A Very Basic Introduction to Logic and Syllogistic Logic

we all want to win arguments i mean sure there are probably those people out there that like losing arguments because that means that they've learned something but usually we want to look cool and smart in front of people that don't really care i mean come on i'd miss my own wedding if it meant winning an internet argument with some random guy in nebraska but in all seriousness being able to analyze different arguments through logic will help us make important decisions in life there's different life philosophies and self-help advice out there some conflicting with others and

perhaps by looking at all this advice more logically we could come to our own conclusions so this video is designed to provide a very basic elementary introduction to logic for someone who knows literally nothing about it the text i'll be using which i was taught in my logic class is harry j gensler's introduction to logic hopefully if this video does its job and gets you more interested in logic you get the book yourself for further reading also this video contains a lot of information so feel free to pause it take notes go back to earlier

sections or whatever else you gotta do now without further ado let's actually start talking about logic so first off we should probably define logic in contemporary culture we kind of just use the word logic interchangeably with reason if anything the word is used as a political tool you know people will talk about how logical they are and their side is while the other side is illogical they'll say their position is logical without even talking about its validity or anything but what really is logic gensler defines logic as the analysis and appraisal of arguments i think

about logic less is a thing but as a method a tool that you could use to look at arguments and determine certain things about that argument we'll talk about those things later but we might as well also understand what an argument is since that's what we're going to be dealing with when we do logic an argument has two components first it has a set of premises which can be seen as supporting evidence and then a conclusion which is based on that evidence now you could have a lot of premises i've seen them go up to

more than a dozen personally but for this video and for syllogistic logic we're going to be dealing with two premises and one conclusion here's a more concrete example of an argument all fish are animals a salmon is a fish therefore a salmon is an animal also those three dots that form a triangle that's just another way to say therefore i just use it instead of writing out therefore because i'm lazy so now we know what an argument is and it might be helpful to think of some argument examples of your own but we've only just

begun we've actually got to test these things i mean consider this example of an argument mcdonald's is healthy all frogs creep me out therefore biking should be illegal i mean it's technically in the form of an argument but something seems seriously wrong here and i'm not talking about the fact that i actually like frogs so when we get an argument like this or any other we have to put it through two different tests we have to test whether an argument is valid and if an argument is sound [Music] so let's start with understanding what a

valid argument is the book states an argument is valid if it would be contradictory impossible to have the premises all true and the conclusion false valid doesn't say that the premises are true but only that the conclusion follows from them if the premises were all true then the conclusion would have to be true so to test for validity we first don't concern ourselves about whether the premises are true we kind of just assume them to be true for now so even if we get ridiculous sounding premises like all giraffes live on mars we don't worry

about whether it's true what we do worry about is the relationship to these assumed true premises and the assumed true conclusion to see if the conclusion necessarily follows from the premises this might sound weird so let's get an example going all cats are evil garfield is a cat therefore garfield is evil so again it may or may not be true that all cats are evil or if garfield is a cat but that's all irrelevant we're only concerned here with whether the conclusion necessarily follows from the premises now i'll explain an actual test to test for

validity later in this video but here's just an illustration i made to show how this argument is valid all cats are evil so the entire category of cats fits into the larger category of evil garfield is a cat so he fits into the cat category and since the cat category is in the evil category it necessarily follows that garfield is evil therefore this is a valid argument but what about an invalid argument what might that look like let's take a classic argument example and modify it a bit to make it invalid all men are mortal

socrates is immortal therefore socrates is a man now this might sound valid on its surface but it's really not here's an illustration to show why so all men are mortal so the men category fits into the larger mortal category now socrates is immortal and while that may mean socrates can fit into the man category he could also be somewhere else like in this fish category because fish are also mortal so you see that even if it's possible for the conclusion to follow from the premises it isn't necessary or forced the conclusion must follow necessarily from

the premises for an argument to be valid so that's what a valid argument is again i'm actually going to give you a way to test for validity later on in this video but first i want to distinguish a valid argument from a sound argument now a sound argument doesn't need much explanation basically a sound argument is a valid argument but the premises are also true remember how we don't really care if the premises are true when we test for validity well here we actually do care an argument could be unsound in either two ways one

it might have a false premise or two its conclusion might not follow from the premises here's the classic example of a sound argument all men are mortal socrates is a man therefore socrates is mortal as you could see it is both valid as an argument and the premises are true don't worry yourself too much though about sound arguments or determining whether the premises are true because in my experience the majority of logic focuses around testing for valid arguments a critical reasoning class might be better suited for judging if a premise is false or not anyway

