hi welcome to an introduction to logic this is a U video series that introduces introduces students um to the basic concepts in logic and in particular we're looking at categorical propositional and predicate logic although you don't need a textbook to watch the videos We are following a textbook and uh we're using the textbook of concise introduction to logic by Patrick Hurley and we're using the 11th Edition this is one of the most widely used textbooks for logic within the country and so I think um a lot of people will find this video helpful um these this textbook is frequently used of course in undergraduate courses um we're going to look at a lot of different concepts throughout this video series there's actually going to be 40 different videos um but in this first one we're just looking at really the basic of basic concepts we're looking at arguments premises and conclusions and um and we're going to be following along with the um Patrick hurly's discussion of that same thing though you'll see that um I don't necessarily agree with everything Hurley says or at least I don't put it the same way Hurley does um but it's a great textbook nonetheless um let's just start off with a real basic question here uh which I think sort of deserves some discussion right from the outset before we sort of get into what arguments premises and conclusions are and let's start with this question what exactly is is logic right um You may have if you've never taken a logic course before I'm sure you've heard the term logic um you know of course Captain Spock and Star Trek he talks about logic what exactly is logic um I think there's a great even though logic goes back all the way to the ancient world with the writings of Aristotle and even Plato um logic is I think the best example or best sort of quick phrase about what logic is comes from a philosopher by the name of John Lock um many of you may in government uh or even your introduction to philosophy courses may have heard of John Lock John Lock uh is a modern philosopher um and he said that logic is the anatomy of thinking of human thought and I think that's a great way of thinking about what logic is so we're going to give this answer logic is the study of the anatomy of thinking uh and for all of you watching out there I'm sorry my handwriting isn't always the best but it's the anatomy of thinking and I think that's a great way to think about it because what exactly is anatomy anatomy is the study of the different um is a is a is a subset of biology and what Anatomy does is anatomy studies the different organs within a body and how those organs function together and in many ways that's what logic is um you even though we can't see them there's certain organs or at least there's certain yeah there's certain organs in our minds that allow us to think in certain ways um and to think correctly and this is an important distinction there is a difference between correct reasoning and incorrect reasoning u whoops he's an ugly guy U correct reasoning versus incorrect reasoning what exactly counts as correct reasoning uh well to reason first and foremost there's lots of different things we do when we think we can imagine uh right and this sort of thing um but we'll see that the sort of thinking that logic is concerned with is the form of reasoning that's contained in its reasoning oops for some reason in argumentation and in fact we'll see that what logicians study essentially are the forms or rather the structures of reasoning that allow us to make arguments now of course what exactly is an argument right we can keep asking this question what is an argument well an argument is essentially um it's composed of two different things first off an argument is always contains a premise at least one but usually multiple premises and the second thing that it contains is a conclusion uh the premise is supposed to support the conclusion right so you can think of the premise as the evidence that we give when we make claims and that's really to put it simple that's what I want you to think of um as an argument argument is essentially when you make a claim you assert something is true right when you say that something is the case and you provide evidence for it that's in the most rudimentary sense what an argument is and we'll see that um logic studies arguments in the most critical basic feature are the premises and the conclusions of our arguments okay um one thing to we should make clear since this this is the first video let me open up quickly open up a new template here one of the things that I want to quickly reference here is the in logic there's logic there's different domains within logic right the first domain of logic the one we're going to be looking at is what's we might call formal logic formal or symbolic logic and I'll talk about what that is in in a minute the other type of logic here generally speaking is informal logic and we'll see that U the basic difference here is that formal logic seeks to analyze whether or not an argument is a good argument whether or not it can support its claims by analyzing the form that that argument takes whereas by contrast informal logic is concerned with the content of our thoughts so let me give an example here because that may sound fairly sort of obscure the difference here between form and content and I want to give you a very classic um argument that comes goes all the way back to Aristotle and it contains three lines three statements U the first statement here is that all men are mortal right Socrates is a man therefore and here just watching the video you'll know what comes next if all men are moral and Socrates is men then therefore Socrates is what is it he's mortal right he's mortal and this is this is a standard form sort of syllogism actually um we we're going to use this term later on especially when we look at categorical logic but an argument that takes this shape that's is known as a syllogism okay all men mortal Socrates is man therefore Socrates is Mortal now why is this interesting here because this argument we'll see is actually a valid argument which means that it's a good argument uses correct reasoning but guess what we can do we can take each one of these two things