Essential Deduction Techniques of Constructing Formal Expressions and Evaluating Attempts to Create Valid Arguments.

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Essential Deduction Techniques of Constructing Formal Expressions and Evaluating Attempts to Create Valid Arguments

Using Claim Variables for Convenience A claim variable is a letter or other symbol that stands for a claim, or proposition. For example... P - Thomas Paine advocates it. Q - Somebody questions it. R - Paul Revere advocates it. In the box above, P, Q, and R are claim variables representing three different sentences.

Consider these arguments... If P then Q P Therefore, Q One argument form is better than the other if it is more reliable. Is one of these argument forms better than the other? If P then Q Q Therefore, P Let us use these variables... P - Thomas Paine advocates it. Q - Somebody questions it.

Modus Ponens If P then Q P Therefore, Q Modus Ponens is a valid deductive form. Any argument that is in this form and has true premises will have a true conclusion.

Affirming the Consequent If P then Q Q Therefore, P Affirming the Consequent is an invalid form. An argument that is in this form and has true premises may or may not have a true conclusion. Invalid arguments are unreliable.

Modus Tollens If P then Q ~Q Therefore, ~P Modus Tollens is a valid deductive form. Any argument that is in this form and has true premises will have a true conclusion.

Denying the Antecedent If P then Q ~P Therefore, ~Q Denying the Antecedent is an invalid form. An argument that is in this form and has true premises may or may not have a true conclusion. Invalid arguments are unreliable.

Chain Argument If P then Q If Q then R So, if P then R The Chain Argument is a valid deductive form. Any argument that is in this form (including any number of premises, as long as they can be arranged as a chain) and has true premises will have a true conclusion.

Reversed Conclusion Chain Argument If P then Q If Q then R So, if R then P The Reversed Conclusion Chain Argument is an invalid (i.e., unreliable) form. An argument that is in this form may have true premises and (unlike a valid form) still have a false conclusion.