hi this is an introduction to logic I'm mark Thor's Bay this course overviews the basics of categorical propositional and predicate logic today in our video we're taking a look at just basic concepts and we'll be looking at the concepts of validity truth soundness strength and currency so for those of you who have been following along with this welcome back it's good to have you today we're going to talking about the concept of validity we're going to see that this issue of validity is really a core concept that goes that we're gonna be talking about throughout the entire course in fact much of logic if not the grand majority of what we do in logic is a test for the validity of certain sorts of arguments so it's pretty key concept so but before we sort of go through and define what the Lydia is let's um let's we'll quickly remind ourselves the distinction we made last time between two types of reasoning again there are two basic forms or two types of reasoning that get employed within argumentation so there's two types of reasoning the first type of reasoning is deductive reasoning and to remind you if you didn't watch our last video you should go watch the previous video which is on the distinction between deductive and inductive reasoning but deductive reasoning is reasoning by necessity reasoning by necessity whereas inductive reasoning by contrast this is reasoning by probability so arguments that are merely probably the case probably true or inductive where deductive arguments argue what has to be the case given a set of conditions it's a the deductive reasoning you can have a hundred percent certainty with your conclusions whereas inductive reasoning you can never be a hundred percent certain though you can be fairly well certain so we're gonna sort of see that the concepts of validity and soundness link up here with deductive reasoning whereas strength and cogent see here go along with inductive using in fact we're gonna see this is that a deductive argument once it's analyzed is either going to be a valid argument or it's going to be an invalid argument or an by contrast an inductive argument is either gonna be a strong argument or it's going to be a weak argument okay let's start with the concept of validity what exactly how should we define validity well since we are following along with the textbook the early textbook take a look at how Hurley defines a valid argument he says quote a valid deductive argument is an argument in which it is impossible for the conclusion to be false given that the premises are true by contrast an invalid deductive argument is a deductive argument in which it is possible for the conclusion to be false that the given that the premises are true okay so what this all comes down here to the idea is that remember arguments should be or one of the key causes we talked about here is the idea of the truth functionality of an argument truth functionality and if an argument is truth functional we're gonna say it's a valid argument and what that means is that if you have true premises you can only get a true conclusion by definition there's no other possibility that's what a valid argument it is such that if you you can imagine if you had a glass of water here right and you have water right and you imagine if you had a second or a sieve or something right if you pour the truth water in truth water comes out right so this is what the truth function is if you pour truth into the premises truth comes out in the conclusion that's truth functionality especially if you have true premises you can never have a false conclusion right a false conclusion is strictly speaking an impossibility in a valid argument whereas an invalid argument by contrast you could have true premises and get out a false conclusion thus that's not going to be the best sort of argument okay so a valid argument is one of which the truths true premises I'll put TP here for true premises leads to a TC a true conclusion or as an in doubt arguing you can have true premises and it's still possible though it's not always the case it's still possible to get a false conclusion ok so that's a deduct that's what a deductive argument a valid deductive argument is now one thing we'll notice here is that the validity of an argument is actually dependent upon the form of the argument hence this is what the linkage we're talking here about formal logic again in formal logic we analyze the form of the argument to determine validity in fact validity is essentially always a function of the form of an argument what this means is that if you have a valid form it is possible to have a valid argument that's not actually true okay and this is where a lot of times people get confused but I think it's gonna make sense here in a minute so let me scroll down here and show you an example here this example comes from the early textbook this is an example of a valid argument you're gonna see why these are the two premises if we were gonna label these this would be premise 1 in fact let me change my color here this is premise 1 this is premise 2 and this is the conclusion okay all television networks are media companies NBC is a television network therefore NBC is a media company ok this is a valid I really because it's impossible for this to be false ok because what this is saying is that they're all television networks we can symbolize it by drawing a circle here that this is the category for all television networks all posts but TV and for television networks are media companies right and then let's draw this a bigger circle here this is our media companies okay so all television networks exist within the frame of media Coney's NBC is a television network so you might just say there's a little dot here or well let's make an X and that X stands for NBC ok therefore NBC is a media company right you can see here despite my poor drawing I apologize for that that this argument