this is here premise this is a premise so there's two premises and then this is the conclusion down here okay but what's what's amazing actually is that logicians going all the way back to Aristotle Aristotle discovered that these take a specific form what if we took uh you'll see that these have different words that sort of reappear over and over right Socrates Immortal and these are what we call terms and what happens if we symbolize the terms with letters so let's do that now and rewrite this it looks like all M are T right and I'm going to slightly change it just to sort of make you a little clear you'll know why later on in the other videos let's say all persons named Socrates are M men therefore all persons named Socrates are t for Mortal you can see here this was our T this was our s this was our M okay so this is essentially what I've done is I've simp symbolized this argument into its form right you can see I've stripped out the content we're not talking about men or mortality more we're just looking purely at the arrangement of the terms and the reason what's fascinating about this is that if I replace any any of these terms with something else totally different right something like all all plants um are things that have cell walls right um pine trees are things that are PL PLS therefore pine trees are things that have cell U um cell walls for instance I can replace any one of these terms with other um with different content in the argument though regardless of what words I use or what terms I use will always turn out to be logical this is um this is 100% um correct reasoning no matter what I'm talking about no matter what I'm talking about now of course uh you can see here this is so what is formal logic study formal logic basically takes all sorts of different arguments puts them into formal analysis and then we mainly just look at the forms and try to determine whether or not the reasoning is correct now let's go back up to here what about informal logic and when I'm talking about content what exactly does that mean well what if I gave a different example what if I took the form of the reasoning but I put in to the um the variables here terms that really that aren't real that are not true for instance what if I wrote If I change the M here by saying that m is unicorns T are one horned animals s here would be Suzy so it looks like this all unicorns are one horned animals all things named all persons all animals identical to Suzie are unicorns therefore all things identical all animals identical to Suzie are one-horned animals see that argument uses the same form of reasoning it's correct in that sense but the content is the problem because since unicorns don't exist that means that I've I've made a logical mistake there I'm talking about things that aren't real okay so informal reasoning and we'll talk about this formal reasoning is concerned with content to a certain degree uh but informal logic studies essentially the content and the ways in which we can arrange our um our arguments in our premises and our evidence and the way we think in fact um what there's a there's a similar difference here though it's not identical between deductive reasoning which is usually associated with formal logic but they don't mean the same thing and also inductive reasoning which is by definition actually informal logic so we're going to talk about that here in another video but I want to get you see this is essentially what logic is and logic provides us with the absolutely fabulous way of assessing arguments ultimately and you may not realize it but everywhere you go people are trying to convince you to believe things everywhere you go on YouTube um your friends at your school at your church on television advertisements everywhere you go in fact perhaps maybe uh more than in any other time in history you're confronted with arguments you're confronted with with or rather you're confronted with claims right to believe people want you to believe things the but unfortunately the majority of the things that people ask you to believe actually use incorrect reasoning and that's what we call a fallacy a fallacy literally means a false argument right um and so what we want to do is we want to assess the claims that we're confronted with in order to determine what we should actually believe and this is really really really important um especially uh think about politics for instance politicians make lots of claims and they give reasons for their claims which means they're giving us arguments but we have to assess those to determine whether or not they're logical so log this is effectively what logic studies okay so let's move down here and make another distinction here these are all claims right right but these are not arguments right in order to fully understand what arguments are we have to also look at what what are not arguments right these are merely statements these are merely statements and you combine statements together to create arguments right and you can see here's the number of do right CH chocolate truffles are loaded with calories melatonin helps relieve jetl political candidates always tell the complete truth now we know that's not true right no wives ever cheat on their husbands that's not true Tiger Woods plays golf and uh Maria Sharapova plays tennis okay these are all statements but they're not arguments they're not arguments because they're just singular statements right um in order to have an argument we have to combine multiple statements together right such that they become they relate right so we have some statements we're going to talk about as premises and some statements we're going to talk here about as conclusions what's the difference the conclusion is the claim you're supposed to believe and the premacy or the premises this is the evidence that you're supposed to that you're supposed to um base the claim off of right so you can see it works like this you have privacies and conclusions now one of the thing that's interesting is in ordinary arguments a lot of times the conclusions and the premises are mixed up we're going to you we're going to see here in logic we're going to abide by what's known as standard form notation which means