Argument is the basic unit of our reasoning and communication. The most idealized form of argumentation is a deductive reasoning according to which a good argument:

  • is a valid argument (there is no way for a conclusion to be false if all the premises are true) and
  • has all true premises.

An argument that is valid and has all true premises is a sound one. Here is the list of the most classically recognized forms of valid arguments.

Simplification

  1. P and Q
    Therefore,
  2. P

Conjunction

  1. P
  2. Q
    Therefore,
  3. P and Q

Addition

  1. P
    Therefore,
  2. P or Q

Modus Ponens

  1. If P then Q
  2. P
    Therefore
  3. Q

Modus Tollens

  1. If P then Q
  2. Not Q
    Therefore,
  3. Not P

Hypothetical syllogism

  1. If P then Q
  2. If Q then R
    Therefore,
  3. If P then R

Constructive dilemma

  1. P or Q
  2. If P then R
  3. If Q then S
    Therefore,
  4. R or S

Destructive dilemma

  1. If P then R
  2. If Q then S
  3. Not R or not S
    Therefore,
  4. Not P or not Q

Bibliography:

Kenyon, Tim, Clear Thinking in a Blurry World, Nelson Education Ltd, 2008.