The philosophical method - logic and argument

right well I think we should get started back everyone nice to see you that you haven't been frightened off today I'm going to talk about something absolutely central to philosophy and that's the methodology of philosophy which is the methodology of logic and argument and just I think I said something last week about this but it bears repeating and in science people do experiments and the experiments they do are constrained by the laws of nature which is why there's some confidence that their experiments are going to give them true knowledge well knowledge the true knowledge is not smaller than mine in philosophy we also do experiments but the experiences we do are not constrained by the laws of nature and we don't do them in laboratories they're not empirical experiments instead we do thought experiments so it's very nice being a philosopher because you don't have to leave the comfort of your armchair you can stay in the library you don't have to get messed up with test tubes and things like that you can just sit there and do it in your head but in the same way as a scientist is constrained by the laws of nature the philosopher is constrained by the laws of logic and that's why we can be fairly sure that when we have knowledge when we think we've got something we know we can be fairly sure we're right especially if we corroborate what we think with other philosophers of course third-person corroboration is as important in philosophy as it is in science and but what I'm going to be talking about today is is the argument the sort of logic that constrains our thought experiments so first of all we're going to talk about what logic is it's not the sort of argument that your teenage children have okay we all know that sort of argument oh you didn't yes I did no you didn't in etc it's nor is it the sort of argument that you laughed at on Monty Python you remember the argument sketch probably and instead the argument is going to be an a set of propositions which we call premises which are put forward is read to believe another proposition which we call the conclusion so here's an argument I want to get London by noon I believe it's a necessary condition of getting to London by noon that I catch the 10:20 train therefore give me the conclusion I must catch the 10:20 train so what you've got is you've got two propositions I want to get to London by noon and I believe it's a necessary condition of getting to London by noon that I catch the 10:20 and together they combine and you will knew immediately what the conclusion had to be because there's only one conclusion that's entailed by these two isn't there and you all got it right and that's because you are all rational animals actually you do logic pretty well as well as I do and that I can do that you can't do is tell you how you do logic what it is that you're doing when you do logic but as rational animals you're doing logic all the time you knew the answer to that the reason you knew is because you do logic logic is is just the if you like the method by which you go from one set of thoughts to another thought it's one way of acquiring knowledge if you like okay so that's that's what an argument is now there are different types of logic because there are different types of argument so and there are all sorts of different types of types as well but one type of argument for example is de ontic logic the logic of moral discourse so if I say to you lying is wrong therefore what's conclusion are you going to give me or I shouldn't lie or something yep something to the effect I should tell the truth why shouldn't I or whatever that's notice that's a different kind of argument because you haven't got two premises there but you have got a premise again and a conclusion I shouldn't lie and but it's interesting because Kant says that's what's peculiar about deontic logic is you go straight from a statement to the effect that something's wrong to the conclusion that you shouldn't do it and Kant thinks that that's a very peculiar thing about morality because for everything else you would need a desire in there as well so if you look again at the first argument I want to get to London by noon it's a necessary condition of getting London to London da-da-da-da-da-da therefore I need to leave on the 10:20 if you took away the desire would you have a good argument left no you just say it's a necessary condition of getting to London by noon that I catch the 10:20 well so what you know unless you want to get to London by noon that doesn't entail anything does it you can do anything you like consistently with that but once you've added that you've got something that requires an action have new so it would be irrational to have that desire and that's belief and not to believe I must catch the 10:20 wouldn't it okay that's true but I have said a necessary condition here so if I'd taken that out you're right but I think as I put that in anticipating that somebody might say something like sorry that's true but if it's a matter of action my belief would be sufficient - wouldn't it because even if I was wrong about that I would still think it's Russia and what's more I'd still be rational to catch the 10:20 wouldn't I if I believed that even if in fact it but I was wrong okay but if you look at this one do you need a desire in there Kant would say no lying is wrong therefore I mustn't lie do you need I don't want to do the wrong thing or I do want to do the right thing Kant would say no because he'd say if you think that you need to add and I want to do right you just don't understand what it is to do something wrong okay think about that for a second if you if you entertain the possibility you need to add I want to do what's right you or implying that you might not want to do what's right and Kant would think that that would show that you didn't actually understand what right means you with me no but and Kant would say they don't understand what's right if you think I understand that ten-year-olds go around licking sweets from from shops because their understanding of right at the moment is is if anyone finds out I'll I'll get into trouble okay I don't wrong is mummy we'll find out and I'll guess smack or something like that Moo how old-fashioned oops it's illegal nowadays in that anyway whatever um just it isn't okay well at least I haven't said anything illegal but immoral maybe um so if you're thinking that for something to be wrong is if I get caught I'll be punished you've got that you haven't yet got the concept of right and wrong have you what you've got is a Prudential concept that may cause you to act in some of the same ways but I bet if I leave my purse here when I go out as I may well do you wouldn't not pinch it because you might be fine found out no you would have other reasons for not pinching it mainly because you'd think it was wrong probably wouldn't occur to you but you'd also if it did occur to you you'd think it's wrong and so there are different ways and if you think about it can do you think you could think that lying is wrong but there's no reason why you shouldn't lie so of course I'd send let's say somebody says to you your builder says to you or your solicitor says to you well of course lying's wrong but that doesn't mean I you know I mean it doesn't mean we shouldn't lie here you isn't there something wrong with that isn't that a contradiction but yeah that's different we're saying if you believe that lying is wrong then you're going to think you shouldn't lie I mean if you don't think lying is wrong then there's no reason not to lies there but if you do think lying is wrong could you also could you consists you believe let's all right let's say if you believe this lie is wrong could you consistently believe that there's no reason for you not to lie I have defined lying in saying you think this lie is wrong so it's not a white lie yeah yeah but a white lie we call them white lies because we don't really think they're wrong do we right no no no that let's not get too away from the topic if we believe that lying is wrong or that this particular lie is wrong even if it's a white lie or not doesn't matter could you consistently think never mind it that doesn't mean I shouldn't do it right yeah okay I'm gonna leave this because maybe deontic logic was a bad idea okay Kant would say that if you believe that you have got to think I shouldn't lie if you think that lying is wrong you might not but if you do then you're going to think you