5.3 Rules and Fallacies

hi this is an introduction to logic I'm mark doors B this course overview is the basics of categorical propositional and predicate logic today we're going to be looking at just the rules and fallacies in fact we're looking at five rules and policies you can use in categorical logic to determine the validity of an argument so we're looking at rules and fallacies today okay let me start off here was sort of a very brief sort of review I usually always start off with a review so we might as well keep with the tradition when I want to start as Latin our last lecture last lesson we looked at Venn diagrams and we found out the Venn diagrams provide us really what is a visual means to inspect whether or not an argument is valid so the Venn diagram is a loss to test for the validity of a categorical syllogism now nearly finish this out so a categorical syllogism remember is any argument has two premises one conclusion it has three categorical terms it again validity is when you have two premises such that if the two premises are true the conclusion necessarily follows it's true now Venn diagrams provided us a way of sort of visually inspecting through sort of really just creating circles I apologize that circles are sort of freehand where we would put the mate the minor term here the major term here in the middle term here and then using either a fill right either a fill an X or even an existential marker we could enter the parentheses and then after enter the premises ask ourselves whether or not we could visualize or really read off the conclusion if we could it's valid if there was any ambiguity or we could necessarily see that the conclusion was represented then the answer was that it was invalid if we use an existential marker or a sort of little x-men symbol here did we discover that it would be conditionally valid okay now that providing us a really nice mechanical means for testing validity but is there another way and the answer is there is in fact we're going to see that there are five rules for testing for the validity of an argument and I'm going to go over these five rules right now and then we'll talk about them we'll see that the first two rules involve the concept of distribution now it is to remind ourselves what is distribution remember we said that in an earlier video and you can watch that video again if you need a refresher we said that a term was distributed if in the categorical proposition we were able to denote learn something about the entire class okay so let's provide ourselves real quick here about which terms get distributed in which propositions now remind ourselves an a statement right says that all SRP right and we said that what term gets distributed here we sort of said that the S gets distributed into the P okay what about an e statement that says that no SRP well in this case we say that each term gets distributed both the subject and the predicate terms get distributed okay now remember why is it the honest because you learned something about all the esses right whereas in the case of no entropy you learn all the asses and all the peas namely that they're always excluded from each other so both terms get distributed in an i statement right which is some SRP in order to figure out what gets distributed ask yourself what do I do I learn anything about in an entire class in the case of some of the answer P all I'm learning that there's all that means is that there's one s in the universe and that s is a P that doesn't tell me about what all of the peas are and it doesn't tell you about what all the esses are for instance imagine for instance if I said that some firefighters or heroes well that tells me about at least one firefighter and it tells me about one set of heroes nearly that this firefighter is a hero but it doesn't tell you about something about all the heroes and all of the firefighters thus nothing gets distributed so like this I'll sort of put an X here to demonstrate to two slashes here nothing gets distributed okay what about the O statement which is that sub s or not P right in this case the P is what gets distributed so I'm going to sort of go I represent it by saying then because when I say that some s or not P I learned something out all of the peas nearly that all of the peas in the world are not assets so words if I said some yeah some politicians are not corrupt right that tells me that if you take all of the corruption all the corrupt politicians that the S is here get excluded so I learned something about the peas so this is the pattern of distribution so what's the rule the rule is that in a syllogism now these the propositions but in a syllogism the middle term must be distributed at least once now remind ourselves once a middle term right and let me sort of just draw one up here if I say all PR M right all m RS therefore all SRP take a look at this statement so the middle term again is the term that gets that is either would like to think of the middle term here is something like the glue it's the glue that binds the subject of the predicate term together depending upon the pattern of distribution so the middle term has to be distributed at least once so let's take a look here does the middle term get distributed here well in all PRM the middle term is not distributed up here right because we said only the S gets distributed to the P what about over here all ever s well yes that the middle term gets distributed right here which means that it passes the rule okay now if you read a syllogism that in which the middle term is not distributed this commits a fallacy and what is a fallacy literally the term policy comes from the Latin which means a false argument or false statements a deceptive statement or argument right so the fallacy of the undistributed middle we're going to see that in order for a syllogism to be considered valid using these rules it has to pass all five rules or at least the first four we'll