Article analysis and discussion

“Reasoning About Morality and Values”

Petrenko Anton, PhD
E-Mail: [email protected]

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This lecture will introduce students to categories of argument, deductive argument forms and validity, and portraying argument structure using arrow diagrams and standard form.
Lecture Objectives

Deductive and non-deductive arguments

Valid and Sound deductive argument

Valid argument forms

Paraphrasing vs. Summary

Diagramming Argument Structure: Arrow Diagrams

Diagramming Argument Structure: Standard Form

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Categories of Arguments
All arguments fall into two main categories: Deductively valid arguments and non-deductively valid arguments. The later subdivides into inductively strong and abductively strong argument.

Deductively valid
(demonstratively valid)
Non-Deductively valid
(non-demonstratively valid)
Abductively Strong
Inductively Strong

Deductively Valid Argument

What is a deductively valid argument?
Definition:
A deductively valid argument is an argument that has the following property, if its premises are true, its conclusion must be true.

Deductive arguments are intended to provide conclusive (certain and final) support for its conclusion. Deductive arguments can be valid and invalid.
Everyone who is a human being has three heads
Socrates is a human being
Socrates has three heads
Example:

Note!
To be valid, the deductive argument DOES NOT HAVE TO BE TRUE OR HAVE TRUE PREMISES!
To be valid, the conclusion of the argument just must follow necessarily from premises.

Assume them to be true for a second, does the conclusion follow necessarily? Then its valid!

Deductive Arguments

If Sam is bald, then Jim is late
Sam is bald
Jim is late
If apples grow on trees, then sky is falling
If sky is falling, then seas are rising
If apples grow on trees, then seas are rising
If Socrates is human, then he is mortal
Socrates is not mortal
Socrates is not human
All dogs hate cats
All cats hate mice
All dogs hate mice
All dogs hate cats
Fluffy is a dog
Fluffy hates cats

If apples are round, then pears are pear-shaped
This pear is pear-shaped
All apples are round

Which ones are valid?

Deductive Arguments

Definition:
A deductively valid argument with all true premises is said to be a sound argument.

But what makes a deductive argument a good argument.

A deductive argument is good when it is both valid and all its premises are in fact true. Such arguments are called sound!

Sound arguments always have true conclusions! These are the best kind of arguments one can have.

Deductive Arguments

If present is the 21st century, then present is not antiquity
Present is the 21st century
Present is not antiquity
If apples grow on trees, then sky is falling
If sky is falling, then seas are rising
If apples grow on trees, then seas are rising
If Socrates is human, then he is mortal
Socrates is not mortal
Socrates is not human
All dogs hate cats
Fluffy is a dog
Fluffy hates cats
If you got an A, you passed the course
You got an A
You passed the course

Which ones are sound?

Valid Deductive Argument Forms

If Sam is bald, then Jim is late
Sam is bald
Jim is late

You might have noticed that the arguments that are valid have some similar general patterns. These are called valid argument forms.

Any argument that has the same valid form will be always valid (although it might not be sound)
If p, then q
p
q
If Socrates is human, then he is mortal Socrates is human
Socrates is mortal

This argument form is called Modus Ponens
If p, then q
Not q
Not p

This argument form is called Modus Tollens
If Sam is bald, then Jim is late
Jim is not late
Sam is not bald

Valid Deductive Argument Forms

If Sam is bald, then Jim is late
If Jim is late, then John is happy
If Sam is bald, then John is happy

If p, then q
If q then r
If p then r
If you As the course, your mom will be glad
If you mom is glad, your life is happy
If you As the course, your life is happy

This argument form is called Hypothetical Syllogism
Either p or q
Not q
p

This is called Disjunctive Syllogism
Either you passed, or you are sad
You are not sad
You passed
Either we will turn up heat or we will freeze
We will not freeze
We will turn up heat

These are only some of a good number of valid argument forms (schema)

Deductive Arguments

If Sam is bald, then Jim is late
Sam is bald
Jim is late
If apples grow on trees, then sky is falling
Sky is not falling
Apples don’t grow on trees
If Socrates is human, then he is mortal
Socrates is not mortal
Socrates is not human
If sun is shining, then life is great
Sun is shining
Life is great
Either dogs hate cats or love them
Dogs don’t love cats
Dogs hate cats

Which argument schemas are used?
If apples grow on trees, then sky is falling
If sky is falling, then seas are rising
If apples grow on trees, then seas are rising
Modus Ponens
Disjunctive Syllogism
Modus Ponens
Modus Tollens
Modus Tollens
Hypothetical Syllogism

Invalid Deductive Argument Forms

If Carla is late, then Jim is sad
Jim is sad
Carla is late

This argument form is called affirming the consequent (second premise affirms the consequent). It is always invalid

If p, then q
q
p
If p, then q
q
p
If Carla is late, then Jim is sad
Carla is not late
Jim is not sad
If p, then q
Not p
Not q
This argument form is denying the antecedent (second premise denies the antecedent). It is always invalid

If Carla is late, Jim will be sad. But he might be sad also for other reasons (so premises can be true but conclusion false—Carla not late)

There are some argument patterns that are always invalid (although might appear valid)

If Carla is late, Jim will be sad. But this also does not mean that he won’t be sad if she shows up on time. All the argument says is that if she does not, he will for sure be sad.

