Lecture on Deductive Reasoning, Validity, and Soundness

uh with respect to what we&#39;re covering well today with deduction uh and validity and soundness it&#39;s extremely important for you to get into the habit of writing out your thoughts and ideally for this class into standard logical form because you have thoughts about political issues surrounding um afghanistan and the refugee crisis there you have thoughts about the geopolitical issues surrounding that and or syria or wherever else right i&#39;m not going to narrow it down to just those two specifics although i start with that as a sort of springboard for you to think about um you have thoughts about what a human is what you are what an animal is and how you&#39;re distinct or not from non-human animals you probably think you are sufficiently morally in a relevant sense distinct from a cow or a pig if you didn&#39;t you probably wouldn&#39;t eat them but if you don&#39;t think you&#39;re relatively different from them then you might in fact find that you don&#39;t eat such things and that&#39;s the reason why and maybe others should follow suit but you have these ideas in your head that are all swirling around and it may be just obvious to you what the answer is what the conclusion is but once you start writing out those premises those reasons in support of your opinions you find very quickly how potentially unclear your thinking was on the matter and so getting into the habit of writing and in philosophy it&#39;s a matter of rewriting get your ideas down get as many of them down as you can give as many premises as you can show that they lead to what you think is the case and then come back to it again and again i don&#39;t know that that&#39;s true i don&#39;t have evidence for this why do i think that&#39;s true even if that&#39;s true it doesn&#39;t lead to this other thing that i thought was true writing in philosophy is about revising and unless your bertrand russell who supposedly wrote out a paper once without any amendments submitted it and it got published without any amendments whatsoever i don&#39;t know if that&#39;s true it&#39;s a story but you&#39;re not bertrand russell don&#39;t pretend to be it&#39;s about rewriting so take your time on that and start thinking about those topics now so my point is look over what the assignment is ahead of time so that you have questions for me next time or via email and i&#39;ll reference this again as we get closer now where are we today oh yes sorry uh i just wanted to ask about sources if there&#39;s a minimum nope no minimum no maximum either but it&#39;s a short argumentative paper it&#39;s not a research paper but it&#39;s likely that you will probably need to get sources information unless you&#39;ve already got all the information you might be able to define what a human is and what an animal is or whatever and present present an argument without needing to research on that that&#39;s possible and that&#39;s fine um but it may lead me to call attention to a particular claim that you make that could be empirical or is based on some fact about the world that needs to be cited how do i know this claim is true you might that might require citing something and if you do that&#39;s fine just cite it uh properly mla format chicago format apa whatever your favorite format is and just stick to that consistently okay uh and also remember where we are with assignments and i&#39;ll reference this at the end so and i&#39;ll email too remind you about that because it&#39;s not until midnight but that that&#39;s good in your time but you could forget all right so to the topic here at hand we&#39;ll look at fallacies there&#39;s only a few that i&#39;m going to focus on there&#39;s a lot of ways of going wrong in formal logic but we&#39;re only going to look at a couple and we&#39;ll look at springboarding from last time where we talked about deductive patterns we&#39;ll look at how we might be able to test what pattern fits a deductively valid form which pattern qualifies as truth preserving and which don&#39;t and importantly why that is so what we&#39;re looking at specifically with validity is testing the inferential strength what are the connections among the premises to the conclusion that is not about facts in other words the facts the truth value in reality what you think to be the case and what you can determine to be the case is irrelevant for the purposes of testing validity and that takes us to this question of two things that you get wrong in an argument the argument can be flawed either because you&#39;ve made a mistake with respect to the inference in other words you&#39;ve engaged in a formal fallacy and formal fallacies only applied to deduction formal logic where you&#39;ve presented the case in such a way that the conclusion does not necessarily follow even if we accept the truth of the premises you&#39;ve made an incorrect inference and as we&#39;ll see with induction the parallel there is you&#39;ve presented a case in which the premises even if true do not give support for the likelihood of the premise of the conclusion being true and we would call that a weak argument with induction with deduction we call an argument that is not truth preserving we call it invalid that&#39;s what we&#39;re focusing on today primarily we&#39;ll look at soundness as well but soundness is actually pretty straightforward so we&#39;ll spend most of our time on validity now the other area of getting things wrong is just simply getting the facts wrong you&#39;re mistaken about what is true or false one of your claims or more of them is in fact false you might get the logic perfect impeccable valid deductive argument truth preserving and that&#39;s what you test first you need to get into the habit of doing this assume for the sake of the of argument and for the sake of testing validity in this case that all the premises are true even if the premises are ridiculous even if you disagree with the conclusion assume that if they were true imagine a possible world in which they were true would they necessitate the conclusion would the conclusion have to be true lest we contradict ourselves when we accept the premises that&#39;s true if so you&#39;ve got a valid argument and then and only then do you go and check do the premises have uh are the premises in the real world outside of our thought experiment actually true that&#39;s questioning the facts and if it is truth preserving valid and the premises and on the argument are all true then it&#39;s a valid and sound deductive inference a deductive argument we&#39;re focusing mostly on number one here um we can give an example of this let&#39;s see do i have one so somebody walks in the room let&#39;s say and we&#39;re not we don&#39;t have windows let&#39;s imagine and somebody walks in soaking wet what&#39;s the first thing that comes to mind that it&#39;s probably raining outside that&#39;s a perfectly decent inference in fact we do that kind of stuff all the time and it&#39;s really impressive that our brains can do this and we don&#39;t really think about it we certainly don&#39;t fill in the premises we don&#39;t say to ourselves hmm well that person looks soaking wet and usually premise two people who look soaking wet are soaking wet and when people walk into a room soaking wet it&#39;s usually because they got rained upon this person probably got rained upon therefore i conclude it rains it&#39;s raining outside we don&#39;t usually go through all that and it sounds silly to say it all but i want you to get into the habit of thinking that way because it&#39;s not always silly to include those premises as i just did and the way that i just represented that by the way is that a deduction or an induction was a deductive argument or an inductive argument inductive why is that because you start off with observations [Music] so anything that starts off with an observation is inductive wait can you say the last line of i&#39;ve forgotten uh uh somebody walks in the person premise one that person looks soaking wet promise to people who looks like you went probably are premise three uh usually when people are soaking wet they come in from outside it&#39;s because they got rained on from is four they got rained on therefore it&#39;s raining outside and that&#39;s not how it has to be that&#39;s just how i present it and you say that&#39;s inductive because i&#39;ll give you a hint you&#39;re correct but why are you correct go ahead oh it doesn&#39;t necessarily necessitate the conclusion it&#39;s only highly probable that that is the case because there are other probabilities like say someone just dumped a bunch of a bucket of water yes good like in the bathroom the sink was gone for the men&#39;s room second floor over there it sprays out really fast but only tiny bits of water and then it gets all over you it&#39;s a stupid sink so sorry i get upset with silly things it&#39;s logically possible you can imagine a scenario in which all the premises are true and yet the conclusion is false it&#39;s not running outside that person just fell into the toilet or they went into the ocean the ocean&#39;s right over there that&#39;s possible or if you know in your background expectation you&#39;ve got in your your background framework that there is scheduled today a campus-wide water balloon fight which would be awesome i just realized who wouldn&#39;t want to be engaged in a campus-wide water villain fight if you knew that that was going on you would not jump to the inference to the conclusion that it&#39;s raining outside the more logical inference would be oh they lost in the water balloon fight uh and that&#39;s an intuitive thing that happens immediately it&#39;s not magical and this is why detectives are really good at what they do and and and uh physicians they&#39;re able to recognize what is relevant they&#39;ve got a larger store of background information to call to pull from to recognize that it&#39;s probably this and not this whereas non-experts don&#39;t have all of that to rely upon we might jump to a conclusion that is based upon a representative bias and we don&#39;t have any other alternatives as we&#39;ll see with expertise the experts have a lot more alternatives in their background framework that they can pull from and recognize when it&#39;s relevant when it&#39;s not relevant so let&#39;s say someone walked in your class right now soaking wet when it&#39;s sunny outside do you think you&#39;d still make that conclusion no good if we&#39;re in the basement of this building i don&#39;t know if it has a basement uh and they walked in soaking wet i don&#39;t think i would infer it&#39;s raining because it&#39;s santa barbara and it hasn&#39;t rained in four years i don&#39;t remember last time it&#39;s rained in santa barbara i&#39;m sure it has like a little bit of a tinkle not tinkle sprinkles sprinkles take on something different the lord has tinkled upon us but no i might actually infer that person who was swimming in the ocean that would actually be a more reasonable inference so that&#39;s a very good point where we are and other background information will play a role in strengthening or weakening that argument but with deduction it&#39;s not a matter of strengthening or weakening deduction in a way is clearer it&#39;s crisper a lot of people like that it&#39;s either valid or invalid there&#39;s no in between it&#39;s not kind of valid but you could with induction say yes this conclusion follows with a high degree of probability add some more premises that are true and in fact that increases the probability you don&#39;t make an argument more valid or less valid it&#39;s either one of the others we&#39;ll see um why am i mentioning this oh because i i looked this up uh when i said somebody what was the example you can get the facts wrong or you can get the logical infants wrong if all the claims we said in that argument actually this is out of order this should be what we see here&#39;s the argument uh uh oh here&#39;s the picture guys yeah this is philosophy uh okay so she looks wet most people don&#39;t look into a philosophy classroom with such uh what&#39;s the word yeah i guess there&#39;s a different word lascivious that&#39;s not it anyway premise one she looks wet usually people who look wet are assuming all those premises are true the conclusion is likely and by the way i say likely there if i had said it&#39;s necessarily true that it&#39;s raining outside would that make the argument all of a sudden deductive well i would think so but it would be an invalid good that&#39;s an interesting way of putting it that&#39;s one way of looking at it another way is to say and here i disagree with uh i think it was herrick and i forgot the page that talks about this in the suggested reading that the indicator words necessarily must absolutely indicate deduction indicate necessity indicate a kind of absoluteness certainty and that&#39;s true up to a point and i disagree with him here where he says uh and likely probably possibly that indicates induction i think he the indicator words work for induction but not for deduction it&#39;s not enough to say in a conclusion it&#39;s necessarily true to make it deductive because psychologically we tend to want to make our arguments appear as strong as possible and so we&#39;ll use language that&#39;s as strong as possible but that doesn&#39;t make the logical inference one of deduction of truth preservation however we don&#39;t typically make our arguments appear weaker than they are so i wouldn&#39;t say all men are mortal socrates as a man therefore probably sacrifice is mortal we wouldn&#39;t do that i mean and even throwing the word probably there actually isn&#39;t going to make that an inductive inference and so there&#39;s a hint within with the indicator words probably likely possibly and you should get into the habit of using those properly if you know you&#39;re making a causal argument an enumerative induction a prediction a generalization an argument by analogy all of which we&#39;ll get to next week it&#39;s a good idea to make it clear that you think your conclusion follows with a high degree of probability don&#39;t fool people don&#39;t try to fool people by saying therefore my conclusion necessarily follows because it doesn&#39;t it never does with induction now i&#39;ll come back to that when we look again at the more of the distinction between deduction and induction i can get the facts wrong the logical inference made here is is a good one that&#39;s a strong inductive argument assuming the truth of the premises the conclusion is likely but of course and i looked this up can you be wrong about the style it could be a style of the wet look and i made a joke about that once and then i found this it&#39;s actually a style it&#39;s uh what&#39;s her name actually i don&#39;t know why i asked doesn&#39;t matter so this person&#39;s wearing that style and it looks like her dress is soaking wet it&#39;s kind of like the you know the pants that my daughter&#39;s wearing today the distressed jeans that have the holes pre-ripped in them which upsets me to no end because i had to throw away i didn&#39;t have to it was suggested that i do i had a pair of pants a pair of jeans that had a hole in them that i caused from years of wear and tear and i threw them away and i realized really the reason i threw them away is because i was told they were not in style because they weren&#39;t skinny enough it just pissed me off lately so they didn&#39;t fit that style it wasn&#39;t because they had holes in them i don&#39;t know this is i&#39;m sorry i&#39;m wasting time uh anyway it&#39;s possible that you could be wrong it&#39;s not actually wet that&#39;s just a style those pants actually aren&#39;t ruined that&#39;s how they were designed to look destroyed or whatever it is so you can get the facts wrong or you can get the logical inference wrong we&#39;re interested in the logical inference the logical inference what is the strength does the premises if true do they lead to the necessity of the conclusion or merely the probability of it and what we&#39;re doing with validity and there&#39;s a lot of different ways of saying this and i&#39;ll be a little repetitive here again because it&#39;s in many respects counter-intuitive with validity it is impossible for the premises to be true and the conclusion false if you find that if you set it up such that the conclusion could be false assuming the truth of the premises it&#39;s invalid when we look at representing other people&#39;s arguments and we&#39;re not sure did this person mean for this to be deductive or inductive you may be able to make a translation such that it sounds