see why in a minute so this is the first world the middle term has to be distributed at least once if if the middle term doesn't get distributed then that's the undistributed middle and I'll give you an example here in a minute of what those fallacies look like let's take a look here at the second the second rule if a term gets distributed in the conclusion then it must be distributed in the premises okay so that and that's quite simple again these first two rules have to deal with distribution so if a term is distributing the conclusion has to be distributed in the premise okay so let's give a sort of example here let's say that no P R M and then we'll say some mr s there for some s are not P okay and let's take a look at this one does this pass the rule well first off you have to look at the conclusion so let's take a look at the conclusion here the conclusion says some s are not P now this is an odd statement right if you recall up here write in an ode statement the P is what gets distributed right so let's scroll back down so that means that the P is distributed here so the question is is the P if the P is distributed in the middle term is it distributed up here because that's where the P is located no PR M this is an e statement in an e statement both the subject and the predicate or dessert so yes this passes the rule okay now what's important here is what happens if you have a notice what if you have no S or P in the conclusion down here both of them have to be distribute so if any term is true inclusion look up and see in the parentheses and make sure it gets distributed up there okay now if you break the rule here then that can commit one of two fallacies either the listed major the illicit minor what's the difference here well it depends on where the premise isn't being distributed so for instance if I have let me give you another example here what if had something like this some PRS I'm sorry some PRM so mrs therefore no s are P this actually brings a whole bunch of rules to stop this argument right but let's take a look at the conclusion in the conclusion both to s and the peer distributed right but up here take a look the predicate term is not distributed because in an I statement both of these are I statements and I say that nothing is distributed so if nothing is true that means that the P is not distributed which means that you've broken in this case since the P is not distributed up here this commits the illicit major because this is the major term and this is the major premise okay now this ironically commits both of them because listen because take a look the S is distributed in the statement because both of them are if you look at this is the minor term and in the minor premise since this is an i statement that nothing is distributed so this actually breaks both the illicit this is the illicit minor fallacy and this is the illicit major fallacy okay I hope that makes sense so those are the first two rules that every valid categorical syllogism must conform to let's take another third one third one here is that two negative premises are not allowed now this is interesting why is this why is this the case we'll see that really the first two rules have to do a distribution the second two rules have to deal with negative parenthesis and conclusions negation okay now why is it the to negative premises are not allowed well in informal logic there's a fallacy known as the fallacy of ignorance an authoritative ignorant basically states that if you if you if your premise says that something is not the case you can't conclude that something is the case okay so let's write this out is that or basically it's simple if you argue that you don't know you can't conclude that you do know something it's pretty simple sorry my handwriting it's sort of poor today because I'm using a different format so so that's the thoughts of ignorance or arguments from ignorance or always fallacious right now that means that if you have a syllogism that the first premise is negative and the second premise is negative the answer is what can you conclude the answer is you can't conclude anything because in order to make a statement in order to make an argument remember an argument is when you say something is the case right and you can't and you can't have two negative premises and say that anything is the case because all you said is that something isn't the case right I don't that makes sense and this is what's called the fallacy of exclusive premises right so for instance let me give you an example what if for instance I said that no Democrats are good politicians right and then I said so like no good politicians are Republicans there are four and then I said something like this some Republicans are Democrats now that's a horrible argument that doesn't make sense I guess it from what Alexa turned out and they could Republican or Democrat can switch but you can see here is that if this is my claim regardless of what R and D stands for right this this can never count as evidence because remember a premise is supposed to be man a premise is supposed to be evidence and if my evidence is simply that I did something is not the case how can I conclude that something is the case and even if this was a negative premise it won't work so you can never have too negative premises so if that's a pretty simple argument let's hear that rule for rule for it also has to deal with vacation right it's also has to toe the negation like rule three and that is that a negative premise requires a negative conclusion and a negative conclusion requires a negative Pro so you can't have two negative premises but of course you can have one negative premise but if you you have a negative presence you have to have a negative conclusion and vice versa right and if you break this rule that commits the fallacy of either drawing an affirmative conclusion from a negative premise or drawing a negative conclusion from an affirmative