Categorical Syllogisms

hi so welcome this is lesson 5.1 on uh standard form categorical cism so what we're doing in this lesson in this chapter that's chapter 5 we'll be basically building on what we discussed and what we learned in our um last module which was on categorical propositions but in this case instead of just talking about inference arguments we're going to be talking about categorical syllogism so let me start off with what a syllogism is a syllogism is a is an argument that has two premises and one conclusion Each of which um Each of which the pr all the premises and the conclusions are all in standard form in terms of standard being standard form propositions essentially the same stuff we learned last time there's a few things you need to learn about a categorical syllogism first off a categorical syllogism categorical syllogism is deductive the second thing is that in order for categorical syllogism to to being a standard form argument there's a few things you have to know right um so we're going to have to talk about a few different terms here that we may they're going to be new to you the first idea is what we call the major term of an argument so let's just throw that up there on the board the major ter term of an argument is determined as the predicate of the conclusion right so the predicate of the conclusion as put C up there there's also the minor term of an argument right and the minor term is the subject of the conclusion right so the minor term is the subject of the conclusion and finally there's a third term which is called the middle term and the middle term is essentially um that term which only appears in the premises right so we'll just put uh a term of the premises right and once we understand what this how these terms operate we'll be in a very good position in order to evaluate whether or not certain sorts of categorical arguments or syllogisms actually are in fact valid um so first off you have to see that so let's just throw an example up here on the board maybe to make sense of this right this is a very simple example right and it's the idea all men are uh mortal right um all persons named Socrates are are are humans or are men therefore all persons named Socrates are mortal right or in other words um all person all men are mortal Socrates is a man therefore Socrates is Mortal so this is in categorical form so here's what we can take a look at but first we look at the conclusion to determine what the major term is right the major term is the predicate right right so in this case it's the idea of mortality right which occurs in the very first line of the argument that's another thing that's necessary for all standard form categorical syllogisms namely that the predicate term occurs in the first line and that the minor term occurs in the second line hence major minor you can just think if it's major it's first if it's minor it's second right so here is the minor term and it's in the second proposition second line of the propos of the argument I'm sorry um now the middle term term conveniently in this case right it's an M right but it's the it's the term that only occurs in the premises right so this is a standard form categorical syllogism now there's four rules and I guess I'll just quickly outline those rules for you there's four rules that in order to make sure that an argument is in standard form the first and this is are located on page 244 of your book I'm actually looking at right now right the first rule is that all these statements are standard form category oral propositions so they have to be in standard form the second is that the two occurrences of each ter term are identical right namely you can't compare non- likee terms the third rule is that each term is used in the same sense throughout the argument and the fourth rule is that the major premise is listed first and the minor premise is listed last and the the conclusions last those are the rules right so that's basically a standard form proposition now there's two other things we're going to talk about right and that's the concept of the mood of an argument and the idea of the figure of an argument all categorical propositions both have a figure and a mood now the mood is essentially identified by three letters right three letters of the proposition right in this case what we're looking at here we have an a proposition an a proposition and an a proposition so we could say is that what we have here is a triple A A A a a right and sorry my handwriting is bad but we have an A AA and this is the mood right now the other question term in which we use to identify this is what we call the figure and the figure is very simple and the figure refers to the location of the middle term now there's actually four possibilities right just to throw these up on the board there's four possibilities for the figure four figures are possible right so we have S well let's start here we have m p s m therefore SP right and this is figure one the other possibility is we have p m s m SP p and this is figure 2 right other possibilities is we have m p MS SP and this is figure three you can see how this next one's going to go probably right and that's going to be we have M I'm sorry we have p m Ms s p and this is figure four so essentially the way in which you can remember this the four figures is by their location right right so figure one 2 3 and 4 what I do in order to keep it to remember myself is I just say 1 2 3 4 right um in order to keep that that'll be backwards for you so for you it's 1 2 3 4 and you can remember the figures in this sense so you just basically have to memorize this now if we went back to our original proposition right uh we had a AA a and our M our middle term was in this sense so we had a triple A1 right so that's the sort of proposition we were looking at an a aa1 right um and if you look in your book there's actually a list of propositions in terms of the figure and the mood which are unconditionally valid um and this is located on page 247 um and this has to do with the figure so let me write these up here for you right hopefully I'm not running out of time with the video right so these are unconditionally valid in terms of the figure right so let's just erase this so these are unconditionally Val and when I say they're unconditionally valid what I mean is they're valid from both the Boolean and the Aristotelian perspective right they're valid for both Aristotle and bull depending upon how um whether or not you commit the existential fallacy right so we have the Triple A A A1 the E A E1 the a I i1 and the E io1 right all of which were unconditionally VI let me see if I can move that for you right and then up here at the figure two right we have the E A E2 the a e E2 the e i O2 and the a o O2 for figure three we have i a i a i i o a o and the e i o and for figure four there's only three that's the a e e the i a i and the e i o4 right so these are always valid no matter what and I'm sorry it's hard to see that but you can look on page 247 right so these so an a aa1 that's our first argument is unconditionally valid right such that if you determine what the argument form is no matter what the terms are you'll know whether or not it's valid now the conditionally valid forms there's there's not as many of them and you'll have to take a look at those on page 247 cuz I think I'm running out of time so uh but obviously there's more conditionally valid ones than there are unconditionally valid and you probably get that just from learning the U the difference between the existential fallacy and the Boolean and the Aristotelian discussion um so I hope this gives you a little bit of sense of what we're talking about when we talk about a categorical syis be basically just an argument in which the major term comes first the minor term comes next and then of course you have the conclusion which is subject predicate and then we have the mood of an argument which refers to the three type of propositions used in the argument and we have the figure which which is correlates to the location of the middle term in the argument okay so this is 5.1 read the lesson U read the book which will give you more details and then try the lesson review and do the homework okay bye

Channel: Mark Thorsby

Views: 71,892

Keywords: Logic, Philosophy, Hurley 5.1

Id: 1sU10dRxnRo

Length: 10min 1sec (601 seconds)

Published: Fri Feb 26 2010