Different Types of Arguments - Marianne Talbot

okay and now we're on week 2 and this week we're going to look at different types of arguments and in particular we're going to look at deduction and induction these are the two basic types of arguments and we'll be looking at different examples of each type welcome back everyone so it didn't put you off entirely last week and you difficult though it was I'm sure it was difficult and let's do a quick recap on last week so we can remember where we were if you remember I said that arguments are sets of sentences such that one of them the conclusion if you remember is being said to be true and the others called the premises are being offered as reasons for believing the truth of the one or reasons for believing the one okay so that's what an argument is and I said it was important to distinguish arguments from two things firstly sets of sentences that aren't arguments and if you remember I gave there two sorts of sets of sentences that are not arguments can only one remember what they are no an assertion isn't an argument an assertion is the second thing from which you should distinguish arguments so I said that there are two sets I think you must understand my question slightly whoever it was then so there are two things from which you distinguish arguments but the first one is sets of sentences and I said that there are two things two types of sets of sentence that you'd need to distinguish from an argument can anyone remember what those two types of sets of sentences were sorry no no no okay maybe that's not a fair question okay the first one is sets of sentences that aren't related at all do you remember I talked about CEA's salt and meld and bail bonds in Australia well until you had their four and a bit of context that's not an argument is it it's just two unrelated sentences and the second type of sets of sentence you should distinguish from arguments of those that are related but not as an argument is related not as the sets of sentences that can constitute an argument are related so in order for a set of sentences to be an argument it's got to be related in the sense that the conclusion is being said to follow from the premises okay that's what an argument is that one of the sets one of the sentences of the set is being said to follow from the others if it's if that relation isn't being said to be there then it's not an argument the second thing from which you must distinguish an argument is a sentence and can anyone remember how you distinguish sentences from arguments or one way at least in which you would distinguish a sentence from an argument what do you mean by premise that a premise has a very particular definition that the definition is that a premise is a sentence that's being offered as reason for believing the truth of the conclusion so what the questions is here is how do you distinguish a sentence or assertion from an argument a sentence you could see as an incomplete argument I suppose but that's not what I was thinking of certainly there's no conclusion nothing being while there is something being postulated if the sentence is being asserted isn't there there's no relation that's right but okay look let me go hang on there's one more matter since again that's right this is just a statement and a statement isn't an argument is it a statement isn't good or bad well it could be I suppose couldn't it a statement is true or false and an argument is good or bad do you remember and vary important that you you shouldn't call arguments true or false because arguments can't be true or false the only thing that can be a true or false is the sentences that make up the argument what an argument is is truth preserving so if you have truth in the premises then and it's a good argument then the conclusion will be true but notice it's the premises that are true and the conclusion that's true not the argument itself the most the argument can be is truth preserving okay so that's a distinguishing arguments from sets of sentences and from sentences themselves what we're going to do today is consider different types of argument and we're going to start using some of the concepts that you've already mentioned this morning so there are two basic types of argument there are deductive arguments and they're inductive arguments this is a very basic type of argument because you'll see later there are lots of other types of arguments in these categories but these two categories are the most important these are the ones you need to get a grip on okay let's look at deductive arguments first now these are such that the truth of their premises guarantees the truth of the conclusion so if the premises are true then the conclusion must be true because if it's a good deductive argument its truth guarantying so here's an adaptive argument you'll be familiar with this one we used it last week it's Friday Mary Ann always wears jeans on a Friday therefore Mary Ann is wearing jeans notice that the conclusion of this argument is is true but neither of the premises are so that that should give you an idea that the argument is a good one the conclusion is true but actually neither of the premises are true so this will be something we'll look at again when we look at what a good argument is next week relating to the real world that's right it's not Friday therefore that premise is false it's not true you'll have to take it from me on authority that I don't always wear jeans on Friday I do have to be wearing jeans today but of course that's irrelevant because it's neither Friday nor is it the case that I always wear jeans on a Friday but what's important about this argument is that it's deductive it's truth guaranteeing at least conditionally upon the truth of the premises can you think of any situation I really try and use your ingenuity here let's see if we get in which that would be true okay it isn't true we know that but we're assuming for the sake of argument that it is true so imagine a situation where that's true and that's true for some reason I always wear jeans on a Friday could that be false can anyone think well well that that would that wouldn't that make that not true no no it doesn't i may not hey may hate wearing jeans that may mean nothing to do with it I may wear jeans as a penance on a Friday because I once did something really ghastly and said to myself right okay from now on I'm always going to wear jeans on a Friday so it doesn't say that I want to can anyone think of a