Logic: The Syllogism

after several weeks of going through the rather grueling and tedious task of diagramming sentences and making sure we are clear on what people are saying we now get to have the fun of linking statements together and learning how to draw proper rational logical conclusions from stated facts you can't just like any old two facts together and draw any kind of a conclusion there are rules to how you do this this is one of Aristotle's contributions to Western civilization just like Plato he remembered and thought about the trial of Socrates and Plato wondered how people could so miss supply the form of justice Aristotle more of a sort of a crisp and scientific thinker began to analyze the nature of arguments themselves to try to understand how people get led astray so part of the result of that was the development of a series of fallacies that people fall into in the midst of debate and the other half of that is the construction of a logical syllogism a syllogism is a three-part argument two premises which are both statements that most people would agree our truthful statements link together in such a way that one may draw a valid conclusion from these statements and push forward a little beyond what had already been known okay for example Aristotle was the first to realize that dolphins are mammals he spend his time on his honeymoon at the beach detecting animals every morning and he realized that all things which give birth to live young or mammals dolphins give birth to live young therefore dolphins are mammals that's two facts that he knows and then drawing a conclusion something that is not immediately obvious to the senses but can be logically supported by those statements to borrow one from one of my favorite historians James Burke as he uses in a video when I lecture my what what has to pass two holes there for my skin has holes in it you can't see the holes logically they have to be there and this is what logic does for you when you start getting into the habit of analyzing very carefully what's being said what statements are known and then linking them together properly you begin to organize your whole view of the world you have a crisper sharper way of knowing how things relate to other things and as we've discussed earlier that is a lot of what your IQ is about seeing patterns and relationships between things in illogical syllogisms this kind of reasoning helps you do that more efficiently and more accurately okay so so far what we have learned is that any statement that you make has to boil down to one of the four propositional forms and ultimately it's going to be such and such amounts of the quantifier of the subject is there is not blank the predicate quantifier subject copula predicate so all cows are mammals the sky is blue I find that my students are fascinating people any statement that you make has to be such a such amount of the subject either is or is not like the predicate category so we've been analyzing those for a couple of weeks and now we need to link this all together to do so we else need to learn a little bit more vocabulary okay so far we have been talking about subjects and predicates and now what we're going to see is that we need to think we need to have names for these terms that indicate their position in a larger argument not just in individual sentences as we have them so a syllogism has three they're called the major premise that is statement of fact number one it is followed by a minor premise statement effect number two and the major the minor premise need to have some term in comments and that links them together so that by looking at the relationship you can draw a third standard a conclusion so you can write this out like a mathematical equation so you have two terms here in that line that leads to the answer also three dots in a triangle is the traditional shorthand symbolism for indicated the conclusion of an argument thank you now these terms these statements are going to have terms within them and they will be called the major term a minor term in the middle let's go ahead and look at an example and diagram it because makes it easier to wrap your head around all of us behold the very first syllogism that Aristotle used in his textbook the very first syllogism that medieval scholars and Cathedral schools encountered when they were learning and tried to recapture the knowledge of what once again the memory of Socrates shows up okay so we have two statements here all men are mortal Socrates is a man okay so this is premise number one premise number two and then hopefully this will lead to a conclusion right first let's analyze them that we've been doing so far as individual statements in the statement all men are mortal what is the subject men then predicate more obviously this is our code below this is our quantifier and what form is this a form okay in our minor premise or such as Socrates our predicate is man where once again a possible form in our conclusion Socrates is more now very importantly we need to know whether these statements are positive or negative assertions and they're all a positive statements and we need to know the distribution factor in any a form statement what is the distribution factor DMU okay at this point now that we're really good and analyzing statements you can actually stop putting SS and peas on top of this basically want to be able to indicate your two categories make sure it's in form and identify the form and then just put your distribution factors up there because that's all you really need to analyze whether or not the argument that they're a part of is found okay all right now looking at this statement notice how each of our statements have two terms in it you've been calling them subjects and presidents right now in terms of the larger argument these are major terms minor terms and middle terms the easiest thing is just find your middle term first plus that makes it clear