like it could be deductive but if it were interpreted as a deductive argument and you were to represent it as a deductive argument it would be an invalid one consider the possibility of reinterpreting it as an inductive argument like we did with the uh the sherlock holmes or the detective example right and by the way on your uh discussions uh even if you get a 10 out of 10 on those um look over my comments on them because i&#39;ll sometimes make comments even if you did really well on it and even if you took like a half point off i don&#39;t take a whole lot of points off for those those are main those are low stakes assignments but you need to do them and get them in on time because they&#39;re related to the readings and i want them to be current but my comments are feed forward as i say now even that sounds strange because i don&#39;t like to say here&#39;s why you got points off i&#39;d rather say here&#39;s how you need to improve this for future arguments because that&#39;s what you&#39;re going to be constantly working on in addition to reflecting on the readings and in addition to constructively criticizing other people&#39;s arguments remember you want to respect respond to two others so look at those comments here are other ways of saying basically the same thing except the last one i think goes a bit further how do i know i&#39;m dealing with a valid argument an argument is valid if the premises cannot all be true without the conclusion also being true an argument is valid if the truth of all its promises forces the conclusion to be true an argument is valid if it would be inconsistent we&#39;ll spend a lot more time on consistency and inconsistency with virtues and vices of beliefs later on it is valid if it would be inconsistent for all its premises to be true in its conclusion false another way of saying that is we&#39;d be contradicting ourselves if we said premise one true premise two true but conclusion false in a valid argument an argument is valid if its conclusion follows with certainty from the premises and an argument is valid if it has no counter example that&#39;s the more interesting one and difficult one if there are no counter examples that is a possible situation think of in terms of thought experiments godunkan spiels remember the german word for thought experiment thought play possible situation that makes all the premises true and the conclusion false we&#39;re not dealing with the actual truth value when you test validity for the sake of argument constantly get that into your head that&#39;s the first thing you want to be thinking about when you hear another person presenting what you think is an argument first figure out what the argument is and then assume that what they&#39;re saying is true and let them know that you&#39;re assuming what they&#39;re saying is true that you&#39;re testing the validity testing the strength of what they&#39;re saying you&#39;re not denying outright their premises because you&#39;ve denied the conclusion you can&#39;t deny their conclusion until you&#39;ve established that the premises don&#39;t lead to it so assume the premises are true you&#39;re not doing yourself a disservice and doing that you&#39;re not saying oh my gosh i&#39;m going to actually going to take on the position of this guy well it&#39;s the mark of an educated mind to be able to entertain an idea without accepting it as is attributed to aristotle that&#39;s what you&#39;re doing here in testing for validity so by way of a test of that can you assume that this claim is true that all fish are religious and if that claim is true and also this claim is true anything that&#39;s religious is a dog what follows if anything necessarily from those two clays yes that all fish are dogs is that true yes valid is it valid is it truth preserving can you imagine a possible scenario in which this claim of fisher dogs is false while assuming one and two are true all fish are religious anything that&#39;s religious as a dog all fish are dogs is it valid it is valid and if you don&#39;t no they&#39;re logical this is obviously everything in it is false every single claim is false which tells you truth or falsity have nothing to do with validity if you sniff this pen enough you&#39;ll come to the conclusion yes man all fish are religious wow i i need to use a different one this is silly there we go low odor do you like the scented markers kind of i do yeah you do a little bit so if you&#39;re not sure look in terms of the euler diagrams these circles we can see this is a categorical syllogism where we have a subject class and we&#39;re saying it&#39;s in whole or in part belongs to a predicate class category if it&#39;s a fish or all fish are things that are religious is how you would phrase that in standard categorical form but we&#39;re not focusing on that premise one says anything that&#39;s a fish is a thing that is religious is that an appropriate way of representing premise one does that seem right you put the fish the f circle inside the larger r circle that&#39;s what premise one says premise two says anything that&#39;s religious or all all religious things uh all religious entities are dogs how do i represent that by by barking did somebody just bark the answer out clever what&#39;s that a circle around of course these different colors here and that says anything that&#39;s religious that&#39;s this category is part of the category the larger category of dogs and notice look i don&#39;t need to do anything else the conclusion that all fish are dogs already embedded within those premises it is impossible for this official dogs to be false if we accept the two premises official religious anything as religious as a dog so it&#39;s deductively valid what else do you know about this argument so far as evaluating it it is the claims the premises one or more of the premises are false so just a reminder arguments as a whole are not true or false only the claims within them the claims within an argument are not valid or invalid sound unsound cogent or uncoaching strong or weak they are true or false so as you noted this is valid it&#39;s truth preserving if the premises were true they would necessitate the truth and conclusion but one of the premises or more in fact every damn thing and it is false but again it can tell you that truth or falsity is irrelevant for testing validity yes excellent question why worry about validity if i can say stupid like this valid so it&#39;s not nothing in there is true that&#39;s a very good question a valid argument i have an analogy later on a valid argument is like a good freezer what do you use a good freezer for food food to preserve it a valid argument is like a good freezer you put in uh fresh meat into a freezer and it&#39;s a in the freezer works the analogy here is it&#39;s a proper form you put true premises into the proper form of an argument though that truth gets preserved in the conclusion you put rancid meat into a freezer even if it&#39;s a good freezer it&#39;s not going to make fresh meat you put false premises into a valid argument you&#39;re not going to get a true conclusion right you&#39;re not it&#39;s not going to automatically give you truth in the end the point of a deductive form is to provide us with a tool to determine truth value when we may not know what it is ahead of time and so this will be useful in in science we&#39;d like to have structures that we can use they&#39;re mechanisms where we can plug in where we&#39;re ignorant of the actual truth value but we can still see that if the claims were were true they would necessitate the conclusion at the end and so we&#39;ve got a kind of structure a form a machine that produced that that uh preserves truth that&#39;s the essence of validity um and importantly i can test somebody&#39;s argument remember the two ways of going wrong logical inference could be flawed or the factuals the claims could be factually incorrect but i don&#39;t even need to test in the real world the muddy gray fuzzy areas of truth value if i can establish that somebody&#39;s argument is invalid so your question is a great one that&#39;s why you start by testing validity you start by testing with induction strength or weakness and you ask yourself if those claims were true would they necessitate the conclusion if not or with induction if those claims were true would they lead to the high degree of probability that the conclusion is true if not then you don&#39;t even have to ask whether the premises are in the real world true because it doesn&#39;t matter even if they were true they wouldn&#39;t follow from the premises given and so the argument because it is invalid is by definition unsound and it saves us time in a way too uh but yes that&#39;s a very good question and here&#39;s a joke so what i say all fish are religious no that&#39;s false but it&#39;s true that some are this is probably right at the border of inappropriateness um this is sometimes referred to as the jesus fish this for those of you taking world religions you know that this symbol was used and it&#39;s a symbol i guess you see it on a lot of cars where it&#39;s the official jesus inside it this is the fallacy of equivocation where i use the same word or idea with that has two different contexts two different meanings in the same argument this is the symbol for christians when they were being persecuted by the romans that where they could be and hold their own uh uh rituals and practices uh uh free from and hiding from the roman persecutors in any case i was just trying to engage in equivocation which we&#39;ll see in a couple of weeks a fallacy of ambiguity oh here&#39;s another one santa claus exists assume that&#39;s true if it&#39;s true and also true that anything exists has a foot fetish what follows [Music] santa has a foot fetish you said that without hesitation or reservation it is a valid argument this is an argument that&#39;s i think it was a logic professor like 30 years ago for me and i just can&#39;t get rid of it can&#39;t get rid of it santa exists if that&#39;s true [Music] bus number two of 40 force class 2 i apologize if it&#39;s true that santa exists and it&#39;s true that anything that exists has a foot fetish it has to be the case that santa has a foot fetish i did have a counter to this once a student said wait a minute premise two anything that exists has a foot fetish that means all existing things have a foot fetish can it be a fetish if everybody&#39;s doing it and i it&#39;s pretty good it&#39;s pretty good that&#39;s questioning the soundness of the argument not validity though what is a sound argument it&#39;s one that is deductively valid and actually has true premises we&#39;re not worried about the real world with validity we&#39;re only testing the logical possibilities is it possible santa exists yes is it possible that anything exists has a foot fetish yes if those two are both presumed to be true it follows necessarily that santa has a foot fetish that is valid obviously it is unsound because one or more of those claims is false which ones actually if one of this is a test here which of those claims is false could premise one be could premise one okay never mind they&#39;re all false i was trying to do something with that forget it they&#39;re all false so previously i had an argument that was comprised of all true claims but it was invalid here we&#39;ve got an argument that&#39;s comprised of all false claims but it is valid or maybe i&#39;ve done that backwards maybe i&#39;m going to show you an example of something that has all true claims but is not valid i think that&#39;s what&#39;s going to happen here&#39;s something that has everything in it that&#39;s false in reality and yet the structure of it to your earlier point the structure of it is valid which means the form is which means anything you put into that anything to plug in there&#39;s santa with a i guess a foot fetish i know i&#39;m sorry i couldn&#39;t find anything better although that&#39;s not true if i really looked i could have found something about santa and foot fetishes quite quickly if i had the if i wasn&#39;t in public and not embarrassed to look such things up a valid argument is truth preserving oh here&#39;s the two to your point earlier about argument is truth preserving uh like good freedoms freezers preserve food if you want a valid argument put it in the freezer and you can&#39;t go wrong that&#39;s a mixed metaphor that&#39;s not as funny as i thought it was this kitten kit kitte is in a freezer your argument is involved [Music] i don&#39;t know i tried to get a combination of argument and freezer together and this is that&#39;s as far as i got anyway forget that testing validity here&#39;s an example if bill arrives then we will have plenty of beer ah there&#39;s plenty of beer bill has arrived has bill&#39;s arrival been necessitated by the two premises being true must we accept the truth of the conclusion that bill has arrived if we accept the truth of the two premises oh we see difference i see shaking of heads and nodding of heads how many think this is valid let&#39;s go with that i saw heads nodding means yes we changed our nut they changed our minds on that does anyone think it&#39;s valid anyone think it&#39;s not valid okay great let&#39;s hear why do you think it&#39;s invalid because they could already have like plenty of beer but maybe bill rex will get a lot more beer yeah we don&#39;t know anything about bill and his connection to beer other than what&#39;s said in this conditional and the conditional along with the connecting claim the chain link here and two don&#39;t necessitate bill having arrived even if it wanted to are true it&#39;s still logically possible that the beer could have come from somewhere else and beer bill arriving still means hey more beer but it doesn&#39;t mean that we have bill&#39;s arrival just because we have plenty of beer and you can translate this although it&#39;s difficult and it sounds weird when you translate this currently it&#39;s a conditional and conditional or hypothetical claims are a little bit more unclear visually but you can retran you can represent them into standard category form with by saying things like all times that bill arrives which is what this first premise is going to say all times that bill arrives that&#39;s the circle our times we have plenty of beer this is a time this circle is the category of times we have plenty of beer here&#39;s the times that bill arrives which means any time bill arrives there is plenty of beer all times bill&#39;s ride the tiny beer premise two says there is plenty of beer meaning now is the time there&#39;s plenty of beer where do i put that x representing 2 plenty of beer where must it go assuming premise 2 is true middle here now is a time let&#39;s call it now now is the time we have plenty of beer it is that that&#39;s true but is it the only option it could be now could be here could it be here could it be outside the plenty of beer circle no because that&#39;s not what it says so the visual kind of euler diagram where you represent things in circles if there&#39;s more than one option of where to put a premise or a conclusion it&#39;s not obviously and necessarily one way or another we know it&#39;s invalid because that tells us this could be false right does bill it does now have to be a time in which bill has arrived it&#39;s unclear there&#39;s more than one option and all it takes is two options all it takes is a logically possible conclusion in which this doesn&#39;t turn out to be absolutely possible excuse me absolutely true and so it is invalid because it is not truth preserving and if it&#39;s invalid it is unsound and we can also see even without doing all this i&#39;ll get him a second we can also see the logical relationship among the parts of a conditional statement show us why it&#39;s invalid why the conclusion doesn&#39;t have to be self because this form if billerize we have plenty of beer if p then q premise 2 there&#39;s plenty of beer that&#39;s q that&#39;s the consequent and remember the parts of a conditional the antecedent provides us with a sufficient condition for the truth of the consequent and the consequent the part that&#39;s after the then provides us with a necessary condition for the truth of the antecedent that&#39;s abstract and confusing but it tells us why this argument is invalid because what are we doing we are affirming that the consequent q there is plenty of beer is true we have affirmed that a necessary condition has been met for the antecedent that bill arrives but just because we&#39;ve affirmed a necessary condition to your earlier point we have not shown that the antecedent has