Causal Arguments

happy Monday everybody how's it going good weekends yeah it's beautiful out right daffodils are coming up crocuses are coming up magnolias are blooming I can't I can't help but feel good when all the plants are waking up unless you have allergies which I don't at least not not those not pollen allergies so sorry to the rest of you guys but I'm feeling good today we're gonna be talking about causal arguments we mentioned them at our last meeting we are talking about fallacies of weak induction I also mentioned that it's not entirely clear that causal arguments are inductive arguments they're definitely likely arguments let's start with that they're definitely likely arguments or they're the sorts of inferences inferences - some kind of causal conclusion are certainly likely at best they're never going to be deductive as to whether they're inductive or not hmm we'll start exploring that not today but on Wednesday today we're going to kind of act as if these are inductive inferences we're gonna look at causal arguments from a direction where it looks plausible to count them amongst all of the other inductive inference is where the main feature of all of these sorts of arguments is there's some sort of pattern recognition going on right we recognize some pattern that apparently is robust and reliable and we say I've observed it in these conditions so I assume it's going to go on beyond the conditions that I've observed it in and something kind of like that is going on with causal arguments well enough talking around it let's let's get right to it right so causal arguments take a look at these two statements I slapped John and he got angry versus John got angry because I slapped him what's the difference between these yeah Shawn the second one yeah articulates it's not just that they both happened right cuz the and statement I slapped John and he got angry just says that they both happen the second one says that there's some sort of relationship between the two namely if we had to describe that relationship what would we call it big hint what kind of arguments are we talking about today causal Eggman's yeah there's some sort of causal connection between these two and the big question that we've got today is all right so what makes a causal claim rationally warranted this does seem pretty plausible if I slap John and then he gets angry immediately after and I was to say something like seems like John got angry because I slapped him most of us would kind of be like seems like pretty good yeah alright but there are other sorts of instances like this where like one thing happens and then another happens and we say oh the first thing caused the second one more like about that so how are we gonna tell the goodies from the baddies right how are we gonna tell the reasonable sorts of inferences the ones that are well supported causal inferences from the ones that aren't so well supported and in order to get into this we're going to revisit our old friend John Stuart Mill we mentioned John Stuart Mill when we were talking about moral arguments does anybody remember that he was one of our the founding fathers of one of the theories that we looked at utilitarian moral theories right so yeah one of one of the two there that's John Stuart Mill he's a handsome fellow I would say he's got a nice bowtie and John Stuart Mill in addition to being a brilliant moral philosopher also brilliant epistemologists and worked out a fairly decent approach to trying to determine when it is that some sort of causal connection is the sort of thing that's warranted is the sort of thing that we could say like yeah there probably is a causal connection there versus what are the instances where it seems like a spurious claim where it seems like it's not very well supported so this is a likely inference I'll stress that again we're never going to have any absolute certainty about causation if any of you guys have taken or are taking modern philosophy this semester you'll know that like causation itself is philosophically really sticky sort of an issue David Hume in particular gets at this is like a serious problem of induction that gets to the root of causation and questions whether or not it can ever be adequately put forward but let's not get into that quagmire let's just say that like that instance that like that example that we looked at in the very first slide I slapped John and then he got angry and everyone goes like yeah that's pretty reasonable - yeah let's let's assume that is something that is reasonable that there is such a thing is a good causal inference or a well justified or a well supported or a reasonable causal inference so again we're back to this question how can we do this well what is it that makes causal inferences stronger more likely to be reliable and we go to maybe advanced a little too quick what are known as Mills methods Mills methods plural Mills methods there are several different methods that mill articulates and says like these are all methods that we can apply to determine whether or not a causal inference seems to be a justified one the first of these methods that we're going to look at is what's known as the method of agreement or Mills method of agreement and mills method of agreement says literally this this is a quote from Mill himself if two or more instances of the phenomenon under investigation have only one circumstance in common the circumstance in which alone all of the instances agree is the cause or effect of the given phenomenon that's that's crystal clear right couldn't be clearer about in English in other words that was English Mill was English like from England English in other words let's put this in contemporary English we find the cases where the effect is happening we look at as many of these as we can or the proposed effect we look for as many of these as we can and if there's only one other feature of the phenomenon in common in all of those cases then it seems like there's good reason or some reason at least this counts as a reason to suspect that these two things are causally linked and notice what Mill says but a the circumstance in which alone all the instances agree is the cause or effect wait which is it is the