Argument: a set of reasons given in support of a conclusion



Argumentation Lecture Notes

1. Argument: A set of reasons given in support of a claim.

2. Conclusion: The claim intended to be supported by the argument is called the conclusion of the argument.

3. Premises: The claims given as reasons for thinking the conclusion of the argument is true are called the premises of the argument.

4. Deductive Validity: An argument is valid if the conclusion necessarily follows from the premises. If the premises are true, then the conclusion must also be true.

5. Soundness: An argument is sound if it is valid and all of its premises are true.

6. Inductive Strength: It is unlikely that the conclusion is false if the premises are true.

Is it valid?

• Assume the premises are true.

• Ask yourself, “Does the conclusion necessarily follow from these premises?”

• If so, the argument is valid.

• Notice that a valid argument can have a false conclusion!

• A valid argument can have false premises.

Re-constructing an author’s argument into standard form

In the simplest case, we may need only to re-arrange the propositions of the argument in order to translate it into a standard-form categorical syllogism. Thus, for example,

"Some birds are geese, so some birds are not felines, since no geese are felines"

1. No geese are felines.

2. Some birds are geese.

3. Therefore, Some birds are not felines.

Identify the premises and conclusions:

The government thinks 18-year-olds are responsible enough to vote and mature enough to fight a war, so why can’t they drink alcohol?

1. 18-year-olds are legally allowed to vote.

2. 18-year-olds can be drafted into war.

C: Therefore 18 year-olds should be allowed to drink alcoholic beverages.

Some common valid forms of deductive argument:

Modus ponens: If p, then q.

p.

Therefore, q.

Modus tollens: If p, then q.

Not-q.

Therefore, not-p.

Hypothetical syllogism:

If p, then q.

If q, then r.

Therefore, if p then r.

Disjunctive syllogism:

p or q.

Not-p.

Therefore, not-q.

Dilemma: p or q.

If p, then r.

If q, then s.

Therefore, r or s.

Inductive Arguments: (may be strong or weak, not valid or sound)

In standard logic, the term “inductive argument” means “an argument that is intended to be strong rather than valid.”

I have never broken any bones in my body. Therefore, I will never break any bones in my body.

Inductive strong argument:

I have never hurt an animal.

C: I will never hurt an animal.

A persuasive argument is a valid argument with plausible, or obviously true, or antecedently accepted premises. It can be inductive or deductive.

1. If I am a student, I am tired.

2. I am a student.

3. I am tired.

1. If I am a teacher, I am fabulous.

2. I am a teacher.

3. I am fabulous.

1. Superheroes have special powers.

2. Wonder Woman is a superhero.

3. Wonder Woman has special powers.

1. Most superheroes have special powers.

2. Wonder Woman has special powers.

3. Wonder Woman is probably a superhero.

Consistency

When a set of propositions cannot all be simultaneously true, we say that the propositions are inconsistent.

If she is a human, then she is a mammal.

She is a mammal.

She is a human.

If they are the state governor, then they are a politician. They are a politician.

They are a state governor.

(Note that I am using “they” as a singular pronoun of non-binary gender.)

If she is a human then she is a mammal.

She is not a mammal.

She is a human.

If they are the state governor, then they are a politician. They are not the state governor.

They are not a politician.

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