shouldn't lie because you cannot think lying is wrong but that there is no reason for you not to lie because for some things to be wrong is itself a reason for you not to do it may not be the final reason it may not be conclusive but it's a reason not to do it and that's deontic logic because you've began got a premise and a conclusion and the premise gives you reason to believe the conclusion so that's what's down here we've got a set of propositions or one proposition a premise put forward as reason to believe another here's another type of argument this is modal logic and I'm sorry it's a bad example but I'm lousy at thinking examples it's not possible for Vixens to be male that's because vixens are defined to be female therefore that vixen is not male okay if you believe that you're going to believe that and that's because if something's not possible then it can't be actual can it okay so so if it's not possible for me to be mailed and then I can't be the case that I am male so you're recognizing that something's not possible it will cause you to believe immediately that nor is it actual because it couldn't be not possible and actual so that's modal logic the logic and modality the logic of necessity and then another type of logic is logical conditionals so um you've probably all heard the saying if it's gold I'm a Dutchman okay that means as we all know that it's not gold doesn't it how do you know that well you'll just have to believe me take it on authority but that's because you know the logic of conditionals and if I were to write the truth table up here for conditionals a truth table gives you the truth of a conditional in every possible world you would see that if it's gold I'm a Dutchman has to be true and therefore it has to be false that it's gold so I'm not going to go into that I'm just going to tell you you know what that means because you know the logic of conditionals because you're a rational animal what you don't know is what I know which is how to draw the truth tables and how to show that that means it's not gold ok finally baffled are you yes all the different words and well some people say that a different possible world is nothing more than a different situation there's a philosopher called Kripke very famous philosopher still alive or if he isn't he's only Jeff it was today or yesterday and I'm very sorry about it he believes that you in order to explain the truth of conditionals like okay if Germany had won the war we would be speaking German now some of you may think that's true and some of you may think it's false we could argue about this we could give reasons for different sides but I'll tell you what doesn't make it true namely that the Germans won the war and we are speaking German because they didn't that's a counterfactual conditional and so we think of conditionals even counterfactual conditionals as true and false all the time and some magicians believe that in order to explain the truth of counterfactual conditionals you've got to postulate other possible worlds now of course there are other reasons in physics for postulating possible worlds in mathematics there are reasons for postulating possible worlds and what is a possible world well Kripke thinks it is literally another place just like our worlds like our universe rather than like our earth but there's no causal interaction between one worlds and other but you can say okay it's there a possible world in which Marianne's wearing jeans tell me the answer yes is that a possible world in which Marianne is male you sure you does anyone think there might be no no no no we're asking question here could Matt could I have been met or could I or I have been male in other words if I if I had to know one another hanger know an x and a y chromosome tell the two x's would I still have been Mary Ann would I still exist okay lots of people think no it's it's an open person some people think no on that some people think yes but notice we do think there's a truth value to it we can ask that question and we can argue about the answer and it's possible that in order to do that we've got to postulate the existence of possible worlds of other worlds that we know about by reason but not by perception do you see what I mean we can see this world we can touch it we can hear it there you heard part of it and but you can't see or touch a possible world but you know they're there because you argue about conditionals is there a world in which I'm male well some of you think yes some of you think no and the more you look at the logic the more you might be able to come up with you're absolutely right it is no the answer or you're absolutely right it is yes or whatever that's what philosophers are doing is there sometimes I talk about it as spinning the possible worlds in order to find out what the limits of possibility are because if you think of what a scientist is doing they're looking to see what the limits of actuality are what is the case in this world where as what philosophers are looking for is what could be the case okay not just in this world but in any world could there be could time-travel be possible for it and it looks as if time travel isn't possible was we know time travel isn't possible at the moment could it be is there a world in which it's possible and if so could this be a world in which it is so we're expanding the worlds and asking okay we know there are possible worlds we know there isn't a world in which there are square circles don't we is there a world in which circles are Square could but could there be could a circle be square exactly it's the concept isn't it if something is a circle it could not be a square end of story so we know that there's no possible world in which circles are square that's not a possible world whereas the world in which Marianne is male may be that is a possible world the world in which Mary Ann's wearing jeans is definitely a possible world so we're trying to limit the possibilities which possible worlds are there and which aren't there and yes but what we're asking is is Mary unnecessarily female or is it just a contingent fact that I'm female in the same way it's a contingent fact that I'm wearing a dress and I might have put jeans on this morning might I have been male okay we know it vixen can't be female because in the same way we know that a bachelor can't be married because it's part of the definition of being a bachelor that you're part of a definition of being vixen is it part of the definition of Mary Anne of me the time female well some people do think so but others think not you do you thought not so there are there are different views on this one and and I could give you other ones that are where we're not sure what's important is there are some cases where it's definite there is such a world some cases where it's definitely there isn't such a world and some cases that we don't know about and the job of a philosopher is to find out about those so that's modal logic and I looked at the logic of conditionals and that there are two main generic forms of argument okay these are these are looking at particular types of discourse and the logic of that sort of discourse so as moral agents you understand something about deontic logic even if you've never heard about it before you also understand something of the logic and modality and the logic of conditionals but here are two very broad sorts of argument deductive arguments and inductive arguments now I want you to ignore the ones under the dotted lines at the moment and just look at the ones on the top now I know you're all reading the ones underneath the dotted line at the moment stop it okay let's look at this one if it snows and they all be late it is snowing therefore the mail will be late the nice thing about deductive arguments is that they give us certainty they don't give us unconditional certainty sadly and if the premises of the arguments are true then the conclusion must be true okay so have a look at these premises there and tell me if that's a deductively valid argument if it snows the mail will be late it is snowing therefore the mail will be date could it be that these premises are true and the conclusion false no okay some people are thinking about it let's let's let them think but yeah but why do we want to do that because I'm giving you an example of a deductive argument and if I change that will too might then I haven't got a deductive argument have I because then the premises could be false without that sorry could be true without