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hello YouTube this video is about conditionals if a then B if you stay up too late then you will be tired in the morning if the moon is edible then the moon is made of cheese and so on what do these statements mean and how do they work well before addressing these questions I need to review briefly some very basic logic ok standard propositional logic I assume you have some familiarity with it here are the connectives that these are the truth tables where T represents true and F represents false so if a is true not a is false if a is false not a is true if a is true B is false a and B is false and so on right arrow is the material conditional or material implication and it's generally interpreted as representing the English construction if-then so a arrow B is usually pronounced if a then B as you can see a arrow B is true just in case a is false or B is true the only time it's false is when a is true and B is false right so a arrow B is essentially a disjunction it means not a or B we say that this connective like all the other connectives here is truth functional all that matters to the truth of a arrow B is the truth value of a and the truth value of B nothing else is relevant right that's a formal logical connective now let's consider the English if-then construction so here are some English conditional statements if the weather holds then we'll go for a walk after dinner if we don't get to the station in five minutes we'll miss the train if a being than which none greater can be conceived exist in the mind than it exists in reality too and so on you can think of your own examples now note that conditionals do not have to explicitly use the words if-then so for example the following are all obviously equivalent to one two one okay they say the same thing as number one here so there are many ways of expressing conditional statements in English that's not really important it's just you know something worth bearing in mind right then in the literature its standard to distinguish indicated and subjunctive conditionals so consider these pairs if Frank Zappa did not write Joe Girardi someone else did if Frank Zappa had not written Joe's Garage someone else would have if David Cameron did not win the election and impostor of him did if David Cameron had not won the election an impostor of him would have well first ones here seem obviously true and the second ones seem obviously false the first are called indicated conditionals and the second are subjunctive or counterfactual conditionals so 4a and 5a indicated 4b and 5b are subjunctive or counterfactual counterfactual because as you can see the the antecedent is what we say counter to fact now there is some debate about whether conditionals should be divided in this way but this is the standard view okay well that's some the preliminary stuff sorted out now the consensus for the last century or so has been that indicated conditionals just our material conditionals so the English indicated if a then B is true just in case a aro B is true arrow is a simple connective so this is a neat little analysis an immediate benefit beyond its simplicity is that we already understand the properties of the material conditional very well it's been pretty much exhaustively studied by auditions but does this analysis hold is this true or is there more tooth if a then B than this simple logical connective so this is what we're questioning in this video is the English can in the of conditional a material conditional when I assert if a then B am I really asserting nothing more than that a is false or B is true I'll call the positive answer to these questions the material analysis of the conditional right now note we are ignoring subjunctive conditionals because the material Isis obviously fails for them so if you consider if Frank Zappa had not written Joe's garage than someone else would have well obviously the antecedent is false but the conditional as a whole is clearly false too so the material analysis fails for subjunctives all we're questioning here are indicated conditionals right then well the paradoxes of material implication are an immediate problem for the material analysis the paradoxes arise from the fact that a arrow B is really a disjunction as I said all that's required for a arrow B to be true is that it is it is a false a or a true B false antecedent or a true consequent now follows from this that all of these conditionals are true if the sky is blue then Frank zapper is a musician if I am dead then I am recording the new YouTube video if the moon is made of cheese then two plus two equals five all of these are true on the material analysis now it strikes people is extremely counterintuitive to say that these are true it seems to many of us that true conditionals should have some sort of relevant connection between the antecedent and the consequent and that this relevant connection is lacking in in these essentially the problem can be stated this way materially anything follows from a false statement and a true statement follows from anything but this is completely at odds with our intuitions about implication let me just emphasize an important point here we're not complaining about arrow as a logical connective the material conditional is what it is and it has a useful function in logic the question is merely does it give the right analysis of the use of if/then in English as a natural language now these paradoxes are certainly a problem can this problem be resolved well first of all perhaps to defuse the problem slightly consider the case of false consequence so if the moon is made of cheese then two plus two equals five the thing is although these