Answer these and send through my email at g_pellejo@yahoo.com before August 28, 2008.

1. In its ordinary usage, the word is often used to refer to a quarrel between two or more parties.
2. In particular, it is a list of statements, one of which is the conclusion and the others are the premises or assumptions.
3. It is the last proposition in the syllogism.
4. These people tend to make assertions without giving reasons.
5. These precede the conclusion in an argument.
6. This is about the logical connection between the premises and the conclusion.
7. In ordinary usage this is often used interchangeably with "true"
8. It is a property of statements but not arguments
9. This is the argument when the argument is valid, and all the premises are true.
10. Its Latin name here simply means "reduced to absurdity".

1. Ralph is four times as old as Frank. In 20 years, Ralph will be twice as old as Frank. How old are Ralph and Frank?
o Ralph is 40; Frank is 10.
o Ralph is 20; Frank is 5.
o Ralph is 60; Frank is 15.
o Ralph is 80; Frank is 20.

2. If Jenny hits a home run, her team will win. Given that this is true, what else also must be true?
o If the team won, Jenny hit a home run.
o If Jenny didn't hit a home run, the team tied.
o If the team didn't win, Jenny didn't hit a home run.
o All of the above.

3. Taking the below statements as a group, which statement is the true one?
o The number of false statements here is one.
o The number of false statements here is two.
o The number of false statements here is three.
o The number of false statements here is four.

4. Neko will go to the movies, only if she can drive. Given that this is true, what else also must be true?
o If Neko didn't drive, she didn't go to the movies.
o If Neko went to the movies, then she drove.
o Both of the above statements.
o If Neko drove, then she went to the movies.
5. Your room is completely dark. You have eight shoes of four different colors, and fifty socks of five different colors. How many shoes and socks must you grab to make sure you have a matching pair?
o 5 shoes, 6 socks
o 6 shoes, 8 socks
o 6 shoes, 10 socks
o 5 shoes, 5 socks

6. No musicians are chefs. No chefs are teachers. Given that these are true, what else also must be true?
o No teacher is a musician.
o Some musicians are teachers.
o Some teachers are chefs.
o None of the above.

7. If QUIZ is written as UYMD, how do you write HEAD?
o MIEH
o MJEH
o LJEH
o LIEH

8. Some tigers are not lions. All lions are mammals. Given that these are true, what else also must be true?
o Some tigers are lions.
o Some mammals are not lions.
o Some lions are not tigers.
o None of these

BONUS BONUS BONUS...

Those who will not attend todays class(8/11/2008 5:30-6:30) will be given 5 pts. This is to check if people are reading our site!!! YOU JUST READ: Argument Analysis, the article below for recitation on Wednesday (8/13/08)

Midterm MODULE: Argument Analysis
An important part of critical thinking is being able to give reasons, whether it is to support or to criticize a certain idea. To be able to do that, one should know how to identify, analyse, and evaluate arguments.
Tutorials
• [A01] Identifying Arguments
• [A02] Validity and Soundness
• [A03] Patterns of Valid Arguments
• [A04] Identifying Hidden Assumptions
• [A05] Inductive Reasoning
• [A06] Good Arguments
• [A07] Argument mapping
• [A08] Analogical Arguments
• [A09] More patterns of valid arguments

UTORIAL A01: Identifying Arguments
A01.1 What is an argument?
To be able to think critically, it is very important that you can identify, construct, and evaluate arguments.
We shall be using the word "argument" in a way that is somewhat different from its ordinary meaning. In its ordinary usage, the word is often used to refer to a quarrel between two or more parties. But here we shall understand an argument as a piece of language. In particular, we shall take an argument to be a list of statements, one of which is the conclusion and the others are the premises or assumptions of the argument.
To give an argument is to provide a set of premises as reasons for accepting the conclusion. To give an argument is not necessarily to attack or criticize someone. Arguments can also be used to support other people's viewpoints.
As an example, suppose I want to convince you that you should be hardworking. I might give the following argument:
If you want to find a good job, you should be hardworking. You do want to find a good job. So you should be hardworking.
The first two sentences here are the premises of the argument, and the last sentence is the conclusion. To give this argument is to offer the premises as reasons for accepting the conclusion.
Dogmatic people tend to make assertions without giving reasons. When they are criticized they often fail to give arguments to defend their own opinions. To become a good critical thinker, you should develop the habit of giving good arguments to support your claims. Giving good arguments is one of the most important ways to convince other people that certain claims should be accepted.
A01.2 Exercises
See if you can give arguments to support some of your beliefs. For example, do you think the economy is going to improve or worsen in the next six months? Why or why not? What arguments can you give to support your position? Or to think about something different, do you think computers can have emotions? Again, what arguments can you give to support your viewpoint? Make sure that your arguments are composed of statements.
A01.3 How to look for arguments
How do we identify arguments in real life? There are no easy mechanical rules, and we usually have to rely on the context in order to determine which are the premises and the conclusions. But sometimes the job can be made easier by the presence of certain premise or conclusion indicators. For example, if a person makes a statement, and then adds "this is because ...", then it is quite likely that the first statement is presented as a conclusion, supported by the statements that come afterwards. Other words in English that might be used to indicate the premises to follow include :