that you actually have the potential for a valid argument the middle term is the term that is shared by the major in the minor premise so what category is shared by each of them and it's convenient just kind of circle them a little bar between them and then we know that okay here's what links these two together so this is our middle yeah once you found the middle term everything else falls in place for diesel this is our major premise that was our main our middle term which means the other term is going to be our major term all major premise a major term means is that it's the first statement in the argument you have to call it something so we call the major the minor you call it the number one term is a number to determine if you want to do we just see the way to indicate okay so that's our major chart now in our minor premise we already have a middle term indicated which means this must be what monitor so each of our premise has a middle term in it and then it has either of the major or the minor term ended just a penny of it's the first of the second statement of the argument now once that's done your middle term has done it's jumped its function was to link the two premises together so that the other two terms can potentially come together in a conclusion so remember your middle term should never show up in your conclusion it's done its job your conclusion if everything is in proper form the way Aristotle president your minor term should become the subject of your conclusion in your major term should come down to become the president so in any properly constructed three-part syllogistic argument you'll have a major term that appears twice the minor term that appears twice in a mental term that appears twice the middle term makes one of carats in each of the premises and the conclusion has the major of the mile minor term linked together and hopefully it will work because of how the premises are linked together okay so all syllogisms have two major terms two minor terms two middle terms no more than us okay yeah the rules of validity once we have gotten to this point we've basically taken the florid flow of words that beguiling nature of language and we have very crisply disciplined grits it's almost like mathematical equations now there's no confusion there's no ambiguity we know that this amount of the subject is part of that predicate category all the way down that also means that we can kind of free ourselves from falling into the flow of the words and just thinking about the components and how they link together one of the most useful things I found in helping students wrap their heads around this and do so much isms properly is to make a six sweater box like this one of those in your notes and think of this box like a game board don't play games aren't chess checkers you know them on a game board you have pieces there are rules for how they can move they can move some ways out in other ways and it's kind of like a game more at this point so we have here are three states we've got men and more we've got Socrates got we got Socrates and we know that all of these are a form statements so I don't even need to look at this as words and sentences anymore I can just look at these as terms and how they link together if I have meant for a subject immoral for a predicate and it's an A+ form my statement must be all man armed or if you can take the act or argument you have and boil it down diagram it and put it in the structure and capture all of the information then you know that you've got a very strictly well-disciplined argument that you've now got well in hand okay if you do this and there's extra words and extra information here that somehow didn't get captured you got a problem you need to fix you should be able to take any argument and structure it up like this now once you have done all this all the tedious stuff is over with you've diagrammed the sentences you found the different terms you figured out your premises and your conclusion you put everything in proper structure you know your distribution factor you know the forms that it's in once all that's done then all you have to do is apply the five rules of validity if it passes all five rules you are on the surest ground possible that you having valid truthful rational argument okay so the rules of the liddie there on page 15 of your reader we're also written down on the board over there rule number one and all these need to be competitive and you cannot have two negative purses do we have two negative vertices No and to positive Percy's so we're both rule one rule 2 I just think if this is the positive negative rule if you have two positive premises your conclusion has to be a positive statement if you have one negative premise then your conclusion must be negative it's kind of like an algebra if you have positive 3 times positive Y with the answer positive 3 1 if you have negative 3 times positive light what's the answer negative 3 1 if you have negative 3 times negative Y we don't care because the first of all orders said you can achieve negative vertices right so don't leave that you can have 2 negative parenthesis a positive portion doesn't work that way the analogy with math breaks down at that point so rules 1 & 2 both involve the positive and negative characteristics of your argument okay and so far it is best both of them we have two positive purposes and a positive conclusion rule number three you must have a middle term right we've already covered that as we were diagramming this we meet your along the way that we had a middle term remember the whole point of this is we're taking two facts and we're going to draw from them a third statement that we're going to hold to be valid and truthful but without a middle term there's no way to do it no way to ascertain the other two things you link together okay so we have a middle term roll-through rules 4 & 5 both involve distribution factor and just as a heads up 