Netto-Deduction

 Some Basic Forms of 
Deduction

Jeff Netto's English 103

Modus Ponens - The Confirmation of a Hypothesis
Premise: If P,then Q Premise: P Conclusion: Therefore, Q	If the butler saw the car approach, then he must be the murderer. The butler did see the car approach. Therefore, the butler is the murderer.

Modus Tollens - The Disconfirmation of a Hypothesis
Premise: If P, then Q Premise: NOT Q Conclusion: Therefore, NOT P	If the butler is the murderer, then he must be left-handed. The butler is NOT left-handed. Therefore, the butler is NOT the murderer.

Disjunctive Syllogism - A Logical Reduction
Premise: Either P or Q Premise: NOT P Conclusion: Therefore, Q	Either the butler or the chauffeur is the murderer. The butler is NOT the murderer because his alibi holds water. Therefore, the chauffeur is the murderer.

Hypothetical Syllogism - Refining a Hypothesis
Premise: If P then Q Premise: If Q then R Conclusion: Therefore, if P then R	If the butler is guilty then he will lie. If the butler lies, then he will blush. Therefore, if the butler is guilty then he will blush.

Generalization - We will cover a few different forms of this, but for the moment we will simply introduce one form of it: the Universal Affirmation.
(For any x) (if x is P, then x is Q) or, more simply All P's are Q's	(For any suspect) (if that suspect has a motive, then that suspect is a prime suspect) All suspects with motives are prime suspects.

Universal Instantiation - Particularizes a Universal Statement
(In the case of a) (if a is P, then a is Q)	In the case of the butler, if the butler is a suspect with motive, then the butler is a prime suspect.