e :
• since
• firstly, secondly, ...
• for, as, after all,
• assuming that, in view of the fact that
• follows from, as shown / indicated by
• may be inferred / deduced / derived from
Of course whether such words are used to indicate premises or not depends on the context. For example, "since" has a very different function in a statement like "I have been here since noon", unlike "X is an even number since X is divisible by 4".
Conclusions, on the other hand, are often preceded by words like:
• therefore, so, it follows that
• hence, consequently
• suggests / proves / demonstrates that
• entails, implies
Here are some examples of passages that do not contain arguments.
When people sweat a lot they tend to drink more water. [Just a single statement, not enough to make an argument.]
Once upon a time there was a prince and a princess. They lived happily together and one day they decided to have a baby. But the baby grew up to be a nasty and cruel person and they regret it very much. [A chronological description of facts composed of statements but no premise or conclusion.]
Can you come to the meeting tomorrow? [A question that does not contain an argument.]
A01.4 Exercises
Do these passages contain arguments? If so, what are their conclusions?
Cutting the interest rate will have no effect on the stock market this time round as people have been expecting a rate cut all along. This factor has already been reflected in the market. [Show answer]
Yes. The conclusion is that this time, cutting interest rate will have no effect on the stock market.
So it is raining heavily and this building might collapse. But I don't really care. [Show answer]
Not an argument. Although the first statement starts with “so” it does not indicate a conclusion.
Virgin would then dominate the rail system. Is that something the government should worry about? Not necessarily. The industry is regulated, and one powerful company might at least offer a more coherent schedule of services than the present arrangement has produced. The reason the industry was broken up into more than 100 companies at privatisation was not operational, but political: the Conservative government thought it would thus be harder to renationalise. The Economist 16.12.2000 [Show answer]
Yes. The main conclusion is that the domination of the rail system by Virgin is not something the government should worry about.
Bill will pay the ransom. After all, he loves his wife and children and would do everything to save them. [Show answer]
The first statement is the conclusion.
All of Russia’s problems of human rights and democracy come back to three things: the legislature, the executive and the judiciary. None works as well as it should. Parliament passes laws in a hurry, and has neither the ability nor the will to call high officials to account. State officials abuse human rights (either on their own, or on orders from on high) and work with remarkable slowness and disorganisation. The courts almost completely fail in their role as the ultimate safeguard of freedom and order. The Economist 25.11.2000 [Show answer]
An argument. The conclusion is that the legislative, executive and judicial systems in Russia are not working properly.
Most mornings, Park Chang Woo arrives at a train station in central Seoul, South Korea's capital. But he is not commuter. He is unemployed and goes there to kill time. Around him, dozens of jobless people pass their days drinking soju, a local version of vodka. For the moment, middle-aged Mr Park would rather read a newspaper. He used to be a brick layer for a small construction company in Pusan, a southern port city. But three years ago the country's financial crisis cost him that job, so he came to Seoul, leaving his wife and two children behind. Still looking for work, he has little hope of going home any time soon. The Economist 25 .11.2000 [Show answer]
Not an argument.
For a long time, astronomers suspected that Europa, one of Jupiter's many moons, might harbour a watery ocean beneath its ice-covered surface. They were right. Now the technique used earlier this year to demonstrate the existence of the Europan ocean has been employed to detect an ocean on another Jovian satellite, Ganymede, according to work announced at the recent American Geo-physical Union meeting in San Francisco. The Economist 16.12.2000 [Show answer]
Not an argument.
There are no hard numbers, but the evidence from Asia’s expatriate community is unequivocal. Three years after its handover from Britain to China, Hong Kong is unlearning English. The city's gweilos (Cantonese for “ghost men”) must go to ever greater lengths to catch the oldest taxi driver available to maximize their chances of comprehension. Hotel managers are complaining that they can no longer find enough English- speakers to act as receptionists. Departing tourists, polled at the airport, voice growing frustration at not being understood. The Economist 20.1.2001 [Show answer]
Yes, it is an argument. The conclusion is that English standards are dropping in Hong Kong.
A01.5 Presenting arguments in the standard format
When it comes to the analysis and evaluation of an argument, it is often useful to label the premises and the conclusion, and display them on separate lines with the conclusion at the bottom :
(Premise 1) If you want to find a good job, you should be hardworking.
(Premise 2) You do want to find a good job.
(Conclusion) So you should be hardworking.
Let us call this style of presenting an argument a presentation in the standard format. Here we rewrite two more arguments using the standard format:
We should not inflict unnecessary pain on cows and pigs. After all, we should not inflict unnecessary pain on any animal with consciousness, and cows and pigs are animals with consciousness.
(Premise 1) We should not inflict unnecessary pain on any animal with consciousness.
(Premise 2) Cows and pigs are animals with consciousness.
(Conclusion) We should not inflict unnecessary pain on cows and pigs.
If this liquid is acidic, the litmus paper would have turned red. But it hasn't, so the liquid is not acidic.
(Premise 1) If the liquid is acidic, the litmus paper would have turned red.
(Premise 2) The litmus paper has not turned red.
(Conclusion) The liquid is not acidic.
In presenting an argument in the standard format the premises and the conclusion are clearly identified. Sometimes we also rewrite some of the sentences to make their meaning clearer, as in the second premise of the second example. Notice also that a conclusion need not always come at the end of a passage containing an argument, as in the first example. In fact, sometimes the conclusion of an argument might not be explicitly written out. For example it might be expressed by a rhetorical question:
How can you believe that corruption is acceptable? It is neither fair nor legal!
In presenting an argument in the standard format, we have to rewrite the argument more explicitly as follows:
(Premise) Corruption is not fair and it is not legal.
(Conclusion) Corruption is not acceptable.
If you want to improve your reading and comprehension skills, you should practise reconstructing the arguments that you come across by rewriting them carefully in the standard format.
A01.6 Exercises
Rewrite these arguments in the standard format.
1. He is either in Hong Kong or Macau. John says that he is not in Hong Kong. So he must be in Macau.
2. If the Government wants to build an incinerator here they should compensate those who live in the area. Incinerators are known to cause health problems to people living nearby. These people did not choose to live there in the first place.


TUTORIAL A02: Validity and Soundness
A02.1 Definition of validity
One desirable feature of arguments is that the conclusion should follow from the premises. But what does it mean? Consider these two arguments :
Argument #1 :
• Barbie is over 90 years old. So Barbie is over 20 years old.
Argument #2 :
• Barbie is over 20 years old. So Barbie is over 90 years old.
Intuitively, the conclusion of the first argument follows from the premise, whereas the conclusion of the second argument does not follow from its premise. But how should we explain the difference between the two arguments more precisely? Here is a thought : In the first argument, if the premise is indeed true, then the conclusion cannot be false. On the other hand, even if the premise in the second argument is true, there is no guarantee that the conclusion must also be true. For example, Barbie could be 30 years old.
So we shall make use of this idea to define the notion of a deductively valid argument, or valid argument, as follows:
An argument is valid if and only if there is no logically possible situation where all the premises are true and the conclusion is false at the same time.
The idea of validity provides a more precise explication of what it is for a conclusion to follow from the premises. Applying this definition, we can see that the first argument above is valid, since there is no possible situation where Barbie can be over 90 but not over 20. The second argument is not valid because there are plenty of possible situations where the premise is true but the conclusion is false. Consider a situation where Barbie is 25, or one where she is 85. The fact that these situations are possible is enough to show that the argument is not valid, or invalid.
A02.2 Validity and truth
What if we have an argument with more than one premise? Here is an example :
All pigs can fly. Anything that can fly can swim. So all pigs can swim.
Although the two premises of this argument are false, this is actually a valid argument. To evaluate its validity, ask yourself whether it is possible to come up with a situation where all the premises are true and the conclusion is false. (We are not asking whether there is a situation where the premises and the conclusion are all true.) Of course, the answer is 'no'. If pigs can indeed fly, and if anything that can fly can also swim, then it must be the case that all pigs can swim.
So this example tells us something :
The premises and the conclusion of a valid argument can all be false.
Hopefully you will now realize that validity is not about the actual truth or falsity of the premises or the conclusion. Validity is about the logical connection between the premises and the conclusion. A valid argument is one where the truth of the premises guarantees the truth of the conclusion, but validity does not guarantee that the premises are in fact true. All that validity tells us is that if the premises are true, the conclusion must also be true.
A02.3 Showing that an argument is invalid
Now consider this argument :
Adam loves Beth. Beth loves Cathy. So Adam loves Cathy.
This argument is not valid, for it is possible that the premises are true and yet the conclusion is false. Perhaps Adam loves Beth but does not want Beth to love anyone else. So Adam actually hates Cathy. The mere possibility of such a situation is enough to show that the argument is not valid. Let us call these situations invalidating counterexamples to the argument. Basically, we are defining a valid argument as an argument with no possible invalidating counterexamples. To sharpen your skills in evaluating arguments, it is therefore important that you are able to discover and construct such examples.
Notice that a counterexample need not be real in the sense of being an actual situation. It might turn out that in fact that Adam, Beth and Cathy are members of the same family and they love each other. But the above argument is still invalid since the counterexample constructed is a possible situation, even if it is not actually real. All that is required of a counterexample is that the situation is a coherent one in which all the premises of the argument are true and the conclusion is false. So we should remember this :
An argument can be invalid even if the conclusion and the premises are all actually true.
To give you another example, here is another invalid argument with a true premise and a true conclusion : "Paris is the capital of France. So Rome is the capital of Italy." . It is not valid because it is possible for Italy to change its capital (say to Milan), while Paris remains the capital of France.
Another point to remember is that it is possible for a valid argument to have a true conclusion even when all its premises are false. Here is an example :
All pigs are purple in colour. Anything that is purple is an animal. So all pigs are animals.
Before proceeding any further, please make sure you understand why these claims are true and can give examples of such cases.
1. The premises and the conclusion of an invalid argument can all be true.
2. A valid argument should not be defined as an argument with true premises and a true conclusion.
3. The premises and the conclusion of a valid argument can all be false.
4. A valid argument with false premises can still have a true conclusion.
A02.4 A reminder
The concept of validity provides a more precise explication of what it is for a conclusion to follow from the premises. Since this is one of the most important concepts in this course, you should make sure you fully understand the definition. In giving our definition we are making a distinction between truth and validity. In ordinary usage "valid" is often used interchangeably with "true" (similarly with "false" and "not valid"). But here validity is restricted to only arguments and not statements, and truth is a property of statements but not arguments:

So never say things like "this statement is valid" or "that argument is true"!
A02.5 Exercises
Question 1 Are the following arguments valid? Why or why not?
1. Someone is sick.
Someone is unhappy.
So someone is unhappy and sick. [Show answer]
Invalid.
2. If he loves me then he gives me flowers.
He gives me flowers.
So he loves me. [Show answer]
Invalid.
3. Beckham is famous.
Beckham is a football player.
Therefore, Beckham is a famous football player. [Show answer]
Invalid.
[Explain]
Beckham might be a
famous chef who is
a football player but
not a famous football player.
4. If it rains, the streets will be wet.
If the streets are wet, accidents will happen.
Therefore, accidents will happen if it rains. [Show answer]
Valid.
5. John was in Britain when Mary died in Hong Kong.
So Mary could not have been killed by John. [Show answer]
Invalid.
[Explain]
Perhaps John shot
Mary on Monday,
and flew to Britain
on Tuesday, but Mary
died on Friday.
6. If there is life on Pluto then Pluto contains water.
But there is no life on Pluto.
Therefore Pluto does not contain water. [Show answer]
Invalid.
7. There were two rabbits in the room last week.
No rabbit has left the room since then.
Therefore there are two rabbits in the room now. [Show answer]
Invalid.
As you know, rabbits
can reproduce.
8. All whales have wings.
Moby does not have wings.
So Moby is not a whale. [Show answer]
Valid.
Question 2
Consider this argument :
If there is a square in the picture then there is a circle as well.
Therefore, if there is a circle in the picture there is a triangle in the picture.
Now look at these four pictures below. Which of them constitute invalidating counterexamples to the argument, and which do not?

[Show answer]
Only the second one from the right.
Question 3 Are these arguments valid?
1. John shot himself in the head. So John is dead. [Show answer]
Not valid. Although the conclusion is very likely to be true given the premise, it is not a logical consequence of the premise. Perhaps a brillant doctor managed to save John.
2. John shot himself in the head. So John shot himself in the head. [Show answer]
Valid. This is a circular argument since the conclusion is also a premise. But it is nonetheless valid since it is impossible for the premises to be true while the conclusion is false.
3. All management consultants are bald. Peter is bald. So Peter is a management consultant. [Show answer]
Not valid. Perhaps Peter is a monk who happended to have shaved his hair.
4. If time travel is possible, we would now have lots of time-travel visitors from the future. But we have no such visitors. So time travel is not possible. [Show answer]
Valid.
5. Jen is either in San Diego or in Tokyo. Since she is not in Tokyo, she is in San Diego. [Show answer]
Valid.
6. Some people are nice. Some people are rich. So some people are rich and nice. [Show answer]
Not valid. Those who are rich might not be the same as those who are nice.
7. If I drink then I will be happy. If I am happy then I will dance. So if I drink then I will dance. [Show answer]
Valid.
8. Every red fish is a fish. [Show answer]
A trick question! This is a necessarily true statement, but it is not an argument and so not a valid argument.
9. The services of mobile phone companies are getting worse as there has been an increasing number of complaints against mobile phone companies by consumers. [Show answer]
Not valid, since the increase in complaints might only be due to increase in the number of mobile phone users.
10. All capitalists exploit the weak and the poor. Property developers exploit the weak and the poor. So property developers are capitalists. [Show answer]
Not valid. Perhaps there are non-capitalists who also exploit.
________________________________________
A02.6 Soundness
It should be obvious by now that validity is about the logical connection between the premises and the conclusion. When we are told that an argument is valid, this is not enough to tell us anything about the actual truth or falsity of the premises or the conclusion. All we know is that there is a logical connection between them, that the premises entail the conclusion.
So even if we are given a valid argument, we still need to be careful before accepting the conclusion, since a valid argument might contain a false conclusion. What we need to check further is of course whether the premises are true. If an argument is valid, and all the premises are true, then it is called a sound argument. Of course, it follows from such a definition that a sound argument must also have a true conclusion. In a valid argument, if the premises are true, then the conclusion cannot be false, since by definition it is impossible for a valid argument to have true premises and a false conclusion in the same situation. So given that a sound argument is valid and has true premises, its conclusion must also be true. So if you have determined that an argument is indeed sound, you can certainly accept the conclusion.
An argument that is not sound is an unsound argument. If an argument is unsound, it might be that it is invalid, or maybe it has at least one false premise, or both.
A02.7 Exercises
Question 1:
Exercise: validity and soundness
Is it possible to have arguments of the following kinds?
If so, provide an example. If not, explain why. It is particularly important to note the highlighted cases.
True conclusion
true premises True conclusion
false premises False conclusion
true premises False conclusion
false premises
Valid & sound arguments [Show answer]
Yes. "Cows are mammals. Mammals are animals. So cows are animals." [Show answer]
No. If the premises are false, the argument is not sound. [Show answer]
No. If the premises are true and the argument is valid, the conclusion must also be true. [Show answer]
No. If the premises are false, the argument is not sound.
Valid & unsound arguments [Show answer]
No. If the premises are true and the argument is valid, the argument is sound. [Show answer]
Yes. "Cows are insects. Insects are mammals. So cows are mammals." [Show answer]
No. If the premises are true and the argument is valid, the conclusion must also be true. [Show answer]
Yes. "Cows are insects. Insects are viruses. So cows are viruses."
Invalid & sound arguments [Show answer]
No. By definition a sound argument has to be valid. [Show answer]
No. By definition a sound argument has to be valid. [Show answer]
No. By definition a sound argument has to be valid. [Show answer]
No. By definition a sound argument has to be valid.
Invalid and unsound arguments [Show answer]
Yes. "Cows are mammals. So the sun is larger than the moon." [Show answer]
Yes. "Cows are insects. So the sun is larger than the moon." [Show answer]
Yes. "Cows are mammals. So the moon is larger than the sun." [Show answer]
Yes. "Cows are insects. So the moon is larger than the sun