that the premises are always going to come first right and um the conclusion will always come last and in a standard form proposition we're only going to always have two premises in one conclusion but I think that is the subject of a video coming up here that's the first thing to think of um by contrast I want you to notice that a lot of the sorts there's lots of different statements in the world that are that um don't count so there's lots of different um things that people can say that don't count as statements right because they don't actually claim anything for instance if you ask a question if you propose something if you suggest if you tell someone to do something if you you know yell out fantastic these are sentences well they're not even sentences let's say they're utterances but they don't actually but there's no claim right right so they don't count right um they are not going to they're not statements in The Logical sense of the term right they're just purely utterances and so one of the things you need to do is you need to we need have to learn slowly and really just through pattern repetition learn to differentiate what matters when we because in an ordinary sort of conversation people are going to tell us a lot of different things they may combine they may have questions combined with evidence combined with suggestion and claims and one of the things we have to do to analyze arguments is we have to sort through and figure out what matters and what doesn't strictly speaking this stuff doesn't matter what matters what you really want to be worried about here are um I'm sorry what you really want to be worried about here or whether or not it makes a claim and is the claim properly supported and then finally of course the subject of logic in its more proper sense when we get to categorical or propositional or predicate logic is whether or not they're formally organized in a way that allows them to be correct forms of reasoning now here's two examples we can take of arguments two examples of arguments here's the first one all film stars are celebrities Haley Barry is a film star therefore Haley Barry is a celebrity okay we could already see that the pre this is the first premise this is the second premise and we would say this is the conclusion okay and even though this is really organized you can see this is organized not in perfect standard form but fairly close right and you can see here the terms film stars celebrities Haley Berry film star right those are the terms okay let's take a look at this one over here let me change the color of my pen here uh first off you can see there's terms uh this is some film stars are men k Diaz is a film star therefore Cameron Diaz is a man now this is a good example right because this is actually organized correctly but you no this is you can see the difference here because this is not true right it's true that uh well let's actually just this is the first premise this is the second premise and this is the conclusion now what's the difference here this is actually a correct form of reasoning if follows and by saying it's correct what we mean is that this argument in terms of its form is what we will call truth functional meaning and this is why I'll explain while this one's wrong and this one's correct right meaning that um since it's organized in a Sur where these terms are in the specific order the way we looked at it earlier um if since it's organized correctly it means a truth functional meaning that if these first two premises are true then the conclusion will also be true necessarily it will always be like that if the premises are true the conclusion will be true now be careful here because if I have a false premise then the conclusion will turn out to be false right so you have to that's that's the content issue there right you have to make sure that film stars are celebrities and stuff like that um now you can see here this may actually be a false premise all film stars are celebrities well I guess if you're a star by definition you are a celebrity so yeah I think it is valid but what about this one this says some film stars are men notice the difference here not all some film stars are men Cameron Diaz is a film star therefore Cameron Diaz is a man you can see here that this has a two premises in a conclusion but it uses um poor reasoning we'll say this is a poor argument why is it poor well because here look at the premises this first premise is true some film stars are Cameron Diaz is is a film star that's true she's not my favorite film star but she is a film star so the the premises are true but look the conclusion here is false which means that this is not truth functional okay so an argument that's a good argument that has uses correct form of reasoning is truth functional it mean it's as if if you pour truth into the premises a conclusion will always spit out that's true whereas the in poor reasoning is when you pour truth in and falsehood comes out at least once right and unfortunately the grand majority of arguments probably that exist u in the media today or maybe in the world are poor arguments they're like this so our goal is to figure out in formal reasoning how what sort of forms are truth functional and then always argue like that and then of course we can use this as a tool to assess how other people argue so these are two different arguments now how how are you supposed to figure out what the conclusion is how you supposed to figure out what the conclusion is the first thing you should do when you actually here read or or um I guess you hear or read an argument is you should figure out what the conclusion is and I would say ask you a simple question um ask this question what is the takeaway what does the person who's arguing whatever it is you're hearing right what is the takeway what is the claim they want you to agree with and believe that's what the conclusion is going to be now usually most conclusions because of the way human language proceeds we use words we're going to call these conclusion indicator words we use certain words that help us to recognize the conclusion the most typical one you'll see is therefore where of I'm sorry wherefore thus consequently we may infer