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

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

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.

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.

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.

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.

Modus Ponens If the glove don't fit, you must acquit. The glove don't fit. Therefore, you must acquit. Modus Ponens is a valid deductive form. Any argument that is in this form and has true premises will have a true conclusion. But if there is an untrue premise, the conclusion could be false.

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 or conclusion must actually be true.

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.

Affirming the Consequent If God wanted to test our faith, there would be a fossil record to make it look like evolution occurred. There is a fossil record that makes it look like evolution has occurred. Therefore, God wants to test our faith.

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".

Modus Tollens If people had an ounce of sense, they would not dump sewage into their drinking water. People dump sewage into their drinking water regularly. Therefore, people do not have an ounce of sense.

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.

Denying the Antecedent If someone thinks alcohol should be legal, then they agree with the principle that some mind-altering substances should be legal. But you don't think alcohol should be legal. So that means you don't agree that some mind altering substances should be legal. Invalid arguments are not completely reliable.

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.

Chain Argument If there's a chance we can balance the budget, we should keep meeting. If we keep meeting, I'll get home late for dinner. If I get home late for dinner, I won't be able to help little Jimmy with his homework. If I don't help little Jimmy with his homework, he will cry himself to sleep. So, if there's a chance we can balance the budget, little Jimmy will cry himself to sleep.

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.