Question 2 : Are the following statements true or false? Why?
1. All invalid arguments are unsound. [Show answer]
True by definition - sound arguments have to be valid.
2. All true statements are valid. [Show answer]
False. Only arguments can be valid.
3. To show that an argument is unsound, we must at least show that some of its premises are actually false. [Show answer]
False. If it is invalid then it is not sound, and we can show that an argument is invalid without showing that some of the premises are actually false.
4. An invalid argument must have a false conclusion. [Show answer]
False.
5. If all the premises of a valid argument are false, then the conclusion must also be false. [Show answer]
False. Make sure you understand why.
6. If all the premises and the conclusion of an argument are true, then the argument is valid. [Show answer]
False. It can still be invalid.
7. All sound arguments are true. [Show answer]
What are true or false are statements, not arguments.
8. Any valid argument with a true conclusion is sound. [Show answer]
Not necessarily.

TUTORIAL A03: Patterns of Valid Arguments

A03.1 Introduction
With valid arguments, it is impossible to have a false conclusion if the premises are all true. Obviously valid arguments play a very important role in reasoning, because if we start with true assumptions, and use only valid arguments to establish new conclusions, then our conclusions must also be true. But which are the rules we should use to decide whether an argument is valid or not? This is where formal logic comes in. By using special symbols we can describe patterns of valid argument, and formulate rules for evaluating the validity of an argument.
A03.2 Modus ponens
Consider the following arguments :
• If this object is made of copper, it will conduct electricity. This object is made of copper, so it will conduct electricity.
• If there is no largest prime number, then 510511 is not the largest prime number. There is no largest prime number. Therefore 510511 is not the largest prime number.
• If Lam is a Buddhist then he should not eat pork. Lam is a Buddhist. Therefore Lam should not eat pork.
These three arguments are of course valid. Furthermore you probably notice that they are very similar to each other. What is common between them is that they have the same structure or form:
Modus ponens - If P then Q. P. Therefore Q.
Here, the letters P and Q are called sentence letters. They are used to translate or represent statements. By replacing P and Q with appropriate sentences, we can generate the original three valid arguments. This shows that the three arguments have a common form. It is also in virtue of this form that the arguments are valid, for we can see that any argument of the same form is a valid argument. Because this particular pattern of argument is quite common, it has been given a name. It is known as modus ponens.
However, don't confuse modus ponens with the following form of argument, which is not valid!
Affirming the consequent - If P then Q. Q. Therefore, P.
Note - When we say that this is not a valid pattern of argument, what is meant is that not every argument of this pattern is valid. This is different from saying that every argument of this pattern is not valid. See if you can figure out why this is the case.
Giving arguments of this form is a fallacy - making a mistake of reasoning. This particular mistake is known as affirming the consequent.
• If Jane lives in London then Jane lives in England. Jane lives in England. Therefore Jane lives in London.
[Not valid - perhaps Jane lives in Liverpool.]
• If Bing has gone shopping then Daniel will be unhappy. Daniel is unhappy. So Bing has gone shopping.
[Not valid - perhaps Daniel is unhappy because he has run out of vodka to drink.]
There are of course many other patterns of valid argument. Now we shall introduce a few more patterns which are often used in reasoning.
A03.3 Modus tollens
Modus tollens - If P then Q. Not-Q. Therefore, not-P.
Here, "not-Q" simply means the denial of Q. So if Q means "Today is hot.", then "not-Q" can be used to translate "It is not the case that today is hot", or "Today is not hot."
If Betty is on the plane, she will be in the A1 seat. But Betty is not in the A1 seat. So she is not on the plane.
But do distinguish modus tollens from the following fallacious pattern of argument :
Denying the antecedent - If P then Q, not-P. Therefore, not-Q.
If Elsie is competent, she will get an important job. But Elsie is not competent. So she will not get an important job.
[Not valid : Perhaps Elsie is incompetent but her boss likes her because she accepts very low wages.]
A03.4 Hypothetical syllogism
If P then Q, If Q then R. Therefore, if P then R.
If God created the universe then the universe will be perfect. If the universe is perfect then there will be no evil. So if God created the universe there will be no evil.
A03.5 Disjunctive syllogism
P or Q. Not-P. Therefore, Q ; P or Q, Not-Q. Therefore, P.
Either the government brings about more sensible educational reforms, or the only good schools left will be private ones for rich kids. The government is not going to carry out sensible educational reforms. So the only good schools left will be private ones for rich kids.
A03.6 Dilemma
P or Q. If P then R. If Q then S. Therefore, R or S.
When R is the same as S, we have a simpler form : P or Q. If P then R. If Q then R. Therefore, R.
Either we increase the tax rate or we don't. If we do, the people will be unhappy. If we don't, the people will also be unhappy. (Because the government will not have enough money to provide for public services.) So the people are going to be unhappy anyway.
A03.7 Arguing by Reductio ad Absurdum
The Latin name here simply means "reduced to absurdity". Here is the method of argument if you want to prove that a certain statement S is false:
1. First assume that S is true.
2. From the assumption that it is true, prove that it would lead to a contradiction or some other claim that is false or absurd.
3. Conclude that S must be false.
Those of you who can spot connections quickly might notice that this is none other than an application of modus tollens. A famous application of this pattern of argument is Euclid's proof that there is no largest prime number. A prime number is any positive integer greater than 1 that is wholly divisible only by 1 and by itself, e.g. 2, 3, 5, 7, 11, 13, 17, etc.
1. Assume that there are only n prime numbers, where n is a finite number : P1 < P2 < ... < Pn.
2. Define a number Q that is 1 plus the product of all primes, i.e. Q = 1 + ( P1 x P2 x ... x Pn).
3. Q is of course larger than Pn.
4. But Q has to be a prime number also, because (a) when it is divided by any prime number it always leave a remainder of 1, and (b) if it is not divisible by an prime number it cannot be divisible by any non-prime numbers either.
5. So Q is a prime number larger than the largest prime number.
6. But this is a contradiction, so the original assumption that there is a finite number of prime numbers must be wrong.
7. So there must be infinitely many primes.
Let us look at two more examples of reductio:
• Suppose someone were to claim that nothing is true or false. We can show that this must be false as follows : If this person's claim is indeed correct, then there is at least one thing that is true, namely the claim that the person is making. So it can't be that nothing is true or false. So his statement must be false.
• One theory of how the universe came about is that it developed from a vacuum state in the infinite past. Stephen Hawking thinks that this is false. Here is his argument : in order for the universe to develop from a vacuum state, the vacuum state must have been unstable. (If the vacuum state were a stable one, nothing would come out of it.) But if it was unstable, it would not be a vacuum state, and it would not have lasted an infinite time before becoming unstable.
A03.8 Other Patterns
There are of course many other patterns of deductively valid arguments. One way to construct more patterns is to combine the ones that we have looked at earlier. For example, we can combine two cases of hypothetical syllogism to obtain the following argument:
If P then Q. If Q then R. If R then S. Therefore if P then S.
There are also a few other simple but also valid patterns which we have not mentioned:
• P and Q. Therefore Q.
• P. Therefore P.
Some of you might be surprised to find out that "P. Therefore P." is valid. But think about it carefully - if the conclusion is also a premise, then the conclusion obviously follows from the premise! Of course, this tells us that not all valid arguments are good arguments. How these two concepts are connected is a topic we shall discuss later on.
We shall look at a few more complicated patterns of valid arguments in another tutorial. It is understandable that you might not remember all the names of these patterns. But what is important is that you can recognize these argument patterns when you come across them in everyday life, and would not confuse them with patterns of invalid arguments that look similar.
________________________________________
A03.9 Exercises
Question 1 Consider the following arguments. Identify the forms of all valid arguments. (To display the correct answer, you need to enable javascript on your browser.)
Q1.1. If Jesus loves me, then I love Jesus. I do not love Jesus. Therefore, Jesus does not love me.

