Lecture Notes.

Module Ten: Session Three
Introduction to Formal Logic  

Deductive Arguments

Defined: An argument where IF the premises were true, then the conclusion would have to be true.

An interesting controversy regarding deduction:

Note: The following definition for deduction is preferred by many who teach logic and critical thinking:

"Any argument where the intent is for the premises to lead to the conclusion with certainty."

Intention is very important in this definition, because it includes certain argument forms which the first definition excludes (see Formal Fallacies). These additional forms are fallacious (i.e., the premises do not actually lead to the conclusion with certainty, but the author erroneously believes that they do). We call these fallacious forms "deductively invalid."

This author prefers the first definition because it does not require one to ascertain intention, but rather focuses on the actual logical structure of the argument. Either it is actually valid (hence deductive) or it is invalid (hence inductive). This is consistent with the definition given in A Dictionary of Philosophy by Antony Flew:

"A valid argument in which it is impossible to assert the premises and to deny the conclusion without thereby contradicting oneself.
Notice that the first definition makes the words "deductive" and "valid" synonyms, where the second definition requires the addition of "valid" or "invalid" to indicate the quality of the argument."


NOT just any argument where the premises ARE true, because inductive arguments can have premises that are true.

This definition sounds a little strange because one can have a deductive argument where the premises are not true and it is still deductive. If those premises WERE true, then the conclusion would have to be true.

Example: If George W. Bush is president, then dogs can fly. George W. Bush is president. Therefore, dogs can fly.

The second premise is true, but the first one isn't. But, IF both premises WERE true, then there is no possible way that the conclusion could be false. It is the FORM that guarantees this.

If the premises are true, and the form is deductive, then the probability of the conclusion being true is 100%.

Deductive arguments draw out conclusions which are already contained in the premises.

Here is an analogy to help you to understand this point. Refrigerators preserve food. If the food that goes into the refrigerator is good, then the refrigerator maintains that goodness. If the food is already rotten when it goes into the refrigerator, then the food remains rotten. Likewise, the truth of reasons is preserved by a deductive argument form. If your reasons are true, then a true conclusion is guaranteed.

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