cause or the effect and this is one of the big weaknesses of Mills method we're not actually going to overcome this today it's not going to be until Wednesday that we start figuring out what the directionality of a causal connection is going to be all we're really going to get today is that there does seem to be some sort of causal connection I'm not sure which is going to be the cause and which is going to be the effect some of the examples that we're going to look at today are ones where it's going to seem obvious others are gonna be ones where it may very well be a little bit ambiguous which is the cause and which is the effect but according to Mills methods we may suspect that there's some sort of causal connection between the two so we gave it an Milly's we also gave it in atom ease who likes pictures I like pictures let's do it with pictures this is what Mill is talking about something like this here's one circumstance where I have a B C and D and also a is happening and I have another instance where H C G and K and also E is happening and notice what we have here in both of the instances in which he occurs C is also occurring and if I have a lot of these instances right if my sample size is large if I'm looking at a lot of cases where he happens and in all of those cases the only other thing that they have in common besides E is C there's good reason to suspect that C and E are causally related make sense this is called the method of agreement why do we call it the method of agreement well because there's something in agreement right when every happens what is the other thing that like is in agreement with E what is the other thing that seems to be coincidental with E and C seems to be an agreement with E they always kind of seem to match up whenever a is present C is also present seems to also be the case that at least in the cases that I'm looking at here whenever C is present he is present so this is good reason to suspect causal connection not just that C happens and it happens but whenever C happens ie happens or whenever he happens C happens make sense and keep in mind also that like one of the things that makes this tick is that the only thing that they have in common is this one other feature if have multiple things in common this gets a whole lot more complicated all right let's look at an example here here's an instance where we're trying to figure out hey what's going on with all the tooth decay in this place that we live in maybe we see like inordinately low rates of tooth decay compared to every place else and we're wondering hey what's what's going on with that I'd like to know what's causing the low rates of tooth decay I'd like to know what sorts of things are causally connected to these low rates of tooth decay and notice what's going on here we have four different cities four different places for different towns dullsville bedroom Town Golf Ville and mega city they all have low rates of tooth decay what else seems to come along with all of these instances of low rates of tooth decay is it a dental education product program sometimes dullsville hazard in mega city has it but bedroom town and golf bill don't what about free dental clinics again some of them have it but some of them don't which seems to suggest that maybe dental education programs and free dental clinics aren't causally connected to low rates of tooth decay because we have low rates of tooth decay say for instance here in bedroom town but no dental education program we have low rates of tooth decay here in dullsville but no free dental clinic what about fluoride in the water all four towns have fluoride in the water and all four towns have low rates of tooth decay and if we check out high salaries for dentists we see the same sort of thing going on with dental education programs and free dental clinics sometimes the high salaries for dentists are associated with the low rates of tooth decay sometimes not so according to Mills method of agreement which of these two things are causally connected fluoride and low rates of tooth decay yeah pretty good all right makes sense right method for cream it's the simplest of these in addition to the method of agreement you might you might have anticipated this there's also a method of difference and the method of difference isn't really that different than the method of agreement but see if you can pick out what the distinction between these two methods is so here's Mill talking about it again we'll start with his quote if an instance in which the phenomena under in bed to Gatien occurs and an instance in which it does not occur have every circumstance in common save one that one occurring only in the former the circumstance in which alone the two instances differ is the effect or the cause or an indispensable part of the cause of the phenomenon again crystal clear but just in case we don't speak Milly's let's put it in the atom language in other words if there are two cases in which one of those two cases has the effect and the other one doesn't and the only difference between the cases where the effect is present and the effect is absent is the absence of one other thing then that thing is probably the cause of the effect and if language is still tripping us up here let's do it with pictures so in this instance he is present in this instance he is absent and we'll notice how these two if instances in addition or aside from the presence and absence of E they look to be pretty much the same this one has a this one has a this one has B this one has B this one has D this one as D but E is present in this case and absent in the other aa but I'll also notice C is present in this case and it's absent in the second case so what does this tell us C is the cause of E or the effect they seem to be somehow causally related we're not exactly sure what the direction is we just know that the presence and absence of C seems to always be coming along with the presence and absence of the e that whenever I take away C I take away e whenever I have C I get me and it's this notice what's going on that like everything is the same in these cases except the absence of something and this is what makes that method of difference different than the method