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Propositions and Arguments

Propositions and Arguments. What is a proposition ?. A proposition is a predicative sentence that only contains a subject and a predicate S is P. Which of these sentences express propositions?. Sydney is north of Melbourne. Is Edinburgh in Scotland?

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Propositions and Arguments

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  1. Propositions and Arguments

  2. What is a proposition? • A proposition is a predicativesentencethatonlycontainsasubject and a predicate S is P.

  3. Which of these sentences express propositions? • Sydney is north of Melbourne. • Is Edinburgh in Scotland? • The moon is made of swiss cheese. • Did you see the eclipse? • Whatan eclipse! • Would that I were good at logic. • Look at the eclipse. • I wish that I were good at logic. • 7+12=23

  4. Arguments • Argumentsineverydaysituationstakeplacebetweenpeople. • Argumentsgivereasonsforbelievingthetruth of a proposition. • Logicstudiestheinformationcontent of thesearguments.

  5. An argument is a list of propositions, called the • premises, • followed by a word such as ‘therefore’, or ‘so’, and then another proposition,calledtheconclusion. • The reasonforacceptingtheinformationintheconclusion is basedonthepremises. • If everything is determined, people are not free. Premise • Peopleare free. Premise • So not everything is determined. Conclusion

  6. Rule Rule Individualinstances Individualinstances INDUCTIVE Arguments DEDUCTIVE Arguments

  7. Rule Most Hungarianscommittaxfraud. Gábor is Hungarian. So, Gábor is likelytocommittaxfraud. • The link betweenthepremisesweaker. • The truth of thepremisesonlymakesthetruthoftheconclusion , butdoesnotguaranteeit • The conclusion is onlypossiblytrue. • TheseargumentsareInductivearguments. Individualinstances P(A|B) = P(A|B) = INDUCTIVE Arguments

  8. AllHungarianscommittaxfraud. Gábor is Hungarian. So, Gábor commitstaxfraud. The premisessupportthetruth of theconclusion: it is impossibleforthepremisesto be true and theconclusionto be false. Thesearecalleddeductivearguments. Rule Individualinstances Peoplecommitingtaxfraud Hungarians DEDUCTIVE Arguments

  9. Valid arguments • An argument is valid if and only if whenever the premises are true, so is the conclusion. • In other words, it is impossible for the premises to be true while at the same time theconclusionis false.

  10. Soundarguments • An argument is sound, just in the case where it is valid, and, in addition, the premises are • all true. So, the conclusion of a sound argument must also be true. • soundnessappealsto the truth of the matter.

  11. Valid ArgumentScheme Allbatsarebirds. H Allbirdsfly. HNotsound ----------------------------------- Thereforeallbatsfly. I Allwhalesaremammals. I Allmammalshavehearts.ISound ---------------------------------- Allwhaleshavehearts. I c A B C All A’s areB’s AllB’sareC’s ----------------- SoallA’s are C’s

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