80% of the mistakes made on the logic exam are rule 4 & 5 mistakes involve distribution okay so focus on these very carefully rule number four the middle term must be distributed at least once what is our middle term here is it distributed at least once yes its distribute into the major premise okay it doesn't have to be distributed both times it doesn't have to match distribution factors don't try to rephrase or simplify the rule anyway simply that it must be distributed at least one time they can be determined both sides that's fine too but if they're both distributed in other words if in both cases you're linking term never accounts for every member of the category you can't draw a short conclusion about that because you're not sure if both of these are distributed if the other terms belong to the parts that didn't touch each other so one of these has to be fully accounted for right fifth and final rule is an if-then statement and again don't try to simplify it any further than this I've done for you already if I could write if a term is distributed in the conclusion then that term must be distributed in the premise work first appeared remember that both terms in your conclusion have already showed up once if one of the purses if you get to your conclusion and you find that your statement is accounting for every member of the category if you're fully distributed in your conclusion then it had to be distributed in the premise work first appeared or in other words you can't make a statement that covers every member of a category of the conclusion if only some of it was covered in the premise when it first appears earlier in the argument you can't say some of it up here but all of it down there okay so again it's an it's not that they have to match necessarily they can be undistributed here distributed up there wouldn't matter the kind of week conclusion but it wouldn't really matter so much and it doesn't mean that everything has to be distributed this is undistributed that's fine right you're simply looking to see any term distributing the conclusion had you have been distributed when it was first introduced and that's it those are the five rules of validity if you know how to properly diagram your sentences put them into this structure in you comprehend distribution factor all you got to do now is go through it apply the five rules at this point we can declare that this is a valid argument our conclusion yeah suppose that Socrates was the name of my pet walk with the conclusion being a good one no not because there's anything wrong with the structure the argument but simply because one of our first sees was not a truthful statement keep in mind that truth and validity are different things a statement is either truthful or it's not truthful an argument is either valid or invalid but truth and validity are different considerations in an argument so if somebody's presenting you some argument and you think there's something bogus and suspicious about it there are two ways to attack the argument either you point out that there's a premise there that is simply not truthful and you can reject the conclusion based on that garbage in garbage out but the real tricky thing is when the premises are in fact truthful agree with the premises but something about the conclusion since wrongly it may be that while the purposes weren't that truthful an improper method of argumentation has been employed so the conclusion is still invalid even though the statements were truthful pollutants so again a statement is truthful or not truthful an argument is valid or invalid right in your notes truth does not equal validity and what the difference between those two things are but at this point I will declare this argument to be valid if we want to diagram this out I showed you boolean diagrams the other day for how to graph out these statements if you take the two that you have and link them together then you can also see it in a more geometrical kind of way so we have in this case all men are mortal and we also know that Socrates is a man now that circle there and that circle there are the same thing right so to combine them together that means Socrates is there so there's Socrates is a man all men are mortal Socrates is mortal you can see that if all men belong to the mortal category and all of Socrates belong to the mini category there's no way that Socrates can't also be in the moral category those of you that like geometry more than algebra you might you know benefit from graphing it out of this way and visualize it better after a while you get so used to you it's gonna do it okay all right clear find out some more all Spartans are brave right you see the movie right Alcibiades it's not so somebody's speeding this up a little bit what are our two categories major premise we have Spartans and Braves minor premise Alcibiades brave conclusion Alcibiades smart right what is the form that the major furnace hey where's the form of the minor Prince eat the form of the conclusion that's possible distribution on a positive is being you and on e statements the in D all right can we all be able to graph this out over here and capture all of this information we have Spartans brave Spidey's brave somebodies this mark right does this capture all that information leaves nothing else right okay so we have a nice strict clean diagrammed argument to consider all right first rule of validity cannot have two negative premises oh boy do you have a problem let's do two negatives here it's that problem why not because that's a conclusion gate the first two are the furnaces right we have a positive and negative we don't have two negatives so we're going on the first rule second rule is a positive negative rule we have a positive or negative premise so we must have negative conclusion and we do do we have a middle turn turn right is our middle term distributed at least once yes it is at the minor premise the middle term is