is going to be true because just by the very structure rather in fact if we wanted to rephrase it it looks something like this right all t RM right that would be the first purpose the second premise here we would say something like all and for all things that are called NBC our t television networks therefore all n r m okay this is a sort of bare-bones ree-ally rewriting of the form of the article this is essentially the form of the argument and this argument is this is always going to be a valid argument now here's the difficulty though what happens if we replace the T the M and the N with things that aren't correct what if for instance because these are all true premises right again if we were to evaluate this we would say that this premise is true this premise is true therefore this premise is true but what happens if we replace these variables with false premises what would happen would we still have a valid argument well the answer ironically and perhaps strangely is yes you would have a valid argument even if the premises are false so let me give you another example here or no no the thumbs sorry that's an example of an invalid argument we'll cover that a minute let's so let's sort of realign these variables let's see if we can do this let's see how I can do this so let's imagine we changed as we said all sports teams are media companies right and we'll say Barack Obama is a sports team right therefore right Barack Obama is a media company okay so here let's erase this thing here now here you can see that if we're going to analyze this we have the exact same form of the argument the form is exactly the same except obviously these premises are false right so let's take a look at it here let's analyze it right all sports teams are media cuz that is false that's not true right Barack Obama is a sports team that is also false Barack Obama is the president of the United States therefore Barack Obama is a media company this is also false so you can see here we have false premises and a false conclusion but the form is identical and in fact what you're gonna see that it may be sort of hard to recognize this at this point in the course is that this is still a valid argument even though it's false and this is the distinction between sound and unsound arguments okay let's scroll back up here let me sort of lay it out for you so you have valid arguments a valid argument is either sound or it is unsound right what does soundness mean a sound argument means that it has the valid form but that apprentices are actually true right that's what a sound argument is what's an unsound argument an unsound argument is an argument that has well an unset all invalid arguments are unsound okay but you can have valid arguments there also in some it has the right form then we can check the form as it found form but the premises are not actually true because obviously Barack Obama is not a sports team I think that's what it was right yeah Barack Obama's not a sports being thus the conclusions false so that's what we call an unsound argument so a valid argument has the right form and a sound argument has the right form and it's actually true okay so that's the difference between sound and unset and soundness and validity soundness means actually true premises and validity means that it has the right form such that if the premises are true the conclusion always has to be true so let me give you an example here of an invalid argument I'll scroll down here cuz that another example this is an invalid argument we can know it's invalid here and ignore the question of soundness for a moment okay all banks are financial institutions well as Fargo is a financial institution therefore Wells Fargo is a bank now at the face of it take a look at it this premise is true this premise is true it's true the Wells Fargo's position and Wells Fargo is make this is the conclusions actually true so are the face of it if you just heard this argument fairly quickly say for instance you're talking to someone and they gave you this argument you think oh yeah okay that makes sense but in order to determine whether or not it's valid you can't just look and see that it has true premises in a true conclusion you have to ask the question is it possible for the conclusion to be false is it possible for this conclusion to be false now if you think about it long and hard and maybe if you walk pause this video and try to figure this out is it possible for this to be false well the quickest way to figure out whether or not this argument could be invalid is to symbolize it again so if we're gonna symbolize it what will we load of look like okay this would be something like all BRF okay all things called Wells Fargo RF therefore all things called Wells Fargo are B okay this is the form of the argument actually think about it for a moment all banks are financial institutions Wells Fargo's a financial institution therefore Wells Fargo's a bank does that really make sense right and you can imagine your what if we put different what if we put different variables here such that we had true premises is it possible to come up with the false conclusion because that's what in validity is the invalidity again is having true premises and a false conclusion and the answer is yes it is think about it for a minute let's draw our sort of circles here are our sort of prototype ends right so let's imagine that we have a circle here and this circle represents banks all banks are financial institutions so the bigger circle here is as well as Fargo is a financial institution so we put the X out here in this therefore Wells Fargo's a bank well wait a second not necessarily right what if Wells Fargo inst is a financial institution that's not a bank because financial institution there's more types of financial institutions than pigs imagine for instance if you had a financial institution that was muley let's say an