of agreement and the method of agreement we are looking for only one thing in common in all of the cases where the proposed effect or like the phenomenon in question is present in this one we're looking at cases where there's a difference between the presence and absence of the effect or cause or the phenomenon in question and we're looking for one additional difference if we can narrow it down to exactly one difference besides the presence or absence of the thing that we're looking at then there's a really good chance that these two things are causally related and again I'm not really sure about the directionality just yet I just know there's some causal connection and again the more cases that I look at in the more diverse those cases are the stronger this argument is going to be yeah William if he was present then C would have to be present right yeah and when e is present C is present and when e is absent C is absent so yeah I guess I guess what what seems to be unclear here in this picture at least is it the absence of C that makes the absence of a happen and the presence of C that makes the presence of E happen or is it the absence and presence of E that makes the absence and presence and C happen and I'm not really sure I kind of maybe bias the picture just a little bit with this directional arrow and the timing of these could be a really big deal right if C happens first and then e happens and we never see doesn't happen I never get e yeah now I've start to I'm starting to get some sense that like if I can establish there's some causal connection between E and C and C always happens before E this is a little quirk of causation that it seems to only go one way in time right you can't cause something backwards in time so we think so far and this may be this may be a little quirk of how our minds work that we only experience time in one direction as well right so yeah we don't necessarily have the directionality just yet but the timing could be a big factor in this all right so that's the method of difference let's look at this at work in one of these tables again in this case we're looking to figure out whether or not alone gets approved Victor crystal tad and Qin are all applying for a loan Victor does not get the loan crystal does get the loan tad does chin does not can we figure out something that seems to be coincidental its presence and absence is coincidental with the presence and absence of the approval of the loan college education nope doesn't work out because they've all got it but not all of them get the loan right what about earning over $80,000 well they've all got it but they don't all get the loan so again no it doesn't work out do they own their own business none of them own their own business but some of them did get the loan so that one doesn't work out either but if we check this out on the declaration of bankruptcy in the past Victor has declared bankruptcy in the past and didn't get the loan Cristal didn't and did get the loan there's a pattern here now right this question of whether or not one has declared bankruptcy seems to be causally linked to whether or not they get the loan makes sense method of difference as opposed to the method of agreement and if we can have a method of agreement and we can have a method of agreement and we can also have the method of agreement and on top of that we can have the method of agreement and as a fourth thing we could have the method of difference why not combine them all method of agreement and difference the method of agreement damn difference isn't really that complicated if you understand the method of agreement and you understand the method of difference it's just both of them at the same time so we're saying in all of the cases where the proposed effect is happening there you only have one other thing in common and it's this this the presence or absence the presence of this this other feature this other phenomenon and in addition to that the only thing that seems to make the effect go away of all the things that I'm tracking is the presence or absence of that same phenomenon then I've got a method of agreement and difference and if the method of agreement gave me good reason to suspect there was a causal connection and the method of difference gave me good reason to believe there was a cause of connection when I can do both of them at the same time now I've got a really strong argument keep this in mind too when you're trying to evaluate whether or not a causal connection an inference to a causal connection is a strong one you want to leave a little bit of room for calling it like a little a little bit of room for saying that it could get stronger you want to like keep in mind that you can critique some of these arguments if you only have the method of agreement or if you only have the method of difference because getting them both is gonna be a much stronger argument does that make sense we got the method of agreement we got the method of difference we got the method of agreement and difference one more method there's actually five but I'm gonna leave the fifth one out we'll just talk about this fourth one and then talk about a couple of other features of causal arguments we have the method of concomitant variation and the method of concomitant variation is fancy talk for trying to analyze these causal cases where I don't have simple presence and absence of my proposed causes in effect I have something like presence and absence to varying degrees right it's not like the effect is there or it's not it's the the effect can be present or absent more or less here's how Mill describes it whatever phenomenon varies in any manner whenever another phenomenon buries in some particular manner is either a cause or an effect of that phenomenon or is connected with it through some fact of causation I'm not even sure if that was a sentence whatever phenomenon varies in any manner whenever another phenomenon varies in some particular matter is yeah that's the subject there's my verb is either a cause or an effect of that phenomenon or is connected with it through some fact of causation and again we have this idea that it's variation you might uh you might recognize this from your intro science