A Crash Course in Formal Logic Pt 6a: Categorical Syllogisms, Terms, Mood and Figure

well everybody and welcome back to my crash course in formal logic in this part we're going to study the crucial topic of categorical syllogisms we're finally going to take categorical sentences in batches and try to draw conclusions from them now last lesson was kind of short but this lesson I'm definitely going to keep to my promise to give you two college-level lectures in one video so hold on to your seats now syllogism is a very broad term it refers to any argument containing two premises and a conclusion categorical syllogism by contrast is a very specific term it's a syllogism but each of the three sentences premises and conclusion have to be categorical sentences to illustrate premise premise conclusion syllogism by contrast categorical sentence categorical sentence to a conclusion of the categorical sentence that's your categorical syllogism so just to give you a concrete example all men are mortal Socrates is a man Socrates is mortal that is a categorical syllogism now it may be a little difficult to see on the surface of it but these are all categorical sentences are the either the AE I or o type we just have to take all men are mortal and swap it out for all men are mortal beings because mortal beings would designate a category and as for Socrates is a man how about instead all persons identical to Socrates that way we have an appropriate subject class in that second premise and just take these two switches and put them into your conclusion instead of Socrates is immortal all persons identical to Socrates are mortal beings you can see that we're moving from an a sentence and an a sentence to an a sentence that makes this a categorical syllogism now let's take a look at these terms that occur in the categorical syllogism Men mortals and Socrates they're kind of links in a chain and the way those terms hook up makes all the difference in the world to whether an argument works or not there's a term that occurs twice in the premises a crucial link that's called the middle term again thinking of these terms as links in a chain there's something special about the one that occurs twice along the premise that is sort of a middle a link up that hooks up the other two terms in the syllogism those other two terms are hooked up in the conclusion in an interesting way those terms are called the mage major term and minor term and they occur in the conclusion so look again the term men occurs twice in the premises and the term mortal and Socrates which also occur in the premises are linked up in the conclusion it's the middle term that's doing that hookup so let's a get a closer look here by deleting some stuff let's take a look at those other terms the other term mortal beings is called the major term it is what occurs one time the premises and once in the conclusion as the predicate remember the major term is the predicate of the conclusion now there's also another term that occurs within the premises one time it's the term persons identical to Socrates here that term occurs one time in the conclusion as the subject so the minor term of the argument which gets linked up to the major term through the middle term is the term that occurs one time in the conclusion as a subject so here you have again three terms each occurring two times in the argument but where those terms occur makes all the difference as to whether they count as major minor and of course the crucial middle now we also have something in addition to the major minor terms in a categorical syllogism we have the major and minor premises because the major term occurs only once in the premises you can spot it as the major premise and because the minor term occurs only one time the premises wherever that term occurs it's going to be called the minor premise again that's just because in contrast to the middle term these terms occur only once in the premises hence they can designate the premises as major a minor in virtue of that fact now now when all the previous conditions for a categorical syllogism are met and the major premise is listed first as of course major things probably should be then the categorical syllogism is said to be in standard form and I'm going to talk a little bit here about standard form so take some notes now standard form categorical syllogisms are all that we're going to need to analyze from here on it's all we're going to study and it may not be obvious to you as to why that's the case look at the argument to the left that we've been studying for quite a while it's pretty much the same as the argument to the right isn't it I just swapped out to the premises one for the other but they're the same premises so if one argument is valid so is the other and yet one of these is approved according to the standards of standard form and the others corrupt why in the world think that and on top of the fact that you just wind up with the same argument when you transform a non-standard into a standard form it's kind of tedious consider this example all watercolours are paintings some watercolors are masterpieces it does follow from this that some paintings are masterpieces but masterpieces as you see from the conclusion is the major term so we got to swap out and put that major premise as the first one well that seems tedious in addition to the fact that it just winds us up with the exact same argument so why even do that well sticking to this standard form reduces the number of moods of arguments that we're going to have to analyze when I refer to moods I'm talking about the order of sentence types when a syllogism is in standard form now you could define mood a little differently just to be any string of sentence types with our Socrates Men immortal argument we end up with an a premise followed by an a premise followed by an ache for a conclusion so our sentence types for this argument and the mood thereof would be a a a or consider the watercolours example we had a particular premise first and a universal premise second followed by a particular conclusion and I a I but this argument in contrast to the last one would give us different moods to analyze to see if it was valid if we allowed