accounting firm write or write an accounting firm where companies hire consultants from this firm right in order to do their to check up on their accounts and make sure they're paying their taxes is that sort of thing they would be count as a finance situation but not a bank so you can see here if what if Wells Fargo was something like an accounting firm this argument would fail in fact because it would be possible for the conclusion to be false right in fact let's just imagine let's just change the scenario let's just change some of the variables here it will use our same example here all banks are financial institutions accounting firms are financial institutions therefore accounting firms are banks okay so you can see here I kept the form of the argument the same but I just changed out the variables here but you can see now what happens if I look at this right well here's what I see is all banks are financial institutions that premise let me see where's my pen here all financial institutions all banks are financial judges that premise is true accounting firms are financial institutions that premise is true therefore accounting firms are banks that's false that is false that is not the case right so you can see here this argument is actually invalid it is invalid because due to the form of the argument it is indeed possible that the conclusion could be false even though you have true premises right and notice here that in the very first version of the argument you had a true conclusion - but it was still false now since it's invalid it's automatically unsound as well right it's an unsound argument because you think unsoundness soundness here refers to something almost like the soundness of architecture right it's not a it's not a structure you can trust right so it's unsound in that sense so that's an example here of that's an example here of an invalid argument okay now take a look here at Hurley's textbook here and then I drew those conclusions from it right now take a look here in fact let me just for the sake of explanation let me take this and sort of highlight it for you okay so here's what we had here is here's here's the possibilities for deductive arts you have valid D document in bad detective arguments right it is possible for a valid argument true premises in a true conclusion right that's what a sound argument is right it is not possible there is no possibility for a valid argument to have true premises and a false conclusion it is possible for about arts have false premises in a true conclusion that's unsound though right because soundness means that everything is true right so there's only one case of soundness here is it possible for a valid argument of false premises and a false conclusion yes but again that's an unsound argument okay but on by contest take a look here the invalidity right it is possible to have invalid arguments to have true premises at a true conclusion true premises and a false conclusion false premises in a true conclusion false premises and a false conclusion in fact you can see here that there are many more possibilities for invalid arguments than there are actually for valid and sad arts now what's the goal would we actually reason because think the goal of logic is to sort through all of the stuff that people are trying to convince us to believe the goal is always to look for sound valid arguments in by contrast totally listen to those aren't until I make sound invalid arguments we're trying to convince others to agree with us okay but you can see here that there is only really one domain out of all of these possibilities that we want to steer towards the grand majority of all arguments are actually either invalid or unsound okay and what and what I want you to I think there is as they go through this through the series of videos and you learn logic as I want you to become increasingly attuned to the idea to listening and hearing and evaluating the arguments that you're actually confronted with let me give you an example here okay here I'll just give you an example here let me open up a new tab here I'm just gonna go to YouTube okay if we go to YouTube here and let's type in a valid argument okay a valid argument right there's all who knows what that is but here's a valid argument there's a whole bunch of people a lot of stuff here a lot of logicians trying to explain and even comedians that looks like talking about valid arguments but I scroll down either Barack Obama is making valid arguments that looks like but oh boom what is this it says there are no valid arguments against gay marriage right he says quote whoever posted this my old teacher my old reteach ur five months ago said quote it is my belief that there are no universally valid arguments against gay marriage those who oppose gay marriage often do so from a blah blah blah blah now from the very title ask yourself is this true is it true that there are no valid arguments against gay marriage well hopefully after this video and knowing a little bit about what a valid argument is a valid argument depends upon the form of the argument right and you can indeed make a valid argument or at least make an argument that has the correct form against gay marriage so actually this is a good example of this person doesn't understand what a valid argument is okay they probably mean there are no sound arguments against gay marriage and maybe we're just quibbling here I know I've never seen this person's video so I don't know what they think here and I'm not against gay marriage so I probably in a certain sense maybe agree with this person but I can't think but here we should see that this sort of statement is actually not true and we should actually believe it to be true though for instance we could be sympathetic their perspective okay so this is this just a good example here that I just want to show you here that you shouldn't even trust everything