Q1.2. Either Jimmy is walking the dog or Cathy is feeding the cat (or both). Cathy is feeding the cat. Therefore Jimmy is not walking the dog

Q1.3. Either Jimmy is walking the dog or Cathy is feeding the cat. Cathy is not feeding the cat. Therefore Jimmy is walking the dog.

Q1.4. If X is a man, then X is a human being. If X is a human being, then X is an animal. Therefore, if X is a man, then X is an animal.

Q1.5. If I do not have Yellow Tail sashimi, then I shall have scallop sushi instead. Now, I have Yellow Tail sashimi. So I do not have scallop sushi.

Q1.6. If some sheep are black, then some ducks are pink. It is not true that some ducks are pink. Therefore, it is not true that some sheep are black.

Q1.7. Either she is right or she is wrong. If she is right, then he is wrong. If she is wrong, then he is also wrong. Therefore, he is wrong either way.

Q1.8. Paul is a bachelor. Paul is single. So at least one bachelor is single.

Q1.9. Either she is in China or she is in Europe. If she is in China, then she is in Beijing. If she is in Europe, then she is sleeping. Hence, either she is in Beijing or she is sleeping.

Question 2 Identify the conclusions that can be drawn from these assumptions. Which basic patterns of valid arguments should be used to derive the conclusion?
1. If God is perfect, then God knows what people intend to do in the future. If God knows what people intend to do in the future, then God can stop people from bringing about evil. [Show answer]
“If God is perfect, then God can stop people from bringing about evil” by hypothetical syllogism.
2. If he is dead, then there will be no pulse. If there is no pulse, then the red light will turn on. There is no red light. [Show answer]
The conclusions are “there is a pulse” and “he is not dead” by two applications of modus tollens.
3. Either Krypto is hot or Pluto is hot. If Krypto is hot, then there is no ice on its surface. But there is. [Show answer]
The conclusions are “Krypto is not hot” and “Pluto is hot” by mod

