In unit two of this course, in our studyof the rules governing the validityof deductive arguments, we've looked atotherways of representing information, otherways besides sentences.We've looked at representing informationusing atruth table, or using a Venn diagram.Now today, in this final lecture of unittwo,I'd like to talk about the advantages ofthese otherways of representing information.What's the point of using truth tables, orusing Venn diagrams?Why did we learn these techniques?And that's the topic of today's lecture.Okay, so let's consider some differentwaysthat we can represent the sameinformation.Consider for example this list of sevensentences.Here's seven sentences.They all represent the very sameinformation,they all mean the very same thing.They just say the same thing in differentlanguages.One is in French, one is in Italian, oneis in Spanish and so on.But even though they're in differentlanguages andthey look different, they all express thesame information.They represent the same information.Well similarly, just as we can usedifferent sentences.To represent that information.We can also use something that is nota sentence at all to represent thatinformation.For instance, here.We can use a truth tableto represent the very same informationthat we were representingby means of those different sentences inthe previous slide.So, look at this truth table for a moment.Now, first.[COUGH].First column of the Truth Table is theproposition Walter likes bourbon,the second column of the Truth Table isthe proposition Walter likes vodka.And the third column is the conjunction ofthose two propositions.Which could naturally be expressed inEnglish,by the sentence Walter likes bourbon andvodka.And now what we can do once we have thistruth tablehere, that shows how the truth or falsityof the conjunction, dependson the truth or falsity of each of theconjuncts, we can circle a particularline, of that truth table To indicate,that this isthe situation, that we're actually in.Okay,now when we circle that particular, row ofthe truth table,what we're doing, is expressing the verysame informationthat we expressed, using one of theseseven sentences earlier.Right.There's no difference in what informationwe're expressing, what information we'rerepresenting.We're just representing it, without usinga sentence.We're representing it, by circling, a rowof the truth table, okay?So it's just a different way ofrepresenting the same information.Now you might wonder, well what's thepoint of representing that sameinformation in different ways?Well, the point of representing thesame information using different sentencesin differentlanguages is just that you can makeyourself understood by different groups ofpeople.You can say it in French to make yourselfunderstood in France.You can say it in Spanish to make yourselfunderstood in Spain or in Latin America.You can say it in Russian to make yourselfunderstood in Russia, and so forth.So, what's the pointof using the truth table?And there's no country where they speaktruth table.So what's the point of using a truth tableto express the very same information?Well the point is That, by using atruth table to represent the very sameinformation, yourepresent that information in a way thatmakes veryclear exactly what deductive argumentsthat use that informationare valid and which ones are invalid.So, for instance, by looking at this truthtable.Looking at our representation of theinformation that uses this truth table, wecan see very clearly that the argumentfrom the premise, Walter likes bourbonand vodka, to the conclusion, Walter likesbourbon, is going to be a valid argument.There's no possible way forthe premise to be true while theconclusion is false.Right?If the premise is true, then theconclusion is also going to have to betrue.But, we can also see that the deductiveargument from thepremise, Walter likes bourbon, to theconclusion, Walter likes bourbon andvodka.Is invalid.There is a possible way,for the premise, Walter likes bourbon tobe true, while the conclusion, Walterlikes bourbon and vodka, is false.So,by looking at the truth table, you cansee, very plainly,why some deductive arguments, that involvetheproposition Walter likes bourbon andvodka, are valid, and other deductivearguments, involving that sameproposition, are invalid.And that's something that you can't seejust as clearly by looking atany of the seven sentences that we can useto represent that information.So, these sentences have some advantagesas away of representing the information thatthey all represent.But they allhave a disadvantage relative to the truthtable, which shows us plainly why certainarguments that use that information arevalid and others are invalid.Sothat's the advantage of using a truthtable to representinformation that could be represented morenaturally by means of sentences.It's not that we make ourselves understoodby more people when weuse a truth table, it's rather that whenwe use a truth table.We can see relations of deductive validitythat we can't just see whenwe use sentences.Okay, now, how about Venn diagrams?Well,consider again.Pieceof information that could representedusing any of these seven sentences, right?One is in French, one is in Spanish, onein is Italian, and so on.Right?All seven of these sentences mean the samething, they express the verysame information, and they represent it.Even though they represent the sameinformation, they're useful in differentsituations.You might use one when you're in Russia,and you want to be understood by Russians.You might use another when you're inIndia, and youwant to be understood by a certainpopulation of people in India.You might want to use another when you'rein Brazilor Portugal, and you want to be understoodby Portugese speakers.But notice, none of these sentences,represent, theinformation that they represent, in a waythatmakes it completely clear, which deductivearguments thatuse that information are valid, and whichare invalid.' Kay, we can make that point clearby representing the same information usinga Venn Diagram.First, we constructa circle to represent the category ofWalter'sdrinks.And second, we construct a circle torepresent the category of,imported, things.[SOUND]And, since these seven sentences all saythat allof Walter dri, all of Walter's drinks areimported, wecan then shade out, the, part of thecircle representingWalter's drinks, that's outside the circleof imported things, right.To show us that, if Walter drinksanything, than whatever it isthat he drinks must be imported, it mustbe inside this region here.[SOUND] Okay.And now, we have a Venn diagram thatrepresents thevery same information that was representedby those seven sentences.But, what's the point of representing thisinformation using a Venn diagram?Well the Venn diagramshows us, which deductive arguments thatuse that information arevalid, and which are invalid.So for instance, consider the argumentfrom, all, Walter's, drinks, are,imported.[SOUND] To all, imported drinks,are Walter's, is thatargument valid or invalid?Well, if you just look at the sentences,itmight not be obvious whether it's valid orinvalid,but if you look at the Venn diagram, youcan see quite clearly that this argumentis invalid.For all of Walter's drinks to be imported,is for this part of the Venn diagram to beshaded in.But for all imported drinks to beWalter's, would befor this part of the Venn diagram to beshaded in.And the question is, is there some way forthe premise to be true while theconclusion is false?And the answer is clearly yes.This part of the Venn diagram could beshaded in even ifthis part of the Venn diagram is notshaded in.And so, this is an example of how wecan use the Venn diagram to show veryplainly, visually.Why certain arguments that use theinformation, all Walter's drinks areimported.Certain of those arguments are valid.And certain of them are invalid.Again, so thepoint of using a Venn diagram to representinformation, is, in that respect,very similar, to the point of using atruth table to represent information.When you want to understand whether aparticular deductive argument is valid orinvalid, sometimes it helps to translatethe information in that argumentinto a form where you can plainly seethe relations of validity or invalidity.Into a form like atruth table, or a Venn Diagram.Where you can plainly see thoserelationships because ordinary languagedoesn't always expose thoserelationships.Okay, so that's why truthtables and Venn Diagrams are usefuldevices for understanding whetherdeductive arguments are valid or invalid.And there are many other devices likethat.But truth tables and Venn diagrams are thetwo simplest ones,and so the two that we focused on in thiscourse.Okay, well have fun with the quizzes, andhave fun with the rest of the course.See you next time.