The philosophical method - logic and argument

right well I I think we should get started welcome back everyone nice to see you that you haven't been frightened off um today I'm going to talk about something absolutely Central to philosophy and that's the methodology of philosophy uh which is the methodology of logic and argument and just I think I said something last week about this but it Bears repeat um in science people do experiments and the experiments they do are constrained by the laws of nature um which is why there's some confidence that their experiments are going to give them true knowledge um

well knowledge the true knowledge is not [ __ ] but never mind um in philosophy we also do experiments but the experiments we do are not constrained by the laws of nature and we don't do them in Laboratories they're not empirical experiment instead we do thought experiments um 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 um

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 um 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 coroporation is is as important in philosophy as it is in science um 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 uh it's not the sort of argument that your teenage children have okay we all know that sort of argument no you didn't yes I did no you didn't Etc it's nor is it the sort of argument that you laughed at on Monty Python you remember the argument sketch probably um instead the argument is going to be um a set of propositions which we call premises which are put forward as reason to believe another proposition which we call the conclusion so here's an

argument um I want to get to London by noon I believe it's a necessary condition of getting to London by noon that I catch the 1020 train therefore give me the conclusion I must catch the 1020 train um 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 to of getting to land by noon that I catch the 1020 and together they combine and you all 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 um that's because you are all rational animals actually you do logic pretty well as well as I do um what 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 you're doing logic all the time you knew the answer to that and the reason you knew is because you do logic um 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 uh because they're different types of argument so um and and there are all sorts of different types of types as well but one type of argument for example is deontic logic the logic of moral discourse so if I say to you lying is wrong therefore what conclusion are you going to give me tell the truth or I shouldn't lie or something yeah something to the effect I should tell

the truth or I shouldn't lie or 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 um but it's interesting cuz K says that 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 K 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 d d da therefore I need to leave on the 10 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 haven't you so it would be irrational to have that desire and that belief and not to believe I must catch the 1020 wouldn't it okay unless you had another way of getting uh that's true but I have said a necessary condition here um 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 that I believe sorry you've only said I believe it is necessary that's true but if it's a matter of action my belief would be sufficient to

wouldn't it because even if I was wrong about that I I would still think it's R and what more I'd still be rational to catch the 1020 wouldn't I if I believed that even if in fact I was wrong okay but if you look at this one do you need a desire in there K would say no lying is wrong therefore I mustn't lie do you need I I don't want to do the wrong thing or I do want to do the right thing K 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're implying that you might not want to do what's right and K would think that that would show that you didn't actually understand what right means are you with me people don't want to do what's right no but and K would say they don't understand what's right if you think I understand that 10-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 Mommy will find out and and I'll get smack or something like that oo how old fashioned oops it's illegal nowadays isn't it anyway whatever um it isn't okay well at least I haven't said anything legal but uh 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 the 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 found 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 you'd also if it did occur to you you'd think it's wrong um 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 say let's say somebody says to you um your Builder says to you or 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 there all sorts of places and opportun you have to lie yeah 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 lie is there but if if you do think lying isong wrong could you also could you consistently 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 you have to Define lying because you have White Lies uh I have defined lying in saying you think this lie is wrong so it's not a white lie I'm just

saying there there times when you lie yeah but uh a white lie we call them lies because we don't really think they're wrong do we well they are because if you're say right no no no no let's let's not get too um 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 that doesn't mean I shouldn't do it but it came up last time with with torture torture is wrong but you can

get a hard case where you could argue yourself and say it was right because you were saving million others yeah okay I'm going to leave this because maybe deontic logic was a bad idea okay K 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 something 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 again 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 there 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 I think you of 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 uh 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 male then then I it can't be the case that I am male so your recognizing that something's not possible is 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 of modality the logic of necessity uh and then another type of logic is the logic of conditionals so um you 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 that 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 okay thoroughly baffled are you yes all the different worlds all the different worlds um well some people say that a