the conclusion being true and and the particular thing about this one is I wanted an example of a deductively valid argument and what I hope I've got is that if these premises are true the conclusion must be true there is absolutely no logical possibility of those premises being true in that conclusion being false is that right yeah okay that's great so we've got a certainty in a deductive argument conditionally upon the truth of the premises and the validity of the argument now here's an invalid deductive argument if it snows the male will be late the male is late therefore it's snowing okay now there's something wrong with that argument isn't there let's wrong with it good and give me another reason yes but can you tell me give me a reason in which puncture good you can't hear ah okay and good I'm glad to say okay well I'll repeat and what was said there and if you've got an an invalid argument what you'll be able to find or at least what you'll be able to say that there is you may not be able to find one because if you like me you're lousy at examples if it snows the male will be late the male is late therefore it's known you should be able to find a counterexample in other words a situation where the premises are true and the conclusions false okay so let's say the mailman had a puncture okay if it snows the male will be late the male is late therefore a snowball no you know it's actually the mailman's had a puncture instead or he got up drunk or even you know whatever happens there are all sorts of reasons why the male might be late in addition to it snowing so we can't go from the confirm the affirmation of the antecedent to the anthem affirmation of the conclusion whereas we can go from this one to that conclusion exactly but the fact is if you have any argument of that form you will have a valid argument whereas if you have any argument of that form you won't let's show you what I mean by that hang on I'll have to find one I haven't written on and then I won't be able to find where I am so you'll have to wait below if P then Q P therefore Q okay can you see that that's a formalization of this argument what does P stand for here sorry not the premise no not well sorry if P then Q formalizes the whole premise doesn't it what does P stand for now you're all too clever you're all too clever no then have a look at that premise and tell me what I've taken out and replaced with a sentence letter thank you it is snowing or it snows yup so P is it snows so if it snows then the mail will be late exactly say so you've got it now you didn't know you could all do logic therefore sorry P so this says it is snowing notice I should have probably put it if it is snowing then the men we'll be late and I didn't but okay it is staying there for the male will be late thank you okay then we've got if P then Q Q therefore P and notice that where is FV or argument to that form it doesn't matter what you put in there that would be valid and it doesn't matter what you put in here it wouldn't be valid would it so if we if we make P let's change the interpretation so if I do this if you were a student doing this you would have to and you gave me these arguments I'd say where's your interpretation and if you hadn't provided one you would lose marks okay so let's give an interpretation P is it is snowing and Q is the male will be late who's going to try to actually I'll try now try and give me another interpretation of those sentence letters okay so forget about snow in the mail give another interpretation think about Mary Ann lecturing or Mary Ann wearing dresses or it's being Monday or do you know what you're doing you're all looking very okay you're just looking serious good it's serious stuff Shh don't yell out you're all trying it I tell you what when you've got one put your hand up and just keep it up to life okay so you're looking for another sentence for P and another sentence for Q which gives you an argument good okay gentleman back there what have you got yeah well you don't need the if because the interpretation is only four P so P is no not if just Obama wins do you see what I mean because if is a logical word here yeah that's right okay and Q is Democrats will be pleased so if we pull that in here we've got if Obama wins then the Democrats will be pleased Obama actually got a problem here haven't we because notice we've got 10 Sid which immediately causes a problem but let's forget that for a minute should I say Obama wins therefore the Democrats will be pleased okay here we've got if Obama wins then the Democrats will be pleased the Democrats are pleased therefore Obama won I mean there must be it as something else that would please them wouldn't it okay how about someone else let's have just one more okay do you want to have a go hang on what's P milkman arrives okay and Q is my dog barks okay so if the milkman arrives in the morning then the dog barks the milkman arrived therefore the dog barks if the milkman arrives then the dog barks the dog barks therefore the milkman has arrived you can see what's going on can't you any argument of this form means that because the thing is P may be a sufficient condition for Q but it's not a necessary condition for Q is it so it's a sufficient condition of the mail being late that the snow that it's snowing but it's not a necessary condition and this fallacious argument here so just sit is a necessary condition and that's why it's never going to work okay well you see you're all doing logic and what's more you're all doing formal logic immediately fantastic okay so that's deduction and the nice thing about deduction is it gives you certainty if the premises are true the conclusion must be true but of course that that's quite a big if isn't it if the premises are true the conclusion must be true often we may not know whether the premises are true or not and and therefore we won't know whether the conclusions true but the fact that we know the argument is valid is nevertheless useful isn't it because the validity will preserve the truth of the conclusion so well then if we can show by scientific methods or whatever that the conclusion that premises are true we will know that the conclusion is true and if we can show by empirical means or whatever that the premise that the conclusion is false then what do we know good one of the premises is false exactly so we learn a lot from a valid argument that has a false conclusion we learn that one of the premises must be false yes you can at least one of the premises because it needn't be more than one just one false premise is quite sufficient to to show that the conclusion might be false not not is false but might be false okay good ah fantastic in fact shame about the deontic logic wasn't it we might have to go back to that as you're proving yourself to be so good at logic okay let's have a look at induction now induction is different an inductive arguments don't give a certainty what they give us is more or less probability so probability is a matter of degree in a way that validity isn't validity is an either/or matter either an argument is valid or it isn't whereas induction and gives us probability and that's a matter of degree okay you can have strong probability or weak probability so if we look at this argument here every den in history the Sun has risen therefore the Sun will rise again I should have put tomorrow in that but tomorrow okay that's a pretty strong inductive argument isn't it in fact we're all pretty well relying on it anyone who's got a lunch appointment tomorrow for example is relying or a dentist's appointment or anything else but of course it's not it doesn't give a certainty does it because we might be wrong tomorrow might be the day when the laws of nature are just going to change the fact that it's always been like that in the past doesn't mean that it's always going to be like that in the future the fact that the laws of nature have always been the same in the past doesn't mean they're always going to be the same in the future it was Hume who pointed out that as a matter of fact I mean it just could be that the hive is strong your deductive argument is it's not going to give you certainty Russell talked about the chicken who every day in the whole of his life the farmer had come out and given him food and the chicken here comes the farmer and he thought oh good him foods coming of course he got his neck wrung now how do we know that we're not in that position with respect to the Sun rising tomorrow and what Hume said is we