TUTORIAL A04: Identifying Hidden Assumptions
A04.1 Introduction
When people give arguments sometimes certain assumptions are left implicit. Example :
Homosexuality is wrong because it is unnatural.
This argument as it stands is not valid. Someone who gives such an argument presumably has in mind the hidden assumption that whatever that is unnatural is wrong. It is only when this assumption is added that the argument becomes valid.
Once this is pointed out, we can of course go on to discuss what this assumption really means and whether it is justified. We might argue for example, that there are plenty of things that are “unnatural” but are not usually regarded as wrong (e.g. playing video games, having medical operations, contraception). Someone who still wants to put forward such an argument might then distinguish between different types of unnatural acts, some of which are supposed to be permissible, others being morally wrong. Pointing out the hidden assumption in an argument can help resolve or clarify the issues involved in a dispute.
In everyday life, the arguments we normally encounter are often arguments where important assumptions are not made explicit. It is an important part of critical thinking that we should be able to identify such hidden assumptions or implicit assumptions.
So how should we go about identifying hidden assumptions? There are two main steps involved. First, determine whether the argument is valid or not. If the argument is valid, the conclusion does indeed follow from the premises, and so the premises have shown explicitly the assumptions needed to derive the conclusion. There are then no hidden assumptions involved. But if the argument is not valid, you should check carefully what additional premises should be added to the argument that would make it valid. Those would be the hidden assumptions. You can then ask questions such as : (a) what do these assumptions mean? (b) Why would the proponent of the argument accept such assumptions? (c) Should these assumptions be accepted?
This technique of revealing hidden assumptions is also useful in identifying hidden or neglected factors in causal explanations of empirical phenomena. Suppose someone lights a match and there was an explosion. The lighting of the match is an essential part in explaining why there was an explosion, but it is not a causally sufficient condition for the explosion since there are plenty of situations where someone lights a match and there is no explosion. To come up with a more complete explanation, we need to identify factors which together are sufficient for the occurrence of the explosion, or at least show that it has a high probability of happening. This might include factors such as the presence of a high level of oxygen in the environment.
A04.2 Exercises
Identify the likely hidden assumptions in these arguments:
1. We should reduce the penalty for drunken driving, as a milder penalty would mean more convictions. [Show answer]
We should increase the number of convictions for drunken driving.
2. Moby Dick is a whale. So Moby Dick is a mammal. [Show answer]
“Anything that is a whale is a mammal”, or “If Moby Dick is a whale it is a mammal.”
3. Giving students a fail grade will damage their self-confidence. Therefore, we should not fail students. [Show answer]
We should not damage students' self-confidence.
4. It should not be illegal for adults to smoke pot. After all, it does not harm anyone. [Show answer]
Anything that does not cause harm should not be made illegal.
5. There is nothing wrong talking on a mobile phone during lectures. Other students do it all the time. [Show answer]
If an action is done by other students (or people) all the time, then there is nothing wrong with it.
6. Killing an innocent person is wrong. Therefore, abortion is wrong. [Show answer]
Abortion involves the killing of an innocent person.
7. Traces of ammonia have been found in Mars' atmosphere. So there must be life on Mars. [Show answer]
"Only living things produce ammonia." (or something similar)
8. There cannot be more than one God. Otherwise, there would be two Gods equally powerful, or one is more powerful than the other. [Show answer]
If something is a God, nothing else can be as powerful or more powerful than it.
TUTORIAL A05: Inductive Reasoning
A05.1 What is induction?
Consider the following argument :
Dipsy bought one ticket in a fair lottery with ten million tickets.
So Dipsy is not going to win the lottery.
This argument is of course not valid, since Dipsy might be so lucky that he wins the lottery. But this is quite unlikely to happen if the lottery is indeed a fair one. If you believe that the premise is true, you probably will accept the conclusion as well. In other words, the conclusion is highly likely to be true given that the premise is true.
Here is another example :
Dylan is a man.
He is 99 and is in a coma.
Therefore, Dylan will not run in the marathon tomorrow.
Again, it is not logically impossible for Dylan to recover from his coma and join the marathon, but if the premises are true this is unlikely to happen.
Although the two arguments above are not valid, we would still regard them as good arguments. What is special about them is that they are inductively strong arguments : the conclusion is highly likely to be true given that the premises are true. With an inductively strong argument, although the premises do not logically entail the conclusion, they provide strong inductive support for it.
There are at least three main differences between an inductively strong argument and a valid argument :
1. As already noted, in a valid argument, the conclusion follows logically from the premises, but this is not the case in an inductively strong argument. It is logically possible for the premises to be true while the conclusion is false.
2. Deductive validity is not a matter of degree. An argument is either deductively valid, or it is not. But inductive support is a matter of degree, depending on the probability of the conclusion being true given the premises.
For example, consider this slightly modified argument :
Dipsy bought X tickets in a fair lottery with ten thousand tickets.
So Dipsy is going to win the lottery.
If we replace X by a very small number, say, 10, then the argument is obviously very weak, since it is very unlikely that Dipsy can win by buying so few tickets. However, if we increase X to say 2000, then the inductive strength of the argument will of course increase. If X is 9999, then the argument is even stronger, since it is extremely likely now that Dipsy will win. So you can see that inductive strength is not an all-or-nothing matter.
3. A related point is that inductive strength is defeasible, whereas validity is not. To say that validity is not defeasible is to say that if you have a valid argument, adding new premises will not make it invalid. If it is indeed true that three people have died, then it follows that at least two people died, and this will remain the consequence whatever new information you acquire.
However, new information can be added to an inductively strong argument to make it weak. Consider the lottery argument again, and suppose we add the new premise that Po has bought 9000 lottery tickets, and have given all of them to Dipsy. Obviously this new argument will is a lot stronger than the old one.
Further reading : Chapter 2 "Probability and Inductive Logic" in Brain Skyrms (2000) Choice and Chance : An Introduction to Inductive Logic Wadsworth.
<< previous page
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In this module:
• Introduction
• [A01] Identifying Arguments
• [A02] Validity and Soundness
• [A03] Patterns of Valid Arguments
• [A04] Identifying Hidden Assumptions
• [A05] Inductive Reasoning
• [A06] Good Arguments
• [A07] Argument mapping
• [A08] Analogical Arguments
• [A09] More patterns of valid arguments
Main modules
• C. About critical thinking
• M. Meaning analysis
• A. Argument analysis
• L. Basic logic
• SL. Sentential logic
• Q. Predicate logic
• V. Venn diagrams
• S. Scientific reasoning
• T. Basic statistics
• G. Strategic thinking
• U. Values and morality
• F. Fallacies & biases
• R. Creativity
Resources
• Further reading
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TUTORIAL A06: Good Arguments
A06.1 What is a good argument?
In this tutorial we shall discuss what a good argument is. The concept of a good argument is of course quite vague. So what we are trying to do here is to give it a somewhat more precise definition. To begin with, make sure that you know what a sound argument is.
Criterion #1 : A good argument must have true premises
This means that if we have an argument with one or more false premises, then it is not a good argument. The reason for this condition is that we want a good argument to be one that can convince us to accept the conclusion. Unless the premises of an argument are all true, we would have no reason to accept to accept its conclusion.
Criterion #2 : A good argument must be either valid or strong
Is validity a necessary condition for a good argument? Certainly many good arguments are valid. Example:
All whales are mammals.
All mammals are warm-blooded.
So all whales are warm-blooded.
But it is not true that good arguments must be valid. We often accept arguments as good, even though they are not valid. Example:
No baby in the past has ever been able to understand quantum physics.
Kitty is going to have a baby soon.
So Kitty's baby is not going to be able to understand quantum physics.
This is surely a good argument, but it is not valid. It is true that no baby in the past has ever been able to understand quantum physics. But it does not follow logically that Kitty's baby will not be able to do so. To see that the argument is not valid, note that it is not logically impossible for Kitty's baby to have exceptional brain development so that the baby can talk and learn and understand quantum physics while still being a baby. Extremely unlikely to be sure, but not logically impossible, and this is enough to show that the argument is not valid. But because such possibilities are rather unlikely, we still think that the true premises strongly support the conclusion and so we still think that the argument is a good one.
In other words, a good argument need not be valid. But presumably if it is not valid it must be inductively strong. If an argument is inductively weak, then it cannot be a good argument since the premises do not provide good reasons for accepting the conclusion.
For more information about inductive strength, see the previous tutorial.
Criterion #3 : The premises of a good argument must not beg the question
Notice that criteria #1 and #2 are not sufficient for a good argument. First of all, we certainly don't want to say that circular arguments are good arguments, even if they happen to be sound. Suppose someone offers the following argument:
It is going to rain tomorrow. Therefore, it is going to rain tomorrow.
So far we think that a good argument must (1) have true premises, and (2) be valid or inductively strong. Are these conditions sufficient? The answer is no. Consider this example:
Smoking is bad for your health.
Therefore smoking is bad for your health.
This argument is actually sound. The premise is true, and the argument is valid, because the conclusion does follow from the premise! But as an argument surely it is a terrible argument. This is a circular argument where the conclusion also appears as a premise. It is of course not a good argument, because it does not provide independent reasons for supporting the conclusion. So we say that it begs the question.
Here is another example of an argument that begs the question :
Since Mary would not lie to her best friend, and Mary told me that I am indeed her best friend, I must really be Mary's best friend.
Whether this argument is circular depends on your definition of a "circular argument". Some people might not consider this a circular argument in that the conclusion does not appear explicitly as a premise. However, the argument still begs the question and so is not a good argument.
Criterion #4 : The premises of a good argument must be plausible and relevant to the conclusion
Here, plausibility is a matter of having good reasons for believing that the premises are true. As for relevance, this is the requirement that the the subject matter of the premises must be related to that of the conclusion. Why do we need this additional criterion? The reason is that claims and theories can happen to be true even though nobody has got any evidence that they are true. If the premises of an argument happen to be true but there is no evidence indicating that they are, the argument is not going to be pursuasive in convincing people that the conclusion is correct. A good argument, on the other hand, is an argument that a rational person should accept, so a good argument should satisfy the additional criterion mentioned.
A06.2 Summary
So, here is our final definition of a good argument :
A good argument is an argument that is either valid or strong, and with plausible premises that are true, do not beg the question, and are relevant to the conclusion.
Now that you know what a good argument is, you should be able to explain why these claims are mistaken. Many people who are not good at critical thinking often make these mistakes :
• "The conclusion of this argument is true, so some or all the premises are true."
• "One or more premises of this argument are false, so the conclusion is false."
• "Since the conclusion of the argument is false, all its premises are false."
• "The conclusion of this argument does not follow from the premises. So it must be false."
A06.3 Exercises
? Question 1 - Answer the following questions.
1. Does a good argument have to be sound?
[Show answer]
A good argument does not have to be valid, and so ...
2. Can a good argument be inductively weak?
[Show answer]
A good argument must be either strong or valid, and so ...
TUTORIAL A07: Argument mapping
An (simple) argument is a set of one or more premise with a conclusion. A complex argument is a set of arguments with either overlapping premises or conclusions (or both). Complex arguments are very common because many issues and debates are complicated and involve extended reasoning. To understand complex arguments, we need to analyze the logical structure of the reasoning involved. Drawing a diagram can be very helpful.
A07.1 Argument maps
An argument map is a diagram that captures the logical structure of a simple or complex argument. In the simplest possible case, we have a single premise supporting a single conclusion. Consider this argument :
Life is short, and so we should seize every moment.
This can be represented in an argument map as follows:

Let us now look at another example:
Paris in in France, and France is in Europe. So obviously Paris is in Europe.
Here is the corresponding argument map:

Note that the two premises are connected together before linking to the conclusion. This merging of the links indicate that the two premises are co-premises which work together in a single argument to support the conclusion. In other words, they do not provide independent reasons for accepting the conclusion. Without one of the premises, the other premise would fail to support the conclusion.
This should be contrasted with the following example where the premises are not co-premises. They provide independent reasons for supporting the conclusion:
[1] Smoking is unhealthy, since [2] it can cause cancer. Furthermore, [3] it also increases the chance of heart attacks and strokes.
Instead of writing the premises and the conclusion in full in the argument map, we can label them and write down their numbers instead:

This diagram tells us that [2] and [3] are independent reasons supporting [1]. In other words, without [2], [3] would still support [1], and without [3], [2] would still support [1]. (Although the argument is stronger with both premises.)
Finally, it is also possible to have a single reason giving rise to multiple conclusions :
[1] Gold is a metal. [2] So it conducts electricity. [3] It also conducts heat.

A07.2 More complicated examples
Now that we know the basics of argument maps, we can combine the templates we learn above to represent more complicated arguments, by following this proceudre:
1. Identify the most important or main conclusion(s) of the argument.
2. Identify the premises used to support the conclusion(s). These are the premises of the main argument.
3. If additional arguments have been given to support any of these premises, identify the premises of these additional arguments as well, and repeat this procedure.
4. Label the premises and conclusions using numerals or letters.
5. Write down the labels in a tree structure and draw arrows leading from sets of premises to the conclusions they support.
Let us try this out on this argument:
Po cannot come to the party because her scooter is broken. Dipsy also cannot come because he has to pick up his new hat. I did not invite the other teletubbies, so no teletubby will come up to the party.
We now label and refomulate the premises and the conclusions:
1. Po cannot come to the party.
2. Po's scooter is broken.
3. Dipsy cannot come to the party.
4. Dipsy has to pick up his new hat.
5. I did not invite the other teletubbies.
6. [Conclusion] No teletubby will come up to the party.
We can then draw the argument map like this:

This is an example of what we might call a multi-layered complex argument, where an intermediate conclusion is used as a premise in another argument. So [1] and [3] are the intermediate conclusions, which together with [5] lead to the main conclusion [6]. This complex argument is therefore made up of three overlapping simple arguments in total. Of course, in this particular case you can understand the argument perfectly well without using this diagram. But with more complicated arguments, a picture can be an indispensable aid.
________________________________________
A07.3 Exercises
Draw argument maps for the following arguments:
? Question 1 -
[1] This computer can think. So [2] it is conscious. Since [3] we should not kill any conscious beings, [4] we should not switch it off.
? Question 2 -
[1. Many people think that having a dark tan is attractive.] [2. But the fact is that too much exposure to the sun is very unhealthy.] [3. It has been shown that sunlight can cause premature aging of the skin.] [4. Ultraviolent rays in the sun might also trigger off skin cancer.]
? Question 3 -
[1. If Lala is here, then Po should be here as well.] [2. It follows that if Po is not here, Lala is also absent,] and indeed [3. Po is not here.] So most likely [4. Lala is not around.]
? Question 4 -
[1. Marriage is becoming unfashionable.] [2. Divorce rate is at an all time high], and [3. cohabitation is increasingly presented in a positive manner in the media]. [4. Movies are full of characters who live together and unwilling to commit to a lifelong partnership]. [5. Even newspaper columnists recommend people to live together for an extended period before marriage in order to test their compatibility.]
? Question 5 -
[1. All university students should study critical thinking.] After all, [2. critical thinking is necessary for surviving in the new economy] as [3. we need to adapt to rapid changes, and make critical use of information in making decisions.] Also, [4. critical thinking can help us reflect on our values and purposes in life.] Finally, [5. critical thinking helps us improve our study skills.]
? Question 6 -
Now extract the premises and conclusions yourself: "The Bible says that life was created by God. The Bible is the word of God so what it says must be true. So the theory of evolution is false, even though many people accept the theory. Besides, the theory says that monkeys and humans have the same ancestors, but this cannot be since we are so different."
• You can check the answers for all the questions here.
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A07.4 More tutorials
If you are interested to learn more about drawing argument maps, you can visit the Australian company Austhink for a set of detailed online tutorials on argument mapping. An earlier version of these tutorials was commissioned by the University of Hong Kong:
• Online argument mapping tutorials
A07.5 Software for drawing argument maps
• ArgMAP is a computer program written by Joe Lau at the University of Hong Kong. It is free for non-commercial use, but this program is no longer under development and its functionality is limited. The last version of ArgMAP is v0.9.1, which you can download from this page. The program was still in beta so save your work frequently and expect mysterious crashes now and then!.
• The Australian philosopher Tim van Gelder has developed a much more sophisticated program Reason!Able. We have obtained a site license for the program and members of the University of Hong Kong can download it for free. Please visit this page for instructions. Your computer has to be within the HKU intranet to access the page. [2007 update] Reason!Able is now replaced by a new version called "Rationale". See the web site for details about getting a trial copy.
• "argumentative" is a free argument mapping software still under development.
These drawing programs can also be used to draw argument maps:
• You can draw flowcharts and other diagrams online for free at http://www.gliffy.com/.
• Many of the argument map diagrams on this web site are drawn using the open-source Graphviz package - a very powerful program.
• IHMC CmapTools is a free program for drawing pretty concept maps. It can be used for argument maps as well
• Visio is a powerful program for drawing all kinds of charts. You can download a trial version from Microsoft.
TUTORIAL A08: Analogical Arguments