to be true in the same way that if i said did you take care of the kids let&#39;s say i&#39;m with the kids for a month i&#39;m by myself god and my wife comes home did you take care of the kids i said yes they have water what have you fed them i gave them water water is necessary is it not yes but not enough you haven&#39;t kept them alive just because you&#39;ve given them this is a terrible example but you see that just to get to how it&#39;s invalid it&#39;s an error in reason i&#39;ve affirmed that a necessary condition has been met and assumed that that&#39;s enough for the antecedent wouldn&#39;t this be more valid if he swapped two and three well be cautious more valid implies there&#39;s degrees to it well i mean so the first one he sets up like what you need and then number three would provide proof to number two good oh so it wouldn&#39;t make it more valid it would just simply make it valid that&#39;s exactly right if i uh did i get it right yeah you said if billerize then we have plenty of beer and you want to switch it bill has arrived as premise 2. and then the conclusion is we have plenty of beer that would be valid in fact there&#39;s a logical form called modus ponens that fits that form that is that form and anything you plug into modus ponens which is if p then q p the antecedent i&#39;m affirming that the antecedent is the case in other words i&#39;m affirming that a sufficient condition has been met for the consequent and if i&#39;ve given you a sufficient condition for something that something is the case therefore if p then q p therefore q is how you presented it and you would be right that&#39;s valid and anything you plug into that would be valid did you take care of the kids yes i gave them water because that&#39;s necessary and cocoa melon [Music] what kids tv show and they were able to watch cocoa melon which is necessary for their survival obviously are those two necessary and jointly sufficient do you see where i&#39;m getting it no they need more than water and cocoa melon i haven&#39;t not heard of that sounds terrible they need water cocoa melon they need food they need sleep yes they need sleep we know we need sleep the military&#39;s tested this they want to try to make troops that don&#39;t sleep you can&#39;t you&#39;ll die if you don&#39;t sleep what is the other thing shelter shelter no no shelter and sleep are different you need you need sleep you need shelter you need oxygen you need full oxygen yeah there it is uh i don&#39;t know how many that is there&#39;s like five or six of them they are necessary independently and jointly sufficient and oh and then a seventh you need you need philosophy or you will die thank you for that heavy silence and recognizing the truth of that claim fallacy of affirming the consequent i&#39;ll get to it a little bit more it looks like the other argument sorry for all the words here you have access to these slides fallacy of affirming the consequent it looks very similar to the modus ponens if p then q p therefore q modus ponens the way of positive i&#39;ll give more examples of that we saw some of those from last class and it looks similar to the modus tollens but with modus tollens where you deny the consequent you say look a necessary condition hasn&#39;t been met but then you are also then denying the antecedent in denying the consequent but that&#39;s not what&#39;s being said in that previous example instead of denying the consequence of the modest tolerance it&#39;s asserting that the consequent is true and when you assert that the consequent in a conditional statement is true you&#39;ve only given us a sufficient condition this only tells us a sufficient condition is met when you assert the consequence which cannot necessitate the truth at the conclusion wait a minute what but instead of denying the concept you&#39;re asserting the concept the consequent provides us with a necessary condition if it&#39;s a cat that&#39;s the antecedent then it&#39;s an animal being an animal is necessary to being a cat it&#39;s not enough because there are animals that are not cats being a cat is enough to be an animal it&#39;s all you need but it&#39;s not uh sufficient so this should be necessary oh good lord i&#39;m glad i caught that now i&#39;ve confused myself that&#39;s correct now so rephrase instead of denying the consequent as with modus tollens we are asserting that the consequent is true and that only tells us that a necessary condition has been met water is necessary therefore my kids are alive uh what no that&#39;s not enough that&#39;s not enough to necessitate the truth conclusion so we have the possibility of all true premises yet a false conclusion that&#39;s always what we&#39;re looking for in testing in validity is it invalid i don&#39;t know can you make it such that it or can you show that the form of it would lead to a false conclusion even though all the premises are true and i&#39;ll show a lot of examples that&#39;ll be somewhat repetitive but it&#39;s useful to have these examples and as always just stop me if something&#39;s unclear so the fallacy of affirming the consequence i&#39;m saying that an unnecessary condition has been met if i am human then i&#39;m an animal and adam premise two i am an animal assuming both of those are true does it necessitate the conclusion that i am a human everything in it is true if i&#39;m human then i&#39;m an animal it&#39;s also true that i&#39;m an animal oh here&#39;s the example i was mentioning earlier everything in this argument is true every premise is true the conclusion is also true but it is not truth preserving because of the incorrect form it is invalid the fallacy of affirming the consequent to get a sense of why that is consider this premise one if i&#39;m a chicken then i&#39;m an animal if p and q if p then q same form if i&#39;m a chicken then i&#39;m an animal i am an animal i&#39;m talking about meat all humans are animals right lola my daughter still doesn&#39;t think that&#39;s the case what are we then we&#39;re humans that&#39;s circular lola you can&#39;t say a human is a human that&#39;s a terrible definition you beg the question that conversation ends very quickly you start that way prayers too i&#39;m an animal what have i asserted this the consequence it must be that i&#39;m a chicken well if i&#39;m a chicken then i&#39;m an animal i am an animal therefore i&#39;m a chicken okay that is false i am not a chicken but these are true true premises false conclusion invalid why is it invalid because i&#39;ve only given us a necessary condition the way to make that valid would be to say if and only if i am a chicken can i be an animal which is to say the only kinds of animals there are are chickens and if that were true and that&#39;s how i wrote it if and only if where that gives the necessary and sufficient conditions for chicken hood or animality animality and i am an animal then i would have to be a chicken because there are no other animals but chickens that&#39;s how i would have to make that valid but of course we know that&#39;s unsound because it&#39;s not true that the only kinds of animals are chickens so to go back to the beer example as this was mentioned immediately and sometimes you can intuitively figure it out this doesn&#39;t work something&#39;s gone wrong what we&#39;re doing now is showing what is the underlying logic that proves why it&#39;s invalid that proves why it&#39;s not truth preserved so uh oh every time bill&#39;s here there&#39;s plenty of fear hey there&#39;s plenty of beer bill must have arrived those two claims don&#39;t preclude the possibility of beer coming from someone else and so the premises could all be true and yet the conclusion false proving that the argument isn&#39;t valid there are other examples oh with bill actually this is the example you gave earlier if bill arrives we have plenty of beer hey bill has arrived we&#39;ve got plenty of beer that&#39;s modus ponens if p then q premise two bill&#39;s arrived p i&#39;m a certain affirming i&#39;m stating that it is the case that the antecedent is true which is to say i&#39;m providing a sufficient condition for the consequent it&#39;s enough and if you found enough you get the thing in question bill arriving is sufficient for there being plenty of beer therefore it&#39;s valid and anything you plug into that modus ponens form is going to be truth preserving no matter what it is no matter how ridiculous it is it&#39;s going to be valid but you&#39;ve got another error that looks similar to those valid forms there&#39;s something called the fallacy of denying the antecedent here&#39;s where i say a sufficient condition is not being met and if that&#39;s the case does it lead to the consequent being false if p is the case then q is the case but p isn&#39;t the case therefore q isn&#39;t the case that abstract variable form is not obvious but when you put it in terms of like this if you like dogs instead of cats here&#39;s that example premise one if i&#39;m a dog then i&#39;m a mammal if pete and cute i&#39;m not a dog not p that&#39;s premise two i&#39;m not a dog therefore i&#39;m not a mammal now you can see that this is clearly false and these are true making this invalid what have i done i&#39;ve denied a sufficient condition but nothing in those two premises precludes me being a mammal these can both be true and yet this is false again unless we assume the only mammals that exist are dogs if that were true if we said that but that&#39;s not what we&#39;re saying if we said if and only if i&#39;m a dog in my enamel then the conclusion would follow when necessary would follow with necessity that i am not a mammal but that&#39;s not what the premise says question no that is the fallacy of denying the antecedent saying that we don&#39;t have a sufficient condition for q therefore q cannot be the case that doesn&#39;t follow and i think i have more examples oh yes oh wow that all came out at once so all capitalists premise one all capitalists are conservatives is that true i don&#39;t know doesn&#39;t matter assume it is carl there&#39;s a little joke here carl is a conservative therefore carl is a capitalist obviously carl marx let&#39;s have a little fun there is it does it follow necessarily the call is a capitalist i don&#39;t know actually it&#39;s hard to tell what is the logical connections between those categories and among those categories here is a counter example with a substitution instance which is to say an exact replica of form since we&#39;re only dealing with form if i can show that that form is the same as this one and this form is invalid i have proven that that form is invalid even though i don&#39;t know who carl is i don&#39;t look out i don&#39;t know much about capitalists and conservatives and so forth i can translate it as premise one all cats are animals assume it&#39;s true premise two i am an animal premise three i am a cat that does not follow this is invalid and it&#39;s the exact same form as that making that invalid and if it&#39;s invalid it&#39;s also what unsound you have can you just correct all of this with just providing more examples are using clearer language like is the following of most of the seems like most of this is just uh dangerous yeah we haven&#39;t gotten to that yet sorry do i want to bring in vagueness yet more or less i do two days yeah it is hard to not introduce yes we all kind of have a sense of what vagueness is good point um so where&#39;s the vagueness here and what a conservative is uh yeah or not providing alternatives um or that there are too many alternatives and you haven&#39;t defined what you&#39;re doing yes and we&#39;ll come to definitions soon you&#39;re right and this is a problem with trying to shoehorn in your case your belief system into a deductive form because it&#39;s very clear this is either valid or invalid but the soundness whether they&#39;re playing whether the claims are true or not and of course it&#39;s only determined to be sound if it&#39;s already valid to begin with but are they sound is it true that all capitalists are conservatives well what do you mean by capitalist and what do you mean by conservative how conservative conservative is vague and what a capitalist is vague chinese government engages in capitalistic acts all the time but i don&#39;t think the chinese government is necessarily capitalistic in the sense that we typically use it so you&#39;re right that&#39;s a problem with induction and it&#39;s a problem with definitions which we&#39;re going to spend a lot of time on so there are ways of avoiding some of the problems with these but technically and all we&#39;re doing here is looking at validity and testing for it this is invalid because it&#39;s not truth preserving as it&#39;s stated and maybe we can fix it oh there&#39;s a cat why do i have hank there uh all cats are animals i have a cat and here i say no i&#39;m not because that&#39;s not me which is actually terrible reasoning on my part since i am not this particular cat i am not a cat does that make sense it&#39;d be like saying i&#39;m not you therefore i&#39;m not a human there are other humans in any case i&#39;m also not a cat that&#39;s just true how about this promise one god if god does not exist objective moral values do not exist premise support promise two objective moral values do exist this is tricky anytime you have negations it gets tricky what follows god exists can anyone guess the form of this put some p&#39;s and q&#39;s in there and mind your p&#39;s and q&#39;s does anyone know where that comes from by the way mind your p&#39;s isn&#39;t and q&#39;s military thing probably i actually don&#39;t know it&#39;s hoping somebody did it well my dad was in the navy and he told me when they were good when they would like dock um off their ships they say like mind your p&#39;s and q&#39;s like when you go to the yes because there so you don&#39;t you don&#39;t get like give me a uh give me a pint well i guess we do call them pints here what am i saying yeah mind your p&#39;s and q&#39;s don&#39;t spill your pints or your quartz he&#39;s drinking a quart of beer so oh right sorry that was a bit of an aside is this valid in what form is it yes yes it&#39;s mother&#39;s tollens because you&#39;re denying a consequence yes and it doesn&#39;t look like you&#39;re denying the consequent because you&#39;re stating something is the case but notice when you state something is the case in premise two it&#39;s denying that something is not the case it&#39;s a double negation if you want to be very very clear you would say if p then q or you could say i don&#39;t like this way of doing it but you could say if p then not q which is not how modus tollens works premise 2 says it is not the case that not p and not q therefore is not the case that not p that&#39;s too confusing unnecessarily so instead you say do i have it if p then q not q premise two the q the consequence says objective moral values do not exist what&#39;s the negation of that that they do this is still not q the conclusion not p in other words therefore god exists why is god exists equal to not p because p is god does not exist do you see and the negation of god does not exist is god does exist so this is if p then q not q therefore not p you&#39;ve denied the consequent you&#39;ve removed the necessary condition that is valid is it sound take philosophy of religion class to find out next semester how about that or write a paper in this class about something like this at the end and that paper can be a springboard into a larger work in the philosophy of religion class next spring or fall spring let&#39;s talk about serial killers shall we all serial killers are shy is that true who cares we&#39;re not dealing with truth value yet all serial killers are shy i resi i represent that by this if it&#39;s a serial killer it&#39;s part of the larger category of shy entities shy people all serial killers are shy that&#39;s premise one smaller circle serial killers into the largest circle of shy people franklin&#39;s a serial killer where does franklin have to go boom what does it tell you i don&#39;t even need to finish it what do you know franklin is shy it necessarily follows it is a valid categorical syllogism is it sound not if ted bundy counts as a counter-example and he defended himself if you&#39;re familiar with ted bundy absolutely wretched human being was a serial killer and was not shy so there&#39;s a counter example to premise one all killers are shot our serial killers are shy that&#39;s false and we only need one counter example to prove that premise one is false so what do we have here a valid but unsound argument it&#39;s valid because it&#39;s truth