sorts of statements seem problematic some statements like this are actually perfectly intuitive and perfectly acceptable suppose John has a test coming up I think he's rather stupid and I know he hasn't bothered doing any revision so I say if John passes the test I'm the Pope another example would be if John passes the test I'm a monkey's uncle we understand these to be expressions of the falsity of the antecedent so John is not going to pass the test that's what I'm saying we're saying that if the antecedent is the case then anything might as well be the case but this of course is exactly how the material conditional works and of course we might object that this kind of use of conditionals is a very special case they're being used and non-standard ly hence it has no relevance for an account of standard conditionals in any case even if this point does defuse some of the paradoxes we're still left with the difficult cases of true consequence like number one and two here so we we still need to address these paradoxes of material implication paradoxes of the material conditional right then let's have a look at some attempt to answer these problems Paul Grice was a defender of the material analysis he held that if a then B and a arrow B have the same truth conditions so one is true just in case the other is he attempted to explain away the paradoxes using the theory of conversational implicature now the basic idea here is that statements can suggest or imply things without literally asserting them suppose I say I was in my friend's house talking to him about modal really last night you probably imagine two people in a company living room having a cultured conversation but you're wrong my friend is actually my dog and I was in the garden in his dog house with him and I was talking to him he wasn't saying anything back but I was talking to him about modal realism now the point is that what I've said is perfectly true but it's misleading the way I phrased it clearly implies a conversation between two humans it's misleading because the friend the word friend typically implies a human the work the verb talking to typically implies a two-way conversation even so I didn't literally lie to you and say what I said was was truthful now many jokes draw on this for example three men walk into a bar ouch okay but three men walk into a bar carries certain implications and then the punchline violates it I spent all morning trying to get the neighbor's cat down from the tree I couldn't get it because I'm a horrible shot I have the words of the world's largest collection of seashells I keep on all the beaches of the world again the initial statement sets up it conveys certain implications and then the punchline violates them but in such a way that the initial statement can be perfectly true well suppose we're talking about a lecturer Jack I say is Jack a good lecturer and you respond well he's got good fashion sense now this statement literally means that he's got good fashion sense all you've asserted there is that he's got good fashion sense but you've also implied or suggested that he's not a good lecturer by responding with a compliment about his fashion sense you're implying or suggesting that he's actually not a very good lecturer so this is conversational implicature as a difference between what a statement literally asserts and what it implies or suggests as you can see it pops up in all sorts of conversational contexts now one of the consequences of conversational implicature is the statement can be entirely true but it may nevertheless be inappropriate to assert it so when did these implicatures come from well Grice claimed the standard discourse was governed by certain Maxim's or rules which developed in order to make discourse easier and more efficient so here are some of the Maxim's he identified give as much information as required do not give more information than required be truthful so don't assert what you believe to be false be relevant avoid ambiguity be concise now these Maxim's explain why it's reasonable to interpret speakers as communicating more than what they explicitly say we assume in standard discourse that people are observing these Maxim's and we use this assumption to draw conclusions from what they say so for example suppose you ask where Jack is and I say Jack is at the cinema you infer from the maxim of truthfulness I believe that Jack is at the cinema or suppose I say he's either at the cinema or he stayed at home even further I believe one of these to be the case but that I'm not sure which I didn't explicitly say that I'm not sure but suppose I confidently believe he went to the cinema I saw him go in there well if I were to respond he's either at the cinema or he stayed at home then yet what I've said is true but it's very unhelpful is unhelpful because it violates the maxim of conciseness and it violates the maxim to give as much information as required by introducing a disjunction then I've made my claim unnecessarily weak i've unnecessarily weakened weakened it and made it less helpful so if i respond with a disjunction then it's it's reasonable for you to infer that i'm unsure whether he went to cinema or stayed at home now conversational implicatures can be cancelled and disjunctions provider a good example of this suppose a friend as to to take something upstairs for them you decide to play a game with them and hide it they demand a clue when you say a case either in the main bedroom or your bathroom now in this case you know exactly where it is but because you're playing a certain kind of game your statement does not imply uncertainty so the notion of of conversational implicature is very useful and it can account for many