premise that's sort of worrying sort of complicated to say but that's essentially the rule right so the rule is is that a valid syllogism right if there is any negation in the conclusion there must be a negative premise if there's a negative premise there has to be a negative conclusion but remember there can only be one negative right otherwise you come into fallacy of the exclusive premises okay I don't really know if I need to write anything out here but that's just the second rule write a negative premise requires native conclusion and a inclusion requires a negative premise so what's the fifth rule right the fifth rule here actually concerns Aristotelian the Aristotelian model of existential fallacy so here we have to remember the difference between Aristotle bool of the existential fallacy remember it I've gone over this over and over by now so I'm sure you've memorized this aerosol thinks that a universal can allow you to conclude a particular who are as bool things that universals can only end with universals they can never end with a with a I'm sorry with a particular okay that's not possible so what is the rulefive rulefive says if both premises are universal the conclusion cannot be particular it cannot be particularly because rule five here conforms to the boolean interpretation which means that if you break this rule you commit the existential fallacy now there's a sort of caveat there is an exception to this rule the exception is if you assume that Aristotle's model for the existential thoughts is correct right which means that for Aristotle you can have universal premises in a particular conclusion okay now what does that mean it means that you can use these five rules and if it if the categorical syllogism passes the first second third and fourth but not the fifth then it's conditionally valid if it passes all five then it is unconditionally valid and if any one of and if any one of these first four broken its invalid and it may even be in thought even if it passes rule five I'm sorry even if if you take the Aristotelian model because River if you make arguments about unicorns you break the existential fallacy regardless okay and that's an important difference here so let me be the sort of review here that means that we have five rules switch colors the first rule again is that the middle term must be distributed once at least words okay the second rule is that if a terms distributing the conclusion it must be distributed in the premise right so I guess all right this is that if a term in the conclusion kids distributed always put D is T here then it must be in the premise ok so these are the first two rules and again these both have to deal with distribution ok third rule right is that there's no is that you cannot have there's no exclusive say what's the what I want to say let me actually I'm sorry about that right to negative premises are not allowed okay the fourth rule is that if they if you have a negative premise all this right like this a negative premise requires a negative conclusion and vice-versa such that if you have a negative conclusion you must have a negative premise okay and then so these two rules have to deal with negation and then the fifth rule to change colors again it has to do with Universal Universal premises require oops Oh here we start out that's Universal premises require a universal conclusion I'll put two Universal premises now they're the this fifth rule has the exception possibly due to the existential fallacy and there's a Tilly model so the every valid still just a must conformed all four of these every unconditionally value syllogism must conform to all five of these right and if any one of these rules gets broken it's either going to be conditionally gone or it's going to be simply in likely it's invalid okay so those are the five rules and of course each of them comes with a fallacy right so the fallacy here would be the undistributed middle the fallacy over here is either the illicit major the illicit minor the third one here is exclusive premises and then this is drawing an affirmative conclusion from negative premise and drawing a negative premise from an Fermin conclusion and this of course is the existential fallacy okay so these are the five rules and so let's sort of do take a look at the homework here and see what you're going to have to do for the homework let's take a look here if you take the book your book gives you examples for each of these fallacies right and it goes over all this stuff okay and also if you want to take a look at the proof the proof is rather sort of laborious so I'm not going to go over the proof for it I just want you to learn at this point what the rules are and learn how to apply them and you'll see that once you get these rules down is going to be much much faster to determine the validity of an argument okay so what you're going to do for me I make this a little bit bigger for you alright so gentle for this first argument for this first section of the homework is they're going to give you form right the figure of the mood and there's a triple a three and you have to figure out whether or not this breaks any of the five rules so all you need to do is sort of reconstruct this it all sort of doing for you real quick I guess okay so let's do this first one here for you so you can see what looks like yes I okay a triple a three now the best way to start this is to always start with the conclusion if you're going to do a reconstruction an a statement is an all s are P so this is going to look like all s are P now this is the next thing to look at when you're reconstructing to take a look at this guy and that's the location of the middle term and you'll remember that the middle term has to this is going to be all the middle term is going to be here for a three are the P is the major term so you put it up here on the major premise yes okay so this is what it looks like so now let's ask does it pass the