Logic: Basic Concepts 1

Argument

A group of statements ( or propositions) of which one ( the conclusion) is claimed to follow from the others ( the premises), which are regarded as providing support or grounds for the truth of that one.

Premises

The statements or propositions that are claimed to provide grounds or reasons for a conclusion

Conclusion

The statements or propositions that is claimed to follow from the premises of an argument

Inference

A process by which one statement is arrived at and affirmed on the basis of some other statement or statements

The Statement

A sentence that is either true or false ( has truth value)

• Different sentences can express the same statement

• Other types of sentences do not have truth value

Different sentences can express the same statement

it is raining

Water is falling from the sky

Il pleut. (French)

Other types of sentences do not have truth values

Make it rain!

Is it raining?

Oh no!

One sentence can contain multiple statements

• The dog barked and ran after the car

• The dog barked and ran after the car, but didn’t catch it

The words “and” and “but” connect distinct statements in a single sentence

Recognizing and Analyzing Arguments

Step 1: [Recognize] Look for an attempt to convince 

Step 2: [Analyze] Find the conclusion 

Step 3: [Analyze] Find the premises 

Some arguments are obvious Example

All humans are mortal

Socrates is human

Therefore, Socrates is mortal

• The above argument is an example of a syllogism

Syllogism

an instance of a form of reasoning in which a conclusion is drawn (whether validly or not) from two given or assumed propositions (premises), each of which shares a term with the conclusion, and shares a common or middle term not present in the conclusion

In real contexts, arguments are presented in all kinds of different, idiosyncratic ways

Premises and conclusions can occur in any order in an argument

You drank my milk, as evidenced by the fact that you have a milk mustache!

Some common conclusion indicators

• Therefore

• Thus

• We can infer that

• Hence

Some common premises indicators

• Because

• Since

• As evidenced by

Sometimes no conclusion or premise indicators are used: Example

You think I drank your milk. You are wrong. I am lactose intolerant

Sometimes premises and conclusions are not put in statement form: Example

You drank my milk! Look at your milk mustache!

Sometimes, what looks like it might be an argument, isn’t an argument 

“Our company has paid the highest dividends
of any Fortune 500 company for the last 5
consecutive years. In addition, we have not had
one labor dispute. Our stock is up 25% in the last
quarter.”

Enthymeme

A “truncated syllogism”, or a syllogism in which one of the premises is not explicitly stated, but implied

Enthymeme Example

Socrates is human. Therefore, he is mortal

What premise is missing here?

• All humans are mortal

Standard Form Definition 

Is an standardized way of presenting an argument

Standard Form

To present an argument in standard form

1. Put the premises and conclusion in a numbered list

2. Put the conclusion at the end of the list

3. Write “therefore” in front of the conclusion

Standard Form Example

1. All humans are mortal (premise)

2. Socrates is human (premise)

3. Therefore, Socrates is mortal (conclusion)