kinds of discourse in this kind of discourse certain kinds of implications that are cancelled it should be fairly clear how this can explain conditionals according to grace the material analysis halts so if a then B is true just in case a is false or B is true so all of the following a true however instant discourse it would be inappropriate to assert them the trouble with saying something like if the sky is blue then Frank Zappa was a musician is that it offends against various Maxim's so by adding if the sky is blue i unnecessarily weaken my claim I make it less concise and I add something completely irrelevant and so on its but that's why it's a silly thing to say and that's why these conditionals seem false to us they're not really false but they are inappropriate to assert and Grace has given us a reason why now bright is basic claim that there are can conversational implicatures that conditionals may be true but inappropriate to assert I think that's pretty much unassailable but there are some problems with his analysis these criticisms come from Frank Jackson who we'll talk about more later firstly there is a significant dissing allergy between true but inappropriate conditionals and other apparently true but inappropriate statements when I say if the sky is blue then Frank Zappa was a musician what I've said does not strike us as being true but on the material analysis this is equivalent to the sky is not blue or Frank Zappa is a musician now this statement strikes most people as inappropriate but it it doesn't strike them as being untrue very few people would have any trouble accepting that this disjunction is true the question is if if then is true functional why does it seem not to be why are we so inclined to confuse truth and assert ability with the conditional but not with the or connective Grice's Maxim's can't account for this and this suggests that there's more to the meaning of if a then B than is given in not a or B that is there's more to the meaning of if a then B than a arrow B to drive this point home recall the conditional if I am dead than I am recording a new YouTube video this is one where we really bought calling it through grace would hold that it's inappropriate to say it because I could say more by inserting simply I am recording a new YouTube video but is it really plausible to suppose that that's all that's wrong with it again compare I am NOT dead or I am recording in a YouTube video where we're using an inclusive or this is silly and inappropriate but it's perfectly true most most of us would accept that this is that this is perfectly true we can see in this case truble inappropriate but with the conditional we don't see that and I don't think grace can explain that so crisis story is at best incomplete because it doesn't account for the difference the very big difference between this conditional and viscous Junction right second problem contra position not be aro not a is the contrapositive of a arrow be logically a arrow B and it's contrapositive say the same thing they are strictly equivalent they're tautologies but if a then B and if not B then not a well but they don't seem to be equivalent they don't seem to say the same thing consider this example from Jonathan Bennett even if the Bible is defiant divinely-inspired it is not literally true Bennet says that he accepts this however he doesn't accept the contrapositive of this but if the Bible is literally true then it is not divinely inspired so in this case we have a case where arguably if a then B is is perfectly suitable but it's contrapositive is not but if we're dealing with the material conditional these two are exactly equivalent so again we we have a problem here why how do we account for this right third problem suppose I'm sure that not a is the case in this case Grice's Maxim's have it that it is inappropriate to assert if a then B in standard discourse and this because I would say more by asserting just not a remember on the material analysis if a then B is just the distinction disjunction not a or B and you should not assert not a or B if you're sure of either disjunct I'll consider another example from Bennett I'm sure that Polynesians didn't originally come from India but it may be entirely appropriate for me to assert if the Polynesians did come from India there have been inhabitants of India whose language was not indo-european this seems perfectly acceptable but grace has to condemn it there's a parallel problem with the with the consequent so suppose I am sure that be again Grice's Maxim's have it that it's inappropriate to assert if a then B again I would say more by asserting just B but imagine we're dealing with a murder case dylan and bob are accused of murdering a man during a burglary now I'm sure that Dylan is guilty however his defense puts forward a convincing case that the fatal blow was struck by Bob now in this case it may be entirely reasonable for me to assert even if Dylan didn't strike the fatal blow he's still guilty of murder the point of this kind of assertion is that the antecedent is irrelevant to the main question the main question being is he guilty of murder now it doesn't matter whether not he struck the fatal blow you don't have to strike the fatal blow to be guilty of murder so I'm sure Dillon is guilty of murder but I can still assert even if Dillon didn't strike the fatal blow he's still guilty of murder Grice's Maxim's condemned it so there's are some problems now despite Jackson's arguments against gryce's theory Jackson herself was a defender of the material analysis now we know that there's more to the meaning of if a then B and simply a arrow B both Grace and Jackson hold that if a then B and a arrow B have the