preserving if the premises were true they would necessitate the truth the conclusion but it is in uh it is unsound not because it&#39;s invalid that would be one reason to make it unsound but it is unsound because one or more of the premises can be uh determined to be false more about serial killers shall we premise one all silicones are shy franklin&#39;s not shy that&#39;s the same structure with the euler diagram franklin&#39;s not shy where does franklin go here yeah maybe here yeah all that that means that means the same thing he&#39;s not in the category of shyness whether he&#39;s there or there that still means not shot and notice he can&#39;t be in there if he can&#39;t even get into the outer circle if he&#39;s not shy then he&#39;s not a serial killer because assuming the truth of premise one all serial killers are shy and if franklin doesn&#39;t fit that category then he&#39;s not a serial killer and that&#39;s what we have here so good for franklin is it true no again it&#39;s unsound because i don&#39;t even need to know anything about franklin i know premise one is false so it&#39;s unsound could you use the same counter in the previous slide not being shy oh yes exactly that&#39;s what makes this exact that would make this unsound uh but it is still valid but it&#39;s just a different structure than the previous argument all right we don&#39;t no we&#39;re not we&#39;re not done with serial killers okay same thing franklin&#39;s not a serial killer okay but different where does franklin go premise two could be there right yeah uh could he be here yeah could he be here doesn&#39;t say that but notice we have two options president is not a serial killer what follows from that that he&#39;s not shy uh maybe but notice this is a possibility and so is this in other words those both might be true i&#39;m sorry those could be assumed to be true and yet this could still be false anytime there&#39;s more than a single option for your conclusion that tells you it&#39;s not necessarily true there are alternatives even when we accept the truth of the premises and this one&#39;s unsound not because the premises are false that&#39;s an additional worry but we&#39;re not even needing to get to that we know it&#39;s unsound already because it&#39;s automatically excuse me it&#39;s automatically unsound because it is invalid because the definition of a sound argument is one that is valid first and in reality has all true promises okay we&#39;re away from serial killers good i think we did this one already all cats are animals oh dogs are animals no we didn&#39;t therefore all cats are dogs i didn&#39;t label this one and it&#39;s not actually in your texts so i&#39;m not gonna i don&#39;t think it is you&#39;re not gonna be responsible for knowing the name of this it&#39;s called the fallacy of the undistributed middle don&#39;t worry about the details of that all cats are animals uh all dogs are animals already i don&#39;t know what the hell to do do i say that do i say that ah this and it gets very confusing notice those are three possibilities premise two says all dogs are animals as long as the category of dogs is within the larger circle of animals we&#39;ve said something that is true with respect to this argument but i don&#39;t know where to put the dog does it overlap the cats or does the cats overlap the dogs or is dogs a separate category altogether still under the larger heading of animal which is probably the case but notice the conclusion all cats are dogs doesn&#39;t follow and you can visually represent why that is and it&#39;s obvious too premise one all cats or animals is true premise two all dogs are animals also true conclusion all cats are dogs obviously false that&#39;s the definition of an invalid argument one of which true premises and a false conclusion and that&#39;s another categorical syllogism you wouldn&#39;t try to interpret that as inductive you wouldn&#39;t try to save it and say maybe this is meant to be merely inductive and we can make it a strong argument no this one is clearly a case of an attempted deduction that fails the example we gave with the detective finding your blood on the scene of the crime and or your dna and video of you stabbing all of that could it seems conceivably have been attempted to be deductive but it could also be interpreted as inductive and there it made the most sense to be charitable and assume they don&#39;t mean this as deductive because if they did it would be invalid and therefore a bad argument but if we interpret it as inductive it&#39;s possible to make it a strong one for categorical socialism is drawing it out just the best way to do it because i know that for conditionals you have [Music] i it depends for some people the visual is a lot easier and that&#39;s why i represented there&#39;s a lot more complexities to testing validity with categorical syllogisms using venn diagrams where you get into more complex categorical claims such as and there&#39;s four different versions of it you could be a universal claim all srp where the s is the subject class and the p is the predicate class that&#39;s a specific type of categorical form you can translate all categorical claims into just four all srp no srp there are there are none of this subject class that are members of the predicate class whatever that class may be some s are not p and some srp those get much more confusing and simple euler diagrams are ill-equipped to test validity using that representative model for our purposes i&#39;m mostly focusing on uh how you can either intuitively or with specific forms tell that&#39;s invalid uh or valid and how a deductive argument is distinct from an inductive argument and in a formal cl formal logic class we&#39;d spend a lot more time on testing validity using truth tables using counter examples using venn diagrams and so forth which can get tedious at times and for others it&#39;s you know this is it&#39;s fun because this that&#39;s the answer it&#39;s not a matter of did i get that right or wrong it&#39;s either right or it&#39;s wrong it&#39;s not a matter of degree here&#39;s an example let&#39;s determine what we have there&#39;s a hint here of what kind of argument it is either classical culture originated in greece or originated in egypt classical culture did not originate in egypt therefore it originated in greece what type of argument is this yes disjunctive syllogism and all destructive syllogisms are deductive is it valid it fits that form and you have a hint that it&#39;s a disjunct because of the either or or the neither nor that&#39;s a hint and anything that fits that either p or q i deny that one of them is the case therefore i&#39;m left with the other one now it may be that the claims are mistaken premise one either pure q it originated in greece or in egypt that&#39;s false it&#39;s false because it&#39;s a false dilemma a false choice there may be a third option it could be babylonia or something like that but that&#39;s testing soundness not validity so that argument is vowel it&#39;s a disjunctive syllogism and it is sound presuming all the premises are actually true just to reinforce that conception of soundness oh here&#39;s another one no vegans eat animal products assume that&#39;s true assume fred&#39;s a vegan therefore he doesn&#39;t consume meat if the first two premises are true is there a way to establish that the conclusion could be false and if there isn&#39;t then you&#39;ve got a deductively valid argument and i don&#39;t think you can i think here there&#39;s no counter example there&#39;s no representation of this such that you could have true premises and a false conclusion is it is it sound uh if the is a defense what&#39;s the definition of a vegan if somebody calls himself a vegan and is eating at holdren&#39;s steakhouse one questions whether they understand those words yes okay well what if you argue that the new vegan like burgers oh well that goes back to the question of definition in vegas yeah what would you define yes you can buy jackfruit and they speak of the fruit the jackfruit as the meat of it that&#39;s confusing so the word meat i i&#39;ve i&#39;ve engaged in a problem here you&#39;ve pointed out a problem i can&#39;t have meat but what kind of meat there&#39;s an equivocation there&#39;s fruit meat i guess what lab-grown meat those are still from animals but notice you can take the cells of an animal replicate that copy that and create meat in its petri dish and the animal is just fine it&#39;s not like homer simpson taking a bite out of the animal as the animal&#39;s just sitting there that harms the animal here you take a cell replicate it and you&#39;ve got petri dish meat yes they like the idea of that technology can solve some ethical problems either they can&#39;t do much yet you don&#39;t have enough petri dish meat to feed a lot of people and i&#39;m not sure it tastes great yet they&#39;ve done they&#39;ve done some good progress oh well maybe there it is we&#39;re gonna go eating today let&#39;s go to the lab let&#39;s go to the lab for lunch how about this if george washington was beheaded then george washington died he was watching did die so therefore he was beheaded and what&#39;s had a medieval philosopher professor say of of a medieval scholar named grossa test and it was just occurred to me rosa test was beheaded and shortly thereafter he died that&#39;s how he phrased it why would you mention that we got it when you said he was beheaded immediately he would have died i assume anyway is this valid what does it look like it doesn&#39;t look like what does it look like first you&#39;re saying it&#39;s not valid but doesn&#39;t it look like a particular valid form we&#39;ve seen ah very good if p then q q what&#39;s the queue george washington was if george washington was beheaded p then he died q premise two george washington died that&#39;s q not p it looks like modus ponens or looks like modus tollens it&#39;s just that if it were modus tollens we&#39;d have to be denying that the q is the case and then denying that p is because nothing here establishes the necessity that washington was beheaded unless there&#39;s only one way of dying and that&#39;s by beheading which is the case i believe for the highlander i&#39;m just kidding i&#39;ve never seen that show but that sounds accurate doesn&#39;t it anyone know what i&#39;m talking about the highlander he can only die if he&#39;s beheaded nobody&#39;s seen this show so this example&#39;s crap sorry my point is that there are other ways of dying than beheading and those other ways of dying are not precluded or not excluded even when we presume the truth of those two premises he could have died from something else let&#39;s do a couple more and then we&#39;ll be done here are some examples of so those are all four that&#39;s that&#39;s a deductive form that looks that has a specific fallacy attached to it the formal policy for the fallacy of affirming the consequence but what about arguments that we can&#39;t tell the form specifically and that&#39;s going to take a little bit of creativity in establishing whether it&#39;s valid or not for example premise one blythe is blanche&#39;s biological muppet premise two meliatha is married to blurt i conclude that blur that&#39;s not a name blurt must be borrowed blanche&#39;s i messed up i should have tried too many of these blurs here blurt must be blanche&#39;s biological father now the question can you come up with a possible world a thought experiment in which all those premises are true those two premises are true but the conclusion is false if you can it&#39;s invalid yes um marriage doesn&#39;t determine biological that&#39;s it exactly that&#39;s a counter example this can all be true but that doesn&#39;t necessitate blurt being blanche&#39;s biological father because he could have been the second husband or third that happens too did you have anything else that i know you were correct it&#39;s invalid and it&#39;s automatically unsound what about this hazel taller than filbert filbert it&#39;s taller than pista you see what i&#39;ve done here a little bit of a motif therefore hey i&#39;m sorry promise too filbert&#39;s taller than pistachio therefore hazel is taller than pistachio what do we do here look for a counter example if there is no counter example it&#39;s valid and you must accept the truth of the conclusion assuming the truth of the premises you would be nuts if you didn&#39;t let&#39;s let that sink in the whole setup was just so i can get to this at this point i want to make sure i get credit for that ah there&#39;s the yes the equivocation on nuts uh how do i do this is it valid does the conclusion have to be true he&#39;s how do i how do i even represent it hazel&#39;s taller than filbert how do i say that how do i represent that you did make a big english okay there it is a smaller app okay we can also do that i guess yeah hazel&#39;s taller than filbert it&#39;s a funny name two philbert&#39;s taller than pistachio you do that what follows hazel&#39;s taller than just yes she is this is an argument i got from the singer johnny cashew forgot i had that one in there you can write that down that might that might be on your test the johnny cashy one johnny all right any questions on why that&#39;s valid that has to be true yes yes [Music] very good if hazel&#39;s taller than filbert no no how would you phrase that into a hypothetical you could yeah you&#39;d have to add something else if because you can do it into a categorical form all this is how you do it all people identical to hazel are people who are taller than people who are identical to fill them that&#39;s how you would rephrase it but we&#39;re not doing that uh so yeah it&#39;ll be tough to i don&#39;t know that would be tough it doesn&#39;t quite fit the forms of categorical versus conditional and so forth how about this since the spanish-american war occurred before the civil war and the civil war happened after the korean war it follows that the spanish-american war occurred before the korean war oh and then i say that huh uh i don&#39;t know what form this fits it&#39;s not obvious we have a premise indicator with since it follows that there&#39;s our conclusion the spanish american war occurred before the korea war must be the case that the spanish american war occurred before the korean war assuming the truth of those premises and again we&#39;re assuming the truth of the premises whether or not they are true if you&#39;re historians you might want to immediately point out they&#39;re not or whatever ignore that what do we think valid or invalid and why and how do we even start testing this yeah i would say it&#39;s valid because expansion did not work anymore but one of the premises is false oh you&#39;re basing it upon truth value remember validity though we don&#39;t want to get to there yet so i see we&#39;re going to that yeah but hold off on that until we get to soundness and and only after we&#39;ve determined that it&#39;s vowel because you don&#39;t test soundness unless it&#39;s first established that it&#39;s valid oh go ahead i would say that invalid because because there&#39;s no premises that states how do you know that well doesn&#39;t it how do i is there a way of visually representing this with time how do we do time can you assign them each a letter just like yes and put them on a timeline time&#39;s going that way let&#39;s assume and promise one says spanish-american war occurred before the u.s civil war that means before it&#39;s over here in time civil war happens i don&#39;t know there let&#39;s say that represents accurately premise one spanish-american war occurred before the civil war and the civil war occurred after the korean war that means the korean war was before the civil war and that goes here here you could have been here at the same time as a spanish american in a terrible time notice what we have with three options there to your point we don&#39;t know for sure whether or not the spanish-american war occurred before the korean war or not since there&#39;s more than one option for that conclusion to to graph that so to speak it&#39;s invalid because validity is about absoluteness the conclusion either does necessarily follow or it does not this one&#39;s for fun if you can figure out what&#39;s going on here good for you premise one if a if a deductive argument has all true premises and a false conclusion it is invalid premise two this deductive argument right here it&#39;s representing itself does have all true prophecies at a false conclusion therefore it is invalid what&#39;s cute about this it fits the valid form of if p then q p therefore q so it&#39;s valid as any argument that fits modus ponens is valid but the conclusion tells us it&#39;s invalid so the conclusion must be false but if the conclusion&#39;s false and the true the premises are all true then it&#39;s invalid and then the premise is true which makes it invalid but it&#39;s valid because it&#39;s p modus opponents think about it all right i know think about it and then review that this is the same slide i posted earlier we&#39;re almost there and remember this what makes a good argument it depends if it&#39;s deductive then we say it&#39;s a valid and sound argument and we remember we don&#39;t use the word valid to refer to particular claims we use valid to refer to entire arguments same thing with soundness same thing with as we&#39;ll see next week strong encode refer to arguments as as a whole we say that the claims the premises are true or false and if you want to know what a good inductive argument is well you&#39;ll have to come to class next time all right i will see you all thank you very much for your presence indeed

