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.”

Inductive, weak argument:

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. 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.

Deductive, valid & persuasive:

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

2. I am a student.

3. I am tired.

Deductive, valid & not persuasive:

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

2. I am a teacher.

3. I am fabulous.

Inductive, strong, persuasive:

1. Most superheroes have special powers.

2. Wonder Woman is a superhero.

3. Wonder Woman has special powers.

Inductive, weak

1. Most superheroes have special powers.

2. Wonder Woman has special powers.

3. Wonder Woman is a superhero.

Consistency

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

Some common invalid forms of argument:

Affirming the consequent (note it looks deceptively like modus ponens):

If p, then q.

q.

Therefore, p.

If she is a human then she is a mammal. She is a mammal. She is a human. (invalid)

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

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

Denying the antecedent (note it looks deceptively like modus tollens):

If p, then q.

Not-p.

Therefore, not-q.

If she is a human then she is a mammal. She is not a mammal. She is a human. (invalid)

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

Other fallacies (improper forms of argument):

Appeal to ignorance: Arguing that a claim is true because it has not been shown to be false. Example (Senator Joseph McCarthy (of HUAC infamy) making the case that a particular person is a communist): “I do not have much information on this except the general statement of the agency that there is nothing in the files to disprove his Communist connections.”

Appeal to authority: Attempting to establish the truth of a claim by appealing to the fact that some alleged authority endorses the claim. This method of argumentation is fallacious only when the alleged authority is or should not be taken to be a legitimate authority on the topic in question. Example: Arguing that the earth is flat because that is what ancient cartographers thought.

Begging the question (aka circular argument): Using your conclusion as a premise in the argument for that conclusion. Example: The Bible is the word of God because its truths were revealed through divine revelation.

Equivocation: Using the same word in two different senses to make a bad argument look like a good one. Example: Men and Women are physically different. Therefore, the sexes are not equal and the law should not treat them as if they are.

Straw man: Misrepresenting an opposing view so that it is easy to refute. Example: People in favor of gun control want to ban all guns.

False dilemma: Presenting a premise of the form “p or q” as though it embraced all relevant possibilities. I.e., ignoring relevant and viable possibilities. Example: Assuming that in this last Presidential election a voter must vote for either George W. Bush or John Kerry, when in fact a voter could have voted for Dennis Kucinich, Ralph Nader, or anyone else.

Slippery Slope: slippery slope involves "if-then" relationships (especially causal connections) which are not (as in the case of deductive logic) 100% absolutely certain.

Example: If you don't get to bed early, you'll be too tired to do well on the GRE tomorrow - and then you won't get accepted into a decent graduate school and then you'll end up a washed-out alcoholic living in a trash-bin.

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