different premise orders notice that if we swapped out the green box in the red box there we'd end up with an AI I mood for the argument why not just stick with the major forms or rather standard forms and that way we'll have fewer moods to analyze when we try to figure out which arguments are valid and which ones are not it's a good argument for sticking with standard form let's review thus far if you have two premises in a conclusion that's a syllogism by definition and if they're all categorical sentences involved then you have a categorical syllogism and if the major premise is listed first followed by the minor then the conclusion you have one that is in standard form and then you can analyze it according to its mood that is the order of sentence types in argument but in order to tell whether or not of the categorical syllogism is valid we're going to need to know more specifically whether or not that mood of a standard form categorical syllogism is valid depends upon figure if you know the arguments in standard form you know roughly where the major minor middle terms are going to show up you know the major term is going to be in premise one in the conclusion for example but figure nails down where these terms show up and that's when we know exactly what type of argument we're dealing with and whether it's valid or not to illustrate the need we use an example before involving water colors being masterpieces and paintings now if this is an eye a eye form as we said before now does the validity of this argument show us that an eye a eye mood of a standard form categorical syllogism will always be valid try this on for size I'm going to swap the positions of the middle and minor term middle and major term in the first and second premise respectively some flying animals are animal mammals I'm sorry all elephants are mammals so does it prove that some elephants are flying animals I don't think that conclusion follows but again we're dealing with an iai mood obviously to find out which IA is are valid or not we need to nail down where the middle term occurs and whether it occurs in the proper spot in each of the premises how are we going to do that well here I'm going to call in a little help from a big friend not a personal friend at all in fact not even a logician multiple-time mr. Olympia Jay Cutler me and look at the size of this guy's back it's a guy who uh may-maybe likes to work on his figure quite a bit so for those in the mood to show off their figures let's use this guy as a rather a mnemonic device to remember what figures there are for us to memorize now there are exactly four figures places that the middle term could show up assuming that the predicate of the conclusion will be in the first premise of the argument the middle term is in Figure one could be listed first and then listed second in premise number two and so on and so forth these pretty well exhaust all the ways that the middle term could show up in the premises of an argument how in the world is jay cutler going to help us remember figure 1 2 3 & 4 well maybe this isn't helpful for you but it sure helps me out an awful lot so thank you Jay Cutler so now what we've done is we've pinpointed where that middle term is going to show up in any given premise and that's what we needed to do to get around that problem with the flying elephants example earlier right so now we can tell which arguments categorical syllogisms that is are going to be valid or we're not that's some good news but there's also some bad news the good news is now that we know can pinpoint where the middle term is thanks to figures we can take an inventory of all the valid categorical syllogisms what uses that though you're going to memorize them all well here comes some more good and bad news in the Middle Ages they did come up with a method to memorize all the valid moods given a figure here you go people somebody made a list of names in the Latin so that under each figure just listed you could tell which mood is going to be a valid one under figure one Barbara is a famous example AAA is valid on one the mood e AE is also valid and so on and so forth so all you have to do guys to memorize which mood is valid on which figure is to memorize Barbara seller aunt dari fari Oh Barbara so on and so forth all the way through isn't that easy heck no it's not easy to make matters worse this covers all the arguments or standard form syllogisms that are valid notice there's a distinction here the ones at the top are very different from the ones at the bottom the ones at the top are unconditionally valid those are the ones that are valid given boolean assumptions namely that universals apremilast italian uh categorical syllogisms the one that are valid on the assumption that the universals carry existential import so in addition to memorizing this list of names you're going to have to memorize the distinctions between what's valid on which assumption oh boy how can we make this easy I guess if you want to make use of mood figure and standard form to tell which arguments are valid or not you've got a lot of memorizing ahead of you don't you well let me help you out here there's a problem and a benefit to this little example listed here in the gray there's a certain form e io that is valid on every single figure and that's what I'm going to make use of to revise this very old and time-honored mnemonic device if it deserves to be called a mnemonic device at all who wants to memorize this list of Latin names for my two cents you shouldn't do it it's obsolete and I'm going to come up with something better the thing that I think is better I call the neighbors mnemonic those are form figures and moods that I listed in the gray they all take the pattern or mood e io e io is valid on every single one of the figures that we studied and I'm going to make use of that to come up with a superior mnemonic device that which has been used throughout the ages so to get our new project going I'm going to need a little help my friends Barbra Streisand known for her political singing and movie career and also Alfonso Roberto who's known for his roles in classic sitcoms and many of you watched and last the Orlando Bloom who's probably best known