on YouTube right here because here you're going to example the very title is wrong right because I can make a valid argument against gay marriage even though I'm for gay marriage right simply by arguing for instance saying that all well you can imagine all I have to do is take this if I wanted to make an argument against gay marriage that was valid all I have to do is go up here and use this argument form right all I have to do is use this argument form it replaced the variables right they talked about gay marriage and stuff like this you could say something like this all persons all gay marriages are things that end in divorce right all persons who get I don't know I can't think of one off the top of it but you can imagine if you replace the variables in such a way you can end up with a valid argument that's against gay marriage of course the question is is it sound right maybe some of you in the YouTube videos if you want you could post an example here of a valid argument against gay marriage or and maybe also post a valid argument for gay marriage because there are valid arguments in both cases then there of course many unsound invalid arguments on both sides of that debate as well okay so this is the difference between validity and invalidity soundness and unsoundness valid arguments have true premises true conclusions and if they're sound they really are true right a valid argument has the right form but the premises of the conclusion itself I'm sorry the premises are somehow false so I would make it unsound invalid arguments are always sound so that's what and that only counts we're only talking about validity ability when we talk about deductive arguments now conversely or at least in lockstep with this sort of the case here let's talk about inductive arguments an inductive argument is an argument by probability right which means that it's probably the case the only way you can know that I'm as strong or weak is to understand what probably is the case and you can't look to the forum to know that you actually have to look to the content now in some cases you will see that certain forms of arguments are better than others but in general you have to look to the content rather than the form a strong argument is one in which the true premises that if you have true premises its profits highly likely it's probably the case that you also have a true conclusion right whereas a weak the inductive argument is one in which if you have true premises it is not here I'll put an X here it is not likely that you will have a true conclusion ok it's so here you have high likelihood and here you have a low likelihood now one of the things to recognize here is that a weak inductive argument because it's based upon likelihood and probability could actually be a good argument it could actually be true right whereas a strong argument is likely to true but not necessarily so here over here with deductive arguments you have a hundred percent certainty at least when you talk about balanced sound arguments but over here you only have you always have let's say less than a hundred percent certainty you can never be totally certain with an inductive argument because it's based on probability right in fact let's take a look here at how that's right let's take a look here how early to funds there's Hurley's definition for sound and the onset of earnest but let's take a look what he says about strong and weak inductive arguments quote he says a strong inductive argument is an inductive argument which it is improbable that the conclusion be false given that the premises are true and by contrast a weak inductive argument is an argument in which the conclusion does not follow probably from the premises even though it's claimed to okay just like we just defined it okay so let's go back down so inductive arguments just because that got a little messy right ending it duck Department is either going to be strong or weak right now a strong argument if it really is true right then it's a cogent argument so a strong argument can either be coated or uncoated right a cogent argument simply means that it is actually true it's actually true whereas an uncoated argument obviously it doesn't isn't necessarily true weak arguments are by definition on Coach and arguments okay so you can see here we have the exact same structural feature of validity invalidity soundness and unsettles except when we talk about inductive Arbenz we use a different language to be precise because it's only based on probability we talk about strong weak cogent uncoachable right or actually true so let me give you some of the examples from the early text here from the early text of some cogent and uncoated strong arguments so let's take a look at here when we talked about the difference well let's just go with this one all time so important I know sort bones discovered to this day I've been at least 50 million years old therefore probably the next dinosaur bone to be found will be at least 50 million years old so ask yourself is this a strong or is this a weak argument well take a look at this because of the regularity of every dinosaur bone we've discovered thus far as 50 million years old that regularity gives it a high likelihood or a high probability that the future dinosaur bones will fall within that time range of age thus we would say this is a strong argument this is a strong argument let's take another example here all meteors found to this day have contained salt therefore probably the next meteorite to be fed will contain salt this is another example that I think was for a ball game let's see what he says right on the face of it this looks like a strong argument all meteorites fantastic contains salt he says the premise this arguments clearly false but if we assume it true they would naturally expect the next mount against us thus the argument struggles so this argument strong but it is uncoated