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

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Consider these arguments... If Thos. Paine advocates it then somebody questions it. Thos Paine advocates it. Therefore, somebody will question it. Note: One argument is better than another if it's more reliable. Is one of these arguments better than the other? If Thos. Paine advocates it then somebody questions it. Somebody is questioning it. Therefore, Thos. Paine must be advocating it.

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Consider using claim variables... 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.

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Consider these arguments formally... 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 We'll use these variables... P - Thomas Paine advocates it. Q - Somebody questions it.

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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.

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IMPORTANT POINT A valid deduction is perfectly reliable. This means that if the premises of an argument are true, the conclusion must be true. And that's pretty much all it means. "Valid" is a word that describes reliable logic. It does not mean the premises are actually true.

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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 not completely reliable.

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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. The "~" means "not".

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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 not completely reliable.

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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.

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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.

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