Examining Deductive Arguments

 

A.  Some Important Terms:

• arguments  occur when a group of statements (or premises) leads to another group of statements  (conclusions)

• a conclusion is the statement or argument designed to be supported or defended

• premises are the starting points of an argument.  They are used to defend the conclusion and are typically affirmed without any defense.

• look for premise indicators such as since, because, and for, which often precede premises.   Likewise conclusion indicators such as therefore, thus, hence, and consequently often precede conclusions.

Examples:

Since all mammals are warm blooded creatures,     [pr. 1]

and since a whale is a mammal,     [pr. 2]

it follows that a whale is a warm blooded creature.  [concl.]

 

If there are millions of habitable planets in our galaxy, then it seems likely that life has evolved on more than just this one.      [pr. 1]

There are millions of habitable planets in our galaxy.     [pr. 2]

Therefore it seems likely that life has evolved on more than just this one.     [concl.]

B.  Some More Important Terms

• a valid argument is one in which the conclusions follow from the premises.

• an invalid argument is one in which the conclusions do not follow from the premises.

  • note:  arguments can be valid or invalid.

• truth and falsity describe the properties of statements alone (i.e., do they accord with the facts)  

  • note:  it is possible to have valid arguments with false statements and invalid arguments with true statements.

• sound arguments are those with true premises and whose arguments are valid.

Examples: 

The assassin of President Kennedy was either Oswald or some other party or parties.      [pr 1]  

It wasn't Oswald.    [pr 2]  

Therefore, it had to have been some other party or parties.  [concl]         

 

[This argument is clearly an example of a valid argument, since the conclusion follows necessarily from the premises.  The only question is whether this argument is also sound.  In order for it to be sound the premises also have to be true.  One could argue against the truthfulness of premise 1 by maintaining that Oswald could have been involved in a conspiracy that included other parties as well.  One could also argue against the truthfulness of premise 2 by maintaining that the assassin was indeed Oswald.   The soundness of the argument could thus be thrown into question by challenging the truthfulness of one or more of the premises.]

 

If a person can face death without bemoaning his or her fate, then that person truly deserves to be called courageous.  [pr. 1]

Sir Thomas More face death without bemoaning his fate.  [pr. 2]

Therefore, St. Thomas More deserves to be called courageous.  [concl]

 

[This argument certainly appears to be sound, since the premises are true and the conclusion follows necessarily from the premises.  Truth + Validity = Soundness]

 

All pigs are cats   [pr. 1]

Babe is a pig   [pr. 2]

Therefore babe is a cat   [pr. 3]

 

[You might be tempted to jump to the conclusion that this is an invalid argument because it looks strange.  It is actually a valid argument, since the conclusion follows from the premises.  It is not sound, however,  because premise 1 and the conclusion are false.]

 

If I bought a ticket on the Queen Elizabeth II, I would be broke.   [pr. 1]

I am broke.   [pr. 2]

Therefore I must have bought a ticket on the Queen Elizabeth II.  [concl]

 

[Let's accept that both premises are true.  The argument is invalid because the conclusion does not follow from the premises.  The person in question could be broke for reasons other than having bought a ticket on the QE II.  The argument therefore most assuredly unsound.]

 

      Ex. 2:   Premises and Conclusions

Molloy College   |    Department of Philosophy     |    Sophia Project 

   © 2000, Michael S. Russo.       For more information contact:  mrusso@molloy.edu