different possible world is nothing more than a different situation um there's a philosopher called kpy very famous philosopher um still alive or if he isn't he's only just it was today or yesterday and I'm very sorry about it um he believes that you uh 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 logicians 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 um what is a possible World well kryp key thinks it it is literally another place just like

our worlds like our universe rather than like our Earth um but there's no causely interaction between one world and another but you can say okay is there a possible World in which maran's wearing jeans tell me the answer yes is there a possible World in which Maran is male no are you sure you does anyone think there might be if you define Maran as a male no no no no we're asking the question here could Mar could I have been M or could I well I have been male in other words if I if I

had two no one hang on no an X and A Y chromosome instead of two x's would I still have been maranne would I still exist okay lots of people think no it's it's an open question some people think no on that some people think yes but notice we do think there's a truth value to it we 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 we can see this world we can touch it we can hear it there you heard part of it um but you can't see or touch a a possible world but you know they're there because you argue about conditionals is there a world in which I male well some of you think yes some of you think no um 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 but that's what philosophers are doing is there sometimes I talk about it as spinning the possible worlds in order to find out um 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 acttion uality are what is the case in this world whereas 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 example I mean it looks as

if time travel isn't possible well 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 um so we're expanding um 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 could there be could a circle be square no exactly it's the concept isn't it if something's a circle it could not

be a square end of story um 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 Marian is male maybe that is a possible world the world in which mariann's wearing jeans is definitely a possible world so we're trying to limit the possibilities what which possible worlds are there and which aren't there and getting back to the you're a female Maran is a female and therefore they couldn't exist as male yes but what we're asking is is Marianne necessarily female or is it

just a contingent fact that I'm female in the same way it's a contingent facts that I'm wearing a dress and I might have put jeans on this morning might I have been male okay we know a vixon 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 maranne of me that I'm female what I well some people do think so but others think not you

do you thought not um 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 definite that 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 okay so uh that's modal logic um and I looked at the logic of conditionals um but 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 of 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 the male will be late it is snowing therefore the male will be late the nice thing about deductive arguments is that they give us certainty they don't give us unconditional certainty sadly um if the premises of the argument 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 knows the male will be late it is snowing therefore the male will be dat 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 to might then I haven't got a deductive argument have I because then the premises could be false without um 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 and that conclusion being false is that right yeah okay that's great so we've got certain 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 SNS 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 what's wrong with it for Reon good and give me

another reason might still be possible to get even if it's snow uh yes but can you tell me Give Me A Reason in which puncture good can't hear you can't hear hear the people looking at you in front of ah okay um you can hear you good I'm glad to say okay well I'll repeats um what was said there um if you've got an an invalid argument what you'll be able to find or at least what you'll be able to to say that there is you may not be able to find one because if you're

like me you're lousy at example um if it snows the male will be late the male is late therefore it's snowing you should be able to find a counter example 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 it's no well no you know it's actually the mailman's had a puncture instead or he got up drunk or 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 confir the affirmation of the uh antecedent to the a affirmation of the conclusion whereas we can go from this one to that conclusion but the first one presupposes some sort of causal relationship between snowing and the male will be late which goes One Direction otherwise it wouldn't always hold if there wasn't the causation whereas the second one the causation simply isn't going to work it's not I mean the doesn't in the first statement doesn't go in the right direction for that

to apply 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 I'll 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 while um if P then q p therefore Q okay can you see that that's a um a formalization of this argument what does p stand for here sorry Prem Prem uh

not the premise no not the sorry if P then Q formalizes the whole premise doesn't it what does p stand for 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 it is snowing or it snows yep so p is it snows so if it snows then the mail will be late exactly so you see you've got it now you you didn't know you could all do logic therefore sorry P so this says it's

snowing it is snowing notice I should have probably put it if it is snowing then the male will be late and I didn't but okay it is snowing therefore the male will be late the male will be late thank you okay then we've got uh if P then q q therefore P that's and notice that where is every argument of 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 uh 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 actually all 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 Marianne lecturing or Maran wearing dresses or it's being