uh with respect to what we&amp;#39;re covering well today with deduction uh and validity and soundness it&amp;#39;s extremely important for you to get into the habit of writing out your thoughts and ideally for this class into standard logical form because you have thoughts about political issues surrounding um afghanistan and the refugee crisis there you have thoughts about the geopolitical issues surrounding that and or syria or wherever else right i&amp;#39;m not going to narrow it down to just those two specifics although i start with that as a sort of springboard for you to think about um you have thoughts about what a human is what you are what an animal is and how you&amp;#39;re distinct or not from non-human animals you probably think you are sufficiently morally in a relevant sense distinct from a cow or a pig if you didn&amp;#39;t you probably wouldn&amp;#39;t eat them but if you don&amp;#39;t think you&amp;#39;re relatively different from them then you might in fact find that you don&amp;#39;t eat such things and that&amp;#39;s the reason why and maybe others should follow suit but you have these ideas in your head that are all swirling around and it may be just obvious to you what the answer is what the conclusion is but once you start writing out those premises those reasons in support of your opinions you find very quickly how potentially unclear your thinking was on the matter and so getting into the habit of writing and in philosophy it&amp;#39;s a matter of rewriting get your ideas down get as many of them down as you can give as many premises as you can show that they lead to what you think is the case and then come back to it again and again i don&amp;#39;t know that that&amp;#39;s true i don&amp;#39;t have evidence for this why do i think that&amp;#39;s true even if that&amp;#39;s true it doesn&amp;#39;t lead to this other thing that i thought was true writing in philosophy is about revising and unless your bertrand russell who supposedly wrote out a paper once without any amendments submitted it and it got published without any amendments whatsoever i don&amp;#39;t know if that&amp;#39;s true it&amp;#39;s a story but you&amp;#39;re not bertrand russell don&amp;#39;t pretend to be it&amp;#39;s about rewriting so take your time on that and start thinking about those topics now so my point is look over what the assignment is ahead of time so that you have questions for me next time or via email and i&amp;#39;ll reference this again as we get closer now where are we today oh yes sorry uh i just wanted to ask about sources if there&amp;#39;s a minimum nope no minimum no maximum either but it&amp;#39;s a short argumentative paper it&amp;#39;s not a research paper but it&amp;#39;s likely that you will probably need to get sources information unless you&amp;#39;ve already got all the information you might be able to define what a human is and what an animal is or whatever and present present an argument without needing to research on that that&amp;#39;s possible and that&amp;#39;s fine um but it may lead me to call attention to a particular claim that you make that could be empirical or is based on some fact about the world that needs to be cited how do i know this claim is true you might that might require citing something and if you do that&amp;#39;s fine just cite it uh properly mla format chicago format apa whatever your favorite format is and just stick to that consistently okay uh and also remember where we are with assignments and i&amp;#39;ll reference this at the end so and i&amp;#39;ll email too remind you about that because it&amp;#39;s not until midnight but that that&amp;#39;s good in your time but you could forget all right so to the topic here at hand we&amp;#39;ll look at fallacies there&amp;#39;s only a few that i&amp;#39;m going to focus on there&amp;#39;s a lot of ways of going wrong in formal logic but we&amp;#39;re only going to look at a couple and we&amp;#39;ll look at springboarding from last time where we talked about deductive patterns we&amp;#39;ll look at how we might be able to test what pattern fits a deductively valid form which pattern qualifies as truth preserving and which don&amp;#39;t and importantly why that is so what we&amp;#39;re looking at specifically with validity is testing the inferential strength what are the connections among the premises to the conclusion that is not about facts in other words the facts the truth value in reality what you think to be the case and what you can determine to be the case is irrelevant for the purposes of testing validity and that takes us to this question of two things that you get wrong in an argument the argument can be flawed either because you&amp;#39;ve made a mistake with respect to the inference in other words you&amp;#39;ve engaged in a formal fallacy and formal fallacies only applied to deduction formal logic where you&amp;#39;ve presented the case in such a way that the conclusion does not necessarily follow even if we accept the truth of the premises you&amp;#39;ve made an incorrect inference and as we&amp;#39;ll see with induction the parallel there is you&amp;#39;ve presented a case in which the premises even if true do not give support for the likelihood of the premise of the conclusion being true and we would call that a weak argument with induction with deduction we call an argument that is not truth preserving we call it invalid that&amp;#39;s what we&amp;#39;re focusing on today primarily we&amp;#39;ll look at soundness as well but soundness is actually pretty straightforward so we&amp;#39;ll spend most of our time on validity now the other area of getting things wrong is just simply getting the facts wrong you&amp;#39;re mistaken about what is true or false one of your claims or more of them is in fact false you might get the logic perfect impeccable valid deductive argument truth preserving and that&amp;#39;s what you test first you need to get into the habit of doing this assume for the sake of the of argument and for the sake of testing validity in this case that all the premises are true even if the premises are ridiculous even if you disagree with the conclusion assume that if they were true imagine a possible world in which they were true would they necessitate the conclusion would the conclusion have to be true lest we contradict ourselves when we accept the premises that&amp;#39;s true if so you&amp;#39;ve got a valid argument and then and only then do you go and check do the premises have uh are the premises in the real world outside of our thought experiment actually true that&amp;#39;s questioning the facts and if it is truth preserving valid and the premises and on the argument are all true then it&amp;#39;s a valid and sound deductive inference a deductive argument we&amp;#39;re focusing mostly on number one here um we can give an example of this let&amp;#39;s see do i have one so somebody walks in the room let&amp;#39;s say and we&amp;#39;re not we don&amp;#39;t have windows let&amp;#39;s imagine and somebody walks in soaking wet what&amp;#39;s the first thing that comes to mind that it&amp;#39;s probably raining outside that&amp;#39;s a perfectly decent inference in fact we do that kind of stuff all the time and it&amp;#39;s really impressive that our brains can do this and we don&amp;#39;t really think about it we certainly don&amp;#39;t fill in the premises we don&amp;#39;t say to ourselves hmm well that person looks soaking wet and usually premise two people who look soaking wet are soaking wet and when people walk into a room soaking wet it&amp;#39;s usually because they got rained upon this person probably got rained upon therefore i conclude it rains it&amp;#39;s raining outside we don&amp;#39;t usually go through all that and it sounds silly to say it all but i want you to get into the habit of thinking that way because it&amp;#39;s not always silly to include those premises as i just did and the way that i just represented that by the way is that a deduction or an induction was a deductive argument or an inductive argument inductive why is that because you start off with observations [Music] so anything that starts off with an observation is inductive wait can you say the last line of i&amp;#39;ve forgotten uh uh somebody walks in the person premise one that person looks soaking wet promise to people who looks like you went probably are premise three uh usually when people are soaking wet they come in from outside it&amp;#39;s because they got rained on from is four they got rained on therefore it&amp;#39;s raining outside and that&amp;#39;s not how it has to be that&amp;#39;s just how i present it and you say that&amp;#39;s inductive because i&amp;#39;ll give you a hint you&amp;#39;re correct but why are you correct go ahead oh it doesn&amp;#39;t necessarily necessitate the conclusion it&amp;#39;s only highly probable that that is the case because there are other probabilities like say someone just dumped a bunch of a bucket of water yes good like in the bathroom the sink was gone for the men&amp;#39;s room second floor over there it sprays out really fast but only tiny bits of water and then it gets all over you it&amp;#39;s a stupid sink so sorry i get upset with silly things it&amp;#39;s logically possible you can imagine a scenario in which all the premises are true and yet the conclusion is false it&amp;#39;s not running outside that person just fell into the toilet or they went into the ocean the ocean&amp;#39;s right over there that&amp;#39;s possible or if you know in your background expectation you&amp;#39;ve got in your your background framework that there is scheduled today a campus-wide water balloon fight which would be awesome i just realized who wouldn&amp;#39;t want to be engaged in a campus-wide water villain fight if you knew that that was going on you would not jump to the inference to the conclusion that it&amp;#39;s raining outside the more logical inference would be oh they lost in the water balloon fight uh and that&amp;#39;s an intuitive thing that happens immediately it&amp;#39;s not magical and this is why detectives are really good at what they do and and and uh physicians they&amp;#39;re able to recognize what is relevant they&amp;#39;ve got a larger store of background information to call to pull from to recognize that it&amp;#39;s probably this and not this whereas non-experts don&amp;#39;t have all of that to rely upon we might jump to a conclusion that is based upon a representative bias and we don&amp;#39;t have any other alternatives as we&amp;#39;ll see with expertise the experts have a lot more alternatives in their background framework that they can pull from and recognize when it&amp;#39;s relevant when it&amp;#39;s not relevant so let&amp;#39;s say someone walked in your class right now soaking wet when it&amp;#39;s sunny outside do you think you&amp;#39;d still make that conclusion no good if we&amp;#39;re in the basement of this building i don&amp;#39;t know if it has a basement uh and they walked in soaking wet i don&amp;#39;t think i would infer it&amp;#39;s raining because it&amp;#39;s santa barbara and it hasn&amp;#39;t rained in four years i don&amp;#39;t remember last time it&amp;#39;s rained in santa barbara i&amp;#39;m sure it has like a little bit of a tinkle not tinkle sprinkles sprinkles take on something different the lord has tinkled upon us but no i might actually infer that person who was swimming in the ocean that would actually be a more reasonable inference so that&amp;#39;s a very good point where we are and other background information will play a role in strengthening or weakening that argument but with deduction it&amp;#39;s not a matter of strengthening or weakening deduction in a way is clearer it&amp;#39;s crisper a lot of people like that it&amp;#39;s either valid or invalid there&amp;#39;s no in between it&amp;#39;s not kind of valid but you could with induction say yes this conclusion follows with a high degree of probability add some more premises that are true and in fact that increases the probability you don&amp;#39;t make an argument more valid or less valid it&amp;#39;s either one of the others we&amp;#39;ll see um why am i mentioning this oh because i i looked this up uh when i said somebody what was the example you can get the facts wrong or you can get the logical infants wrong if all the claims we said in that argument actually this is out of order this should be what we see here&amp;#39;s the argument uh uh oh here&amp;#39;s the picture guys yeah this is philosophy uh okay so she looks wet most people don&amp;#39;t look into a philosophy classroom with such uh what&amp;#39;s the word yeah i guess there&amp;#39;s a different word lascivious that&amp;#39;s not it anyway premise one she looks wet usually people who look wet are assuming all those premises are true the conclusion is likely and by the way i say likely there if i had said it&amp;#39;s necessarily true that it&amp;#39;s raining outside would that make the argument all of a sudden deductive well i would think so but it would be an invalid good that&amp;#39;s an interesting way of putting it that&amp;#39;s one way of looking at it another way is to say and here i disagree with uh i think it was herrick and i forgot the page that talks about this in the suggested reading that the indicator words necessarily must absolutely indicate deduction indicate necessity indicate a kind of absoluteness certainty and that&amp;#39;s true up to a point and i disagree with him here where he says uh and likely probably possibly that indicates induction i think he the indicator words work for induction but not for deduction it&amp;#39;s not enough to say in a conclusion it&amp;#39;s necessarily true to make it deductive because psychologically we tend to want to make our arguments appear as strong as possible and so we&amp;#39;ll use language that&amp;#39;s as strong as possible but that doesn&amp;#39;t make the logical inference one of deduction of truth preservation however we don&amp;#39;t typically make our arguments appear weaker than they are so i wouldn&amp;#39;t say all men are mortal socrates as a man therefore probably sacrifice is mortal we wouldn&amp;#39;t do that i mean and even throwing the word probably there actually isn&amp;#39;t going to make that an inductive inference and so there&amp;#39;s a hint within with the indicator words probably likely possibly and you should get into the habit of using those properly if you know you&amp;#39;re making a causal argument an enumerative induction a prediction a generalization an argument by analogy all of which we&amp;#39;ll get to next week it&amp;#39;s a good idea to make it clear that you think your conclusion follows with a high degree of probability don&amp;#39;t fool people don&amp;#39;t try to fool people by saying therefore my conclusion necessarily follows because it doesn&amp;#39;t it never does with induction now i&amp;#39;ll come back to that when we look again at the more of the distinction between deduction and induction i can get the facts wrong the logical inference made here is is a good one that&amp;#39;s a strong inductive argument assuming the truth of the premises the conclusion is likely but of course and i looked this up can you be wrong about the style it could be a style of the wet look and i made a joke about that once and then i found this it&amp;#39;s actually a style it&amp;#39;s uh what&amp;#39;s her name actually i don&amp;#39;t know why i asked doesn&amp;#39;t matter so this person&amp;#39;s wearing that style and it looks like her dress is soaking wet it&amp;#39;s kind of like the you know the pants that my daughter&amp;#39;s wearing today the distressed jeans that have