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Argument Analysis. Truth-Table Test for Validity. Example. Consider the argument (P & ~Q) ├ (Q → P). Premise: (P & ~Q) Conclusion: (Q → P) . Write Down ALL the Possibilities. Write Down Premises. Write Down Conclusion. Write Down Truth-Table for Premise.
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Example Consider the argument (P & ~Q) ├ (Q → P). Premise: (P & ~Q) Conclusion: (Q → P)
Multiple Premises Sometimes arguments have multiple premises, like: (P v Q), ~P ├ Q Premise: (P v Q) Premise: ~P Conclusion: Q
Failing the Test Not all arguments pass the test. This argument is called “affirming the consequent”: (P → Q), Q ├ P Premise: (P → Q) Premise: Q Conclusion: P
Failing the Test Whenever an argument form fails the truth-table test for validity, then some arguments with that form are invalid. P = There is no food in Hong Kong. Q = Michael will move out of the country
Failing the Test Whenever an argument form fails the truth-table test for validity, then some arguments with that form are invalid. Premise: If there is no food in Hong Kong, then Michael will move out of the country. Premise: Michael moved out of the country. Conclusion: There is no food in Hong Kong.
Failing the Test However, not every argument of this form is invalid. P = One person is happy. Q = Two people are happy.
Failing the Test However, not every argument of this form is invalid. Premise: If one person is happy, then two people are happy. Premise: Two people are happy. Conclusion: One person is happy.
Tautologies Some arguments/ argument forms have no premises. If an argument with no premises is valid, then we call the conclusion a tautology. Example: ├ (P v ~P) Premise: Conclusion: (P v ~P)
Contradiction The opposite of a tautology is a contradiction. Its truth-table is always false.
Interesting Case Since there are no F’s on the table, the argument is valid. Every argument with a contradictory premise is valid (though none are sound). Every argument with a tautology for a conclusion is valid.
The Deduction Theorem Whenever P ├ Q is valid, ├ (P → Q) is valid (and vice versa). If you really want, you can avoid the truth-table test for validity. • If you need to figure out if φ ├ ψ is valid, just write a truth table for (φ → ψ). • If you need to figure out if φ, χ ├ ψ is valid, just write a truth table for (φ → (χ → ψ)) • If your conditionals are tautologies, you know the argument’s valid.
Premise vs. Conclusion Real-world arguments are not like logic arguments. They almost never tell you which sentence is the conclusion of the argument. You’re left to figure that out yourself.
Conclusion Discourse Markers • Thus • So • Therefore • Hence • Consequently
Premise Discourse Markers • Since • Because • For • [colon] :
Identifying the Conclusion Most companies would agree that as the risk of physical injury occurring on the job increases, the wages paid to employees should also increase. Hence it makes financial sense for employers to make the workplace safer: they could thus reduce their payroll expenses and save money
Identifying the Conclusion Most companies would agree that as the risk of physical injury occurring on the job increases, the wages paid to employees should also increase. Hence it makes financial sense for employers to make the workplace safer: they could thus reduce their payroll expenses and save money Conflict
Thus The English word ‘thus’ has two meanings: it can either mean the same thing as ‘therefore’– and in this sense it indicates a conclusion. But it can also mean ‘in this way’ or ‘by doing this.’ That’s what it means in this passage.