counter example okay so it's true it would be Friday on that day but would this be true no it wouldn't would it so we've given what we've given there is a falsification of that not a counter example to the argument okay do you see where I'm getting at with what we're doing is we're distinguishing the truth of the premises from the truth preserving nasai argument lots of us can think of situations where that's false or where that's false but that's not what I'm asking you to do what I'm asking you to do is to think of a situation where that's true and that's true and that's false it is isn't it yep well very on a couple of others at examples here let's try one so I'm on the moon or something like that very ingenious I think what we do what we're talking about is a situation where all these are so these two are true together do you see what I mean and what you're giving me is one where it's not Friday aren't you really you're trying to make it not Friday somehow by shifting me out of its time zone in which it is Friday no won't do but we don't need to guarantee it because all we're doing we're saying this is true if this is true and if this is true we're not saying this is true and this is another very important distinction when you're doing logic you're you're not talking about the actual truth value of a sentence okay so the truth value of that could be either true or false do you see what I mean so that's the value of its truth it's either true or false and we're not saying it is true but we're saying if it's true and if this is true this can't be false and as you rightly said actually if these two are true it's impossible for this to be false it really is isn't it well if we're looking at an argument we're saying we're asking ourselves two questions the questions are does the conclusion follow from the premises and in asking that what we're asking is if the premises were true would the conclusion be true if the premises are true would the conclusion be true and if we look at these two premises and we asked that question we're not asking whether the premises are true we're saying if they're true would the conclusion be true and the answer is yes can everyone see that this is a deductively valid argument its truth preserving and therefore it's very very useful because we know that if the premises are true the conclusion must be true now in this particular case this is not very useful because it's all hypothetical but can you imagine if this was something that we didn't know but we were wanting to test then we could say okay it's Friday Marianne always wears jeans on a Friday therefore Marianne is wearing jeans then if you see that I'm not wearing jeans what do you know one or other of these isn't true exactly so if you see that Marianne isn't wearing jeans you know either that it's not Friday that that one's false or that Marianne always wears jeans on a Friday is itself false so you know either your hypothesis is false or your observation is false oh sorry but you're quite right all both that's right so if you have a valid argument a deductively valid argument the conclusion to which is false you know that one of the premises must be false and that's why truth preserving nough sizz useful whatever the situation is even if it turns out that the conclusions false anyway again that's something we'll talk about more next week the only thing that's important for now is that you understand what a deductively valid argument is you understand that it's truth preserving that if the premises are true the conclusion must be true okay everyone happy with that let's move on okay you should note incidentally that deduction is an either/or thing either an argument is deductive a deductively valid or it's not okay there's no in-between there it's one or the other a good deductive argument gives us conditional certainty certainty conditional upon the truth of the premises well done I can feel you're getting it now okay a bad one tells us nothing because if the argument isn't a good one if it isn't truth preserving then the conclusion could be either true or false and we really don't know okay so that's deduction let's move to induct an induction inductive arguments is such that the truth of their premises makes the conclusion either more or less probable okay it doesn't give a certainty makes the conclusion more or less probable now this means that inductive arguments can be either weak or strong okay so here's an example of a strong inductive argument the son has written written every day in the history of the universe therefore the Sun will rise tomorrow okay that's a strong inductive argument why isn't that a deductive argument so what may not be true because arguments can't be true of course can they this may not be true okay but but we're saying if this is true then this will be true so why is that not deductively certain okay so this could be true and yet this false and yet this is a good argument yep good well done and that's exactly right the the hallmark of a strong inductive argument is even though you've got a very strong argument I mean if the Sun has risen every single day in the history of the universe so far I have no idea how the old the universe is but some it's a it's old right if if the Sun has risen every day in the history of the universe then it's hugely likely that the Sun is going to rise tomorrow isn't it and and then you say but we can't be a hundred percent certain because who knows the Sun may explode tomorrow or maybe the law that ensures that the Sun rises every morning and she has a bit of a dogleg in it so it's saying okay what the law is is every morning the Sun will rise except on the 7th of October 2009 it's something going to miss a day and it from then on it's only going to rise every other day okay for the rest of the history of time do we know that that isn't what the lawyers do we know that the Sun that the law that ensures that the Sun has risen every morning the history of the universe so far won't tomorrow miss a day the well it makes it weaker but it means that we haven't got certainty this could be true and this false but it's a different type of argument you mustn't think that because deductive arguments are certain an inductive arguments aren't that they're for inductive arguments are somehow inferior because actually they're dealing with different things this is the sort of argument that science deals with isn't it you observe that nature has been like this all the times before and then you