distributed so now fifth rule we check the conclusion anything distributed here must be distributed up top where it first appeared I'll supply these distributed distributed there as well spartans distributed distributed there as well so here's a valid argument but one that has a negative conclusion to it okay and it follows the rules of validity is what again if you were to graph the cell we have all of our Spartans along the category of people who are brave Alcibiades does not belong in the brave category he's out here somewhere with Enoch breaking people and if all the Spartans are within here and also by Diaz outside of there there's no way he can be a smart right visually diagram okay so that's a couple of valid syllogisms whether the positive over the negative complete now let's break the rules a little bit to see people can be sneaky with you all Spartans are brave Socrates it's not smart so I guess Socrates is not brave 30% of Americans with Flint said that argument and say yes right you must recover let's check it out all right our components are Spartans brave Socrates Spartan Socrates brave was the form of the major purse a positive one of the minor for us negative form a conclusion okay so this is the same structure as the last one he possibly not going to be negative and it was battle before let's see if it is this time all right so we know that eight statements are distributed in a distributed and then e statements are both terms distributed so is that all that different we got Spartans and brave we've got Socrates now rather than Alcibiades and we're comparing them first of all to Spartans and then we're saying that well I guess Socrates is not right so just a couple little tweaks on something that we know already worked out is about merriment let's see if it works out this time do we have two negative vertices no me obeying the positive negative rule yes do we have a middle term what's up going to turn or smartness is our middle term distributed at least once way it's distributed both times that problem no super good well I can super saw one rule for another problem Socrates is shipping it here shove it in their brain distributed and violated rule 5 we have a term distributed in the conclusion that had not been distributed to the premise where it first appeared therefore this argument is invalid and when you're doing this as homework or on the exam tell me it's invalid and tell me what role did violence roll 5 it's deadly the way fresh yourself and I have put these rules together and your written logic packet is the way that we decided was only the cleanest simplest way for you to remember them if you look at another logic book or go to some online loving website you might find those rules structured a little bit differently but they all add up to the same set of rules so if you remember it the way we have it just take number 5 if you're not sure right thing out so you've got a term distributed conclusion that's not a difference what is this look like diamonds all Spartans are brave Socrates is now not excluded from the braided category as well somebody's was he's only excluded from the Spartan category so we know that Socrates is not a Spartan there's our Spartans your Socrates they don't overlap but just because Socrates is not a Spartan doesn't mean that he can't even break maybe he's here maybe he's here we actually can't say for sure we cannot take these two statements and determine whether or not Socrates is brave or not all we can determine is that the conclusion that po2 is not valid it is not supported by the premises that have led to it and if you want to feel like a medieval Latin schoolboy you can declare at this point non sequitur which is Latin for it does not follow these might be truthful statements but the conclusion does not follow from the premises non secretary that's none of those Latin expressions and people use generally that you are now alright let's do some more Finian's are Greek Athenians are sparkles by Sarah comparing the Spartans Greeks vidiians also Greeks or Athenians and Spartans related what is the form of our conclusion all right distribution D nu D u u at a glance you can already tell that what rule can't possibly be a problem for us we got all positive statements so we know immediately what rule one's not gonna be a problem there's no negatives in there also our conclusion everything is undistributed so whether the rule can't possibly be a problem for us rule 5 exactly so if nothing is distributed the conclusion I don't even need to go check up top we're not making a really strong statement at the conclusion here well let's check them all so we're fine for a little one the final rule to the positive the negative rule so we have a middle term Greece is our middle term distributed at least once no it is not so this one is invalid for rule number four what would this look like basically we've got a whole bunch of Greeks versus Spartans there's some Athenians Spartans are Greeks Athenians are greats but if we've never fully accounted for a middle term we have no idea if these two are related to each other we happen to know as a matter of fact that Athenians and Spartans are not the same thing even though they vote to share being Greek right so with somebody who's trying to link things together that you're not sure about but that middle term is never fully accounted for sometimes you just sort of make an association that doesn't really pan out is it another appearance Greek about our military but it is never distributed therefore we're invalid for finian leaders eight Socrates lady please it's obviously something suspicious in that statement yes so in our major premise what is the major term what is their second finding the leaders are predicates hate Socrates and said what form is it distribution all of them and our minor prince if such a Plato he's an ebony now in conclusion Plato must be among those people in the heat sacrifice