A08.1 Using analogies
To give an analogy is to claim that two distinct things are alike or similar in some respect. Here are two examples :
• Capitalists are like vampires.
• Like the Earth, Europa has an atmosphere containing oxygen.
The analogies above are not arguments. But analogies are often used in arguments. To argue by analogy is to argue that because two things are similar, what is true of one is also true of the other. Such arguments are called "analogical arguments" or "arguments by analogy". Here are some examples :
• There might be life on Europa because it has an atmosphere that contains oxygen just like the Earth.
• This novel is supposed to have a similar plot like the other one we have read, so probably it is also very boring.
• The universe is a complex system like a watch. We wouldn't think that a watch can come about by accident. Something so complicated must have been created by someone. The universe is a lot more complicated, so it must have been created by a being who is a lot more intelligent.
Analogical arguments rely on analogies, and the first point to note about analogies is that any two objects are bound to be similar in some ways and not others. A sparrow is very different from a car, but they are still similar in that they can both move. A washing machine is very different from a society, but they both contain parts and produce waste. So in general, when we make use of analogical arguments, it is important to make clear in what ways are two things supposed to be similar. We can then proceed to determine whether the two things are indeed similar in the relevant respects, and whether those aspetcs of similarity supports the conclusion.
So if we present an analogical argument explicitly, it should take the following form :
(Premise 1) Object X and object Y are similar in having properties Q1 ... Qn.
(Premise 2) Object X has property P.
(Conclusion) Object Y also has property P.
Before continuing, see if you can rewrite the analogical arguments above in this explicit form.
A08.2 Analogical arguments and induction
It is sometimes suggested that all analogical arguments make use of inductive reasoning. This is not correct. Consider the explicit form of analogical arguments above. If having property P is a logical consequence of having properties Q1 ... Qn, then the analogical argument will be deductively valid. Here is an example :
(Premise 1) X and Y are similar in that they are both isosceles triangles (an isosceles triangle is a triangle with two equal sides).
(Premise 2) X has two equal internal angles.
(Conclusion) Y has two equal internal angles.
Of course, in such a situation we could have argued for the same conclusion more directly :
(Premise 1) Y is an isosceles triangles.
(Premise 2) Every isosceles triangle has two equal internal angles.
(Conclusion) Y has two equal internal angles.
What this shows is that :
• Some good analogical arguments are deductively valid.
• Sometimes we can argue for a conclusion more directly without making use of analogies. This might reveal more clearly the reasons that support the conclusion.
Of course, analogical arguments can also be employed in inductive reasoning. Consider this argument :
• This novel is supposed to have a similar plot like the other one we have read, so probably it is also very boring.
This argument is of course not deductively valid. Just because the plot of novel X is similar to the plot of a boring novel Y, it does not follow logically that X is also boring. Perhaps novel X is a good read despite an unimpressive plot because its pace is a lot faster and the story telling is more gripping and graphic. But if no such information is available, and all we know about novel X is that its plot is like the plot of Y, which is not very interesting, then we would be justified in thinking that it is more likely for X to be boring than to be interesting.
A08.3 Evaluating analogical arguments
So how should we evaluate the strength of an analogical argument that is not deductively valid? Here are some relevant considerations :
• Truth : First of all we need to check that the two objects being compared are indeed similar in the way assumed. For example, in the argument we just looked at, if the two novels actually have completely different plots, one being an office romance and the other is a horror story, then the argument is obviously unacceptable.
• Relevance : Even if two objects are similar, we also need to make sure that those aspects in which they are similar are actually relevant to the conclusion. For example, suppose two books are alike in that their covers are both green. Just because one of them is boring does not mean that the other one is also boring, since the color of a book's cover is completely irelevant to its contents. In other words, in terms of the explicit form of an analogical argument presented above, we need to ensure that having properties Q1, ... Qn increases the probability of an object having property P.
• Number : If we discover a lot of shared properties between two objects, and they are all relevant to the conclusion, then the analogical argument is stronger than when we can only identify one or a few shared properties. Suppose we find out that novel X is not just similar to another boring novel Y with a similar plot. We discover that the two novels are written by the same author, and that very few of both novels have been sold. Then we can justifiably be more confident in concluding that X is likely to be boring novel.
• Diversity : Here the issue is whether the shared properties are of the same kind or of different types. Suppose we have two Italian restaurants A and B, and A is very good. We then find out that restaurant B uses the same olive oil in cooking as A, and buys meat and vegetables of the same quality from the same supplier. Such information of course increases the probability that B also serves good food. But the information we have so far are all of the same kind having to do with the quality of the raw cooking ingredients. If we are further told that A and B use the same brand of pasta, this will increase our confidence in B further still, but not by much. But if we are told that both restaurants have lots of customers, and that both restaurants have obtained Michelin star awards, then these different aspects of similarities are going to increase our confidence in the conclusion a lot more.
• Disanalogy : Even if two objects X and Y are similar in lots of relevant respects, we should also consider whether there are dissimilarities between X and Y which might cast doubt on the conclusion. For example, returning to the restaurant example, if we find out that restaurant B now has a new owner who has just hired a team of very bad cooks, we would think that the food is probably not going to be good anymore despite being the same as A in many other ways. .
A08.4 Analogical arguments in morality
Analogical arguments occur very frequently in discussions in law, ethics and politics. In a very famous article, "A Defense of Abortion", written in 1971, philosopher Judith Thomson argues for a woman's right to have an abortion in the case of unwanted pregnancy using an analogy where someone woke up one morning only to find that an unconscious violinist being attached to her body in order to keep the violinist alive. Thomson argues that the victim has the right to detach the violinist even if this would bring about the violinist's death, and this also means that a woman has the right to abort an unwanted baby in certain cases. For further discussion on the role of analogy in moral reasoning, see this article.
A08.5 Exercises
Question 1 Evaluate these arguments from analogy. See if you can identify any aspects in which the two things being compared are not relevantly similar :
• 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. [Show answer]
Weather reports do not change the weather, but newspaper reports and the public media can influence people and have an indirect effect on moral standards.
• Democracy does not work in a family. Parents should have the ultimate say because they are wiser and their children do not know what is best for themselves. Similarly the best form of government for a society is not a democractic one but one where the leaders are more like parents. [Show answer]
There are many relevant ways in which a family is different from a society. First, the government officials need not be wiser than the citizens. Also, many parents might care for their children out of love and affection but government officials might not always have the interests of the people at heart.
• "Wives, submit yourselves to your own husbands, as unto the Lord. For the husband is the head of the wife, even as Christ is the head of the church." - St. Paul, Ephesians 5:22. [Show answer]
Should a husband be regarded as the head of his wife?
• In the early 17th century, astronomer Francesco Sizi argued that there are only seven planets: "There are seven windows in the head, two nostrils, two ears, two eyes and a mouth; so in the heavens there are two favorable stars, two unpropitious, two luminaries, and Mercury alone undecided and indifferent. From which and many similar phenomena of nature such as the seven metals, etc., which it were tedious to enumerate, we gather that the number of planets is necessarily seven."