Monday all do you know what you're doing you're all looking very okay you're just looking serious good it's serious stuff pres sh don't yell out you're all trying it I'll tell you what when you've got one put your hand up and just keep it up till I okay so you're looking for another sentence for p and another sentence for Q which gives you a an argument good okay gentlemen at that there what have you got me yeah um if Obama wins the Democrats will please uh well you don't need the if because the interpretation is

only for p so p is if Obama wins no not if just Obama wins do you see what I mean cuz if is a logical word here yeah that's right okay and Q is the Democrats will 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 we got a problem here haven't we because notice we've got tent Sid which immediately causes us 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 one I mean there must be something else that would please them wouldn't it okay um how about someone else let's have just one more okay do you want to have a go when when the Milkman arrives in the morning my dog hang on what's P the mil arriving Milkman arrives okay and Q is my dogs my dog barks okay so if the Milkman arrives um in the morning then the dog barks the Milkman arrived therefore the dog barks

uh 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 as 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 male being late that the snow that it's snowing but it's not a necessary condition and this fallacious argument here suggests it 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 um 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 um and therefore we won't know whether the conclusion is 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 conclusions so we'll then if we can show by scientific methods or whatever that the conclusion the premises are true we will know that the conclusion is true and if we can show by empirical means or whatever that the Prem that the conclusion is false then what do we know one of the Prem good one of the premises is false exactly so we learn a lot from a a valid argument that has a false conclusion we learn that one of the premises must be false can can we say

at least one of 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 uh 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 um inductive arguments don't give us 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 or it isn't um whereas induction um 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 day in in history the sun has risen therefore the sun will rise again I should have put tomorrow in that but uh 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 um 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 um uh as a matter of fact I mean it just could be that the however strong your deductive argument is it's not going to give you certainty Russell talked about the chicken who uh every day in the whole of his life the farmer had come out and given him food um and the chicken here comes the farmer and he thought oh good food's coming and of course he got his neck rung now how do we know that we're not in that position with resp

respect of 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 been like the past it always has been like the past you know there's

there's not it's like trying to hop around on one leg here can I ask a question of course um that means surely that an inductive argument is based on what has happened in the P yeah imag inure no um it's certainly true that that in induction um you're going from something observed or something that has happened to a a your um oh what's the word mine's gone blank no when you project into the future extrapolate whoever said extrapolate that's what I meant you're extrapolating into the future aren't you so for example here's another inductive argument

I think you'll agree it's not a terribly strong one every time you 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 um next time you see me I'll be wearing earrings now that is an inductive argument isn't it there's some probability there um but I think you'd agree it's not as strong as that one um because next time you see me it might have been as I'm going out to get the paper in the morning before I even put clothes on dressing

gown on or something I don't wear earrings with my dressing gown um and anyway we know too much about human beings to 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 present to something else so um 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 there there's just a you know and and is that a good inductive argument well it's it's sort of no it's not very good is it uh certainly no 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 um K believes that's a deductive argument okay because the the premise

entails the conclusion if the premise is true the conclusion can't be false now some people disagree with K in which case that wouldn't be a deductive argument um wouldn't obviously be an inductive one either incidentally there are other types of argument there's um ah this is where I'm um 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

an analogy can anyone tell me what it is Blinder the blind watch maker 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 uh but it's a an argument from analogy um what you do with an argument from analogy is is you find something that's like something else and so if a you've got a is p okay a has this property p uh 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 too and of course there the the premise of similarity is absolutely crucial because if you haven't got the the similarity there then you C you haven't got the conclusion either um 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 causation 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 um what's important about uh 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 is the argument valid and um 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 if you're asking is it the case that the premises provide good reason to believe the conclusion so how strong a reason do the premises provide us to believe the conclusion um so those are the the two questions you've got to ask it doesn't matter what the argument is if you're reading deart uh or you're reading the leader in today's newspaper um what you've got to do is try and firstly analyze the argument in other words set it out