all right three positive statements you know one rules one a and to or fine right there's no negatives every time do we have the middle turn the fini and is our time to serve at least once yes and I'm conclusion the only thing to suit it is Plato so we check up top Plato is also distributed that's undistributed so it doesn't really matter if it was covered and the premise or not wait a minute is that me Plato Socrates all right I just sneakily like to say is there a difference absolutely absolutely correct if vidiian leaders and Athenians are not the same thing so remember I said subjects and predicates think about a fence pull up some stuff you're trying to decide if they're related to each other so here's a big ol fence full of Athenians it's a little tiny fence full of athenian leaders all right so here our middle terms don't really match you have two slightly different categories of thing they're trying to sneaky make it sound like they're the same thing and lead to this absurd conclusion in fact we violated all opinions are drink our philosophers some Greeks all right all the Finian's are great is that truthful statement yes subject run a kid before is that before was it hey both our distribution Deenie and reminder purpose some Athenians are philosophers is that a truthful statement yes it is but what for was in it mindful distribution you you our conclusion some Greeks are not philosophers is that true sure they can't all be philosophers we've met a few Greeks that were not exactly philosophers so some Greeks are not philosophers what form is that distribution is gonna make you okay so what we have three statements that I think we all agree are truthful statements that does not mean that the conclusion logically derives from these two premises and that's where you can also get confused you might look at the conclusion decide what y'all know that's true and assume that the argument is true well what you're stating is that your conclusion is a truthful statement not that the argument is about different things here let's go through the rules do we have two negative purposes no are we having the positive negative rule no we have two positive vertices that we're leading to a negative conclusion this is invalid rule number two should we stop there no always test for all five rules because often an argument can have more than one violation of validity do we have the middle term yes we did he's our middle term distributive at least once yes it is and our conclusion do we have anything distributed philosophers is distributed this is so many in the premise our first appear so this is actually in Bella for two reasons rule 2 in rule Fox we have a negative conclusion drawn from two positive vertices we have a term distributed in the conclusion that was not distributed the premise very first appeared so we know that all opinions are Greeks we know that some Athenians are philosophers but does that mean that we can say that some Greeks are not philosopher we simply can't draw any kind of conclusion about these folks we know that some Greeks since all Athenians are Greeks and some of these are philosophers we could say some Greeks are philosophers we could draw that conclusion right Olinda needs of Greeks Athenians are philosophers so can we conclude seven Greeks are philosophers yeah because that would make this positive taking care of this problem and that would mean this was undistributed taking care of that problem and what you'll find is that the more you start doing these the more you see were like a little crystalline structure the syllogism is pokin here there's an effect there there's a little consequences we're a little Rubik's Cube but you're sitting there working out so everything you do is gonna have an effect on something else in our original statement we simply can't draw a conclusion we know that some Greeks are philosophers since all of the names are Greeks that some of them are but as for the other ones who knows to assume otherwise is to basically make the fallacy of assuming the converse but we're going to say that some of them are philosophers I guess the rest of them or not what I'm talking about the ones that are not only talking about the ones that are remember that logical statements are about the amount of the subject that they say that they're about don't make assumptions about the other parts breaking the greets little bit let's see no horses cows toucher no cows or goats better house goes up the same thing right because it goes so no horses please again do we have pre truthful statements here yes all right so we got cows and goats and horses and cows and horses entrance these are all the wood form you know so everything is distributed basically we have a diagram that looks like this gals [Music] because horses yeah cows are not goats horses are not cows cows my good nothing is nothing so what is the rule we're violating rule number one if everything is distributed we new rules four and five we're going to work we do have a middle term it's cows and you can't really break rule one in two at the same time you could break one into the other so it's only rule one that we're bringing we have two negative vertices why can't you have two negative vertices if you know that cows are not goats you know that horses are not cows then horses are not ghosts they're all separate from each other no relation you've not a sandwich any relationship between anything there exactly and to make it even more obvious let's say we didn't like this no cows are goats no horses are cows no horses are good let's say we said no will to take goats out of here we'll say no cows are equines instead so now we have no towns our equine that's true no horses our cows that's true does that mean no horses are at once no in fact our little circle of horses goes inside there so cow's neck ones aren't related horses and cows aren't related but horses a neck lines are intimately related right so