Memorize: affirming the consequent or denying the antecedent is invalid!

So, now that we have some idea of how some premises can be linked together in deductive arguments, we can analyze passages to determine the argument structure
Diagramming Arguments

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Analyzing Long Passages
When you are evaluating longer arguments, there are a number of obstacles:
1. Only a small part might contain claims, premises, or conclusions (most will be descriptions, narrative, illustrations)
2. The premises and conclusions might be implicit.
3. Many long works contain few or no arguments at all.

1. Read the passage and circle inference indicators
2. Examine each sentence for its role in the passage
(premise, conclusion, background, illustration, digression, definition)
3. Identify the main point of the passage
4. Check conclusion against the rest of the passage. How do the other claims fit with this claim?

5. Identify the structure of the argument by relating reasons to conclusion

6. If there are unclear, ambiguous, or vague words central to the passage, clarify them.

Identifying Relevant to the Argument Claims

(1) Background information about the controversy

[ The debate over the gay marriage has become particularly heated over the last past two years. ] [ By gay marriage, I mean the right of same-sex couples to enter into a legal union that give them the rights normally shared by heterosexual couples who marry. ] [ Gay men and women have demanded they be given the legal right to marry. ] [ Many conservatives have rejected the idea on the grounds it will undermine the sanctity of marriage. ] [ I contend we should allow gay marriage] because [ if we do not we will be denying a significant segment of the population the basic rights shared by the rest of the population. ]
(1)
(2)
(3)
(4)
(5)
(6)
(2) Defines key term (gay marriage)
(3) Presents a position of one of the parties in the debate
(4) Presents a contrary position in the debate
(5) Presents controversial claim (conclusion)

(6) Presents reason for the truth of the controversial claim (premise)

Diagramming Argument Structure: Arrow Diagrams

Barack Obama has great ideas for preserving the natural environment. You bet he does! Therefore Obama being elected is good for Canada.”
Step 1:
Step 2:
Step 3:
Step 4:
Read the passage and circle any premise or conclusion indicator words.
[2]
[1]
[3]
Number all the claims in the passage in the sequential order.
Examine each sentence for its role in the passage
(premise, conclusion, background, illustration, digression, definition)
Cross out extraneous (redundant) claims in the passage which are neither premises nor conclusions.
Step 5:
Draw a diagram with the conclusion at the bottom and premises at the top. Draw arrows from premises to the conclusions they support.
3
1

Diagramming Argument Structure: Arrow Diagrams

What do you think of shopping at the Bay? I’ll tell you! They’ve got great prices, and they’ve got a good selection of men’s clothes. So, the Bay is a great place to shop!”
[2]
[1]
[4]
[5]
4
3
5
Both premises 2 and 3 give independent reason to believe the conclusion is true. If one turns out to be false, the other can still support the conclusion.
This is called a convergent argument (premises are independent).
Step 1:
Step 2:
Step 3:
Step 4:
Read the passage and circle any premise or conclusion indicator words.
Number all the claims in the passage in the sequential order.
Cross out extraneous (redundant) claims in the passage which are neither premises nor conclusions.
Step 5:
Draw a diagram with the conclusion at the bottom and premises at the top. Draw arrows from premises to the conclusions they support.
Examine each sentence for its role in the passage (premise, conclusion, background, illustration, digression, definition)

[3]

Diagramming Argument Structure: Arrow Diagrams

If Marla buys a house in the suburbs, she will be happier and healthier. She is buying a house in the suburbs. So, she will be happier and healthier.
Step 1:
Step 2:
Step 3:
Step 4:
Read the passage and circle any premise or conclusion indicator words.
Number all the claims in the passage in the sequential order.
Cross out extraneous (redundant) claims in the passage which are neither premises nor conclusions.
Step 5:
Draw a diagram with the conclusion at the bottom and premises at the top. Draw arrows from premises to the conclusions they support.
[1]
2
1
3
[2]
[3]
Premises 1 and 2 are called linked premises (or dependent premises).

Linked premises support the conclusion together (can’t do it without each other), and must be considered together.

Examine each sentence for its role in the passage
(premise, conclusion, background, illustration, digression, definition)

Diagramming Argument Structure: Arrow Diagrams

There is no question in my mind. I therefore maintain that Colonel Mustard is the murderer. Because if he did it, he would probably have bloodstains on the sleeve of his shirt. The bloodstains are tiny, but they are there. Any observant person can see them. Also, the murder weapon was within his reach before the crime. And since of all the people in the house he alone does not have an alibi, he must be the killer.
[2]
[1]
[3]
[4]
3
6
4
[5]
[6]
[7]
[8]
7
8
Premises 3 and 4 are linked premises (or dependent premises).