don't there is nothing you can do to show that there's anything more than probability here because that argument rests on the idea that nature is uniform why do you believe that nature is uniform in other words that the future will be like the past because the future always has been like the past hasn't it well that's no argument because that is itself an inductive argument isn't it why is the future being like the past it always has been like the past you know that it's like trying to hop around on one leg here of course yeah no it's certainly true that in induction you're going from something observed or something that has happens to a your REM uh what's the word mind's gone blank no when you project into the future extrapolate whoever said as travel a that's what I meant you're extrapolating into the future aren't you so for example here's another inductive arguments I think you'll agree it's not a terribly strong one every time you've seen me I've been wearing earrings that's probably true is it especially if you've only seen me last week and this week and next time you see me I'll be wearing earrings now that is an inductive argument isn't it there's some probability there but I think you'd agree it's not as strong as that one because next time you see me it might have been as I'm going out to get the paper in the morning before I've even put clothes on dressing-gown or something I don't wear earrings with my dressing young and and anyway we know too much about human beings to assume that that's a good inductive argument so in deduction you get certainty and it doesn't need to be about the past or the future it can be about anything at all with induction you are extrapolating from not necessarily the past you could extrapolate from the presence to something else so all the chairs in this lecture room are blue therefore the chairs in the next lecture room are going to be blue now there's no time element in that is that there's just a you know and is that a good inductive argument well it's it's sort of no it's not very good as it certainly no is not as good as that one okay so these are two types of argument and whether you've got deontic logic or conditional logic or modal logic or whatever you'll get arguments of this kind for example the argument I was trying to convince you of lying is wrong therefore you shouldn't lie can't believe that's a deductive argument okay because the premise entails the conclusion if the premise is true the conclusion can't be false now some people disagree with can't in which case that wouldn't be a deductive argument wouldn't obviously be an inductive one either instantly there are other types of argument there's some are this is where I'm had that one haven't we and we've had that one okay there's arguments by analogy anyone tell me what one of those is give me a very famous one perhaps to do with watches anyone read Dawkins book The God Delusion he talks about a very famous argument from analogy can anyone tell me what it is the blind watchmaker exactly so so the universe is like a watch a watch has a maker therefore the universe has a maker okay Dawkins thinks that's an appalling argument and he's probably right but it's a an argument from analogy and what you do with an argument allergies is you find something that's like something else anew so if a you've got a is P okay a has this property P a is like B or B is like a therefore B has P as well okay so a has this property B is like a therefore B has this property - and of course their the the premise of similarity is absolutely crucial because if you haven't got the similarity there then you cut you haven't got the conclusion either and of course there are arguments from causation if a causes B then you don't get an a without a B okay and the reason that that's a valid argument is that you assume that brings correlation if a causes B and you get an a without a B then that shows you that a doesn't cause B because an a isn't sufficient for a B okay right well let's let's move on from there those are the types of arguments and what's important about any argument whatever sort of argument it is is that if you want to evaluate it you've got to ask two questions and the questions you've got to ask are these are the premises true and it's the argument valid and in a case of a deductive argument what you're asking is is it the case that if the premises are true the conclusion must be true okay that's what you're asking if the argument is deductive and if it's inductive you're asking is it the case that the premises provide good reason to believe the conclusion so how strong a reason to the premises provide us to believe the conclusion so those are the the two questions you've got to us it doesn't matter what the argument is if you're reading Descartes or you're reading the leader in today's newspaper what you've got to do is try and firstly analyze the argument in other words set it out logic book style identified it that first thing you go for is a conclusion identify what it is this person is arguing for okay that's the conclusion and then find out what he's using as his reasons and once you've identified those you've got the premises so you should be able to set it out premise one premise two conclusion and then you ask okay what do I think of these premises are they good premises what do I think of this argument is it is it valid in other words if the premises were true would the conclusion have to be true or do the premises provide me with at least good reason to believe the conclusion and if either of the answers so if the question - I'm sorry the car answer to either of these questions is no then you don't have a good argument if the answer to both those questions is yes you might have a good argument it's not sufficient let me give you an argument that satisfies both of these so I'll get lost again okay now is the premise okay here's the premise here's the conclusion okay it's the premise of this argument true you oath okay it says whales and mammals therefore whales are mammals okay the premise is true okay is there any possible situation in which the premise is true and the conclusion false there isn't is that how could there be the conclusion is the same as the premise okay that is a circular argument a circular circular arguments are valid how could they not be if the premise is amongst its or if the conclusion is amongst the premises then then there can't be any situation in which the premises are true and the conclusion false so that's a valid argument but what's wrong with that is its circular you're not going to learn anything from that argument so the fact that you answer yes to both those questions isn't sufficient for it being a good argument but it's certainly necessary and and that as a philosopher those are the two questions that are well actually as a philosopher that's the one that bothers you it's it's often scientists who are interested in that one so for example every Swan I've ever seen has been white therefore all swans are white okay well it may be true that every Swan I've ever seen has been white I need to find out now whether that's a sufficient reason for thing King that the Swan in the next room is white and if it's true that all swans are white this one in the next room will be white won't it but my job is to go into the next room and see if it's white and if it isn't what do I know well either that it isn't a swan okay or that it's not the case that all swans are white and maybe we would say it isn't a swan I mean you must have heard when mrs. Thatcher in people saying she's the best man in the cabinet okay here's the argument all women are passive mrs. Thatcher is a woman therefore mrs. Thatcher is passive here there's the argument while mrs. Thatcher clearly isn't passive therefore either she's not a woman or not all women are passive but you know them do you see how it works he'll not often depends on logic precisely because it tells us what we ought to think and then somehow confounds us are the same yeah well therefore actually just marks the conclusion of an argument it says I am the thing about an argument is its its premises giving reasons for a conclusion and we can give any premises as reasons for any conclusions so if I say Melbourne is in Australia the sea is salt therefore Paris is the capital of France okay now that sounds like a really bad argument doesn't it and but I could tell you a story about how here we are we're all not only we all terribly ignorant really very badly ignorant and we