Deductive Arguments

Question

A deductive argument can be:

a. neither valid nor sound.
b. sound with a false conclusion.
c. sound but not valid.

 

If a deductive argument is valid, its conclusion is:

a. a logical consequence of its premises.
b. sound.
c. true.

Answer 1

1. A valid argument is one where the premises may or may not be true, but the argument is correct.  So if the premises are false, the conclusion may be true or false, but if the premises are true, then the conclusion must be true.

 

A sound argument is one where the argument is valid AND the premises are true, so the conclusion must also be true,

 

So a sound argument cannot have a false conclusion.  And it must be valid.  So a is correct by elimination.  It's also true by definition.  If the argument is not valid, then it cannot be sound.  So in that case the argument would be neither sound nor valid.

 

2. If an argument is valid, then the conclusion is true if the premises are true, so a seems right.  But we can also eliminate b and c:

 

b - A conclusion is not said to be "sound".  "Sound" is used to define the argument, not the conclusion.

c - In a valid argument, the truth of the conclusion depends on the premises, so you can't say that a conclusion is true just because the argument is valid.