there's simply no way to establish a relationship in our two terms and our conclusion based on two negative parenthesis you never selvage any kind of a connection so you can't draw any kind of conclusion positive or negative the whole point of a logical syllogism is that you are establishing connections at least one positive connection so that you can then take your other two terms that are in the middle term it makes some assertion about the mental include okay all right all clear so far and that's pretty much it what I have to do now is practice this for a while until you get used to the structure how about a real world example I'm talking about Grayson farm and a rule if to negative purposes but that's why you can't have two negative verses okay all right your real-world example I used to know the person who's the kind of person that probably ought not to have the internet because then she would go on and believe every conspiracy theory bit of nonsense you can imagine she would send me emails of how Obama's this secret Muslim got born in this country and all the surprises and for a while several years ago for a while she was infatuated with one of those right-wing conservative talk shows I won't say the name but the guy that would the big Chuck Lorre used to cry a lot anyway she tell me how can i watch the show i watch the show and explain everything it's so clear you know you know she wanted me to know the truth so I could teach my students the truth so I finally humor I said okay fine I'll watch one episode right and I watch it and it's just rambling illogical nonsense but I didn't watch this episode and it did give me this nice real-world example of how people lied to you with facts this was a show about the dangers of people that talk about social justice you've heard that phrase before right social justice right did you know how evil that so it goes on like this it says well Lonnie you might go to church and it could be that your pastor talk social justice and that might seem like a good thing at all but you know who else talked about social justice take a while yes Hitler yeah that's what Nazis were talking about as well Nazis talk social justice so according to this person who used to have a TV show that millions of people watched their pastor is talking about social justice yes way your pastor is kind of sort of thought you went to hear about Jesus okay I did my best to explain what's wrong with this argument I don't think I made much headway let's diagram showing in our media press was the subject nonsense what is the project talk social justice okay in our minor presence what is the subject your pastor yeah somehow okay what former all these statements in all right now that was the same structure as Socrates is mortal we know that three positives can work sometimes but doesn't work here distribution all the way across the D in you all right so three positive statements here roles one and two and over fine do we have a middle term talk social justice is it distributed once no it is not and the only thing shouldn't inclusion is your pastor also distributed so that's not a problem but it isn't valid for a role number four we've never fully distributed our middle term diagram the sound what does it look like of all the people to talk about social justice it may well be that Nazis talked about social justice that does not make nor posture not see we're not able to establish a connection between these two groups based on one undistributed middle term this my friends is one of the most common one of the most pernicious ways that people lie to you in politics in fact this one is so commonly used that it has its own name this is called the fallacy of the unbounded middle the fallacy of the unmounted build or a rule for violation it's when you try to disparage your opponent by associating them with some obviously negative person because of some trivial or connection that is not fully accounted for you might as well say Hitler breathes oxygen dr. Brooks breathes oxygen so I guess dr. Brooks is like Gilbert makes no sense when you think about but to the untrained listener you hear somebody go on or on about this and it's like oh that's just what these bad people used to do and it's persuasive to people that have not learned to think clearly in a discipline their reasoning process right we could say for example fire trucks on red strawberries are red strawberries are like fire trucks well they are both red but if your house is on fire you're gonna call the strawberries to come Thunder now are you gonna slice up some fire truck on your summer salad no this is ridiculous this is a sign of sloppy thinking and unfortunately your world is full of sloppy thinking I used to believe that if you had a TV show if you were important enough done you know speak to millions of people that you would have you know gone in college and learned to think clearly but that's not the case and there are liars and damned Liars all over in your world we're gonna lie to you your whole life even though they might start with a couple of truthful statements they lied to you by giving you arguments there's simply not valid this is nonsense so this is what logic does free when you get into the habit of using logical reasoning either through a syllogistic process of connecting your facts together and then determining whether these conclusions are valid or simply understanding how in the midst of argument people fall into emotional sloppy kinds of fallacious arguments and learn to identify them you need to do these things to defend yourself and there's a world full of liars that we live in and that ultimately is what logic does morning provides you with a bull it tells you where to push them

Channel: George Brooks

Views: 3,862

Rating: 4.963964 out of 5

Keywords: Brooks, Valencia, Humanities, Logic, Syllogism, Validity, Aristotle

Id: 0Z9-kcnk7lc

Length: 49min 11sec (2951 seconds)

Published: Tue Mar 12 2019