.

This is an argument asserting how something is to be achieved. Given a causal statement, we know that if we want to achieve a certain result we need to bring about the cause.

1. Reduction in swelling causes relief of pain. (Causal generalization statement) 2. Therefore, if relief of pain is desired, reduce the swelling. (Prescription)

Causal Conclusion: An argument consisting of a premise in support of a causal statement.

This type of argument provides evidence for concluding that one event causes another.

1. Whenever swelling is reduced, pain is relieved. (Premise) 2. Therefore, reduction in swelling causes relief of pain. (Causal statement)

Conclusion:

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In this lecture, we have learned the major aspects of logical thinking. Here are the important notions:

1. Logic is the study of the principles of good reasoning. Logicians, unlike psychologists, are not interested in what motivates thinking. Rather, logicians are interested in the structure of arguments, what makes an argument good or bad, what makes one valid and another invalid.

2. There are two distinct forms of reasoning, deduction and induction. A deductive argument is one whose conclusion is claimed to follow necessarily from the premises. An inductive argument is one whose conclusion is never necessary, but rather probable.

Furthermore, deductive arguments can be valid or invalid, sound or unsound; inductive arguments can be weak or strong, cogent or uncogent.

A deductive argument is valid if, and only if, given the premises, the conclusion follows necessarily. A deductively valid argument that has true premises is called sound. A deductively valid argument that has at least one false premise is called unsound. A deductive argument is invalid just in case given the premises the conclusion does not follow at all—even if the premises are true. A good deductive argument is a sound argument.

An inductive argument is one whose conclusion is inferred (rather than being deduced) from the premises. That is to say, an inductive argument is one whose conclusion always follows probably. Depending on how probable the conclusion is given the premises, an inductive argument may be weak or strong. Weak inductive arguments are known as uncogent. Also, strong inductive arguments that have at least one false premise are uncogent. A strong inductive argument that has all true premises is known as cogent. Cogent arguments are good inductive arguments.

As we have seen, there are 3 main types of inductive arguments: (1) Arguments that begin with an observation, which is known as sample, and then move to a generalization about the sample. (2) Arguments that rely on an analogy between two or more things or events and then move to a conclusion about one of those things or events, a conclusion claimed on the basis of the analogy. (3) Arguments whose conclusion relies upon the notion of causation (i.e. cause and effect).

Finally we have learned about informal logical fallacies. These are logical errors of reasoning. Often people commit these errors that do not depend on the structure of the argument, but on certain other issues.

(CSLO 1, CSLO 3, CSLO 4)

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