same truth conditions and that in asserting if a then B you assert nothing more than a arrow B of course we do not just assert we also implicate now Grice as we saw argued that the implicit is involved in if they then be arose from general Maxim's of discourse that's conversational implicature we've seen the problems of this theory Jackson held that the implications of a different source Jackson defends conventional implicature what is conventional implicature or consider these two statements Bertrand is a philosopher and he is friendly Bertrand is a philosopher but he is friendly very arguably these statements have the same truth conditions they're both true just as long as each conjunct is true nothing else matters but no there's a significant difference in their meaning the first one simply attributes two properties to Bertrand so does the second but the second also suggests due to its use of the word but that it's unusual for somebody to be both the philosopher and to be friendly the second implies a contrast between the conjuncts whereas the first does not imply any contrast now consider this one not even Peter found that film scary again arguably this is true just in case Peter didn't find the film scary all you assert in asserting this statement is that Peter didn't find the film scary but it implicates more than this due to the word even it implicates that Peter is easily scared imagine that Peter did not find the film scary but also the Peter is not easily scared then not even Peter found the film scary is certainly misleading but it doesn't seem to be false and this suggests that Peter is easily scared is implicated not outright asserted by the statement now conversational implicature was as we saw about general Maxim's general rules of discourse conventional implicature deals with the meanings of individual words we obviously can't explain the implicature that Peter is easily scared by appealing to general Maxim's it arises due to the meaning of the individual word even the same with the contrast in Bertrand is a philosopher but he is friendly that doesn't arise because of general Maxim's general rules it arises because of the meaning of the word but an important differences between conversational and conventional implicature these are perhaps not so relevant in this video but I do want to note two primary differences conversational implicature is cancelable but not detachable conventional implicature is detachable but not cancelable consider again Jack the lecturer I say is Jack a good lecturer you respond while he's got good fashion sense this conversationally implies that Jack is not a good lecturer but then you add not to suggest that he isn't a good lecturer he's excellent what you've done here is cancel the implication generally you can't do this with conventional implicature if I say Bertrand is a philosopher but he is friendly he knows no good to say not to imply that most philosophers aren't friendly because by using the word but Ivan I've implied it whether I like it or not now on the other hand with conventional implicature some words can say the same thing without the implication so Bertrand is a philosopher and he is friendly says the same thing but does not implicate the contrast as Bertrand is a philosopher but he is friendly so conventional implicatures are detachable you see that if I ask Jack a good lecturer any way of responding that his fashion sense is good will convey the implication that he's not that he's not a good lecturer there's no way to say the same thing and not to convey the implication so those are two differences we have conversational implicature which you can you can cancel it but you can't detach it whereas conventional implicature you can detach it you can say the same thing without the implication but you can't cancel it that's the general view as I said maybe not so important here but it's worth being aware of those differences so according to Jackson when I say if a then B all I assert is a aro B that is not a or B however I also implicate due to the particular meaning of the if-then construction that the consequent is robust with respects the antecedent what does that mean what does robust mean well the concept of robustness was introduced by Jackson himself take two statements a and B we say that B is robust with respect to a just-in-case B has a high probability on the supposition that a is true that is there is a high probability of B given a in other words if you came to believe that a you would continue to believe that B Jackson gives this example suppose I'm reading with paper and there's just been an election and I knew who won in that it's between say 10 20 candidates who are all equally likely you ask me who won I read that Hyperion won in the election but I say either Hyperion or hydrogen won the election now all of us would agree that what I've said is perfectly true but misleading misleading because it implies that I'm uncertain when I'm not Jackson would say that the trouble with saying this disjunction is that the disjunction is not robust with respect to the negation of its first disjunct in other words on the supposition that the first disjunct is false I would stop believing this disjunction since the only reason I believed it in the first place was my belief that the first disjunct was true so if I came to believe that the first disk jump is false I'd stop in the disjunction hence it's not robust with respect to the negation of its first disjunct and that explains why I shouldn't assert this disjunction now consider us like a different case I have very bad eyesight and when reading the paper I can only make out the first letter of the name so I CH and then a blur but I know that