classes as kind of a proportionality or inverse proportionality if like when one thing goes up another thing goes up and one thing goes down and another thing goes down or even if we wanted to make it a little more complicated when one thing goes up another thing goes down and the other one goes down the other one goes up like say I don't know ideal gas law for example when pressure goes up temperature goes how's your intro chemistry whole when pressure goes up temperature goes up when pressure goes down temperature goes down that's why if you have like an aerosol can and you're spraying it the pressure is going down as you're spraying the stuff out you'll notice the can gets a little colder chemistry if the volume goes down what's gonna happen to the pressure if I have the same amount of gas and I constrict the volume the pressure is gonna go up these things seem to be causally connected and it doesn't matter that when one goes up the other one goes up or one goes that the other one goes down there seems to be as Millwood put it some sort of concomitant variation the variation seems to match up either proportionally or inversely proportional II here's the sort of scenario we might be looking at notice I didn't even try to draw a picture of this we'll just skip right to the table we're trying to figure out what's going on with a crop he'll what sorts of things effect causally affect crop yield we have I'm a farmer I have plot a plot B and plot C plot a I have a crop yield of eight crop units clearly I know a lot about farming plot B I have 12 crop units plot C I have 16 crop units so it seems to be going like as I go from plot a to plot B to plot C the crop yield is going up what are their concomitant variations can I pick out there maybe it's the amount of water that's causing this plot a is the lowest plot B is the highest then plot C goes down again lower than plot a but that doesn't match the variation that I see in the yield amount of sunlight same thing I go it's the highest in plot a even though the crop yield is the lowest it's in the middle for plot B yeah yeah okay maybe I have some inverse proportionality but notice this plot B and plot C are really close to one another they're almost the same yet I have a fairly large difference in crop yield so that doesn't seem like a very good candidate either however if I look at the amount of fertilizer it seems like we have some direct proportionality between the amount of fertilizer used in my crop yield by method of concomitant variation and this sort of scenario I can say there seems to be some sort of causal link between the amount of fertilizer and the crop yield and if we were guessing at this would you say the amount of fertilizer causes the high crop yield or would you say the high crop yield causes the amount of fertilizer probably the first way right yeah we'll get it on like I said on Wednesday we'll get into like how it is that we can like what sorts of reasons can we apply to figure out the directionality and again temporal temporality is one of them if I'm putting the fertilizer in the ground before the crops come up that's a really big clue all right that's the method of compliment and difference as always for any sort of inductive argument and as I mentioned it's not clear that these are inductive arguments but they're close enough we can look at them as if they are inductive arguments we're going to have the following sorts of concerns a quantitative concern more cases more relevant factors I'm examining in these methods of agreement difference agreement and difference or concomitant variation the more different factors I'm looking at the more cases I'm looking at the stronger these arguments are going to be and also had this qualitative concern that in with arguments by analogy it was about the relevance of the similarities and differences when it was about generalizations it was about this question of whether or not I suspect that my sample might be biased not just that it's big or small but it is it representative and when we were looking at statistical syllogisms the question was do we have reason to suspect there's an exception to the rule and that there's a rule that determines when we have an exception to the rule here we're looking at the same sort of idea and it has to do with this question of whether or not we can be assured that we haven't ignored any conflating factors that all of the features of the phenomena that we're looking at are in fact all of the relevant features it seems silly to describe every little detail of the phenomenon we just want to capture the ones that seem like they might be causal candidates but I want to get them all otherwise ignoring that might kind of undermine the reliability of the causal inference that I'm making and last but not least what counts as a strong inference is going to depend in part on what's on the line these are always going to be likely inferences at best I'm always going to be taking a chance on maybe and so this question that I have to keep asking myself whenever I make one of these like inferences is is it worth it to take a chance on maybe make sense so far things to worry about we just talked about some things to worry about but also remember this in terms of some of the fallacies that we just looked at in our last meeting because this is going to add some new wrinkles that we haven't seen before so I want to make sure that I'm not miss identifying any irrelevant factors as relevant that is pretty much the same as stuff that we saw in the last slide I don't want to be enchanted by coincidence I don't want to say that like just because two things seem to be happening together therefore they must be causally related I really want to make sure that I'm rigorous in my application of these methods that millas is suggesting this kind of gets at this issue of the post hoc ergo propter hoc fallacy that we talked about at our last meeting just because one thing happens and then another thing happens does not necessarily mean that they're causally linked though I can start teasing this out by the application of Mills methods I want to make sure that I'm not confusing the temporal conjunction with causation this is another way of talking