extrapolate into the future to assume it's going to be like that in the future so every daffodil you've ever seen in your life so far has been yellow you're going to assume that the next daffodil you see will be yellow there's another bad example you see but you see what I mean I hope Oh because there's a oops sorry I'm going the wrong way this is the argument write an argument is a set of sentences there are three sentences in this argument the argument claim that's being made by this sentence is that if this is true and this is true then this will be true this will be true okay and this one the inductive argument is saying if this is true this will be true okay now in this case we can say that there could be a counter example to this the counter example might be that the Sun explodes tomorrow or or that the law of nature has had written into it from the history of time that it'll change tomorrow of all days we know that this doesn't give a certainty but it gives us a jolly good reason for thinking that this is true doesn't it I mean I could give you an inductive argument that goes like this in fact let me give you one every time I've seen Mary Ann she's been wearing earrings therefore next time I see Mary Ann shall be wearing earrings okay now juice is that a strong inductive argument no well it's not very strong is it I mean the next time you see me you might have come knocking on my door at seven o'clock in the morning and I've just got up and I don't wear earrings in bed so the next you know we know too much about the world about people about earrings and things like that to know that that's good inductive argument well let's go back to this one and notice that here we're arguing from this not to it okay this is a premise in our argument not a conclusion okay whereas if we're looking here oh now I'm going the wrong with the other way I know actually what I was just about to tell you there isn't gonna work how did we get to this what we've seen the Sun Rise every single day we see lots of observations and therefore we naturally extrapolate to a generalization like this this is a different form of reasoning this is inductive reasoning and it's the same reasoning that causes us to say something like this but in this case the same reasoning isn't as strong here's another one who takes a lucky rabbit's foot into an exam if they ever go into it was am who used to take a lucky rack and rabbit's foot into exam who has a lucky red jumper or something like that we've all had the experience of something's really nice happening to us and we were wearing something or carrying something and we think you know maybe I'll wear that again I'll be lucky again because we extrapolate from what's happened in the past to what's going to happen in the future I've lost you I can see I can look at your faces and you've gone right the only thing you need to remember is that a deductive argument you've got certainty because if the premises are true the conclusion must be true in an inductive argument you haven't got certainty you've only got probability okay this argh this premise gives you probable reason to believe this if this premise is true this conclusion is probably true okay but it's not certainly true and if this premise is true then this conclusion is not even probably true isn't is it this is a very weak inductive Argan this this gives you some reason for believing this but not very much have a look at these go through I'm good to give you a couple of minutes to do them on your own so you really try and work this out for yourself decide which of those are deductive arguments and which of those are inductive arguments and then we'll have a look at them together so the Sun is coming at well actually let's do them together I think that's probably easier at this point let's have a look at the Sun is coming out so the rain should stop soon which is the conclusion of that oh okay well right well let's do it the canonical way shall we just so we've all got it which is the conclusion of this argument the range should stop soon that's what we're we're claiming and the reason we're giving for that claim is the Sun is coming out so the premises the Sun is coming out therefore the range should stop soon now does the truth of that premise make the truth of the conclusion certain no you can't have more or less certain sorry this more or less probable but not more or less certain okay so is it inductive or deductive put up your hands if you think it's inductive yay you see I knew got it really okay good that's inductive what about this one let's do it the canonical way what's the conclusion right I'm going to make you do the things that I make undergrad you're used to make undergraduates - and notice there's a can you make that a proper sentence John won't be at the party that's right it's obvious what the sentence should be isn't it so okay the conclusion is John won't be at the party and the premises are good there are two prints two premises here one is Jane is at the party and the other is if Jane is that the party John won't be at the party notice that that's a complex sentence that's constituted of two sub two sentences within the sentence but you don't separate those two to make them two different premises because this sentence being asserted as if Jane is that the party John won't be that's the premise good okay so we've got an argument that goes if Jane is that the party John won't be at the party Jane is at the party therefore John won't be at the party is that deductive or inductive put up your hand if you think it's inductive okay put up your hand if you think it's deductive well done okay so you are getting this okay it's the Siot the house is a mess therefore Lucy must be at home what's the conclusion just Lucy must be at home the zetas therefore just marks the conclusion rather than being the conclusion okay Lucy must be home premise the house as a mess inductive or deductive put up your hand if you think inductive well done can you give me a counter example to that argument yes that's right okay so the house is a mess but Lucy isn't at home you've had burglars instead good okay either he's in the bathroom or the bedroom he's not in the bathroom so he must be in the bedroom conclusions obvious it must be in the bedroom and the two premises either he's in the bathroom all the bedroom he's not in the bathroom okay deductive or inductive deductive well done okay dog would have barked if it saw a stranger it didn't bark so it didn't see