now that we have distinguished between a valid and sound argument let's now introduce a certain type of logic which is arguably the most famous and accessible [Music] shout out to aristotle it's surprising that we haven't talked about him yet on this channel but he is the inventor of syllogistic logic now there are three parts to an argument in syllogistic logic or syllogisms for short there's the major premise such as all men are mortal there's the minor premise such as socrates as a man then there's the conclusion such as socrates mortal pretty straightforward the thing is

though when working with logic you're probably not going to be dealing with full words but rather letters that represent a word usually you just substitute the word for the first letter so instead of all men are mortal you'd put all m is o with o representing mortal because we already have an m but wait why are we saying all m is o instead of all m r o well that's because there's specific language used for syllogisms specifically there are five words used in these sentences those words are all no sum is and not and when

you combine the letters that represent a thing with these words you get stuff like all f is h or no g is d these are called well-formed formulas but in class we just called them woofs for short here are some examples of wolves used in syllogisms and underneath them are some non-wolfs notice how the non-woofs underneath use language that isn't limited to our five words now there's also the issue of capitalization because as you've probably noticed some letters are capitalized and others aren't so in each wolf there are two letters now for the first letter

if the wolf begins with a word such as some all or no then both letters get capitalized however if the wolf begins with a letter and not a word then the first letter is lowercase but in this second case where the first letter is lowercase what do we do about the second letter well if the term you're representing is a general term then you use a capital letter so for example eats ice cream would be a capital e and soccer players would be a capital s now if the term you're representing is singular and points

to a specific person or thing then you should use a lowercase letter for example amygdalavids would be a lowercase a and nietzsche would be a lowercase n now with all this in mind see if you could convert this sentence here into a woof pause the video if you need to okay assuming you pause the video and you have an answer here is the correct answer as you can see we only use those five words that are available to us and our letter capitalization meets the rules we previously established finally now that we understand wolf's and

syllogistic logic we can now go over a method for testing the validity of a syllogism [Music] so let's start by converting this argument on the left into a syllogism using wolves no rabbits eat meat bugs bunny is a rabbit therefore bugs bunny doesn't eat meat for the first part we could translate this into no r is e with r representing rabbits and e representing eat meat remember we capitalize both because this woof starts with a word next we can translate the second part into b is r with b for bugs bunny being lower case because

this wolf begins with a letter and r for rabbit being uppercase because it is a general term finally we could translate this conclusion into b is not e alright nice job guys we have our syllogism next we want to underline any letter that is distributed but what does it mean for a letter to be distributed an instance of a letter is distributed in a woof if it occurs just after all or anywhere after no or not so here are some examples of distributed letters and wolves that are underlined again pause the video if need be

but let's now look at our example since our first wolf starts with no any letter after that is distributed so we underline both the r and the e our next line has no distributed letters according to our rules so nothing gets underlined finally for our conclusion b is not underlined but e is because it comes after the word not so our syllogism with underlined distributed letters should look like this next we need to star certain letters star premise letters that are distributed and conclusion letters that aren't distributed so for our example here our first premise

has both letters distributed so we star both of them none of the letters in our second premise is distributed so nothing gets starred finally in our conclusion we only star b because it is not distributed this is now what our syllogism looks like both distributed and starred last step here we check if every capital letter is starred exactly once and then we check if there is exactly only one star on the right hand side so checking over our example we see that r and e our only capital letters are starred exactly once so it passes

that test next we check if there is exactly one star on the right hand side and there is on the e in our first premise and since it passes those two tests the argument is valid the syllogism is valid if and only if every capital letter is starred exactly once and there is exactly one star on the right hand side now i don't expect you all to get this immediately which is why i highly recommend the book of this stuff interests you because there are also practice problems to help you fully grasp all this as

to why the star method works i really don't know and i would expect it to be extremely tedious to try and learn how it just does in the end but just to recap hopefully you've learned what logic is the difference between a valid and sound argument the basics of syllogisms and well-formed formulas or wolves as we've called them and the star test to test for validity don't ask me to go further with logic because it's really not where i focus much in my education however just learning some basics has really helped me greatly in life

if you got any value out of this video then feel free to subscribe and hit the bell to be the first ones notified when i drop another video hit the like button if you've learned anything and i wish you all a beautiful rest of your day you