about post hoc ergo propter hoc I want to make sure that I'm not confusing cause and effect and let let me just kind of reiterate this I've mentioned it several times already Mills methods don't necessarily give us directionality they just tell us that there is some causal link if you go beyond that and say a is causing B you're going to need some additional reasons besides method of agreement method of difference or method of concomitant variation I want to make sure that I don't mistake any kind of third common cause or don't mistake like the causal connection between two things for a causal connection to some third thing the example that I use when I was talking about this in terms of causal fallacies was I got a fever and then I got a rash so the fever must have caused the rash and we suggested that maybe you have a virus and the virus caused both the fever and the rash so just because they come together it means that they're causally linked but it doesn't even necessarily mean that one is the cause of the other or the other is the cause of the one it could be some third thing that's causing them both and last but not least I don't want to oversimplify cases of complex causation and this gets into a whole different concern that gets its gets its own slide in fact I suspect this might be the last slide we'll find out it is rare that any actual effect in this world that any actual phenomenon that gets caused has only one cause and I want to be careful when I'm making some sort of causal inference that I don't extend beyond saying that there is something causally linked to this thing that there is a cause with saying that it's the cause is the difference clear enough when I say that something is a cause I'm suggesting that it's one of many causes that are kind of coming together in a complex fashion to cause the effect when I say that something is the cause I'm saying it's the only cause and that's rare to have an effect with only one cause and one way that we can kind of like tease this out one way that I can think about the difference between a cause and the cause is by coming back to our old friend necessary and sufficient conditions so for example unnecessary causal connect all conditioned is going to be one that I can't get the effect without it right that's what necessity means if I have a causal condition I say this one is necessary for this then that means I can't get the effect without it and the method of difference is always going to be tracking necessary conditions think about that for a second and check to make sure that it makes sense to you the method of difference is going to help me identify whether or not a causal connection is picking out a necessary causal condition because the method of difference says when the cause goes away the effect goes away when the cause is present the effect is present yeah but when the cause goes away the effect goes away this is telling us there's some sort of necessary condition between the cause and the effect a sufficient causal condition is one where we're gonna say as long as the causes present the effect is going to be present but that doesn't necessarily mean that when I take the cause away the effect is gonna go away it just means that every time the cause happens the effect happens and the method of agreement is going to track this and if I use the method of agreement and difference together what am I gonna get a causal connection that's tracking both both necessary and sufficient conditions so for example let's look at one example and then we'll jump into the worksheet let's say I have an office plant that I'm watering every few days and I expose it to plenty of sunlight and I periodically even fertilize the soil I get some of those little miracle grow sticks that pop it in the pot every now and again the plant flourishes and it produces beautiful flowers bless you is the water in the scenario that I just gave let's look at it again I water it every few days I expose it to plenty of sunlight I periodically fertilize the soil and I get beautiful flowers is the water necessary or is it sufficient for getting the flowers necessary do I know this what sort of tests would I run to determine whether or not it's necessary if I don't water the plant will the flowers go away I don't have that yet exactly right but if I applied the method of difference that's what I would get right if I took away the water and all the flowers went away I would say like aha yes I've identified the water as a necessary condition if whenever I water I get flowers would I say that I have a sufficient condition yeah perhaps but those of you have any experience with plants you would know that I can't just water and get flowers right if I water and keep the plant in a dark closet no flowers are gonna happen right yeah so the water is a necessary condition what about the sunlight is the sunlight necessary sufficient condition seems to also be necessary right because I can have plenty of sunlight but if I don't keep it water or fertilizer I'm not gonna get flowers but if I don't have the sunlight I'm not gonna get the flowers either yeah sunlight seems to be a necessary condition what about the fertilizer if I have the fertilizer but none of the other things I'll get the flowers fertilizer with no water and no sunlight is the fertilizer necessary to get flowers some of us might be thinking or ourselves like yeah depends on how good your soil is yeah maybe it's neither right maybe we might get some concomitant variation there where we would say like it's a contributing factor and how many flowers that you get more fertilizer might give you more flowers but you'll get some without it and all three causes together we might say that they are jointly necessary for getting like a big flower yield out of my plant which isn't to say that any one of them is sufficient they might be jointly necessary we might also be able to say that they're jointly sufficient that as long as I get water sunlight fertilizer maybe I'll tack on an extra one good air circulation if I have those four things that's enough each of those four things is necessary and if I have all four of them I'm definitely getting flowers then they're both they're all four of