the holes pre-ripped in them which upsets me to no end because i had to throw away i didn&amp;#39;t have to it was suggested that i do i had a pair of pants a pair of jeans that had a hole in them that i caused from years of wear and tear and i threw them away and i realized really the reason i threw them away is because i was told they were not in style because they weren&amp;#39;t skinny enough it just pissed me off lately so they didn&amp;#39;t fit that style it wasn&amp;#39;t because they had holes in them i don&amp;#39;t know this is i&amp;#39;m sorry i&amp;#39;m wasting time uh anyway it&amp;#39;s possible that you could be wrong it&amp;#39;s not actually wet that&amp;#39;s just a style those pants actually aren&amp;#39;t ruined that&amp;#39;s how they were designed to look destroyed or whatever it is so you can get the facts wrong or you can get the logical inference wrong we&amp;#39;re interested in the logical inference the logical inference what is the strength does the premises if true do they lead to the necessity of the conclusion or merely the probability of it and what we&amp;#39;re doing with validity and there&amp;#39;s a lot of different ways of saying this and i&amp;#39;ll be a little repetitive here again because it&amp;#39;s in many respects counter-intuitive with validity it is impossible for the premises to be true and the conclusion false if you find that if you set it up such that the conclusion could be false assuming the truth of the premises it&amp;#39;s invalid when we look at representing other people&amp;#39;s arguments and we&amp;#39;re not sure did this person mean for this to be deductive or inductive you may be able to make a translation such that it sounds like it could be deductive but if it were interpreted as a deductive argument and you were to represent it as a deductive argument it would be an invalid one consider the possibility of reinterpreting it as an inductive argument like we did with the uh the sherlock holmes or the detective example right and by the way on your uh discussions uh even if you get a 10 out of 10 on those um look over my comments on them because i&amp;#39;ll sometimes make comments even if you did really well on it and even if you took like a half point off i don&amp;#39;t take a whole lot of points off for those those are main those are low stakes assignments but you need to do them and get them in on time because they&amp;#39;re related to the readings and i want them to be current but my comments are feed forward as i say now even that sounds strange because i don&amp;#39;t like to say here&amp;#39;s why you got points off i&amp;#39;d rather say here&amp;#39;s how you need to improve this for future arguments because that&amp;#39;s what you&amp;#39;re going to be constantly working on in addition to reflecting on the readings and in addition to constructively criticizing other people&amp;#39;s arguments remember you want to respect respond to two others so look at those comments here are other ways of saying basically the same thing except the last one i think goes a bit further how do i know i&amp;#39;m dealing with a valid argument an argument is valid if the premises cannot all be true without the conclusion also being true an argument is valid if the truth of all its promises forces the conclusion to be true an argument is valid if it would be inconsistent we&amp;#39;ll spend a lot more time on consistency and inconsistency with virtues and vices of beliefs later on it is valid if it would be inconsistent for all its premises to be true in its conclusion false another way of saying that is we&amp;#39;d be contradicting ourselves if we said premise one true premise two true but conclusion false in a valid argument an argument is valid if its conclusion follows with certainty from the premises and an argument is valid if it has no counter example that&amp;#39;s the more interesting one and difficult one if there are no counter examples that is a possible situation think of in terms of thought experiments godunkan spiels remember the german word for thought experiment thought play possible situation that makes all the premises true and the conclusion false we&amp;#39;re not dealing with the actual truth value when you test validity for the sake of argument constantly get that into your head that&amp;#39;s the first thing you want to be thinking about when you hear another person presenting what you think is an argument first figure out what the argument is and then assume that what they&amp;#39;re saying is true and let them know that you&amp;#39;re assuming what they&amp;#39;re saying is true that you&amp;#39;re testing the validity testing the strength of what they&amp;#39;re saying you&amp;#39;re not denying outright their premises because you&amp;#39;ve denied the conclusion you can&amp;#39;t deny their conclusion until you&amp;#39;ve established that the premises don&amp;#39;t lead to it so assume the premises are true you&amp;#39;re not doing yourself a disservice and doing that you&amp;#39;re not saying oh my gosh i&amp;#39;m going to actually going to take on the position of this guy well it&amp;#39;s the mark of an educated mind to be able to entertain an idea without accepting it as is attributed to aristotle that&amp;#39;s what you&amp;#39;re doing here in testing for validity so by way of a test of that can you assume that this claim is true that all fish are religious and if that claim is true and also this claim is true anything that&amp;#39;s religious is a dog what follows if anything necessarily from those two clays yes that all fish are dogs is that true yes valid is it valid is it truth preserving can you imagine a possible scenario in which this claim of fisher dogs is false while assuming one and two are true all fish are religious anything that&amp;#39;s religious as a dog all fish are dogs is it valid it is valid and if you don&amp;#39;t no they&amp;#39;re logical this is obviously everything in it is false every single claim is false which tells you truth or falsity have nothing to do with validity if you sniff this pen enough you&amp;#39;ll come to the conclusion yes man all fish are religious wow i i need to use a different one this is silly there we go low odor do you like the scented markers kind of i do yeah you do a little bit so if you&amp;#39;re not sure look in terms of the euler diagrams these circles we can see this is a categorical syllogism where we have a subject class and we&amp;#39;re saying it&amp;#39;s in whole or in part belongs to a predicate class category if it&amp;#39;s a fish or all fish are things that are religious is how you would phrase that in standard categorical form but we&amp;#39;re not focusing on that premise one says anything that&amp;#39;s a fish is a thing that is religious is that an appropriate way of representing premise one does that seem right you put the fish the f circle inside the larger r circle that&amp;#39;s what premise one says premise two says anything that&amp;#39;s religious or all all religious things uh all religious entities are dogs how do i represent that by by barking did somebody just bark the answer out clever what&amp;#39;s that a circle around of course these different colors here and that says anything that&amp;#39;s religious that&amp;#39;s this category is part of the category the larger category of dogs and notice look i don&amp;#39;t need to do anything else the conclusion that all fish are dogs already embedded within those premises it is impossible for this official dogs to be false if we accept the two premises official religious anything as religious as a dog so it&amp;#39;s deductively valid what else do you know about this argument so far as evaluating it it is the claims the premises one or more of the premises are false so just a reminder arguments as a whole are not true or false only the claims within them the claims within an argument are not valid or invalid sound unsound cogent or uncoaching strong or weak they are true or false so as you noted this is valid it&amp;#39;s truth preserving if the premises were true they would necessitate the truth and conclusion but one of the premises or more in fact every damn thing and it is false but again it can tell you that truth or falsity is irrelevant for testing validity yes excellent question why worry about validity if i can say stupid like this valid so it&amp;#39;s not nothing in there is true that&amp;#39;s a very good question a valid argument i have an analogy later on a valid argument is like a good freezer what do you use a good freezer for food food to preserve it a valid argument is like a good freezer you put in uh fresh meat into a freezer and it&amp;#39;s a in the freezer works the analogy here is it&amp;#39;s a proper form you put true premises into the proper form of an argument though that truth gets preserved in the conclusion you put rancid meat into a freezer even if it&amp;#39;s a good freezer it&amp;#39;s not going to make fresh meat you put false premises into a valid argument you&amp;#39;re not going to get a true conclusion right you&amp;#39;re not it&amp;#39;s not going to automatically give you truth in the end the point of a deductive form is to provide us with a tool to determine truth value when we may not know what it is ahead of time and so this will be useful in in science we&amp;#39;d like to have structures that we can use they&amp;#39;re mechanisms where we can plug in where we&amp;#39;re ignorant of the actual truth value but we can still see that if the claims were were true they would necessitate the conclusion at the end and so we&amp;#39;ve got a kind of structure a form a machine that produced that that uh preserves truth that&amp;#39;s the essence of validity um and importantly i can test somebody&amp;#39;s argument remember the two ways of going wrong logical inference could be flawed or the factuals the claims could be factually incorrect but i don&amp;#39;t even need to test in the real world the muddy gray fuzzy areas of truth value if i can establish that somebody&amp;#39;s argument is invalid so your question is a great one that&amp;#39;s why you start by testing validity you start by testing with induction strength or weakness and you ask yourself if those claims were true would they necessitate the conclusion if not or with induction if those claims were true would they lead to the high degree of probability that the conclusion is true if not then you don&amp;#39;t even have to ask whether the premises are in the real world true because it doesn&amp;#39;t matter even if they were true they wouldn&amp;#39;t follow from the premises given and so the argument because it is invalid is by definition unsound and it saves us time in a way too uh but yes that&amp;#39;s a very good question and here&amp;#39;s a joke so what i say all fish are religious no that&amp;#39;s false but it&amp;#39;s true that some are this is probably right at the border of inappropriateness um this is sometimes referred to as the jesus fish this for those of you taking world religions you know that this symbol was used and it&amp;#39;s a symbol i guess you see it on a lot of cars where it&amp;#39;s the official jesus inside it this is the fallacy of equivocation where i use the same word or idea with that has two different contexts two different meanings in the same argument this is the symbol for christians when they were being persecuted by the romans that where they could be and hold their own uh uh rituals and practices uh uh free from and hiding from the roman persecutors in any case i was just trying to engage in equivocation which we&amp;#39;ll see in a couple of weeks a fallacy of ambiguity oh here&amp;#39;s another one santa claus exists assume that&amp;#39;s true if it&amp;#39;s true and also true that anything exists has a foot fetish what follows [Music] santa has a foot fetish you said that without hesitation or reservation it is a valid argument this is an argument that&amp;#39;s i think it was a logic professor like 30 years ago for me and i just can&amp;#39;t get rid of it can&amp;#39;t get rid of it santa exists if that&amp;#39;s true [Music] bus number two of 40 force class 2 i apologize if it&amp;#39;s true that santa exists and it&amp;#39;s true that anything that exists has a foot fetish it has to be the case that santa has a foot fetish i did have a counter to this once a student said wait a minute premise two anything that exists has a foot fetish that means all existing things have a foot fetish can it be a fetish if everybody&amp;#39;s doing it and i it&amp;#39;s pretty good it&amp;#39;s pretty good that&amp;#39;s questioning the soundness of the argument not validity though what is a sound argument it&amp;#39;s one that is deductively valid and actually has true premises we&amp;#39;re not worried about the real world with validity we&amp;#39;re only testing the logical possibilities is it possible santa exists yes is it possible that anything exists has a foot fetish yes if those two are both presumed to be true it follows necessarily that santa has a foot fetish that is valid obviously it is unsound because one or more of those claims is false which ones actually if one of this is a test here which of those claims is false could premise one be could premise one okay never mind they&amp;#39;re all false i was trying to do something with that forget it they&amp;#39;re all false so previously i had an argument that was comprised of all true claims but it was invalid here we&amp;#39;ve got an argument that&amp;#39;s comprised of all false claims but it is valid or maybe i&amp;#39;ve done that backwards maybe i&amp;#39;m going to show you an example of something that has all true claims but is not valid i think that&amp;#39;s what&amp;#39;s going to happen here&amp;#39;s something that has everything in it that&amp;#39;s false in reality and yet the structure of it to your earlier point the structure of it is valid which means the form is which means anything you put into that anything to plug in there&amp;#39;s santa with a i guess a foot fetish i know i&amp;#39;m sorry i couldn&amp;#39;t find anything better although that&amp;#39;s not true if i really looked i could have found something about santa and foot fetishes quite quickly if i had the if i wasn&amp;#39;t in public and not embarrassed to look such things up a valid argument is truth preserving oh here&amp;#39;s the two to your point earlier about argument is truth preserving uh like good freedoms freezers preserve food if you want a valid argument put it in the freezer and you can&amp;#39;t go wrong that&amp;#39;s a mixed metaphor that&amp;#39;s not as funny as i thought it was this kitten kit kitte is in a freezer your argument is involved [Music] i don&amp;#39;t know i tried to get a combination of argument and freezer together and this is that&amp;#39;s as far as i got anyway forget that testing validity here&amp;#39;s an example if bill arrives then we will have plenty of beer ah there&amp;#39;s plenty of beer bill has arrived has bill&amp;#39;s arrival been necessitated by the two premises being true must we accept the truth of the conclusion that bill has arrived if we accept the truth of the two premises oh we see difference i see shaking of heads and nodding of heads how many think this is valid let&amp;#39;s go with that i saw heads nodding means yes we changed our nut they changed our minds on that does anyone think it&amp;#39;s valid anyone think it&amp;#39;s not valid okay great let&amp;#39;s hear why do you think it&amp;#39;s invalid because they could already have like plenty of beer but maybe bill rex will get a lot more beer yeah we don&amp;#39;t know anything about bill and his connection to beer other than what&amp;#39;s said in this conditional and the conditional along with the connecting claim the chain link here and two don&amp;#39;t necessitate bill having arrived even if it wanted to are true it&amp;#39;s still logically possible that the beer could have come from somewhere else and beer bill arriving still means hey more beer but it doesn&amp;#39;t mean that we have bill&amp;#39;s arrival just because we have plenty of beer and you can translate this although it&amp;#39;s difficult and it sounds weird when you translate this currently it&amp;#39;s a conditional and conditional or hypothetical claims are a little bit more unclear visually but you can retran you can represent them into standard category form with by saying things like all times that bill arrives which is what this first premise is going to say all times that bill arrives that&amp;#39;s the circle our times we have plenty of beer this is a time this circle is the category of times we have plenty of beer here&amp;#39;s the times