five rules okay it may be helpful here to sort of draw it out like this here's the five rules I'm not going to write about because my handwriting is horrible on this this computer right now for the first one here was a middle term has to be distributed at least once well in an aid statement the first term gets distributed so the middle term does gets tributed we passed that rule second one if it turns distributed the conclusion it has to be distributed in the premise right so let's take a look at it all s are P this the S is distributed right here does the asket that is distributed in the conclusion is it distributed in the premise no it is not because look the asses in the second position and in the first one only the subject term is distributed not the predicate term so no it didn't pass this and so what fallacy gets committed because I but they're going to ask you well since the that it was the minor term there was distributing the conclusion and it's not during the minor pros this clip commits the illicit minor fallacy they listed minor okay invalid therefore now see wasn't that faster and easier then looking it up in the table in or drawing a Venn diagram now we could draw a Venn diagram to test if you want I won't do it but that's how you're going to do the homework here now remember when you reconstruct these always start at the conclusion then take a look at the middle term then sort of fill it in and run through the rules okay it's pretty simple in that regard okay the next thing oh let's say they say oh they actually want you to come check yours just by constructing a Venn diagram so I guess you can go ahead and do that but it always works out okay we have to do the second one now this the second section has used the five rules return whether the following standard form soldiers were valid from the boolean standpoint both in the Aristotelian standpoint or invalid okay so you need to see if there they are going to be conditionally valid unconditionally knowledge or just simply invalid okay so let's do another one here and then they want you to construct a Venn diagram for this so maybe I will do it all for you so let's take this first one right here okay okay so nebulous clouds of our clouds of gas some clouds of gas or objects invisible to the naked eye therefore some objects invisible naked are nebulas as a nebulous and it nebulas okay first thing to do here is to just recognize what we're actually looking at here and in fact it may be easier than sort of you could say that this is N and this is C this is C and this is I guess oh and then this is o and then this is our and right so what does this look like let's reconstruct it and you can also take a look at this is an eye some clouds of objects are invisible to the naked eye that's an eye and then times we are that's a tie so we have a triple eye okay where's the middle term let's hear the middle terms right here right that's one two three sorry one two three four so that's a triple line four okay so is this ballot well let's sort of write it out here some inner see some see our Oh there for some Oh our in okay so is this dog let's use our rules again one two three four five all right first rule in right the middle term has to be treated somewhere right the middle term has to be distributed least ones but wait a second in an i statement nothing is ever distributed right remember distribution for the date the a the eo8 turn in the a that Vaska distributed in the e s and the PS route and i nothing is distributive so right away you can see that this breaks the very first rule right and what thought is that commits it commits the undistribute middle now one of the things that's interesting here is that means that any argument that starts with the double I is always invalid right because that means the middle term can never be distributed so in fact once you just look and see that if you ever seen Ariana starts with some blah blah blah some volleyball are blah right that means that always going to be invalid okay now they want us to do a Venn diagram I'll sort of try to draw one real fast here just to show you what you want to do here so this is going to be O and C right so some of the answer C's so some of the answer C's that means you have to put the X here here I don't know where so let me change my color here so I'm going to put the X on the line right for that premise now if I need to diagram the sagging press some of the CRO some of the C zeros I don't do this going to go here it's going to go here I don't know so it goes on the line you can see here in both cases it's sort of unknown what the case is so when it says that some O are n I have no idea because but maybe these X's are supposed to go here right which means that I have no idea this is an invalid argument and our Venn diagram proves that as well all right so I hope that makes sense so that's what you have to do for that okay let's move here to the third section in the over there's just true or false it's going to ask you sort of questions I won't answer those and that's what those are the five basic rules now you'll see that once you get a handle using those five rules things are going to be much much easier for you in terms of ability it's much easier to check your work especially your Venn diagrams and I'm sure that some of you when you actually started doing the Venn diagrams after our last video actually found that they're more difficult to interpret and actually to perform than you probably thought so these five rules you should just commit them to your memory and get used to using them it's going to make your life a whole lot easier okay thank you very much for watching that I'll see you guys online okay bye

Channel: Mark Thorsby

Views: 32,292

Keywords: Screencast-O-Matic.com, Categorical Logic, Districbution, Negation, Exclusive Premises, Undistributed Middle, Existential

Id: Y2ZaVg1ZubI

Length: 30min 5sec (1805 seconds)

Published: Thu Sep 06 2012