them together are jointly necessary and jointly sufficient and this is starting to get into scenarios where I have complex causation right where it's more than one cause is causing the effect but they're all contributing to something all right let's forget about that and we're back to our first slide and we have a worksheet and in this worksheet you're given a variety of causal inferences and I want to know how strong they are before you tell me how strong they are I want you to tell me which of Mills methods that we've discussed is being applied here is it the method of agreement is it the method of difference is it both the method of agreement and difference or is it the method of concomitant variation shall we start with the first one all together as usual okay five factory workers are found to be inefficient relative to others who are doing the same work the efficient workers and the inefficient workers were found to be similar in all relevant ways except one the inefficient workers were not part of a profit sharing plan it is likely therefore that profit sharing causes efficiency method of agreement method of difference both or the method of concomitant variation method of difference and why method of difference is there anybody who was like I wasn't really sure can we rule out method of concomitant variation because we're not talking about like more or less presence it's just presence or absence of profit-sharing or efficiency we're pretending as if efficiency is something that either you got it or you don't so what a method of difference rather than the method of agreement yes yeah everything else is the same in both cases the only two differences in these cases are the presence and absence of the profiteering and the presence or absence of the inefficiency so the only differences that are being tracked here are these two things that we're proposing are causally related to one another this is the method of difference what would you say about the strength of this argument therefore profit-sharing caused efficiency and think in these terms could it be stronger there's one very obvious way in which could be stronger we have method of difference what else what what could make it stronger was that yeah if I had method of agreement on top of method of difference it would be stronger so like immediately I'm gonna I'm not gonna go like oh it's a great argument well it could be stronger right I could get method of agreement in there as well anything else yes yeah we were it is v factory workers have found to be inefficient sample size was bigger I'm gonna be a lot more confident in this this is kind of a small sample size so I'm kind of like yeah it's alright it's maybe enough to this might be enough to get me to take a closer look right this might be enough to say like we should probably study this and if somebody was wondering like should I fund that study we'll say like we kind of got a proof of concept already but I'm not really super willing to commit to it I'm not willing to for example put hundreds of thousands of dollars into a prop sharing program just because I think it's going to get me more efficiency anything else I say that the profit sharing is causing the efficiency I'm asserting a directionality does it seem plausible that the direction goes that way that it's profit sharing that causes efficiency and maybe not the other way around yeah we're not really sure how this works out right if some of the workers are in a profit hearing program are sent and some of them aren't we might wonder like well why how come some are in it and some aren't maybe the ones who are inefficient we just say that you don't get to be part of the profit sharing if you're inefficient in which case the causal direction is pretty clear right then it would be the efficiency that causes the participation or lack thereof in the profit sharing program which would be backwards from what I've asserted on the other hand if we said something like employees can participate in the profit sharing at will they can decide to or not decide to and the ones who decide to end up being more efficient and the ones who don't decide to end up being less efficient that's right I don't know how many yeah I don't have a method of agreement at work just yet right if I had a method of agreement I'd feel stronger about this yeah and I'm not really sure I mean this is what's on the line I'm not really sure what's causing the participation in the profit sharing program right is it worker efficiency that's causing it or is it something else we might also consider the possibility of a third cause that like some employees are highly motivated and the highly motivated and engaged employees are the ones that see a profit sharing program they're like yes please I'll do that and there are also more efficient workers there's some third cousin it's just maybe just some character trait of the workers and the ones who are I don't know just kind of generally lazy and apathetic workers they see the profit sharing program and they say like yeah do I have to fill out paperwork to be a part of it I do uh no no and also they're inefficient workers on top of that and maybe both of these are being caused by some third thing so the directionality is suspect this argument could be better but it's not nothing at all right we're not pulling the causal connection just like out of nowhere something is going on here and perhaps we want to take a closer look we'd want to apply more methods we want to have a closer more rigorous investigation this makes sense more or less all right there are six arguments on this worksheet let's do the remaining five everybody by themselves we'll check in see how everybody does share our intuitions and if there is any time left over although we're kind of getting close to in a class there's any time left over we can just leave early or you can ask any questions that you might have all right go for it

Channel: Adam Rosenfeld

Views: 2,467

Rating: 4.8571429 out of 5

Keywords: Critical Thinking, Induction, Causal Arguments, Mill's Methods, Method of Agreement, Method of Difference, Method of Concomitant Variation

Id: 0Nv-4CXeyJc

Length: 38min 12sec (2292 seconds)

Published: Mon Feb 20 2017