have been told that these two sentences are such that if they are true this third sentence is true okay the first sentence is the Sears salt ii sentences mel burns in australia so i say okay you go off and find out whether spheres salt okay you go off and find out whether melbourne is in australia so off you scurry and you find the nearest encyclopedia or dictionary and so on you come back you say the sea is salt you come back and say melbourne in australia and i say therefore Paris is the capital of France okay do you see then there is an argument there and what's made those premises provide us with reason for the conclusion is the context isn't it by providing a context I could make those apparently completely irrelevant sentences an argument so the therefore just stands for a conclusion to say I am saying that that is reason to believe that now notice something else if I had lots of other sentences in here am I going to change the fact that this arguments valid well let's put in it's not the case that mammals whales are mammals it's not the case that whales are mammals whales are mammals therefore whales and mammals now is there any situation where both those premises are true and that conclusions false actually that's a they can't both be true can they so is this argument valid yes yes it is because there's no possible situation in which the premises are true so how can there be a possible situation in which the premises are true and the conclusion false and I'm going to do a truth table here which is probably asking for trouble but let's let's do it show me let's some okay this is using the notion of possible worlds to explain something okay I've got if P then Q P therefore Q no I don't want that hold on sorry I'm changing my mind let's try this okay each of the each sentence can be either true or false can't it okay most I mean let's assume for the moment if you've got a sentence the cat sat on the mat or Mary Ann's wearing a dress or something like that it could either be true or it can be false if it's contingent sentence so this truth table represents every possible world with respect to the combination of truth values here okay two visited world in which P is true and Q is true okay this is the world in which tummy good okay this is the world in which that's right and this is the world in which they're both false absolutely that's oh you do you're really doing well here yeah you've been most often undergraduates can't do that and it's because they haven't separated the possible worlds because each these possible worlds is quite separate from me from the other okay now in the world where if we just take P here in the world where P is true then the premise here is going to be true isn't it okay and in the world where P is true here the premise is going to be true okay and in the world where P is false and false again exactly so okay and that's going to be the same here because we've got exactly the same letter here okay now do we know whether this arguments valid while looking at e structure in turn is this the world in which the premise is true and the conclusions false no okay so that's okay it's valid there is this a world where the premise is true and the conclusion false hang on this is number two the second world is this a world where the premise is true and the conclusion false no it isn't that's okay is this a world where the premise is true in the conclusion false no and is this a world where the premise is true and the conclusion false no hang on who said yes look is this a world where the premise is true and the conclusion false no so there's no possible world there's each of these as a possible world and these are all the possible worlds and there isn't one where the premise is true and the conclusion false is there this is a circular argument so we know that this argument is valid now I'm going to add not P in here so I should've added Q at all I've just complicated things by adding Q ignore it let's add not P okay what's the truth you hear please true so in this world not P is false good so that's a not that is not okay in this world P is true so not P is false again in this world P is false so not P is true you really do well okay and in this world P is false so not P is true okay so now we're looking at two premises and let's see if we can find a world in which the premises are true and the conclusion false okay so this world the world number one we've got two premises is this a world where the premises are both true and the conclusion false no because the premise is not both true this one's false isn't it so okay this is valid that's all right here's one where okay is this a world where the premises are both true in the conclusion false no it isn't is it okay is this a world where the premises are both true and the conclusion false no and is this a world in which the premises are both true incorrigible so it's the argument valid yes good really good a circuit the thing is you can add any premise to a circular argument and it remains valid so it may be there's a circular argument when I look at that therefore you think this isn't an argument it's so obviously not valid now if I were a politician wanting to kick sand in your face the best way to do it would be to offer you a circular argument but in the middle blind you with science hide the premise that is the conclusion in amongst lots of other premises so you wouldn't see you know the therefore would sign fine to you then because it looks as if you'd have an argument but actually it wouldn't change the validity would it you as a rational animal would recognize the validity what you wouldn't recognize is that the argument is valid because it's circular are you with me so circular arguments are jolly useful if you're trying to confuse someone and the reason they're useful is because you as rational animals are validity detectors that's what you do you know if we're in the pub and I'm giving you an argument you're sitting there thinking is that a good argument is she right it's very you're asking yourself whether my argument is valid you're setting yourself to validity detection mode yeah yeah yeah you you know you could use it the thing about that is it's self referential because the liar if I say I'm telling the truth and you don't know whether I'm a lying or a liar or not you don't know whether that sentence is true but yes you could use truth tables for that yep yeah you could you could use that were you being confused by the fact I put Q in there do you think or where you've been confused by the fact I wrote that out first well there's not models there for Wales and not mammals yeah okay yeah if you look at it that that's truth table I've just done is exactly that argument if we provide the interpretation that says P is whales are mammals do you see because when you look at that piers whales are mammals not P sorry this is yuppie as whales mammals this says it's not the case of the whales are mammals and this says whales are mammals so that's the truth table for that argument yeah and I drew that and I then didn't do it because I realize it wasn't circular but if I do the truth table for that one what's going to happen does anyone recognize this argument if P then Q P therefore Q is that going to come out valid it's not circular because the Q isn't a premise the Q is part of a premise and that's different that's okay so that's not circular if you had Q in here it would be a circular argument and it would be valid for that reason what's this argument you've seen it today already or rather this is a formalization of an argument you've seen today spoo thank you exactly so if it's known the male will be late it is snowing therefore the male will be late and if I write out the truth table and you'll just have to take these four poops yes that's right okay there's the therefore is this a world in which the premises are all true in the conclusion false nope okay so that's right is this a will but the premises are all true and the conclusion false nope is this one where the premises are all true and the conclusion false nope is this one no okay so that arguments valid but if I change this to a Q sorry I'll get another pen because it's okay is this a world where the premises are all true and the conclusion false okay is this a world where the premises are all true in the conclusion false no is this a world where the premises are all true in the conclusion false it is isn't it okay that is quite sufficient to show that this argument any argument of that form