the only two candidates whose names begin with H are Hyperion and hydrogen well in this case when I assert either Hyperion or hydrogen won the election what I say is fine because the disjunction is robust with respects the negation of either the first or the second disjunct not both of course the point is if I came to know that Hyperion is not the winner I will still believe the disjunction is true and similarly for hydrogen my confidence in this in the disjunction will be unshaken since I if I discover that one disjunct is false I'll believe the other it's worth noting here but Jackson is not suggesting that conventional implicature can entirely replace conversational implicature well consider again the election but suppose that Hyperion and hydrogen are the only serious candidates it's like an American presidential election the only serious candidates in the last election were Obama and Romney nobody expected anyone else to win so I read that Hyperion has won and when you ask me who's won I say either Hyperion or hydrogen won the election now note that this disjunction is robust with respect to the negation of its first disjunct if I came to believe that the newspaper reported incorrectly and Hyperion did not win the election I would believe that hydrogen one being the only other serious candidate and hence I would still accept the disjunction and what I say of course is still unhelpful it's unhelpful this time for greicy and reasons so conversational indicator still has a role to play Jackson just denies that this royal Canon fully expert Kait conditionals he denies that some that's all that's going on here right so back to conditionals I uh I say if a then B all I assert is a arrow B but the if-then construction unlike the arrow carries a conventional implicature that the consequence is robust with respect to the antecedent when I assert if a then B I imply that I'm confident that if a is true B will remain true to so that is I I Accord be a high probability on the supposition that a is true the important point for Jackson is the use of conditionals in modus ponens arguments of the form if they then be a therefore B modus ponens is always a valid form but validity is a different question than our ability to actually use the argument in practice consider the argument a therefore a well that form is perfectly valid it is absolutely valid but it's completely useless right we could what can you do with that in practice nothing now the conditional if a then B is completely useless for the purposes of modus ponens if I accept it merely because I reject a or merely because I accept B if I reject a then obviously I will reject the second premise here so I will consider the argument on the sound if I accept B well then I already accept the conclusion the paradoxes of material implication if the moon is made of cheese and two plus two it was five of Frank Zappa if the skies blue that Frank Zappa R is a musician these are true but useless if I came to believe that the moon is made of cheese I would reject this conditional because I hold that two plus two equals five is false and coming to believe that the moon is made of cheese wouldn't change that if I came to believe that the moon is made of cheese I would still believe that two plus two equals five is false this conditional the consequence of this conditional is not robust with respect to the antecedent on the other hand if I if I came to believe that the sky is blue well I already do believe that the sky is blue but that has no bearing on the probability of zappers being a musician I accept this merely because I accept the consequent I accept it merely because I accept that Zappa is a musician neither of these conditionals are robust hence they have no use in argument the only reason to accept either of these conditionals is that I are either reject a or I accept B and in that case they are are useless for the purposes of modus ponens now Jackson's theory does seem to be an improvement on gryce's but it does have some problems of its own so this first one isn't a serious objection but it is quite interesting consider again the cases of conditionals with false antecedents so if the moon is made of cheese and two plus two plus five well I noted earlier in the video that the defender of the material analysis might have an easy answer to this because we often use conditionals like this to express disbelief in the antecedent if John has a test coming up I think John is stupid so I say if John patters the test I'm the Pope now the trouble is that Jackson can't allow conditionals like this to be assertable because I mean the Pope is not robust with respect to John passes the test should John and pass the test I won't even slightly raise the probability that I'm the Pope I would just reject that conditional so Jackson's defense of the material analysis is actually hampered not helped by our use of such conditionals his responses is quite simple he points out as we did earlier that the use of silly conditionals to express this belief in the antecedent is non-standard and his theory is of course a theory of standard conditionals so in other words given the standard use of conditioner was like if John passes a test and I'm the Pope if that was used standardly well then no it's not asserted well according to Jackson the reason why we sometimes asserted is that we're using it non-standard ly and um um yeah that's that's a reasonable point I'm sure none of us would really disagree with that okay more serious problem we we can ask how do we determine whether some part of a word meaning is a matter of conventional implicature rather than assertion so that is how do we determine that a but B merely implies but does