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3 Types of arguments

  1. Deductive Arguments
  2. Inductive Arguments
  3. Abductive

 

Deductive Arguments

A valid deductive argument is truth preserving.

Truth Preserving – If the premises are true the conclusion is guaranteed to be true. The premises cannot be true and the conclusion false. They preserve the truth of the claims being made.

Validity and Soundness

 

Validity – A deductive argument is valid if it is in the correct logical form. Validity refers only to the logical form of the argument and has nothing to do with whether the premises or the conclusion are true.

An argument can be valid but the conclusion can be false and an argument can be invalid but nevertheless have a true conclusion.

An argument can be valid but have a false conclusion because one or more of the premises may be false. If one or more of the premises are false we say that the argument is not sound.

A valid argument with a false conclusion:

  1. If I don’t do the readings for this class, then I will get a good grade.
  2. I won’t do the readings for this class.
  3. So, I’ll get a good grade.

Let me assure you this conclusion is false J This argument is valid but unsound because one of the premises is false.

Soundness – A deductive argument is sound if all the premises are true.

So, if an argument is valid and sound we know for sure that the conclusion is true, which means that when evaluating an argument we need to check for validity and soundness and when constructing arguments we should make sure our arguments are valid and sound.

An invalid argument with a true conclusion:

  1. Roses are red.
  2. Violets are blue.
  3. So, thirty plus two is thirty-two.

The conclusion happens to be true but the “argument” does not guarantee the conclusion to be true because the conclusion does not actually follow from the premises.

The difference between the first and second argument is that the first is in valid logical form but the conclusion is false because one of the premises is false and the second argument is not in valid logical, despite the conclusion being true.

Logical Form – The logical structure of an argument.

Common Valid Forms of Arguments

Modus Ponens

  1. If P then Q.
  2. P.
  3. Therefore, Q.

Example:

  1. If it is raining out then there are clouds in the sky.
  2. It is raining outside.
  3. Therefore, there are clouds in the sky.

This argument is valid as it is in a correct logical form. And it is sound, both premises are true, so, we know that the conclusion is true.

Modus Tollens

  1. If P then Q.
  2. Not-Q.
  3. Therefore, not-P.

Example:

  1. If it is raining out then there are clouds in the sky.
  2. There are not clouds in the sky.
  3. Therefore, it is not raining.

This argument is valid as it is in a correct logical form. And it is sound, both premises are true, so, we know that the conclusion is true.

Exercise: With your partner come up a sound and unsound examples of a modus ponnens and a modus tollens argument.

Common Invalid forms of Argument

Affirming the Consequent:

  1. If P then Q.
  2. Q.
  3. Therefore, P.

Example:

  1. If it is raining out then there are clouds in the sky.
  2. There are clouds in the sky.
  3. Therefore, it is raining.

Denying the Antecedent:

  1. If P then Q.
  2. Not-P.
  3. Therefore, not-Q.

Example:

  1. If it is raining out then there are clouds in the sky.
  2. It is not raining.
  3. Therefore, there are not clouds in the sky.

Exercise: With your partner come up an example of an argument that makes the mistake of affirming the consequent and an argument that makes the mistake of denying the antecedent.

 

Logically Syllogism – Also known as a Syllogism in Barbara. Dates back 2,500 years to Aristotle, the father of logic in the Western philosophical tradition.

  1. All A’s are B.
  2. C is an A.
  3. Therefore, C is a B.

Example:

  1. All men are mortal.
  2. Socrates is a man.
  3. Therefore, Socrates is mortal.

 

Logical Fallacies

Equivocation:

Example 1:

  1. Man is the only rational animal.
  2. No woman is a man.
  3. Therefore, no woman is rational.

Using the same word multiple times with a different meaning each time or switching back and forth between meanings is called equivocating.

When we using a more precise word than man it becomes clear that the conclusion does not actually follow from the premises.

Example substituting biological species definition of man:

  1. Homo sapiens are the only rational animal.
  2. No woman is a homo sapien.
  3. Therefore, no woman is rational.

Or

Example substituting gender definition of man:

  1. Male homo sapiens are the only rational animal.
  2. No woman is a male homo sapien.
  3. Therefore, no woman is rational.

Begging the Question/Circular Reasoning

“Begging the question” is a technical term in philosophy and should not be used casually without care as to its definition in philosophy. This fallacy is also known as circular reasoning.

Begging the Question – An argument begs the question when the conclusion is stated or assumed in one or more of the premises.

Example:

  1. It is always wrong to kill an innocent human being.
  2. A fetus is an innocent human being.
  3. Therefore, it is always wrong to kill a fetus.