logic book style identify the the first thing you go for is the 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 uh 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 to if the question to I sorry the 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 um satisfies both of these get lost again okay now is the premise okay here's the premise here's the conclusion okay is the premise of this argument

true you oh Sor okay it says whales are mammals therefore whales are mammals yes 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 there how could there be conclusion is the same as the premise okay that is a circular argument all circum circular arguments are valid how could they not be if the premise is amongst sorry 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 it's 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 um well it may be true

that every Swan I ever seen has been white um I need to find out now whether that's a sufficient reason for thinking that the swan in the Next Room is white I mean if it's true that all swans are white the swan 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 by Mrs therim people saying she's the best man in the cabinet okay well here's the argument all women are passive Mrs Thatcher is a woman therefore Mrs Thatcher is passive there's the argument well Mrs thater clearly isn't passive therefore either she's not a woman or not all women are passive but you know do you see how it works humor often depends on logic um precisely because it tells us what we ought to think and then somehow confounds us what me sort of in a sideways way

is the use of the word therefore in that one um I don't know what I I'm really getting at but it just feels that it can't be a proper argument because um because the two are the same are the same yeah well um therefore actually just marks the con conclusion of an argument it says I am the thing about an argument is it's it's premises giving reasons for a conclusion and we can give any um premises as reasons for any conclusions so if I say um Melbourne is in Australia the sea is salt therefore um

Paris is the capital of France okay now that sounds like a really bad argument doesn't it um but I could tell you a story story about how uh here we are we're all not only are we all terribly ignorant really very badly ignorant um we have been told that these two sentences are such that if they are true this third sentence is true okay um the first sentence is the sea is salt and the second sentence is Melbourne's in Australia so I say okay you go off and find out whether the sea is salt okay

you go off and find out whether Melbourne's in Australia so off you scurry and you find the nearest encyclopedia or dictionary and so on you come back and you say the sea is salt and you come back and say Melbourne's 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 add lots of other sentences in here am I going to change the fact that this argument's 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 M mammals therefore whales are mammals now is there any situation where both those premises are true and that conclusion is 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 um I'm I'm going to do a truth table here which is probably asking for trouble but let's let's do it shall we let's um okay this is um using the notion of possible worlds to explain something um okay I've got if P then q p therefore Q uh no I don't want that hold on sorry I'm changing my mind um 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 Marian's wearing address or something like that it could either be true or it can be false if it's a contingent sentence so this truth table represents every possible world with respect to the combination of truth values here okay so this is the world in which p is true and Q is true okay this is the world in which tell me is good okay this

is the world in which is false and is true that's right and this is the world in which they're both false absolutely that's you're doing you're really doing well here you've been M often undergraduates can't do that um it's because they haven't separated the possible worlds because each of these possible worlds is quite separate from from the other um 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 argument is valid well looking at each structure in turn is this a world in which the premise is true and the conclusions false no Okay so that's okay that 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 no it isn't that's okay is this a world where the premise is true and 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 is a possible world and these are all a 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 shouldn't have added Q at all I've just complicated things by adding Q ignore it let's add not P okay what's the truth value here p is true so in this world not P isal false good sorry 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're really doing