for his role as Legolas in the Lord of the Rings series notice the neat thing is each of these persons has a name that corresponds a modern and not a Latin name that corresponds to some of the valid moods on each of the figures the eh eh eh eh oh oh and the Oh a o I what if we can use this in order to memorize our valid moods given a figure think of this first Barbara's neighbors naming feared I'm not asking you why Barbara has neighbors who fear maiming just remember that sprays Barbara's neighbors maiming fear - notice I'm using the word neighbours here look at figure number one and the moods that are valid on it under boolean assumptions Barbara's neighbors naming feared covers each and every one of these in the English not with those ridiculous lists of Latin names your one step towards getting all the valid moods given figures one through four let's see if we can make the rest of those leaps we'll make that next little jump with Alfonso's help Alfonso's neighbors apparently don't like to have jobs don't ask me why but i'll fons those neighbors for your careers just as much as Barbara's neighbors naming feared so if you can remember that Alfonso's neighbors for your careers you're just one step closer to memorizing all of the valid moods given a figure only this time it's going to be figure number two on figure number two I'll farms those neighbors Maine feared careers corresponds in terms of the vowels in it to the vowels listed in each one of the Latin names in Figure two congratulations you're one step closer can we make the last two leaps to figure three and figure four in fact we're going to do both of them at the same time with a little help from Orlando Bloom Orlando's neighbors disdain naming and disdain careers for neighbors I got a whole bunch of people showing disdain towards careers up in my little uh picture here I hope you can remember it it's goofy and just goofy enough to be remembered but if you can remember that Orlando's neighbors disdain naming and dispute staying careers for neighbors then you've gotten all the way towards memorizing The Ballad moods given figures which figure does that handle figure three and four together notice the figure three has four valid moods on boolean assumption and figure four has three valid moods so while this isn't a perfect example or illustration or mnemonic device Orlando's neighbors disdain naming corresponds to all the vowels listed under figure three in the names thereof and disdain careers for neighbors as long as you can list four as not a extra word after all what sort of valid mood would have just one oh fo r get rid of that you have to stain careers neighbors and that corresponds in terms of its valves to all of the valid moods under figure four congratulations you're done so remember instead of barbarous element dari Ferriero and all this other stuff that comes under the green portion that is the portion of this diagram that lists valid boolean moods let's just take it a different route how about instead barbers neighbors maiming feared Alfonso's neighbors for your careers Lando's neighbors disdain maiming and distinct careers for neighbors there you go you're done now isn't that mnemonic a little silly I guess we can answer that question forthrightly it's about as silly as it comes barbers neighbors naming fear the Fonz's neighbors fear careers Orlando's neighbors disdain naming and disdain careers for neighbors I just memorized out of all the valid moods and it's not as silly as trying to remember all those Latin lady names unless you have just a good memory in Latin and one last big note there's another advantage to mind a mnemonic device apart from that mnemonic that's better than the mnemonic device where you memorize all those Latin for any word that I use in that mnemonic device for example word feared it's used to denote that ei e is valid on a particular figure and I never repeat any other word where ei e is going to be valid any place you find feared is where ei e is going to be valid any place you don't find the word feared ei e is invalid and that goes for every word and every possible combination of vowels in the mnemonic device pretty helpful huh well we still have one last issue here my little pneumonic device just taught you how to memorize all the moods given a figure that are valid under boolean assumptions but what about all those that are valid under Aristotelian assumptions notice that in these Latin names when you look at the vowels in red you start off with a and E or E and a or a and a universals and then you move to eyes and O's for conclusions in other words the universals must have existential import because you're reaching a conclusion that's an iron oh sentence and those are known to have existential import is there any way for memorizing these I want to point out one thing that may be helpful in memory Fernando in his plane and he's being chased by some other pilots captain Hernando likes to go upwards with his plane all these other pilots are trying to attain his trajectory if they're trying to attain our Nando's trajectory then remember this there are only three valid Aristotelian moods for any figure if you go back to all those names that were listed under the Aristotelian valid moods in the yellow in the previous slide you only found three combinations of vowels that worked eh eh I II AO and AEO are the only combinations that are ever going to turn out valid regardless of figure hope this pneumonic device turns out helpful for you well I hope this has been a helpful lesson for you it certainly helps you memorize the concepts of categorical syllogism mood figure and all the other related concepts and it gives you a helpful mnemonic device to take all that knowledge and put it to some practical use so just stick to it and you're going to memorize a whole lot and get good A's in your college courses and you're going to do so really quickly in the meantime as usual hang around for my exercises on this lesson and my next logic lesson which will be coming up soon thanks guys bye bye

Channel: PhilHelper

Views: 94,127

Keywords: categorical syllogism, syllogism, mood, figure

Id: KcNESCrkIiQ

Length: 19min 49sec (1189 seconds)

Published: Mon Jul 15 2013