accordingly we may conclude I mean the conclusions right there right it must be that for this reason so this is a very U I'll Circle the ones that are common so and therefore these are fairly entails that hence it follows that right that's also known implies that as a result so one of the first thing you use ask just for when you read an argument first what is the takeaway and if you can't figure the takeaway um number two search for the indicator term search for the indicator term right because even though this formal logic we we we're going to take arguments that are explained in ordinary language formalize them and analyze them but we have to figure out the conclusion is so you got to look for that indicator term if you can't find an indicator term or you can always look for the premise indicator terms oftentimes the Pres the premise remember a premise are counts as the reasons you the reasons you give for the claim right um in the premise these words usually come right before the premise you say for you say um dogs are great animals since right there's a premise indicator term since they've biologically evolved with human beings right so human beings that I'm sorry evolved with human beings is the premise to the conclusion that dogs are great pets or something okay since as indicated by because this is probably the most common in that may be inferred as given that seeing that for the reason that that's pretty common uh I think since is a common one too so you can always number three right after you've looked for the um what do we have up here after you've asked what the takeway is and search for the indicator term um I guess then you take a look at the premise indicators right so number three search for the premise for the premises by taking a look at the indicator terms okay that's the sort of me scroll down here okay so let's give some examples here these are some basic core examples you need to take a look at um let's take this argument ex expected mothers should never use recreational drugs since the use of these drugs can jeopardize the development of the fetus okay so first off ask yourself one what's the takeaway way we say read it again expected mothers should never use Rec recreational drugs since us of these drugs can jeopardize the development of thes the takeaway is that pregnant women shouldn't use drugs okay which means that in notice here there was no indicator term we can just sort of sit back and figure out what it is best thing to do when you see this is underline the conclusion if you're if you're using a textbook or something like that underline the conclusion now let's take a look where's the premise uh well notice there's there is a premise indicator term since the use of these drugs can jeopardize the development of fetus so this is we'll say this is premise one let's erase that and this is conclusion one there's only one conclusion one premise here okay so that's an example of how you can do these problems let's do another one here it's vitally important that Wilderness areas be preserved for Wilderness provides essential habitat for wildlife including in dangerous species and it is a natural Retreat from the stresses of daily life okay this one is right as this thing says this one is a little bit more difficult right um so let's say first off let's ask ourselves what's the takeaway okay let's read it again it's Vally important that Wilderness areas be preserved for Wilderness Aries provides okay this word for this is a premise indicator term right this is what what comes after this is going to be a premise or a reasoning for Wilderness provides essential habitat for including the endangered species and look here we have another term and it is a natural Retreat from the stresses of daily life so we see here is that this this first statement it is Vally important area that it is Vally important the Wilderness areas be preserved this is the conclusion actually we's put C1 for conclusion and then here we have for Wilderness areas provide essential and is natural tree from da life this here is going to be premise you know to make it simple I'll Circle the conclusion here right this is premise one and then this thing here this is premise 2 now what is this thing right here this is this is an indicator term but what's this and this in is going to be known as a conjunctive um and don't worry too much about that right now but a conjunctive it means that it's a term that allows us to conjoin two different premises together right so but you can see here the best thing to do because in the homework you do after this is you really just have to stop and just think slowly about what's being said here okay here's another example the Space Program deserves increased expenditures in the years ahead not only does the National Defense depend on it but the program will more than pay for itself in terms of technological spin-offs furthermore at current funding levels the program cannot fulfill its anticipation ated potential okay what's the conclusion the conclusion like the other ones we've looked atop sorry i s erased it is this first statement the Space Program deserves increased expenditures in the years ahead okay so this is the conclusion now not only does National Defense spinoff but the program will more than pay for itself in terms of spin-offs you can see this is sort of a complicated one but this thing here is a premise right because this is trying to support the conclusion that we need more money for it right and then this furthermore this is another one of these conjunctive terms right at the current funding levels the program cannot fulfill its anticipated presedential this is also a premise right this one was a little bit more tricky but again I think the simplest way is really to sit back and ask yourself what's the takeaway now you'll notice here I want to make a distinction here between statements let's just put this this is a distinction that you should know a difference a distinction is just talking about to a differentiation something way two ways two concepts that are different statements versus propositions okay and this is actually a very critical distinction within logic now what's a statement a statement is really the actual