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 and 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 and the conclusion false so is the argument valid yes good really good um a a Circ 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 to kick sand in your face the best way to do it would be to offer you a circular argument but in the M blind you with science hide the premise that is the conclusion in a amongst lots of other premises so you wouldn't see you know the therefore would sound 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 um if you're trying to to um 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 is right you're asking yourself whether my argument is valid you're setting yourself to validity detection mode would you relate that you know that kind of old I don't know what you call it quiz kind of

thing of somebody there's two doors and one's a liar and one's a Toth person yeah and you've got to ask him one question work out which yeah is the is that the same use yeah you you you could use it the thing about that is it it's self-referential because the liar if 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 say that the outcome is still true yeah one

is doesn't work with the other um Prem you know but two different answers still give you I was just a bit confused by the first bit before when it was like one they sorry but you could use that you could you could use that were you being confused by the fact that I put Q in there do you think or were you being confused by the fact I wrote that out first no no just the first the initial statement that said whales are not mammals and whales Ms whales are not mammals therefore whales are not

mammals yeah that was notams are mams are mammals okay that's still true but yeah if you look at it that that 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 cuz when you look at that P is whales and mammals not P sorry this this is um yeah p is whales and mammals this says it's not the case that whales are mammals and this says whales are mammals so that's the truth table for that argument Y and I drew that and

I then didn't do it because I realized it wasn't circular but um 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 um because the Q isn't a a premise the Q is part of a premise and that's different that's okay so that's not circular um 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 or rather this is a formalization of an argument you've seen todaynow snow thank you exactly so if it's snowing the mail will be late uh it is snowing therefore the mail will be late and if I write out the truth table and you'll just have to take these for um uh oops yes that's right uh okay there's the therefore is this a world in which the premises are all true and the conclusion false no okay so that's all right is this a world where the premises are all true and the conclusion false no

is this one where the premises are all true and the conclusion false no is this this one no okay so that argument's valid but if I change this to a [Applause] q sorry I'll get another pen cuz it's uh uh okay is this a world where the premises are all true and the conclusion false okay is this is this a world where the premises are all true and the conclusion false no is this a world where the premises are all true and 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 only need one counter example 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 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 um I wanted to point out that there are two sorts of logic uh so far we've been looking at formal logic um but I also want to say something about philosophical logic um because that's a bit different but firstly just to say something a bit more about formal logic you've got to distinguish form from content the form of the argument from the content of the argument so this is the form of the argument up here the content is supplied by the interpretation

so you notice that you could 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 actions that produce the greatest happiness of the greatest

number are right that action produced the greatest happiness the greatest number therefore that action was right now can you see that these two arguments completely different subject matter aren't they this is about mortality and and Socrates and that's about um ethics the greatest happiness 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 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 word well they're all English words but leave The Logical words in provide an interpretation for the non-logical words don't worry if you're finding 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 guessing that the same as symbolic yeah symbolic logic because the the form is captured in symbols good okay we've got a few do you want to have a go I have a go all a is B okay hold on surely somebody could invent something better than this don't you think called a crayon what it's called a crayon a crayon yes yes would work wouldn't it all a all a is B all A's are B can I can I change it yeah okay all A's are b s is a s

is a therefore is give the girl a gold star fantastic do you see it all A's are b s is an a therefore s is a b and what about up there let's provide the interpretation for each of these arguments okay so the interpretation says what does a mean what does B mean and what does s mean and we've got two arguments so we need to provide two inter interpretations what is a here uh oh you're doing the if we do the first argument first uh X is a man is what it is actually I'll

I'll put that in because these are predicates is a man is a predicate so you need to have a a placeholder X is a man B is moral X is Mortal yeah and S Socrates well done okay and the interpretation here a is X is it's a bit long winded this one uh 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 the 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 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 of Mind a philosophy of biology a philosophy 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 no actually