not assert a contrast between a and B in fact Jackson himself acknowledges that all we have to go on when making judgments about convention at Decatur are our intuitive responses so that is when Jackson says that a and B and a but B have the same truth conditions and that the rats are only implies but does not assert a contrast his justification for this view is simply that it seems intuitively plausible but we can ask is that is that really the case suppose Bertrand is a friendly philosopher and that most philosophers are friendly I say berkland is a philosopher but he is friendly now the question is is it more plausible to say that that's misleading and proven that it's misleading and false well to be fair a natural response to this statement would probably be something like yes that's right I hope though I wouldn't agree that most philosophers aren't friendly so perhaps there is reason to think that this is an example of conventional implicature because if somebody were to assert this if somebody was to say Bertrand is a philosopher but he is friendly although I disagree although I wouldn't agree that most philosophers aren't friendly it would be odd to say that this statement is false it would it's more reasonable it seems to say that it's misleading so in that case our intuitions seem reasonable enough but that does seem to me to be a problem with putting so much stock in our intuitions given that our intuitions would rule conditionals such as if I'm dead then I'm recording a new youtube video is simply false it doesn't seem even remotely plausible this is true in which case there's a difficulty with supposing that it's inappropriateness is a matter of implication rather than assertion so as long as we hold the judgments about whether meaning is a matter of implicate you are than assertion are justified by appeal to intuition there is a problem with saying that this conditional is true but misleading right then probably the most serious problem the jacksons theory is that there's a significant difference between the usual sources of conventional implicature and indicated conditionals and the problem is that all other sources can be deleted without altering what is asserted though this is really a consequence of the fact that common conventional implicatures are detachable so if I say Bertrand is a philosopher but he is friendly I can assert the same thing without the implication by saying Bertrand is a philosopher and he is friendly or I can just delete the conjunction entirely Bertrand is a philosopher Bertrand is friendly if indeed if it's true that the contrast between philosophers and friendliness is only implied and not asserted by the word but then I can simply remove the word but and I will say the same thing without the implication of a contrast as we can see in these two statements here and this is the case for all such conjunctions so I can delete all of these versions have lots of fun nevertheless he is friendly however he is friendly yet he is friendly even so he is friendly all of these on the theory of conventional implicature all of these conventionally imply a contrast between being a philosopher and being friendly but note that I can just I can just delete all of them and then I'll say the same thing without the implication or consider for another example not even Peter found the film scary now again we can delete the even we can say Peter did not find the film scary or it is not the case that Peter family felt scary these say the same thing without implying that Peter is easily scared Julia's sleep is still sleeping this implies that she was sleeping earlier we can delete the still and have Julia sleeping same assertion without the implication John managed to pass the test but possibly implies that we didn't expect him to pass the test but we can delete the managed and just have John passed the test same assertion without the implication shut the bloody door that implies that the speaker is frustrated about the door being open we could say the same thing without the implication by saying shut the door so those are some possible though certainly not uncontroversial sources of conventional implicature we can disagree whether these really are sources of conventional implicature you know but these are sort of some standard examples and in each case we can delete the word and remove the implication without changing the assertion again conventional indicators are detachable and we can simply remove the words that convey them the trouble is that we simply can't do this with if-then the conditional if Bertrand is a philosopher then he is friendly and the two statements Bertrand is a philosopher Bertrand is friendly they say something completely different if then is not deletable and that's a very significant structural difference between the usual sources of conventional implicature and between the conditional now Jackson himself acknowledges this problem his response is that actually there are other standard sources of conventional implicature that are not deletable the only example he gives is unless so it gives the example of unless a unless B and it is true you you can't delete unless if you had a unless B that says something completely different to a and B or just you know stating a and then stating be the trouble is that this is a fairly lame response since a unless B is generally held to mean the same thing as if not B then a so a unless B is itself a conditional so it's no surprise that we can't delete the unless you know that's that's a poor response we'd have to find a standard source of conventional implicature that does not seem to be a conditional for this kind of response to work right those are some problems with with