Arguments

• Arguments: premises provide grounds for the truth of the conclusion

• Two different ways a conclusion may be supported by premises.• Deductive Arguments• Inductive Arguments

Deductive Arguments

• Aim: logical necessity; the truth of the conclusion follows necessarily from the truth of the premises.

• Succeeds: Valid• Fails: Invalid

Validity

• Valid Argument: the truth of the premises guarantees the truth of the conclusion; if the premises are true the conclusion must be true

If Socrates is a philosopher then he isn’t a ballerina.Socrates is a philosopher.So, Socrates isn’t a ballerina.

Invalidity

• Invalid Argument: the truth of the premises does not guarantee the truth of the conclusion; it’s possible for the conclusion to be false if the premises are true.

If Socrates is a philosopher then he isn’t a ballerina.Socrates isn’t a ballerina.So, Socrates is a philosopher.

Validity & Truth

• Validity: Arguments• Truth: Propositions

• Every argument makes a claim about the relation between its premises and the conclusion

• Truth or falsity of conclusion doesn’t determine its validity or invalidity; the logical form of the relation does that

Valid Argument w/False Conclusion

If Frazier keeps Ali from hitting him in the left eye, he wins the Thrilla in Manilla. Frazier keeps Ali from hitting him in the left eye.Therefore, Frazier wins the Thrilla in Manila.

Invalid Argument w/True Conclusion

If I broke the bank at Monte Carlo, then I would be wealthy.I didn’t break the

bank at Monte Carlo.Therefore, I’m not wealthy.

Disjunctive Syllogism

Either you love me or you leave me.It’s not the case that you love me.Therefore, you leave me.

Disjunctive Syllogism

Either human beings want peace or war. Clearly history shows they don’t want peace. Therefore, they want war.

ConditionalMaterial Implication

Implication: the relation that holds between the antecedent and the consequent of a conditional.

There are different kinds of implication.

Logical Implication

Consequent follows logically from antecedent.

If all humans are mortal and Socrates is a human, then Socrates is mortal.

Definitional Implication

Consequent follows from its antecedent by the definition of the term.

If Johnny is a bachelor, then Johnny is unmarried.

Causal Implication

Consequent follows causally from its antecedent.

If this piece of blue litmus paper is placed in acid, then this piece of blue litmus paper will turn red.

Decisional Implication

Consequent follows from the antecedent given a decision one makes.

If my sister asks me one more time when am I going to give her a little niece or nephew, I’m slitting my wrists.

Modus PonensIf my sister asks me one more time when am I going to give her a little niece or nephew I’m slitting my wrists. My sister asks me one more time when am I going to give her a little niece or nephew. So, I’m slitting my wrists.

Modus TollensIf Sarah Palin becomes president then I’m moving to the Negev desert to live amongst the Bedouin. I am not moving to the Negev desert to live amongst the Bedouin. Therefore, Sarah Palin doesn’t become president.

If people are entirely rational then all of a person’s actions can be predicted in advance. Not all of a person’s actions can be predicted in advance. Thus, people are not entirely rational.

Hypothetical SyllogismIf Sarah Palin becomes president then I’m moving to the Negev desert to live amongst the Bedouin. If I move to the Negev desert to live amongst the Bedouin then I’ll be certain to tie my camel. If Sarah Palin becomes president then I’ll be certain to tie my camel.

If people are entirely rational then all of a person’s actions can be predicted in advance. If all of a persons’ actions can be predicted in advance then the universe is essentially deterministic. So if people are entirely rational then the universe is essentially deterministic.

Affirming the Consequent

If my sister asks me one more time when am I going to give her a little niece or nephew, I’m slitting my wrists. I’m slitting my wrists. So, my sister asks me one more time when am I going to give her a little niece or nephew.

Denying the Antecedent

If Sarah Palin becomes president then I’m moving to the Negev desert to live amongst the Bedouin. Sarah Palin doesn’t become president. Therefore, I’m not moving to the Negev desert to live amongst the Bedouin.