a stranger deductive good no one in Paris understands me so my French must be rotten all the Parisians are stupid which I got this from a book inductive ok it's difficult that one but it is inductive you're quite right because what's the conclusion that's right it's actually a complex conclusion isn't it my French must be rotten all the prisons are stupid and the premises no one in Paris understands me so it may be the case that if that's true these are true but but there are other reasons for nobody understanding me on there as well ok good so you have actually got it even if we got tied up in a few knots there and no I'm not going to sail to write logicians study deduction by did a study invaded argument forms and now here it's very important to distinguish form from content ok and arguments are deductively valid in virtue of their forms rather than their contents now that's not true of all deduction but it's true of most deduction so let's have a look what I mean here all men are mortal Socrates of a man therefore Socrates is mortal ok all actions that produce the greatest happiness of the greatest number I got very bored writing it out so the greatest happiness of greatest number all actions that produce the greatest happiness the greatest number a right morally right that is that action produced the greatest happiness of the greatest number therefore that action was right ok can you see that the form of those two arguments is exactly the same can you see that so the content of the two arguments is quite different this is an argument about Socrates and mortality and this is an argument about morality and the greatest happiness to the greatest number completely different topics completely different content but each of the arguments has the same form can anyone try and write down the form tell me the form of that argument this the structure of it do not know what I mean no ok let's do it together all a s RB s is an a therefore s is a B did you get that all A's are B so a a let's do an interpretation here a equals let's do it properly here X is a man X is mortal s is Socrates and the form this is all A's are V s is an a therefore s is a B go with me let me do it again can you see outside that so if this is the interpretation this is I've just changed the words four symbols here and the symbols are only letters so a a of X says X is a man X is mortal is B and s is Socrates so all A's are B s is an a s is a therefore s is a be with me so sitting do that for the other argument what would we have to say that a is there good a X is a is an action B X is difficult it's gone produce no okay all men are mortal all actions that produce the greatest happiness grace number are right okay so actually a isn't actions is it it's actions that produced no not right actions actions that produce the greatest happens greatest number so all men are mortal and all actions that produces greatest happens the greatest number are right you with me so all A's or men are B's mortal all A's actions that produce the race have disgraced number all right okay and then the next one that action produced the greatest happiness of grace number you've got Socrates here is a particular thing just as that action is a particular thing okay and you're saying that particular thing is a man ie falls into this class here and therefore he falls into the other class too okay so both those arguments have the form all A's RB s is an a therefore s is a B now the point of this is just to get you to distinguish form and content can you see that an argument can have different forms and yet the same content sorry different contents and yet the same form okay so these are two arguments of exactly the same form different contents what's important about this is that logic is topic neutral once you've learned how to do logic it doesn't matter what you're doing it with or on it's always the same logic is the same whether you're talking about the color of chairs whether you're talking about biochemistry whether you're talking about the philosophy of time doesn't matter what you're talking about if an argument is valid it'll be valid by virtue its form whatever the topic is you're talking about so logic is the ultimate transferable skill if you've learnt logic you can do it with whatever you happen to be talking about whatever it is you're interested in whether it's art history or fashion right okay let's have a look at a few argument forms here's a valid argument form if P then Q P therefore Q what piece standing in for here what type of thing is it standing in for can anyone tell me a good or a sentence I was going to say but a premise is even better yes well done so this is one sentence what's this uh no no not even that it's a oh actually I've that'sa premise actually that's a premise that's only a sentence can you see why that's right okay so if P then Q is one premise P is the other premise and Q is the conclusion so all we've done there instead of thinking about actual sentences we've just put in what are called sentence letters any letter will do doesn't matter just so long as you get the form of the argument right can you think of an argument that fits that form okay just think for yourself now of an argument that fits that form you could use one that we've already used you could use one to do with the colors of the chair in this room quite difficult but see if you can think of one go on try it give her a clap well done that's exactly right can anyone think of another one no there's no all there no do just if the impossible cannot happen then no you're not quite getting the idea here now this will be happening to lots of you this is not just just you the form is if sentence then sentence sentence therefore sentence and these two have got to be the same sentence and these two have got to be the same sentence so the form of this has got to be if P then Q P therefore Q think of another one think you think to yourselves first and then then when you feel confident that you've got it put your hands up and we'll try this is really doing logic so do the if you find it odd that's right it's in the nature of the beast are you well sit down and think for yourself and then try again no you've just said oh no you didn't know sir okay go on you say one no that was an if P and Q wasn't it and we're looking for an if P then Q the these words that are left are the logical words and it's getting the logical words right if then and or not that's hugely important have you got one good