utterance um or right or say sentence this is the actual utterance jesz that's horrible handwriting isn't it it's the actual utterance or it's the sentence itself whereas the proposition isn't the utterance but we would say that the proposition is what is meant by the sentence or the utterance we're talking about the meaning okay so Pro statements right essentially this is is the grammar this is that the sentence whereas the proposition here is the meaning it's the meaning of the claim so for instance think about like this let me say it like this we can take this statement here the Space Program deserves increased expenditures in the years ahead and but the meaning is not the same as that right or it doesn't have to be that way because think I could actually say that same thing differently I could say for instance NASA uh needs a greater budget um so that NASA needs to spend more money I guess let me say this NASA deserves to spend more money in the future right that NASA needs to spend more money in the future means the Space Program deserves increased expenditures in the years ahead right so I can have two different statements that are actually the same proposition and the reason that that's really actually important is because one of the things you're going to see in here is that as we go through um as you go through this course is that often times when you read when you read a full argument let's say in a newspaper or something like this let's say you read a newspaper editorial right where some sort of argument is being made often times people will say um the same thing in multiple ways which means they'll give multiple propositions right uh they'll give multiple sentences but all of them combined really there's just one proposition or just a handful uh just we'll put a handful of propositions right so one of the tasks you have to do when you evaluate arguments is figure out what the meaning of it is figure out what the propositions are and actually analyze the form that the propositions are given rather than the syntax the grammatical sentence structure right so this is a pretty important distinction to make as well um and because some so we've talked here about the idea that statement that arguments and statements can have truth values there's such of things as non- statements there's conclusion and premise indicator terms and also the difference here between propositions um and one thing I forgot to mention that is in this chapter that's worth remarking here is the concept of inference right and this is sort of one of the things that's really exciting about this course one of the things I think you'll find is that if you do well in this course you actually have to sort of get interested and excited about this stuff and see it something as as sort of a game and rather than a boring dry subject um an inference what is an inference I said that um right correct reasoning forms in such a sense that arguments can have truth functionality right and that means that the truth can flow from the premis is necessarily to the conclusion this this notion of flow that I'm talking about is what I mean is really inference so that means that you can infer from the premises the conclusion okay so inference is the technical term here to talk about how um truth can flow from the premises to the conclusion so that's what I want you to think of when we talk about inference it's maybe not the most technical term for reference uh technical definition but I think it's a very helpful one let's see here I want to show you let's exit this let's see here okay here I'm sorry let me show you this u in fact let me give you the let me give you the exact definition here of the con inference in the narrow sense of the term is the reasoning process expressed by the argument or analogously a proposition in the narrow sense is the meaning or information content of a statement okay so that's the sort of General sense here about what an inference and a proposition are okay now there is a there is a note here about the history of logic U that I'd like you to read in your book I'm going to cover this more in uh another lecture so most of the lectures here that I'm posting are purely just about the mechanics of learning logic and the basic concepts we will be talking about the development of logic though um and I'd like you to read these in the textbook and we'll be talking about them later this mainly talks about the idea sort of gives you a brief overview of the history of logic beginning with Aristotle and I think working all the way up into contemporary mathematicians like U Kurt girdle um or for instance beron Russell temporary in the larger sense of the sense right they lived in the 20th century um so but this sort of gives you an overview but you'll see here that um now that you've listened to this video if you have the textbook and you're following along with the text then I'd like you to go here to exercise 1.1 or if you're using APPA you can use you can work on the the problems that are assigned for you you can see that what are you supposed to do in these exercises U the first thing you're going to do is look for conclusions and premises right and you're going to sort of um get arguments and then what you need to do is you need using the letters P and C identify the premise U and conclusion of each argument often times it's helpful to Circle as a result for instance to Circle these indicator terms right as a result was that a conclusion or a premise indicator term do you remember I hope you do okay and you can see that that's essentially what most of your homework is to for this section 1.1 is essentially taking a look at these sort of um core really simple arguments and then from there doing a short analysis uh in the second section here and what's interesting is these are really real arguments that people have made okay and the following arguments in the second section what you're going to need to do is um in order to fully understand you have to rephrase the conclusion right you have to move away from looking at the sentence or the statement in order to determine what the proposition is and then figure out it from there okay so that's essentially what your homework is for 1.1 now