I'm sure there is a philosophy of accountancy and actually if there there are I'm sure philosophical issues in there um there is a philosophy of everything because of this okay logic is the methodology of philosophy and it can be applied to any subject at all and that's because logic is topic neutral okay let's move down so what we do in formal logic as 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 um test

mechanically for validity here that's one way of testing mechanically for validity okay now the trouble with that is what happens if I add another premise here so I have an r as well it's just 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 um 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 uh I can find a 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 um 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 um 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 a in an hour or so um to get this um okay that the conditions under which that are that is true that are true that is true are there are two 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 translate it into 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 to see again how it works the invalid one is if P then q q therefore P so 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 sets consisting of the premises plus the negation of the conclusion well that's true just in case not P or Q again um 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 PQ 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 you give magic isn't it well yeah P it is snowing Q the male is late do you see what I mean I I was just doing exactly the same example don't don't worry if you're getting confused here that you don't know the these rules you have no idea why I've um represented the truth conditions of that

like that um and I would have to tell you that and I'd also given that that's actually quite difficult to understand I'd 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 Isn't it nice are you doing it because would you be doing it trying to show in it wasn't the p is that why you using uh are you understanding that as there you said P therefore Q yeah that's not a therefore it's it's an implication not an entailment that's saying if P then Q not P therefore Q um I mean don't worry too much about that the therefore would be said me orig so what I was asking is just would you be using I'm just trying to get an idea use that

kind of diagram is it because you're you be trying to challenge somebody's argument to say well in fact yeah it's not the case if 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 snowing 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 deart for example and I think okay he what he's saying is that um it's possible that all our beliefs about the external world are 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 I would drew 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 in the 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 it might 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 an if it's a philosophical argument but it might be an empirical argument in which case the truth of premises isn't your business um you know we don't go around getting our hands dirty if this stff

has existed for centuries why don't all philosophers submit their own ideas to it they do and then but so so everything you can analyze all the philosophers statements and say it's all true it's all true it's all true no it doesn't work like that because firstly you've got to be able to formalize an argument and there are there are huge problems if if this is the class of all arguments in the world okay all arguments here um you can formalize um oh I don't 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 deontic logic you can formalize that many in modal logic this lot you can't formalize 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 um couple of hundred years years ago Aristotle developed syllogistic logic but it took frager to develop um predicate logic and and that was a huge leap forward modal logic has only been developed well it's still

being developed the logic of probability ditto deontic logic we're still working on it so um you know you're right at The Cutting Edge here um I've given you the the ndy calculus um 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'd know that if I if I made you do some because it's really really difficult to

translate from English into a symbolic language um and there are lot of things left out and it's very frustratingly inaccurate and so there are there are real problems but 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 than you might think there must be cases Prem yeah be p p p 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 10 premises here I could still apply these rules way many of premes no no you you you only need one that's false and that's quite sufficient to show that the uh even if the argument's valid the conclusion may be false yeah so the number of premises that are true is not very relevant it's the if there's at least one that's false here's a valid argument with a false conclusion [Music] um think I wrote it down hang on I've written it here uh if it's Tuesday then Maran isn't lecturing it is Tuesday

therefore marann isn't lecturing okay well that's a valid argument isn't it do you want to hear it again if it's Tuesday then maranne isn't lecturing it is Tuesday therefore maranne 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 um 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 pre 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 um in some ways the servant of Science in other ways of course science is the servant of logic um I mean they they work together but doesn't tell you anything 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 but it's the if the if is if this is true yeah then this is true if this is true then this happens whatever but we don't know it's true because you got shows that you don't know it's true um well let's say I'm a scientist and I say well um if the higs 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 hick boson doesn't exist I've

wasted all that money well you know they may may show me a few other things but it won't tell me about the higs boson so if statements are 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 um therefore I need some onions or something like that um there I haven't got any you're 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 you are talking about different to the logic that you find the computers it's just the same yeah absolutely the same exactly so yeah yeah no all all I mean what you're doing when you're doing the applying those truth tables and the um Tableau rules is is acting like a computer you're you're making like a computer or if you say something like if the world is getting warmer this this this this implies but if there is a blip in a tendency towards new