okay if he gets a bus then he's eco-friendly he does get a bus therefore he's eco-friendly good well done Paul oh it's something wrong with that what was wrong with it now that that the sentences were great say it again though okay okay so P is it is raining okay and Q is I raise an umbrella now what P my umbrella is up what was P it's raining so what you need there instead it is raining then for your do see what you were doing those who are committing the fallacy of affirming the consequent very common fallacy will do fallacies next week I think so but you see it has to be you have to have the letters in the right order because what you gave me initially wasn't a valid argument but a valid argument could easily be made from it just by transposing those do you have another then I'll take my dog for walk it's sunny therefore I'll take my dog for what exactly so P is it is sunny Q is I'm taking my dog for a walk and the argument is if it's sunny then I'm taking my dog for a walk it is sunny therefore I'm taking my dog for a walk okay now that has to be valid doesn't it as sorry that as if those premises are true that conclusion has to be true because any argument of this form must be a good argument is deductively valid anyone else want to try another one good okay if the postman is striking then we will have no letters the postman are striking therefore will have no letters so P is the postman strike no not if because see if okay the postman striking and Q is we will have no letters so if the postman is striking them will have no letters the postman are striking therefore will have no letters good okay one more and then we'll move on this is looking good that's right if he's breathing then he's alive he is breathing therefore he's alive okay yep good okay it's dead easy isn't it once you get the idea of it and here's the sorry sales again the light third parrot of the dead parrot yes I'm sure we could meet one there here we are if there are no chance factors in chess then chess is a game of skill there are no chance factors in chess therefore chess is a game of skill what's P here good what's Q good well done here's another argument okay that was modus ponens by the way so you know how to do new modus ponens here's modus tollens the mode of denial if P then Q not Q therefore not P okay if P then Q not Q therefore not P so this is saying in effect that P is sufficient for Q and sorry have I got it wrong way around no I have got it right way around it some what we're saying is here is that Q is necessary for P and so if Q isn't the case then P isn't the case I well let's have a look at the example and then you can come up with your own actually this example is wrong because that shouldn't be in there but let's do it if the dog didn't know the visitor well the dog would have barked okay the job didn't bark therefore the dog did know the visitor that shouldn't be in there that's the one that I was saying I got wrong before we started so if you take that not out I won't draw on the screen there so on your handouts make sure that you take that not out on slide 16 write that down now I think it's 16 yep because that's that sink rate but you do see how that argument is valid if it's true that if the dog didn't know the visitor well the dog would have barked it's a good guide dog got guard dog guard dog my dog and it didn't bark therefore it must have known the visitor well mustn't it okay so see if you can come up with something of that form now I'll take the example out so it's not confusing you have you come up with an already well done fantastic absolutely right so appears I have money Q is I would be in the pub sat right I'm not in the pub therefore I have no money if I had if I had money so the having money would be sufficient for you to be in the pub okay but you're not in the pub therefore you haven't got any money okay anyone else wants to have a go gentlemen they're good you've got it I think does anyone else want to have a go or does everyone feel that they've got that where was it sorry say it again okay so P is the Sun is out and Q is I'll take my dog for a walk ah I'm sorry those of you who saw the error that's quite right okay what should be here I'm not taking my dog from out for a walk therefore the Sun is not out yep that's right good okay try one more then as we got that as I got that wrong yes okay it had not in the wrong place there didn't we have how did it go again if I'm hungry then I won't concentrate I write it would be I will write this one down because there are knots in there that we need to get right because as you see ok so P is I am hungry Q is I can't concentrate ok notice that we've changed Q the Q is actually a negative here that's where where it's very easy to get tied up so be very careful of this negatives immediately make things quite difficult so but nobody can do it ok so curious I can't concentrate now not Q therefore is I can concentrate therefore I'm not hungry are you with me do you see how that works so you had the right sentences you you were just not using the negative to the right we're forgotten who said this so I'm looking at that all the wrong people but ok one more on this one because it's quite difficult Paul Oh actually we have had you Paul so did we have you before ok good ok if I if I catch my train no so I start again if I miss my train I'll be late I'm not late therefore I haven't missed my train I you don't have to use the same words as long as you now this is this is actually the important point you don't have to use the same words as long as the words have to say meaning or do you see what I mean but it's a very when you're learning logic it's a very good idea to use the same words because it cuts out one area of complication do you see that it just you know why you why change your language when what it's going to do is confuse you keep things as simple as possible this is quite hard enough without adding layers of complication in okay good you did that well so what have I got oh well I we've already tried that good let's try another one this is a disjunctive syllogism P or Q not P therefore Q okay have a go at that one P or Q not P therefore Q okay oh good look at you hands going up immediately now brilliant okay it's either raining or it's sunny it's not raining therefore it's sunny good well done one at the back there good well done anyone else good okay I think you've got it one good well done okay you've got notice that that works if you've got a an exclusive or