Linked premises support the conclusion together (can’t do it without each other), and must be considered together.

The other two premises (6 and 7) provide independent support to the conclusion. If one is false, the other can still provide support.

Diagramming Argument Structure: Arrow Diagrams

The famous trial lawyer Clarence Darrow (1857-1938) made a name for himself by using the “determinism defense” to get his client acquitted of serious crimes. The crux of his argument is that humans are not really responsible for what they do because they cannot choose freely—they are determined or predestined by nature (or God) to be the way they are. They have no free will. But Darrow is wrong about human free will for two reasons. First, in our moral life, our common-sense experience suggests that sometimes we are free to make moral decisions. We should not abandon what common-sense tells us without good reason, and Darrow did not give a good reason. Second, Darrow’s determinism is not confirmed by science, as he claims—it actually conflicts with science. Modern science says there are many things (at the subatomic level) that are not determined at all. They just happen.
5
8
6
9
4
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
7
Sometimes premises lead to a conclusion that in turn functions as a premise for another conclusion. We call such a premise an intermediate conclusion. Premise 8 is intermediate conclusion.

Premises 4, 5, and 6 are linked premises. They support the conclusion together.

Diagramming Argument Structure: Arrow Diagrams

Most philosophers are nerds, and Chris is a philosopher. Therefore, Chris is probably a nerd. Therefore, Chris probably has poor social skills, because most nerds have poor social skills.
4
1
3
5
[1]
[2]
[3]
[4]
[5]
2
The only valid reasons for dishonorably discharging someone from Canadian Armed Forces are health problems and violations of military regulations. So, if Amal says he was dishonorably discharged for simply being gay, he is either lying or he is mistaken. He is not lying. So, he is mistaken.
[1]
[2]
[3]
[4]
1
2
3
4
Canadian Armed Forces
Philosopher nerds

Diagramming Argument Structure: Arrow Diagrams

If an individual in a coma is no longer a person, then giving him a drag to kill him is not a murder. Such an individual is in fact not a person.
Therefore, giving him the drug is not a murder.
1
3
2
“Grow accustomed to the belief that death is nothing to us, since every good and evil lie in sensation. However, death is the depravation of sensation. Therefore… death is nothing to us.”
Coma
[1]
[2]
[3]
[1]
[2]
[3]
[4]
2
4
3
Death

I think City Council should pass a by-law prohibiting smoking in all restaurants and bars. It won’t be a popular move, but its clearly the best thing from a public-health point of view. By passing such a by-law, City Council would be setting a good example and reminding everyone what a serious risk smoking poses
[1]
[2]
[3]
[4]
1
3
4

Diagramming Argument Structure: Arrow Diagrams

There are at least two main views regarding the morality of war. Pacifism is the view that no war is ever justified because it involves the taking of human life. Just-war theory is the view that some wars are justified for various reasons—mostly because they help prevent greater evils (massacres, ethnic cleansing, tyranny) or because they are means of self-defence. I think our own moral sense tells us that occasionally (as during WWII) violence is morally justified. It would be hard for anyone to deny that a war to prevent something like a Holocaust is morally right. Just-war theory is correct ((Implied conclusion)
[1]
[2]
[3]
[4]
[5]
5
4
[6]
6

Diagramming Argument Structure: Standard Form

[ (1) In all wars there is the chance innocent people will be killed], and [ (2) we should never kill innocent people, even for a good cause]. So, [ (3) we should not participate in this war.]

1 In all wars there is the chance that innocent people will be killed.
2 We should never kill innocent people.

 3 We should not participate in this war.
1
3
2

[(1) Some people justify deception as simply a part of good business practice]. However, [(2) good business practice is built upon trust]. And [(3) trust is undermined by deception]. So, [(4) good business practice should not be built upon deception].

2 Good business practice is built upon trust.
3 And trust is undermined by deception.

 4 Good business practice should not be built upon deception.
2
4
3

Diagramming Argument Structure: Standard Form
3
2
5

(1) es should work to improve the labour conditions of their workers in developing countries. (2) This will improve their socioeconomic conditions. (3) Some people argue that to prevent tragedies like the one that happened in Bangladesh, the companies should withdraw from the host country. (4) But withdrawing from the host country will produce much greater suffering in the long run due to slower economic development and unemployment. (5) Therefore, business should stay and improve conditions.
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Squiggly arrows are used to represent objections in more complex argument structures. In the example given, statement (3) is an objection to the conclusion that business should stay in the host country, so a squiggly arrow connects it to the conclusion (objections could also connect to the premises within the argument).

The author defends the conclusion by presenting a counter-objection (4) to the original objection (3).