Exercise: Discuss with your partner how it might be that this argument assumes the conclusion.

Other dubious methods of arguing

Straw man Argument – A straw man argument is when instead of arguing against the actual argument one sets up a “straw man”, which is an argument that looks similar to the original but different is some important way, and then attacks the straw man while claiming to have show the original argument unsound or invalid.

Ad Hominem – Often times arguments resort to attacking the other person’s character in an attempt to discredit them, but this is not a logically acceptable way of arguing. When doing philosophy we should just focus on the argument being presented and leave the character of the person making the argument out of the picture.

 

Example: Anyone who says abortion is right/wrong is just stupid and evil and should never be listened to or taken seriously by anyone.

 

Arguing from authority – Appeals to authority, whether a particular person or religious tradition, are not acceptable methods of arguing in philosophy.

 

Example: Einstein believed in God so God must exist.

 

 

Other Types of Arguments

Inductive – Inductive arguments are the type of arguments used in science, such arguments are also called empirical arguments as they rely on information derived from the senses and draw conclusion based on our experiences. No inductive argument is ever one-hundred percent guaranteed the way a deductive argument is.

Example:

  1. The sun has risen every morning in recorded history.
  2. Therefore, the sun will rise tomorrow.

Example:

  1. Every swan I have ever seen is white.
  2. Therefore, all swans are white.

As you can see inductive arguments are stronger or weaker depending on the evidence and sample size whereas deductive arguments are either valid or invalid.

However, it is very important to note that many deductive argument rely on an empirical premises, which may give us reason to doubt the conclusion if the argument is valid.

Consider the previous example wherein we had a deductive argument where one of the premises was that “All men are mortal” which is an empirical claim.

Abductive – Abductive arguments, also called inference to the best explanation (IBE), also play an important rule in scientific inquiry. Many scientific facts are inferences to the best explanation.

Example: Previous to Galileo it was thought that the sun orbited the earth, this was thought to be the best explanation of certain facts. However, this explanation didn’t properly explain the movement of the other planets so Galileo hypothesized that the Sun was the center of the universe and that all the planets orbited the Sun and not the earth.

This type of thinking is also employed constantly in everyday life.

  1. My sandwich is gone from the refrigerator.
  2. My roommate is the only one in the apartment.
  3. Therefore, my roommate ate my sandwich.

Review

 

Types of Arguments:

  1. Deductive
  2. Inductive
  3. Abductive (IBE)

 

Validity and Soundness

 

Logical Fallacies:

  1. Equivocation
  2. Begging the Question
  3. Straw man Argument
  4. Ad Hominem Argument
  5. Arguing from Authority

 

Other Terminology:

Conditional – an if-then claim i.e If P the Q.

Antecedent – the first part of a conditional.

Consequent – the second part of a conditional

Conclusion – the conclusion of a argument, denoted by the use of “so” or “therefore” and the last line of the argument is generally underlined to show that the next line of the argument is the conclusion

 

Logic Quiz

Question 6

A deductive argument is valid if all of its premises are true? T/F

 

Question 6

A deductive argument is sound if it is in the correct logical form? T/F

 

Question 6

If a an argument is valid then its conclusion is true. T/F

 

Question 6

In the statement, “If the lamp is on, there is power in the outlet,” which part is the consequent?

 

Question 6

If P then Q. Not-Q. Therefore, not-P. Valid/Invalid

 

Question 6

If P then Q. Not-P. Therefore, not-Q. Valid/Invalid

 

Question 6

If P then Q. Q. Therefore, P. Valid/Invalid

 

Question 6

If P then Q. P. Therefore, Q. Valid/Invalid

 

Question 6

Is the following argument valid Y/N Is it sound? Y/N

If turtles are mammals then tigers are amphibians.

Turtles are not mammals.

So, tigers are not amphibians

 

Question 6 

Is the following argument valid Y/N Is it sound? Y/N

If chairs are evil then tables are good.

Chairs are evil.

So, tables are good

 

Question 6

Is the following argument valid Y/N Is it sound? Y/N

If Joey is a kangaroo then Joey is not a reptile.

Joey is a kangaroo.

So, Joey is not a reptile.

 

Question 6 Is the following argument valid Y/N Is it sound? Y/N

  • If abortion is wrong, then Greece is not in Europe.
  • Greece is Europe.
  • Therefore, abortion is not wrong.

 

Question 6

 

What  logical fallacy does this argument makes: Man is the only rational animal. No woman is a man. Therefore, no woman is rational.

 

Question 6

Explain the logical fallacy this argument makes: It is always wrong to kill an innocent human being. A fetus is an innocent human being. Therefore, it is always wrong to kill a fetus.

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