because or is actually an ambiguous word in English it can mean either or or it can mean not both and if this was a either this has got to be either/or hasn't it as if it were not both you couldn't get the conclusion could you so that that's where English can lead lead us astray a little bit because English is itself ambiguous okay here's my example either this is actually a Bertrand Russell example either we hope for progress through improving morals or we hope for progress from improving intelligence we can't hope for progress through improving morals therefore we must hope for progress through improving intelligence what this should tell you instantly we've been looking at very simple ones but actually these forms is can be very complicated one of the things I'm going to ask you to do this week while you're at home is when you read your newspaper you listen to your television or argue with your friends in the pub or whatever you happen to do I want you to try and identify arguments that come up whenever you hear the words if then and or not if and only if all these logical words all is lovely logical words just you're got to be sensitized to them this week because I want you to hear you if you had to every time you hear an if/then I want you identifying the form of the argument in which you because it might not be in an argument might it might be just a free-standing assertion but have a look see if there is an argument there second the second sentence yes II each of the premises is asserted sentence a sentence that's being asserted isn't II so Russell is saying you know it's true that either we hope for progress this way or we hope for it this way okay there's no other option we can't hope for it this way he's asserting therefore we must hope for it that way okay Watson correction hang on what's false here so is it the first premise let's start to use the language now is it the first premise that false or the second what improve intelligence isn't a sentence and it appears here and here so what so is that the false premise all that one right I think we I'm going to put this on one side because a we're not really looking at the truth of the the premises and be you've got to take the premises as they are here this is what's being asserted so we're not saying this is true or that this is true what we're saying is if this is true and this is true then this must be true okay these conditionals are very important presupposition rod we'll get onto that later on so what I want to get up there just sensitizing us now to deduction an induction and to the form of an argument that that's what we need to get today okay let's move on here's another one live knits law a is f a equals B therefore B is f I'll give you my example of that because it's quite difficult one Jane is tall Jane is the bank manager therefore the bank manager is tall if these are true is that true has to be doesn't it can't be anything else don't think of a couple of examples of that one go for it don't know don't think it's going to work why is that not going to work let's see what why is this not going to work well Dobbs Park doesn't have the form a is there a SF is the chair is blue Maryann is tall the board duster is lost etc not dumb you could say the dog the dog is barking but dogs bark is saying of one class of things that they fit another class of things and that's not the form of that sentences it gone not quite know what we've got here this is a very interesting ambiguity here is is a very slippery word in English is you can have the is of predication and the is of identity and your attempted argument there and don't worry about this at all this is a perfectly reasonable mistake to make you equivocated between these two is is so you said this chair is blue is that right it right and then you said this chair is comfortable okay now this well actually those those are both is is of predication aren't they whereas what we're looking for here is an is of identity isn't it a is B is the very same thing as B so here we've got an a predication haven't we a is f a has a certain property and here we have and this thing a is the same thing as this thing B therefore B is F okay do you see how that has to be true this is a it's a law of logic this one isn't it the sly blitz law it is a law of logic if a is F if Mary Ann is tall oh I'm just giving you the same example so let me give it to you if Jane is tall and Jane is the bank manager here's an is of prezi Capretta keishon so we're predicating tallness of Jane aren't we you with me and here we've got the is of identity haven't we Jane is the bank manager okay if that's true and that's true that has to be true doesn't it because the bank manager is Jane isn't she yes that's exactly that's what we're doing we're looking at examples of deductively valid arguments arguments that are valid by virtue of their form okay good one last one I think here's a syllogism now this should be easy all fcg a is an F therefore a is G all Ford's are cars okay a is a Ford therefore a is a car yep well done that's that do anyone else want to give one more example and we'll move on good I see where you're getting - yeah the grammar got a bit mixed up but yes okay so all my clothes are wet that pair of jeans is one of my clothes sort of therefore it is wet I see where you're coming from okay you've got one you go KQ under all miracles are impossible resurrection is a miracle therefore okay it works doesn't it well done we knew we'd get there somewhere it's deadly there's let me just give you a logical problem with that just because I think you might enjoy it and you said the resurrection is a miracle therefore the resurrection is impossible and there's something very logically fishy about negative X true negative existential sentences isn't there if we say Pegasus doesn't exist aren't we picking out something by the word Pegasus in order to say of it that it doesn't exist in which case how can a negative existential be true see what I mean Hamlet doesn't exist you're picking out something Hamlet in order to say of him that he doesn't exist well how can you do that you shouldn't be able to do that I'll just leave you with a little conundrum because that's philosophical logic and we're not doing that here we're doing symbolic logic here so now you know two different types of logic oK we've this there's the canonical example for that one all men are mortal da da da da now said that some arguments are deductive valid deductively valid but