I age then all the proceedings exactly 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 theory is the correct one do you see all reasoning you cannot do without if statements um and I can tell you under exactly what conditions if statements 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 way a laboratory can tell me um that's a wonderful example You' got because I I believe there's global war because of our activities but some people don't so and they're saying so do you see that now we have we have scope for going into the laboratory or the Arctic or wherever we go to find out but without that bit of reasoning first you wouldn't even know what you were looking for um and 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 is in serious trouble because you know why should I fund him okay moving on because we've only got five minutes left but that's all right because um okay I was going to talk very briefly about philosophical logic um I've 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 Phil philosophy of logic is as you can imagine pretty damn important uh to philosophers because the philosophy of L logic um 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 Central well what is truth go on tell me you've all sat there looking intelligent as we've talked about truth so I assume you understand the word tell me what is truth

something that's correct something that's correct what's correct then I mean you just giving me a synonym there aren't you whoever it was okay so opposite of false what in this case opposite of false okay what's false then there's no one without the others no okay but that doesn't tell me what either are it's true you can't have truth without falsehood you can't have falsehood without truth but what is truth fact a fact fact okay what's a fact hang hang on let's let's what is a fact certain knowledge is it is knowledge a 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 aren't there so so facts are nothing to do with knowledge but does truth have to conform with reality and then Define reality of uh 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 what is a fact something you can prove 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 of 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 you've all been dealing with truth what is it it has to be something that corresponds to uh to something we know then how do we know it it may not be sense experience it no we don't need to know it at all no you 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 and they're two quite separate things what were you going to belief uh no because a belief is usually to

do with knowledge rather than because there might be facts about which we have no belief belie 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 or okay uh but there's still a fact about my middle name that's kind irrefutable you at it it's always irrefutable is to do with proof again isn't it say premis 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 um key theories about truth actually here's another one there's some belief that truth truth is nothing that 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 when you're saying not p and no I'm not I'm saying not not P aren't I cuz if if p is true then then not p is false so if if I'm saying P I'm saying not not P not p is truth demonst

you too can do this eventually is truth demonstrable not always no no definitely not it covers moral what we regard as moral judgments as opposed to factual uh well I think there are facts about values so so I don't think there's any opposition between fact and value um so I think there are moral truths and that what make a moral truth is that there are moral facts you can't proove truth no you think of pro proof again think proof is to do with knowledge anyway one one PE some people think that there's no more to

truth than coherence what makes one belief true is that it coheres with your other beliefs other people think well 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 won't it but which is true so coherence can't be the Right theory reality uh well no because truth truth seems to be a property of sentences and beliefs doesn't it yes reality doesn't 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 there sentences Express beliefs okay if I believe that that your what's your name de dear is wearing red I just expressed that belief in saying dear Dre is wearing red if there were no beliefs there'd be no sentences if there were neither beliefs nor sentences there would be no truth but there'd still be reality isn't that just semantics means truth or it means truth conditions yeah yeah that truth is something that exists despite you know

no matter that's because you're thinking of what makes things true um but of course truth is still the property of the sentence that you've uttered I mean what's true is the sentence the reality is what makes it true this is this is really difficult stuff here um how just talking about semantics and syntax at the moment if we look at one of the truth trees again um 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 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 we've got we've got TR is either redundant or coherence with other beliefs oh okay another one correspondence um correspondence so you've actually we've already looked at that truth is um 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 that's AJ um oh goodness it's lots of people yeah not AJ would certainly be one of them I think um so what is truth answer I don't know uh 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 entailment a minute ago um and you weren't very happy with it

here's another two um well it would be if I can find them um we're running over our time if anyone wants to go they're most welcome um no I'm not going to be able to find it if I say um the grass is green therefore 2 + 2 equals 4 that's a valid argument because there's no possible situation in which that conclusion is false so how could there be a possible situation in 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 magicians would like to know is why is our definition of 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 higs BOS on on our logic so so our logic isn't totally wrong how do we deal with it okay we're going to stop right there you know nothing about our identity but that's all right I'm sure we can talk about

that some other time