okay this is a strong argument that's uncoated because it's not actually true okay so that's I want you to just get a sense here of this differentiation here here's another example here Don Perignon champagne which is made in France sells over 100 dollars per bottle marquis de la tour is also a French Champagne they offer probably eight to sells for over 100 dollars per bottle now is this a strong or a weak argument I think it's actually a weak argument why because domperidone champagne is a very expensive champagne but we know that not all champagnes are very expensive right if you've ever been to a cheap wedding you know that's the case so just because a champagne is me in France doesn't mean that it's expensive so this is a this is even though this sort of has the same sort of language as a strong argument it's actually a weak argument since its weak we would say it's also uncoded okay so this is the the basic differentiation here and you can see here that many let's go back here to this sort of example here that it's very similar to when we looked at valid arguments whoops let's new table one point two for inductive arguments take a look at this okay you can see here the same thing exists now here we have strong arguments and weak arguments you can see here that we there's only one category of cogent and strong urns that's where you have true premises in a probably true conclusion do you have true premises that are probably false conclusion well none of those exists because that by definition is a weak argument is it possible of a strong argument that has false premises and a probably true conclusion yes it is but that's an cogent argument is it possible to have a strong argument that is false premises are probably false conclusion yes because of the the sake of probability that would also be an uncoded argument now weak arguments are all uncoated by definition right so they're all armed Koecher I don't know how that actually helps explain anything so sorry but you can see here that and these are great examples he gives here all the tales and I'm not gonna read them to you cuz you read them on your own right but these are all all you can have weak artists to have true premises in a probably true conclusion that seems sort of odd but it is in fact possible okay because the conclusion could probably be true for other reasons take a look at his example a few US presidents were lawyers there for probably the next u.s. president will be older than 40 ok now you can see here that the premise here and the conclusion don't relate right these are not related since they're not related it's a weak argument even though this premise is true and this is actually probably a true conclusion since the grand majority of all presidents have been over 40 like maybe all of them actually don't know off the top of my head but probably all of them I know you have to be 35 to be the president but all of them I can think of a bit over for you right so notice that you can actually have true Provost inspiron to inclusion the question is whether or not the premises actually provides support or evidence for the conclusion being probably the case ok and you can see here you can have encouragement arguments and all these other domains ok so this is an example here I hope this makes sense and I know it maybe we've labored a bit long here on the difference of all this stuff you can take a look at the book here where he gives this he gives examples of all of this stuff so real quick just as a quick overview here all right so take a look at this you can see here that what do we discuss so far in our logic ORS is that there are statements a statement can either be true or false right let me so you can have statements a statement is either true or false this is known as the principle of by valence right in a group of saving can either be an argument or invalid argument arguments do that your deductive or inductive and then out of deductive arguments through their valid or invalid invalid are all unsound and if they're valid either sound or unsound an inductive arguments are either strong or weak cogent and run codes you can see or what I kind of though I think that this could be sort of made to look a little bit clearer here well we're building up here is really sort of a stratification for evaluating arguments and this is why this is really key and critical here to the basic understanding of the whole structure of logical arguments now in these exercises these are acts of exercise are actually really fun because you're gonna see is that the first section here are their deductive arguments and you have to determine whether or not they're valid or invalid and the majority here I think are actually from real things and then the next here he's going to give you in dog departments and you have to figure out whether they're strong or weak okay and then here you have to determine whether or not the art you have to evaluate the argument totally right to turn whether following our votes or inductive or deductive and then if they're deductive or inductive figure out their strong weak valid or invalid and then finally the last one here is it's going to ask you to define terms and sort of evaluate these it's actually a really fun sort of series of exercises to do and it's really good practice because ultimately and remember this may seem sort of dry and boring but it's really fun it's really important rather because the because as you get better and better with these arguments you'll be able to actually be able to determine whether or not the arguments you hear in your ordinary life are valid or invalid deductr inductive ok in our next video here we're going to be taking a look at argument forms and how we can prove invalidity ok because obviously in doubt argument you want to avoid how can we prove those ok so that's our next video I'll see you then thanks for tuning in ok bye