not in virtue of their form here is just a couple that are valid in virtue of their content apparently deontic logic now this is cutting-edge stuff we are know very little about deontic logic logic deontic logic is the logic of morality okay what we're trying to look at is the area of discourse in which we talk about morality and say how does it work logically how can we get a valid argument form from a talk of morality now look at this argument lying is wrong therefore we shouldn't lie now that looks like a deductively valid argument doesn't it in other words if that's true surely this must be true as well but if so it's not true in virtue of its form it's true in virtue of its or could you say lying is wrong but I'm going to like well we all know that you could lie but yeah if you truly believe that lying is wrong you're also going to believe you shouldn't lie now that doesn't mean you won't lie but you'll feel guilty you'll feel madam that's just what I said I said if you believe lying is wrong then you're going to believe you shouldn't lie aren't you do you think you could possibly believe that lie really believe that lying is wrong and yet not believes that you shouldn't lie well I think that if you find it okay if you lie either you're going to feel shame which manifests your belief that lying you do think lying is wrong or you don't going to feel any shame at all which manifests manifests the fact that you don't believe that lying is always and everywhere wrong oh don't get me on that I'm not going to follow that one up at all oh it's very important yes but we're not but but actually we can safely leave it on one side here you if you're a Kantian you think that this entails that instantly my wants to put another premise in here you might want to say we shouldn't do things that are wrong did someone want to do that okay and Kant would say if you did that you're you're manifesting the facts that you think that they you could believe that something's wrong without believing you shouldn't do it and that just shows you don't understand what wrongness is to Kant to have the proper moral concept which is that you know lying is wrong or something like that you cannot believe that something is wrong without also believing you shouldn't do it so it doesn't mean you won't do it because we all know that we do things we believe to be wrong but but your belief that it's wrong will manifest itself as guilt and if it doesn't it manifests the fact you don't believe the first thing that lying is wrong so anyway we're not going to get into morality I just wanted to say there is a logic a type of logic called deontic logic and it looks at that sort of inference and noticed that that's can't them we can't give you a form for that that's the very meaning of the word wrong there's something very special about the meaning of the word wrong logically here's another one modal logic modal logic is the logic of necessity and possibility it's necessarily the case that there are no square circles in other words there's no possible world in which there's a square circle if it's square it's not circular and so on therefore it's not possible that there are square circles so if P is necessarily true then not P is not possible can you hear that your your capacity for reason would follow that quite quickly if a is necessary there not a is not possible not to be the case hasn't it so again we have a deductively valid argument but it's not deductively valid at least actually we're a lot further on with modal logic than we are and a ontic logic we can do quite a lot with modal these days and here's a bit of temporal logic for you it's raining today therefore tomorrow it will have been raining yesterday is that true ok if that's true then that must be true mustn't it yeah couldn't not and that's because the temporal logic the way the logic of time works ok let's move on to make short of time here let's we'll move on to inductive arguments now inductive arguments you remember what's the hallmark of an inductive argument is if the premises are true the conclusion might be true probably is true that's right ok then so the premises give us reason for believing the conclusion but not in this case certainty they don't give us conclusive reason for the conclusion and that's because inductive arguments rely on the assumption of the uniformity of nature that's what Hume called it David Hume the idea that the future will be like the past so if we've seen the Sun Rise every day in the history of the universe we expect it to rise tomorrow if every time we've come here for Mary Ann's lecture on Monday 2 o'clock and Mary Ann's been lecturing it two o'clock we'll come on we'll carry on doing that and if we come on the seventh week we'll be disappointed sadly ok but it was quite a good reason for believing that Mary Ann would be lecturing on Monday at 2:00 that she has been lecturing at 2:00 every Monday for the last six weeks but it's not conclusive and so on so we're we are one of the biggest problems of philosophy in fact is how do we justify can we justify this assumption the assumption that the future is going to be like the past why should we think that the future has been like the past can anyone give me a reason exactly because it has always been the case that the future has been like the past in the past so that's a circular yes exactly if every time you try and justify the the belief that the future is going to be like the past you'll find yourself arguing in a circle the only reason we think that that works is because it always has worked in the past therefore we assume it will work that way in the future but human beings just cannot not argue like that it's very interesting I was playing with my cat the other day and I noticed that it doesn't go in for inductive reasoning if you do that with a cat if you do it with a human being the human being will keep going and expect you to keep going with the cat doesn't if you stop it it stops you don't catch it just slightly if it was interesting anyway that's what inductive arguments rely on okay tell me why this one tell me what it is we're assuming actually this is a silly question in fact I don't like this question I'm going to skip it and you can see why the assumption here is that because the son has always done this it'll always continue doing that in the future and the assumption here is that because in your experience Maryann's always done this in the future Mary Ann will always do this but our backgrounds