Jackson's theory then now there are some problems that both Jackson and grace face the most serious concern is embedded conditionals that is conditionals that our constituents of more complex statements Stephen Reed gives an example of a debate about Churchill I say Churchill ordered the bombing of Dresden and you denying now I'm sure we all agree that the conditional if I am right the new Iran is true and assertable and I'm sure we all agree that the conditional if I am right then you're right even if that's true which it may be on the material analysis it's certainly not assertable of course it would be odd to say that the earth but it's true but we've seen how both Grise and jackson deal with that but now consider the following either if I am right the newer right or if you are right then I am right this is this is a proposition of the form if a then B or if B then a now this disjunction is clearly false there's no way that either disjunct is true you explicitly denied why I said so neither conditional can hold but think about it materially if I'm right then the second disjunct is true since it has a true consequent and if you're right then the first disjunct is true since it has a true consequence hence the disjunction as a whole is true one or the other of these must be true this may be a problem on the other hand I wonder if this just begs the question against the material after all if you're okay with accepting that if I am right the newer right might be true but not assertable I'm not sure why you shouldn't say that the disjunction that this disjunction here is also true but not as suitable perhaps on missing Reid's point Reid himself says that it does no good to argue that one of the conditionals is true but not assertable because neither conditional was asserted only the disjunction was asserted I'm not sure what difference this makes to be honest all you need to establish the truth of the disjunction is that one of the conditionals is true and a defender of the material analysis will obviously accept this much a more problematic example comes from gibbard imagine you see someone holding a cup a few inches off the floor afterwards you say if the cup broke if it was dropped then it was fragile formally and materially this conditional is written the cup was dropped arrow the cut broke arrow the cup was fragile you might object then I'm swapping the statements around here but I'm not think about it the cup broke if it was dropped means the same as if the cup was dropped then the cup break so there's nothing there's no funny business going on here and that now suppose that the cup was not dropped did not break and is not fragile now note we have a in that case we have a false antecedent here and a false consequent here making the conditional as a whole this conditional as a whole true but then we have a true antecedent here and a false consequent here making this conditional as a whole making the whole conditional false but the original statement if the cup broke if it was dropped then it was fragile that does not seem to be false at all that seems to be true that doesn't seem to be anything wrong with that now note that neither Grice nor Jackson can account for this their approach try to certain try to show why we find it difficult to accept conditionals which on the material analysis are true but in this case we have a conditional which we all accept and which seems to be true but which on the material analysis is false so this is a big problem as was the problem of what we can derive given the material conditional how the material conditional actually works in arguments here are two examples from Graham priest in standard propositional logic the following arguments hold this symbol here this turnstile that just means entails so you know not if a then B entails a that's how you read that now the second argument here that's just part of the definition of the material conditional the material conditional is false only if the antecedent is true and the consequent false so from a false conditional you can derive that the antecedent is true the trouble is that if we hold up the English if-then is equivalent to arrow then the following two arguments will be valid if you close switch X and closed switch Y the light will go on therefore it is the case either but if you close switch X the light will go on all of if you closed switch Y the light will go on imagine that the two switches are in a series so both must be closed for the light to go on second argument it is not the case that if there is a good god the prayers of evil people will be answered therefore there is a good God these two arguments are not simply counterintuitive like the earlier paradoxes they're straightforwardly invalid and this and this suggests that the English conditional is not Material again the second argument form not if a then B therefore a or it is not the case that if there is a good god the prayers of a group it will be answered therefore there's a good god that's that argument form is part of the definition of the material condition or even if you do accept some non classical logic in which the the first argument fails the second form must hold or was simply not dealing with the material conditional at all and even if you believe in God I'm sure you'll agree that's a pretty poor argument for God well anyway that's something to think about there so that's an introduction to the material truth functional analysis of indicated conditionals as you can see it's surprising just how much debate can be generated by a construction as simple as if a then B and believe me we have only scratched the surface anyway I hope you found it interesting thanks very much for watching goodbye