Patterns of Arguments Examples

• If it rains, the ground will be wet.

• It is raining.

• Therefore, the ground is wet.

Modus Ponens

• If the car’s battery is dead, the engine won’t start.

• The engine does start.

• Therefore, the battery is not dead.

Modus Tollens

• Either we will go to the beach or we will go to the mountains.

• We will not go to the beach.

• Therefore, we will go to the mountains.

Disjunctive Syllogism

• If I study hard, then I will pass the exam.

• If I pass the exam, then I will graduate.

• Therefore, if I study hard, then I will graduate.

Hypothetical Syllogism

• Either the manager will approve the project or the board will reject it.

• If the manager approves it, the team will start working.

• If the board rejects it, the team will look for alternatives.

• Therefore, either the team will start working or the team will look for alternatives.

Constructive Dilemma

• Assume that there is a largest prime number.

• Then you can construct a larger prime by multiplying all known primes and adding 1, which is itself prime or divisible by a prime not in the list.

• This contradicts the assumption of a largest prime.

• Therefore, there is no largest prime number.

Reductio ad Absurdum