that bill arrives which means any time bill arrives there is plenty of beer all times bill&amp;#39;s ride the tiny beer premise two says there is plenty of beer meaning now is the time there&amp;#39;s plenty of beer where do i put that x representing 2 plenty of beer where must it go assuming premise 2 is true middle here now is a time let&amp;#39;s call it now now is the time we have plenty of beer it is that that&amp;#39;s true but is it the only option it could be now could be here could it be here could it be outside the plenty of beer circle no because that&amp;#39;s not what it says so the visual kind of euler diagram where you represent things in circles if there&amp;#39;s more than one option of where to put a premise or a conclusion it&amp;#39;s not obviously and necessarily one way or another we know it&amp;#39;s invalid because that tells us this could be false right does bill it does now have to be a time in which bill has arrived it&amp;#39;s unclear there&amp;#39;s more than one option and all it takes is two options all it takes is a logically possible conclusion in which this doesn&amp;#39;t turn out to be absolutely possible excuse me absolutely true and so it is invalid because it is not truth preserving and if it&amp;#39;s invalid it is unsound and we can also see even without doing all this i&amp;#39;ll get him a second we can also see the logical relationship among the parts of a conditional statement show us why it&amp;#39;s invalid why the conclusion doesn&amp;#39;t have to be self because this form if billerize we have plenty of beer if p then q premise 2 there&amp;#39;s plenty of beer that&amp;#39;s q that&amp;#39;s the consequent and remember the parts of a conditional the antecedent provides us with a sufficient condition for the truth of the consequent and the consequent the part that&amp;#39;s after the then provides us with a necessary condition for the truth of the antecedent that&amp;#39;s abstract and confusing but it tells us why this argument is invalid because what are we doing we are affirming that the consequent q there is plenty of beer is true we have affirmed that a necessary condition has been met for the antecedent that bill arrives but just because we&amp;#39;ve affirmed a necessary condition to your earlier point we have not shown that the antecedent has to be true in the same way that if i said did you take care of the kids let&amp;#39;s say i&amp;#39;m with the kids for a month i&amp;#39;m by myself god and my wife comes home did you take care of the kids i said yes they have water what have you fed them i gave them water water is necessary is it not yes but not enough you haven&amp;#39;t kept them alive just because you&amp;#39;ve given them this is a terrible example but you see that just to get to how it&amp;#39;s invalid it&amp;#39;s an error in reason i&amp;#39;ve affirmed that a necessary condition has been met and assumed that that&amp;#39;s enough for the antecedent wouldn&amp;#39;t this be more valid if he swapped two and three well be cautious more valid implies there&amp;#39;s degrees to it well i mean so the first one he sets up like what you need and then number three would provide proof to number two good oh so it wouldn&amp;#39;t make it more valid it would just simply make it valid that&amp;#39;s exactly right if i uh did i get it right yeah you said if billerize then we have plenty of beer and you want to switch it bill has arrived as premise 2. and then the conclusion is we have plenty of beer that would be valid in fact there&amp;#39;s a logical form called modus ponens that fits that form that is that form and anything you plug into modus ponens which is if p then q p the antecedent i&amp;#39;m affirming that the antecedent is the case in other words i&amp;#39;m affirming that a sufficient condition has been met for the consequent and if i&amp;#39;ve given you a sufficient condition for something that something is the case therefore if p then q p therefore q is how you presented it and you would be right that&amp;#39;s valid and anything you plug into that would be valid did you take care of the kids yes i gave them water because that&amp;#39;s necessary and cocoa melon [Music] what kids tv show and they were able to watch cocoa melon which is necessary for their survival obviously are those two necessary and jointly sufficient do you see where i&amp;#39;m getting it no they need more than water and cocoa melon i haven&amp;#39;t not heard of that sounds terrible they need water cocoa melon they need food they need sleep yes they need sleep we know we need sleep the military&amp;#39;s tested this they want to try to make troops that don&amp;#39;t sleep you can&amp;#39;t you&amp;#39;ll die if you don&amp;#39;t sleep what is the other thing shelter shelter no no shelter and sleep are different you need you need sleep you need shelter you need oxygen you need full oxygen yeah there it is uh i don&amp;#39;t know how many that is there&amp;#39;s like five or six of them they are necessary independently and jointly sufficient and oh and then a seventh you need you need philosophy or you will die thank you for that heavy silence and recognizing the truth of that claim fallacy of affirming the consequent i&amp;#39;ll get to it a little bit more it looks like the other argument sorry for all the words here you have access to these slides fallacy of affirming the consequent it looks very similar to the modus ponens if p then q p therefore q modus ponens the way of positive i&amp;#39;ll give more examples of that we saw some of those from last class and it looks similar to the modus tollens but with modus tollens where you deny the consequent you say look a necessary condition hasn&amp;#39;t been met but then you are also then denying the antecedent in denying the consequent but that&amp;#39;s not what&amp;#39;s being said in that previous example instead of denying the consequence of the modest tolerance it&amp;#39;s asserting that the consequent is true and when you assert that the consequent in a conditional statement is true you&amp;#39;ve only given us a sufficient condition this only tells us a sufficient condition is met when you assert the consequence which cannot necessitate the truth at the conclusion wait a minute what but instead of denying the concept you&amp;#39;re asserting the concept the consequent provides us with a necessary condition if it&amp;#39;s a cat that&amp;#39;s the antecedent then it&amp;#39;s an animal being an animal is necessary to being a cat it&amp;#39;s not enough because there are animals that are not cats being a cat is enough to be an animal it&amp;#39;s all you need but it&amp;#39;s not uh sufficient so this should be necessary oh good lord i&amp;#39;m glad i caught that now i&amp;#39;ve confused myself that&amp;#39;s correct now so rephrase instead of denying the consequent as with modus tollens we are asserting that the consequent is true and that only tells us that a necessary condition has been met water is necessary therefore my kids are alive uh what no that&amp;#39;s not enough that&amp;#39;s not enough to necessitate the truth conclusion so we have the possibility of all true premises yet a false conclusion that&amp;#39;s always what we&amp;#39;re looking for in testing in validity is it invalid i don&amp;#39;t know can you make it such that it or can you show that the form of it would lead to a false conclusion even though all the premises are true and i&amp;#39;ll show a lot of examples that&amp;#39;ll be somewhat repetitive but it&amp;#39;s useful to have these examples and as always just stop me if something&amp;#39;s unclear so the fallacy of affirming the consequence i&amp;#39;m saying that an unnecessary condition has been met if i am human then i&amp;#39;m an animal and adam premise two i am an animal assuming both of those are true does it necessitate the conclusion that i am a human everything in it is true if i&amp;#39;m human then i&amp;#39;m an animal it&amp;#39;s also true that i&amp;#39;m an animal oh here&amp;#39;s the example i was mentioning earlier everything in this argument is true every premise is true the conclusion is also true but it is not truth preserving because of the incorrect form it is invalid the fallacy of affirming the consequent to get a sense of why that is consider this premise one if i&amp;#39;m a chicken then i&amp;#39;m an animal if p and q if p then q same form if i&amp;#39;m a chicken then i&amp;#39;m an animal i am an animal i&amp;#39;m talking about meat all humans are animals right lola my daughter still doesn&amp;#39;t think that&amp;#39;s the case what are we then we&amp;#39;re humans that&amp;#39;s circular lola you can&amp;#39;t say a human is a human that&amp;#39;s a terrible definition you beg the question that conversation ends very quickly you start that way prayers too i&amp;#39;m an animal what have i asserted this the consequence it must be that i&amp;#39;m a chicken well if i&amp;#39;m a chicken then i&amp;#39;m an animal i am an animal therefore i&amp;#39;m a chicken okay that is false i am not a chicken but these are true true premises false conclusion invalid why is it invalid because i&amp;#39;ve only given us a necessary condition the way to make that valid would be to say if and only if i am a chicken can i be an animal which is to say the only kinds of animals there are are chickens and if that were true and that&amp;#39;s how i wrote it if and only if where that gives the necessary and sufficient conditions for chicken hood or animality animality and i am an animal then i would have to be a chicken because there are no other animals but chickens that&amp;#39;s how i would have to make that valid but of course we know that&amp;#39;s unsound because it&amp;#39;s not true that the only kinds of animals are chickens so to go back to the beer example as this was mentioned immediately and sometimes you can intuitively figure it out this doesn&amp;#39;t work something&amp;#39;s gone wrong what we&amp;#39;re doing now is showing what is the underlying logic that proves why it&amp;#39;s invalid that proves why it&amp;#39;s not truth preserved so uh oh every time bill&amp;#39;s here there&amp;#39;s plenty of fear hey there&amp;#39;s plenty of beer bill must have arrived those two claims don&amp;#39;t preclude the possibility of beer coming from someone else and so the premises could all be true and yet the conclusion false proving that the argument isn&amp;#39;t valid there are other examples oh with bill actually this is the example you gave earlier if bill arrives we have plenty of beer hey bill has arrived we&amp;#39;ve got plenty of beer that&amp;#39;s modus ponens if p then q premise two bill&amp;#39;s arrived p i&amp;#39;m a certain affirming i&amp;#39;m stating that it is the case that the antecedent is true which is to say i&amp;#39;m providing a sufficient condition for the consequent it&amp;#39;s enough and if you found enough you get the thing in question bill arriving is sufficient for there being plenty of beer therefore it&amp;#39;s valid and anything you plug into that modus ponens form is going to be truth preserving no matter what it is no matter how ridiculous it is it&amp;#39;s going to be valid but you&amp;#39;ve got another error that looks similar to those valid forms there&amp;#39;s something called the fallacy of denying the antecedent here&amp;#39;s where i say a sufficient condition is not being met and if that&amp;#39;s the case does it lead to the consequent being false if p is the case then q is the case but p isn&amp;#39;t the case therefore q isn&amp;#39;t the case that abstract variable form is not obvious but when you put it in terms of like this if you like dogs instead of cats here&amp;#39;s that example premise one if i&amp;#39;m a dog then i&amp;#39;m a mammal if pete and cute i&amp;#39;m not a dog not p that&amp;#39;s premise two i&amp;#39;m not a dog therefore i&amp;#39;m not a mammal now you can see that this is clearly false and these are true making this invalid what have i done i&amp;#39;ve denied a sufficient condition but nothing in those two premises precludes me being a mammal these can both be true and yet this is false again unless we assume the only mammals that exist are dogs if that were true if we said that but that&amp;#39;s not what we&amp;#39;re saying if we said if and only if i&amp;#39;m a dog in my enamel then the conclusion would follow when necessary would follow with necessity that i am not a mammal but that&amp;#39;s not what the premise says question no that is the fallacy of denying the antecedent saying that we don&amp;#39;t have a sufficient condition for q therefore q cannot be the case that doesn&amp;#39;t follow and i think i have more examples oh yes oh wow that all came out at once so all capitalists premise one all capitalists are conservatives is that true i don&amp;#39;t know doesn&amp;#39;t matter assume it is carl there&amp;#39;s a little joke here carl is a conservative therefore carl is a capitalist obviously carl marx let&amp;#39;s have a little fun there is it does it follow necessarily the call is a capitalist i don&amp;#39;t know actually it&amp;#39;s hard to tell what is the logical connections between those categories and among those categories here is a counter example with a substitution instance which is to say an exact replica of form since we&amp;#39;re only dealing with form if i can show that that form is the same as this one and this form is invalid i have proven that that form is invalid even though i don&amp;#39;t know who carl is i don&amp;#39;t look out i don&amp;#39;t know much about capitalists and conservatives and so forth i can translate it as premise one all cats are animals assume it&amp;#39;s true premise two i am an animal premise three i am a cat that does not follow this is invalid and it&amp;#39;s the exact same form as that making that invalid and if it&amp;#39;s invalid it&amp;#39;s also what unsound you have can you just correct all of this with just providing more examples are using clearer language like is the following of most of the seems like most of this is just uh dangerous yeah we haven&amp;#39;t gotten to that yet sorry do i want to bring in vagueness yet more or less i do two days yeah it is hard to not introduce yes we all kind of have a sense of what vagueness is good point um so where&amp;#39;s the vagueness here and what a conservative is uh yeah or not providing alternatives um or that there are too many alternatives and you haven&amp;#39;t defined what you&amp;#39;re doing yes and we&amp;#39;ll come to definitions soon you&amp;#39;re right and this is a problem with trying to shoehorn in your case your belief system into a deductive form because it&amp;#39;s very clear this is either valid or invalid but the soundness whether they&amp;#39;re playing whether the claims are true or not and of course it&amp;#39;s only determined to be sound if it&amp;#39;s already valid to begin with but are they sound is it true that all capitalists are conservatives well what do you mean by capitalist and what do you mean by conservative how conservative conservative is vague and what a capitalist is vague chinese government engages in capitalistic acts all the time but i don&amp;#39;t think the chinese government is necessarily capitalistic in the sense that we typically use it so you&amp;#39;re right that&amp;#39;s a problem with induction and it&amp;#39;s a problem with definitions which we&amp;#39;re going to spend a lot of time on so there are ways of avoiding some of the problems with these but technically and all we&amp;#39;re doing here is looking at validity and testing for it this is invalid because it&amp;#39;s not truth preserving as it&amp;#39;s stated and maybe we can fix it oh there&amp;#39;s a cat why do i have hank there uh all cats are animals i have a cat and here i say no i&amp;#39;m not because that&amp;#39;s not me which is actually terrible reasoning on my part since i am not this particular cat i am not a cat does that make sense it&amp;#39;d be like saying i&amp;#39;m not you therefore i&amp;#39;m not a human there are other humans in any case i&amp;#39;m also not a cat that&amp;#39;s just true how about this promise one god if god does not exist objective moral values do not exist premise support promise two objective moral values do exist this is tricky anytime you have negations it gets tricky what follows god exists can anyone guess the form of this put some p&amp;#39;s and q&amp;#39;s in there and mind your p&amp;#39;s and q&amp;#39;s does anyone know where that comes from by the way mind your p&amp;#39;s isn&amp;#39;t and q&amp;#39;s military thing probably i actually don&amp;#39;t know it&amp;#39;s hoping somebody did it well my dad was