and knowledge comes in to say whether you think it's a strong argument or a weak argument and I think you'll see that given what we know about physics about astronomy about the laws of nature etcetera that is a strong argument given what we know about people and what they wear that's a weak argument but both of them rely on the assumption of the principle of the uniformity of nature and there are sub categories within the category of inductive arguments here's one an argument from an analogy a is like B a is F therefore B is F okay a is like B and notice these smaller lowercase letters stand in particular things whereas letters like this stand in for either properties or sometimes sentences but I tend to use PQR for sentences and a for Oh actually that should spoil the case now now started explaining it that should be smaller case ah scrub that okay is like BASF therefore B is f you see how that works and here's an example the universe is like a pocket watch a pocket watch has a designer therefore the universe has a designer you will be familiar with that Pascal's no it's not pestle what is it Paley thank you so the universe is like a possitive pocket watch a is the universe B is a pocket watch a is F I've got this the wrong way around haven't I here's your homework take that argument and put it into into proper canonical logical form come back and tell me where I've got that wrong user I've got several quite interesting little errors in there some of them are just in the logic that I'm using and some of them are I've just transposed various things it should be easy for you to see where I've gone wrong do it and come and if you want to come check that with me next week I'm very happy to have a look at it ok do you want to come up with your own argument from analogy got time for one or two perhaps Aion there's someone over here who hasn't had a chance to so far yes okay that would do one of your premises isn't true well actually no yes one of your well I suppose our universe is like a cabbage that in a roughly so shape wise okay well they that would work yep one more sorry cert again Tricia's like sylvia good yep absolutely that'll do good we've got that let's have a look at another inductive on can you see how that's inductive by the way why is that why does that depend on the principle of the uniform uniformity of nature well it again we're assuming if one thing is like another in some ways then it'll be like another in other ways so we're it we're assuming the uniformity of nature aren't we so if it's like that in one way it'll be like that in another way as well here's a another argument an argument from Authority Einstein is brilliant physicist Einstein says relativism is true therefore relativism is true of course we could put in a different thing here Einstein says pacifism is the right creed therefore pacifism is the right Creed what are we done there we've changed a good argument to a bad argument why is one good one bad because he is an authority on physics that's right and he isn't an authority on politics so but we'll be looking at good and bad arguments from now on after next week ok causal arguments we looked at causal arguments briefly last week every time an a occurs a B occurs therefore A's cause B now we have a huge tendency and in fact that tendency was manifested here last week in this very room wasn't it where we assumed that where there's a correlation there's also a causal relation well we know that that's not true is it we know that there can be correlations without causal relations but even so we tend our evidence for causation tends to rest on a correlation so if every time an a occurs a B occurs we'll tend to think that a z' cause B's so we argue from observation of a correlation to an assertion about a a causal relation and just to say quickly that causal arguments can be deductive or inductive depending on whether we're arguing from a causal claim or to one so a scause be there was an a therefore there will of be there will be a B every time every observed a has been followed by a be there for a s cause B which of these is deductive left or right my left hook that's left deductive inductive yep that's right can use that's we're taking calls here what we're saying wick we're arguing to a causal plane aren't we from observations of correlation and here we're arguing from a causal claim indeed the conclusion of that one to a particular claim okay so that's deductive well you should be able to do this okay that's the adaptive because if that's true if that's true and that's true then that must be true okay this is this might be true and yet this be false but even so that is reason to believe that isn't it okay it's just not conclusive reason whereas these are conclusive reason to believe that right your task for the week ahead and see if you can find in in your newspaper magazine or a book or or wherever and I've said for but that's entirely arbitrary just see if you can find some arguments that fit the patterns that we've been looking at today and you might also notice in your own behavior as you're talking to people you'll find yourself and I'm hoping to sensitize you to these logical words so that they can't go with go past without your thank you so when you find yourself saying if-then that's a particularly good one if then or therefore or since or things like that catch yourself and try and work out what your argument was now some of your arguments going to be far too complicated to work out like that at the moment stick to simple one see if you can find yourself offering a simple argument if you did I said if you don't clean your room then this would happen you did not clean your room therefore you know this this sort of thing is what you're trying to find out for and have a look and see if you can fit them into the forms that we've given here okay and next week we're going to look at actually identifying arguments and setting them out logic book style we've been doing that today but we're going to do that with some rather more complicated arguments next week we're going to look at arguments that you might make in the pub or in a newspaper or something like that we'll look at a few magazine leaders and things like that sorry newspaper leaders that's it

Channel: University of Oxford

Views: 43,696

Rating: 4.818182 out of 5

Keywords: yt:stretch=16:9, philosophy, arguments, critical reasoning, argument, reasoning

Id: cff4jr8CCLA

Length: 71min 7sec (4267 seconds)

Published: Fri Oct 22 2010