is invalid because here's a world just here's a possible world in which the premises are true and the conclusion false and all the rest becomes irrelevant because you and you need one counterexample and we can even say what the counter example is because that argument is invalid in the world where P is false and Q is true so if we put in the interpretation we had before what was P it's snowing and Q is the male is late so in the world where P is false in other words it's not snowing but the male is late because of that puncture that's the counter example to this argument do you see do you see how useful logic is it's fantastic and you see you're doing it now okay you've got a fair amount of help here but um it wouldn't take me long to show you how to do this yourself the really difficult bit is the interpretation from English into formal logic that's that's the really difficult bit but this bit dead simple once you know how to do it and and this is formal logic okay right actually that takes me quite neatly on to the next slide because I wanted to point out that there are two sorts of logic so far we've been looking at formal logic and but I also want to say something about so fickle logic because that's a bit different but personally just to say something a bit more about formal logic you've got to distinguish form from contents the form of the argument from the content of the arguments so this is the form of the argument up here the content is supplied by the interpretation so you notice that you give this a completely different interpretation but the form would still be the same and that's actually very important because what that tells us is that logic is topic neutral once you know how to do logic it doesn't matter what subject you're talking about the logic will work for any subject at all so let's look at this one let's look at here are two arguments sorry I'll move this over all men are mortal Socrates is a man therefore Socrates is mortal all elections that produce the greatest happiness of greatest number aright that action produced the greatest happiness of the greatest number therefore that action was right now can you see that these two arguments completely different subject matter only this is about mortality and Socrates and that's about ethics the greatest happiness of the greatest number etc but they've got the same form and now I want you to practice your logic by telling me what the form of this argument is okay work it out for yourself and then put your hands up when you've got it without yelling it out work out what the form of that argument is remember that there are logical words and there are English words and it's the logical words you want to leave in and the English work well they're all English words but leave the logical words in provide an interpretation for the non logical words don't worry if if I knew this difficult this is difficult stuff put up your hand if you think you've got it let me give you a tip that all is a word that you leave in and is is a word that you'll leave in put up your hand if you think you've got an answer good we're getting that yep symbolic logic because the form is captured in symbols good okay we've got a few do you want to have a go okay hold on surely somebody could invent something better than this don't you think what a crayon yes yes would work wouldn't it all all a is B all A's are B can I can I change it yeah okay all A's are B SS a therefore gives a girl a gold star fantastic do you see it always RB s is an a therefore s is a B a lot of us up there wait let's provide the interpretation for each of these arguments okay so the interpretation says what does a mean what does be mean and what does s mean and we've got two arguments so we need to provide two interpretations what is a here you do the same if we do the first argument first X is a man is what it is actually I'll put that in because these are predicates is a man is a predicate so you need to have a placeholder X is a man B is X is mortal yeah an S Socrates well done okay and the interpretation here a is X's a bit long-winded this one a is an action an action that produces the greatest happiness of the greatest number and B is is right X is right well done and s is well done well done that action because that action is a designator isn't it that action it picks out one particular thing in this case an action in the same way that Socrates is a designator it picks out one particular thing Socrates so we're saying first one anything that's a man is mortal so anything that has this property also has that property Socrates has this property the first one therefore Socrates has the other one okay and we're saying exactly the same thing in that one except we're talking about something completely different we're talking about actions and and whether they produce the greatest happiness of the greatest number or not so do you see why logic is topic neutral once you've learned logic it doesn't matter what you're thinking about you can think clearly about it and this is one of the joys of being a philosopher as far as I'm concerned because it means you can put your nose in anywhere it really doesn't matter what you're talking about there's a philosophy in mind a philosophy of biology of loss fear of chairs probably somebody was trying to persuade me to run a weekend school on the philosophy of accountancy yesterday if anyone would like to do that they can share it has no actually I'm sure that then there is a philosophy of accountancy and actually if there are I'm sure philosophical issues in there and there is a philosophy of everything because of this ok logic is the methodology of philosophy and it can be applied to any subject at all and that's because logic is topic neutral ok let's move down so what we do in formal logic you've seen is we strip an argument of its content we're not interested in the content we reveal its form and then we can test mechanically for validity and you've seen me test mechanically for validity here that's one way of testing mechanically for validity okay now the trouble with that is that happens if I add another premise here so I have an R as well it's to see it's going to get unwieldy isn't it and just for fun I always get undergraduates to do one with four or five premises in so that their truth table goes on and on and on and it's very very boring to work it out and then I show them that they can do this instead I can find okay now you'll just have to believe me that that arrow means if then okay so that that formula there means if P then Q and that little sign there means it is not the case so that means not Q and what I've done here you remember the argument we had if P then Q P therefore Q I've got the premise there the first premise there the second premise there and I've negated the conclusion okay because the argument was if P then Q P therefore Q and I'm saying well let's pretend that we've got if P then Q P and not Q in other words a situation in which the premises are both true and the conclusions false let's see if I can find an argument like that or a situation like that and I then apply completely mechanical rules that I could again teach you in an hour or so to get this okay that the conditions under which that are that is that are true that is true are though situations it's true just in case not P or Q and you can't there is no possible world with both Q and not Q in it so that's not a possible world there's no possible world with not P and P in it so that's not a possible world there is no possible world in which the set consisting of the premises and the negation of the conclusion are true together okay now you won't have understood that but I hope you can see that I know what I'm talking about and that it would be very easy to teach you how to do this so that all you have to do is any argument at all if you can translate it into symbols and that's the biggest if if you can introduc translate it in symbols there is a set of rules such that you can apply these rules and test it just as I have done and say quite categorically this is a situation in which sorry this is an argument that's valid and let's do the invalid one just see again how it works the invalid one is if P then Q Q therefore piece I'm negating P because that's the conclusion and I want to see if there's a possible world in which these are all true together that set consisting of the premises plus the negation of the conclusion well that's true just in case not P or Q again but we don't have any