In Logic, what are Sound and Valid Arguments?

There are several types of arguments, and one of the most common are deductive arguments. Deductive arguments are those who contain a string of related statements that taken in totality prove or establish a conclusion.

Such deductive arguments can be attacked on two different fronts: 1) call into question the premises of the argument itself, 2) call into question the structure of the argument, specifically that the conclusion does not follow from the premises.

This leaves us with four different possibilities for any deductive argument:

• Invalid and unsound: at least one premise is false, and conclusion does not follow from the premises. Example:
  
  
  • All GPS satellites are positioned underwater.
  • Everything positioned underwater becomes wet.
  • therefore, GPS satellites are dry.
• Invalid: premises may be true but conclusion does not follow from them. Example:
  
  
  • Mangosteen is a fruit.
  • Mangosteen is purple.
  • Therefore, all fruit is purple.
• Valid but unsound: conclusion follows from the premises but at least one of the premises is false. Example:
  
  
  • All art movements started in India.
  • Bauhaus was an art movement.
  • Therefore, Bauhaus started in India.
• Sound: all premises are true and conclusion follows from the premises. Example:
  
  
  • Investment strategies may be profitable
  • "Dogs of the Dow" is an investment strategy
  • therefore, the "Dogs of the Dow" strategy may be profitable.

Note that in all four of the examples above, the conclusion can be true. Even an invalid and unsound argument can have a true statement as its conclusion - its just that the conclusion may not follow from the premises, or that the premises that the conclusion is based on are not true. Let us imagine a non-sequitor, for example that is unsound and invalid, but the conclusion is true:

• non-sequitor:
  
  
  • The Curse of the Bambino will never end.
  • Sputnik was launched by China.
  • Therefore, en-passant is a move in chess.

Also, arguments themselves are neither true or false, they are to be judged on their validity and soundness. It is the statements within an argument, namely the premises and conclusion that can have truth and falsity.