contradictions here do we see we've got not P not P Q there's one possible world in which that set are all true the sentences in that set are all true and we've got Q not P Q so that's another world in which the set consisting of the premises plus the negation of the conclusion are all true so either of these any situation in which Q and not P is true is a counter example to that argument and you go to your interpretation now you find out what Q is you find out what not P is and you know what your counter example is magic isn't it well yeah P it is snowing Q the mail is late do you see what I mean I was just doing exactly the same example don't don't worry if you're getting confused today you don't know these rules you have no idea why I've represented the truth conditions of that like that and I would have to tell you that and I'd also given that that's actually quite difficult to understand how to have to convince you that that is the case but I would be able to do it I promise you and once I'd done it you would then be able to take any argument and and show whether or not it's valid or invalid and one if if you showed it was invalid you'd also be able to give me the counter example because you would know which world is such that the premises are both true and the conclusion false it's did nice are you understanding that as therefore you said P therefore Q yeah that's not R therefore it's it's an implication not an entailment that's saying if P then Q not P therefore Q and I mean don't worry too much about that the therefore would be okay yep yeah well what I'd be saying is if anyone made this argument this is the argument they'd make they'd be saying if P then Q and P then Q so if these are true then Q is true so if it's if it's true that if it's known the male will be late and it's true that it's snowing then it must be the case that the male is late and I would do this sort of diagram and I'd say you know you're right that's absolutely right but then if somebody tried the other argument so as I'm reading deck hearts for example and I think okay he what he's saying is that it's possible that all our beliefs about the external world of false okay and one of his premises is this one of his premises is that one of his premises is this is it true that that conclusion really follows from those premises so I would do the truth table and I would say no it isn't true or yes it is true and that would enable or you could look at the reader and leader in tonight's paper and say okay here's the argument premise one premise two premise three I'll now formalize the arguments I'll strip the content out of it and formalize it and then I'll apply the rules of the predicate calculus would probably be needed this is the propositional calculus but you'd need a slightly more sophisticated one predicate calculus and and you'd be able to determine whether the argument is a good one or not of course what you're determining is that the argument is a good one or not that still doesn't tell you whether the conclusion is true does it why not exactly in my the fact that an argument is valid isn't telling you that the premises are true so as a philosopher what you're interested in is the validity of the argument you're also interested in the truth of the premises if it's enough it's a philosophical argument but it might be an empirical argument in which case the truth of premises isn't your business you know we don't go around getting our hands dirty they do no it doesn't work like that because firstly you've got to be able to formalize an argument and there there are huge problems if this is the class of all arguments in the world ok all arguments here and you can formalize all right I mean I'm making this up but let's say you can formalize that many in the predicate calculus you can formalize that many in the in day on take logic you can formalize that many in modal logic this lot you can't form lies at all and therefore you can't apply the rules now what we hope as formal logicians is that we will learn how to formalize those and for example the predicate calculus was developed only a couple of hundred years ago Aristotle developed syllogistic logic but it took Frager to divert predicate logic and that was a huge leap forward modal logic has only been developed well it's still being developed so the logic of probability dito deontic logic still working on it so you know you're right at the cutting edge here I've given you the the knotty calculus if you want to go and do it for yourself you'll you'll have to do a lot more than I've given you here but you'd know that I mean so no it's not the case and of course also the the real skill is in translating the argument and you know that if I if I made you do some because it's really really difficult to translate from English into a symbolic language and there are lots of things left out and it's very frustrating ly inaccurate and so there aren't there are real problems but we all do it all the time believe me I I sit in my study doing tables like that it's much more interesting that if you might think yeah well I mean there are more there's more than one premise in the arguments I've been doing of course that's one premise that's another premise and of course there could be I mean there could be ten premises here I could still apply these rules no no you you only need one that's false and that's quite sufficient to show that the even if the arguments valid the conclusion may be false yeah so the number of premises that's true is not very relevant it's than if there's at least one this fall so here's a valid argument with a false conclusion you can write it down hang on I've written it here if it's Tuesday then Mary Ann isn't lecturing it is Tuesday therefore Mary Ann isn't lecturing okay well that's a valid argument isn't it if you want to hear it again if it's Tuesday then Mary Ann isn't lecturing it is Tuesday therefore Mary Ann isn't lecturing now if those premises were true the conclusion would be true wouldn't it okay but the premises aren't true are they neither is the conclusion so you can have a valid argument with a false conclusion if you then know that the conclusion is false of course you can go back and say one of the premises must be false but there are often situations where we actually don't know whether the prep the conclusion is true or false and therefore we don't know whether the premises are true or false you know I mean this is logic is is in some ways the servant of science in other ways of course science is the servant of logic I mean they work together oh yes it tells you a lot it tells you whether an argument is valid and you know that if okay think of the difference between something's generating truth and something's preserving truth logic doesn't generate truth if you haven't got truth in the premises you won't have it in the conclusion but if you have got truth in the premises you preserve it in the conclusion by using a valid argument and that's what you hope you because there are things that we know about the world and there are things that we want to know about the world so we want to extend our knowledge from what we already have to what we don't already have and one of the ways of doing that is is by using logic if this is true and this is true then this must be true the if is yeah yeah um well let's say I'm a scientist and I say well if the Higgs boson exists then my building this whacking great Hadron Collider at cost of millions and millions and millions of pounds might enable me to find it of course if the if the Higgs boson doesn't exist I've wasted all that money well you know I may show me a few other things but it won't tell me about the Higgs boson so if statements are actually we use them all the time I mean if you think of any of your practical reasoning that says okay I want to do liver for supper tonight therefore I need some onions or something like that there I haven't got any linens that you're using if statements to generate conclusions about actions or conclusions about knowledge or you can't you can't reason without if statements this is yeah I mean it was when this was developed that computing became possible yeah yeah absolutely the same exactly so yeah yeah no I mean what you're doing when you're doing the applying those truth tables and the tableau rules is is acting like a computer you know you're making like a computer I mean you might have two conflicting theories and you're saying if this is true then this will be the results let's see if this is the result but if this is true this will be the result and if we can find out whether it's this or that then I know which there is the correct one do you see it all the reasoning you cannot do without if statements and I can tell you under exactly what conditions if state would be true I might not I might need to go into the laboratory to see if an if statement is true actually I wouldn't because there's no where laboratory can tell me so do you see that now we have we have scope for going into the laboratory or the Artic or wherever we go to find out but without that bit of reasoning first you wouldn't even know what you were looking for and the thing is if logic can rule out something then there's no point in going to the laboratory at all I mean if I can show an argument is invalid then any scientist who's trying to get funding on the back of that argument is in serious trouble because the yeah what why should i fund him okay moving on because we've only got five minutes left but that's all right because ok I was going to talk very briefly about philosophical logic and I talked about formal logic but philosophical logic is the philosophy of logic I said there are philosophies of everything including biology accountancy whatever but the filip philosophy of logic is as you can imagine pretty damn important to philosophers because the philosophy of log of logic looks at the notions without which logic can't work so we've talked about truth a lot today haven't we I've drawn truth tables I've drawn truth trees I've said if this is true that's true so the notion of truth is absolutely essential well what is truth gon tell me you've all sat there looking intelligence as we've talked about truth so I assume you understand the word tell me what is truth something that's correct what's correct then I mean you're just giving me a synonym there aren't you whoever it was okay so what okay what's false then no okay but that doesn't tell me what I there are it's true you can't have truth without falsehood you can't have falsehood without truth but what is truth a fact okay what's a fact hang on let's let what is a fact certain knowledge is it it's knowledge of fact I mean there's the knowledge that I'm wearing a dress and there's the fact I'm wearing a dress are they the same thing no because there are facts of which we know nothing out there so facts are nothing to do with knowledge but well reality sounds like a synonym for truth here a fact is actually something that makes a true sentence true isn't it think about it what are what is a fact no there are facts you can't prove I mean are there three consecutive sevens in the decimal expansion of pi if there aren't then you can't prove it I'm told there are by the way so that's out of date but just imagine the decimal expansion pi is an infinite expansion if there aren't three consecutive sevens there's no way we'd be able to prove it but it would still be a fact wouldn't it so knowledge of a fact and a fact are two quite different things and what is a fact a fact is something that makes a true sentence true so talking about facts doesn't tell me anything about truth so come on come on you've all been dealing with truth what is it no we don't need to know it at all no you're all confusing not all of you maybe epistemology and metaphysics here epistemology is what we know and metaphysics is what is the case and there are two quite separate things what were you going to know because a belief is usually to do in knowledge rather than because there might be facts about which we have no beliefs I mean you have no beliefs about my middle name I shouldn't think you don't even have the belief that I have one how do you know whether I have one home okay but there's still a fact about my middle name irrefutable is to do with proof again isn't it yeah yeah no that's again to do with epistemology no the fact is truth is a very very difficult you mentioned correspondence there are two key theories about truth actually here's another one there's some belief that truth is nothing but the truth is completely redundant because if I say P is true I'm not saying anything more than P am i if I say P is true aren't I am I saying anything more than P I'm not I'm saying not not P aren't I because there if if P is true then then not P is false so if I'm saying P I'm saying not not P not P you two can do this yeah eventually its truth demonstrable not always no no definitely not well I think there are facts about values so so I don't think there's any opposition between fact and value so I think there are moral truths and that what making moral truth is that there are moral now you can sing approach proof again so in proof is to do with knowledge anyway that one one people some people think that there's no more truth and coherence what wakes one belief true is that it coheres with your other beliefs other people think we'll hang on I can have a set of beliefs here all of which are coherent and then if I negate them all that'll be another set all of which are coherent weren't it but which is true so coherence can't be the right theory well no because truth truth seems to be a property of sentences and beliefs doesn't it well reality isn't a property of your beliefs is it or of your sentences exactly but truth seems to be a prop if there weren't any beliefs in this world there wouldn't be any sentences would the sentences express beliefs okay if I believe that that you're what's your name Deirdre is wearing red I just expressed that belief in saying Deirdre is wearing red if there were no beliefs there be no sentences if they were neither beliefs nor sentences there would be no truth but they'd still be reality semantics means truth or means truth conditions yeah yeah that's because you're thinking of what makes things true but of course truth is still the property of the sentence that you've uttered I mean what's true is the sentence that reality is what makes it true this is this is really difficult stuff here and just talking about semantics and syntax at the moment if we look at one of the truth trees again I have stripped the semantics out of the arguments there I've left the syntax all I've left is the shape if I want to put the meaning back in I've got to put semantics back in and in putting semantics back in what I'm putting in is conditions of truth and falsehood that's what semantics is and that's that's what meaning is anyway we've done it now that's logic that's your lot on logic um I oh okay correspondence correspondence so you've actually we've already looked at that truth is correspondence between a sentence and a fact but what's wrong with that is is what is a fact other than something that makes a true sentence true and therefore it that's just a circular definition it gets you absolutely nowhere oh goodness it's lots of people ya know that a chair would certainly be one of them I think so what is truth answer I don't know I know more than you do obviously but I don't know because this is still an ongoing question what is truth that's what philosophical logic looks at we also I mean validity I gave you one of the paradoxes of entailments a minute ago and you weren't very happy with it here's another two although it would be if I can find them we're running over our time if anyone wants to go they're most welcome no I'm not going to be able to find it if I say the grass is green therefore two plus two equals four that's a valid argument because there's no possible situation which that conclusion is false so how could there be a possible situation which the premise is true and the conclusion false there couldn't be that's one of the paradoxes of entailment and one of the things that philosophical traditions would like to know is why is our definition entailment faulty in that way because that surely that argument isn't valid and yet our definition of valid makes it valid so there's something wrong with our definition of validity and yet somehow we can run computers that run large hadron colliders and find the Higgs boson on our logic so our logic isn't totally wrong how do we do with it okay we're going to stop right there you know nothing about identity but that's alright I'm sure we can talk about that some other time

Channel: Oxford University Department for Continuing Education

Views: 98,638

Rating: 4.8773007 out of 5

Keywords: Logic (Field Of Study), Argument, Philosophical Method, marianne talbot, philosophy

Id: M14ReHfPFUw

Length: 94min 42sec (5682 seconds)

Published: Wed Jun 26 2013