in the navy and he told me when they were good when they would like dock um off their ships they say like mind your p&amp;#39;s and q&amp;#39;s like when you go to the yes because there so you don&amp;#39;t you don&amp;#39;t get like give me a uh give me a pint well i guess we do call them pints here what am i saying yeah mind your p&amp;#39;s and q&amp;#39;s don&amp;#39;t spill your pints or your quartz he&amp;#39;s drinking a quart of beer so oh right sorry that was a bit of an aside is this valid in what form is it yes yes it&amp;#39;s mother&amp;#39;s tollens because you&amp;#39;re denying a consequence yes and it doesn&amp;#39;t look like you&amp;#39;re denying the consequent because you&amp;#39;re stating something is the case but notice when you state something is the case in premise two it&amp;#39;s denying that something is not the case it&amp;#39;s a double negation if you want to be very very clear you would say if p then q or you could say i don&amp;#39;t like this way of doing it but you could say if p then not q which is not how modus tollens works premise 2 says it is not the case that not p and not q therefore is not the case that not p that&amp;#39;s too confusing unnecessarily so instead you say do i have it if p then q not q premise two the q the consequence says objective moral values do not exist what&amp;#39;s the negation of that that they do this is still not q the conclusion not p in other words therefore god exists why is god exists equal to not p because p is god does not exist do you see and the negation of god does not exist is god does exist so this is if p then q not q therefore not p you&amp;#39;ve denied the consequent you&amp;#39;ve removed the necessary condition that is valid is it sound take philosophy of religion class to find out next semester how about that or write a paper in this class about something like this at the end and that paper can be a springboard into a larger work in the philosophy of religion class next spring or fall spring let&amp;#39;s talk about serial killers shall we all serial killers are shy is that true who cares we&amp;#39;re not dealing with truth value yet all serial killers are shy i resi i represent that by this if it&amp;#39;s a serial killer it&amp;#39;s part of the larger category of shy entities shy people all serial killers are shy that&amp;#39;s premise one smaller circle serial killers into the largest circle of shy people franklin&amp;#39;s a serial killer where does franklin have to go boom what does it tell you i don&amp;#39;t even need to finish it what do you know franklin is shy it necessarily follows it is a valid categorical syllogism is it sound not if ted bundy counts as a counter-example and he defended himself if you&amp;#39;re familiar with ted bundy absolutely wretched human being was a serial killer and was not shy so there&amp;#39;s a counter example to premise one all killers are shot our serial killers are shy that&amp;#39;s false and we only need one counter example to prove that premise one is false so what do we have here a valid but unsound argument it&amp;#39;s valid because it&amp;#39;s truth preserving if the premises were true they would necessitate the truth the conclusion but it is in uh it is unsound not because it&amp;#39;s invalid that would be one reason to make it unsound but it is unsound because one or more of the premises can be uh determined to be false more about serial killers shall we premise one all silicones are shy franklin&amp;#39;s not shy that&amp;#39;s the same structure with the euler diagram franklin&amp;#39;s not shy where does franklin go here yeah maybe here yeah all that that means that means the same thing he&amp;#39;s not in the category of shyness whether he&amp;#39;s there or there that still means not shot and notice he can&amp;#39;t be in there if he can&amp;#39;t even get into the outer circle if he&amp;#39;s not shy then he&amp;#39;s not a serial killer because assuming the truth of premise one all serial killers are shy and if franklin doesn&amp;#39;t fit that category then he&amp;#39;s not a serial killer and that&amp;#39;s what we have here so good for franklin is it true no again it&amp;#39;s unsound because i don&amp;#39;t even need to know anything about franklin i know premise one is false so it&amp;#39;s unsound could you use the same counter in the previous slide not being shy oh yes exactly that&amp;#39;s what makes this exact that would make this unsound uh but it is still valid but it&amp;#39;s just a different structure than the previous argument all right we don&amp;#39;t no we&amp;#39;re not we&amp;#39;re not done with serial killers okay same thing franklin&amp;#39;s not a serial killer okay but different where does franklin go premise two could be there right yeah uh could he be here yeah could he be here doesn&amp;#39;t say that but notice we have two options president is not a serial killer what follows from that that he&amp;#39;s not shy uh maybe but notice this is a possibility and so is this in other words those both might be true i&amp;#39;m sorry those could be assumed to be true and yet this could still be false anytime there&amp;#39;s more than a single option for your conclusion that tells you it&amp;#39;s not necessarily true there are alternatives even when we accept the truth of the premises and this one&amp;#39;s unsound not because the premises are false that&amp;#39;s an additional worry but we&amp;#39;re not even needing to get to that we know it&amp;#39;s unsound already because it&amp;#39;s automatically excuse me it&amp;#39;s automatically unsound because it is invalid because the definition of a sound argument is one that is valid first and in reality has all true promises okay we&amp;#39;re away from serial killers good i think we did this one already all cats are animals oh dogs are animals no we didn&amp;#39;t therefore all cats are dogs i didn&amp;#39;t label this one and it&amp;#39;s not actually in your texts so i&amp;#39;m not gonna i don&amp;#39;t think it is you&amp;#39;re not gonna be responsible for knowing the name of this it&amp;#39;s called the fallacy of the undistributed middle don&amp;#39;t worry about the details of that all cats are animals uh all dogs are animals already i don&amp;#39;t know what the hell to do do i say that do i say that ah this and it gets very confusing notice those are three possibilities premise two says all dogs are animals as long as the category of dogs is within the larger circle of animals we&amp;#39;ve said something that is true with respect to this argument but i don&amp;#39;t know where to put the dog does it overlap the cats or does the cats overlap the dogs or is dogs a separate category altogether still under the larger heading of animal which is probably the case but notice the conclusion all cats are dogs doesn&amp;#39;t follow and you can visually represent why that is and it&amp;#39;s obvious too premise one all cats or animals is true premise two all dogs are animals also true conclusion all cats are dogs obviously false that&amp;#39;s the definition of an invalid argument one of which true premises and a false conclusion and that&amp;#39;s another categorical syllogism you wouldn&amp;#39;t try to interpret that as inductive you wouldn&amp;#39;t try to save it and say maybe this is meant to be merely inductive and we can make it a strong argument no this one is clearly a case of an attempted deduction that fails the example we gave with the detective finding your blood on the scene of the crime and or your dna and video of you stabbing all of that could it seems conceivably have been attempted to be deductive but it could also be interpreted as inductive and there it made the most sense to be charitable and assume they don&amp;#39;t mean this as deductive because if they did it would be invalid and therefore a bad argument but if we interpret it as inductive it&amp;#39;s possible to make it a strong one for categorical socialism is drawing it out just the best way to do it because i know that for conditionals you have [Music] i it depends for some people the visual is a lot easier and that&amp;#39;s why i represented there&amp;#39;s a lot more complexities to testing validity with categorical syllogisms using venn diagrams where you get into more complex categorical claims such as and there&amp;#39;s four different versions of it you could be a universal claim all srp where the s is the subject class and the p is the predicate class that&amp;#39;s a specific type of categorical form you can translate all categorical claims into just four all srp no srp there are there are none of this subject class that are members of the predicate class whatever that class may be some s are not p and some srp those get much more confusing and simple euler diagrams are ill-equipped to test validity using that representative model for our purposes i&amp;#39;m mostly focusing on uh how you can either intuitively or with specific forms tell that&amp;#39;s invalid uh or valid and how a deductive argument is distinct from an inductive argument and in a formal cl formal logic class we&amp;#39;d spend a lot more time on testing validity using truth tables using counter examples using venn diagrams and so forth which can get tedious at times and for others it&amp;#39;s you know this is it&amp;#39;s fun because this that&amp;#39;s the answer it&amp;#39;s not a matter of did i get that right or wrong it&amp;#39;s either right or it&amp;#39;s wrong it&amp;#39;s not a matter of degree here&amp;#39;s an example let&amp;#39;s determine what we have there&amp;#39;s a hint here of what kind of argument it is either classical culture originated in greece or originated in egypt classical culture did not originate in egypt therefore it originated in greece what type of argument is this yes disjunctive syllogism and all destructive syllogisms are deductive is it valid it fits that form and you have a hint that it&amp;#39;s a disjunct because of the either or or the neither nor that&amp;#39;s a hint and anything that fits that either p or q i deny that one of them is the case therefore i&amp;#39;m left with the other one now it may be that the claims are mistaken premise one either pure q it originated in greece or in egypt that&amp;#39;s false it&amp;#39;s false because it&amp;#39;s a false dilemma a false choice there may be a third option it could be babylonia or something like that but that&amp;#39;s testing soundness not validity so that argument is vowel it&amp;#39;s a disjunctive syllogism and it is sound presuming all the premises are actually true just to reinforce that conception of soundness oh here&amp;#39;s another one no vegans eat animal products assume that&amp;#39;s true assume fred&amp;#39;s a vegan therefore he doesn&amp;#39;t consume meat if the first two premises are true is there a way to establish that the conclusion could be false and if there isn&amp;#39;t then you&amp;#39;ve got a deductively valid argument and i don&amp;#39;t think you can i think here there&amp;#39;s no counter example there&amp;#39;s no representation of this such that you could have true premises and a false conclusion is it is it sound uh if the is a defense what&amp;#39;s the definition of a vegan if somebody calls himself a vegan and is eating at holdren&amp;#39;s steakhouse one questions whether they understand those words yes okay well what if you argue that the new vegan like burgers oh well that goes back to the question of definition in vegas yeah what would you define yes you can buy jackfruit and they speak of the fruit the jackfruit as the meat of it that&amp;#39;s confusing so the word meat i i&amp;#39;ve i&amp;#39;ve engaged in a problem here you&amp;#39;ve pointed out a problem i can&amp;#39;t have meat but what kind of meat there&amp;#39;s an equivocation there&amp;#39;s fruit meat i guess what lab-grown meat those are still from animals but notice you can take the cells of an animal replicate that copy that and create meat in its petri dish and the animal is just fine it&amp;#39;s not like homer simpson taking a bite out of the animal as the animal&amp;#39;s just sitting there that harms the animal here you take a cell replicate it and you&amp;#39;ve got petri dish meat yes they like the idea of that technology can solve some ethical problems either they can&amp;#39;t do much yet you don&amp;#39;t have enough petri dish meat to feed a lot of people and i&amp;#39;m not sure it tastes great yet they&amp;#39;ve done they&amp;#39;ve done some good progress oh well maybe there it is we&amp;#39;re gonna go eating today let&amp;#39;s go to the lab let&amp;#39;s go to the lab for lunch how about this if george washington was beheaded then george washington died he was watching did die so therefore he was beheaded and what&amp;#39;s had a medieval philosopher professor say of of a medieval scholar named grossa test and it was just occurred to me rosa test was beheaded and shortly thereafter he died that&amp;#39;s how he phrased it why would you mention that we got it when you said he was beheaded immediately he would have died i assume anyway is this valid what does it look like it doesn&amp;#39;t look like what does it look like first you&amp;#39;re saying it&amp;#39;s not valid but doesn&amp;#39;t it look like a particular valid form we&amp;#39;ve seen ah very good if p then q q what&amp;#39;s the queue george washington was if george washington was beheaded p then he died q premise two george washington died that&amp;#39;s q not p it looks like modus ponens or looks like modus tollens it&amp;#39;s just that if it were modus tollens we&amp;#39;d have to be denying that the q is the case and then denying that p is because nothing here establishes the necessity that washington was beheaded unless there&amp;#39;s only one way of dying and that&amp;#39;s by beheading which is the case i believe for the highlander i&amp;#39;m just kidding i&amp;#39;ve never seen that show but that sounds accurate doesn&amp;#39;t it anyone know what i&amp;#39;m talking about the highlander he can only die if he&amp;#39;s beheaded nobody&amp;#39;s seen this show so this example&amp;#39;s crap sorry my point is that there are other ways of dying than beheading and those other ways of dying are not precluded or not excluded even when we presume the truth of those two premises he could have died from something else let&amp;#39;s do a couple more and then we&amp;#39;ll be done here are some examples of so those are all four that&amp;#39;s that&amp;#39;s a deductive form that looks that has a specific fallacy attached to it the formal policy for the fallacy of affirming the consequence but what about arguments that we can&amp;#39;t tell the form specifically and that&amp;#39;s going to take a little bit of creativity in establishing whether it&amp;#39;s valid or not for example premise one blythe is blanche&amp;#39;s biological muppet premise two meliatha is married to blurt i conclude that blur that&amp;#39;s not a name blurt must be borrowed blanche&amp;#39;s i messed up i should have tried too many of these blurs here blurt must be blanche&amp;#39;s biological father now the question can you come up with a possible world a thought experiment in which all those premises are true those two premises are true but the conclusion is false if you can it&amp;#39;s invalid yes um marriage doesn&amp;#39;t determine biological that&amp;#39;s it exactly that&amp;#39;s a counter example this can all be true but that doesn&amp;#39;t necessitate blurt being blanche&amp;#39;s biological father because he could have been the second husband or third that happens too did you have anything else that i know you were correct it&amp;#39;s invalid and it&amp;#39;s automatically unsound what about this hazel taller than filbert filbert it&amp;#39;s taller than pista you see what i&amp;#39;ve done here a little bit of a motif therefore hey i&amp;#39;m sorry promise too filbert&amp;#39;s taller than pistachio therefore hazel is taller than pistachio what do we do here look for a counter example if there is no counter example it&amp;#39;s valid and you must accept the truth of the conclusion assuming the truth of the premises you would be nuts if you didn&amp;#39;t let&amp;#39;s let that sink in the whole setup was just so i can get to this at this point i want to make sure i get credit for that ah there&amp;#39;s the yes the equivocation on nuts uh how do i do this is it valid does the conclusion have to be true he&amp;#39;s how do i how do i even represent it hazel&amp;#39;s taller than filbert how do i say that how do i represent that you did make a big english okay there it is a smaller app okay we can also do that i guess yeah hazel&amp;#39;s taller than filbert it&amp;#39;s a funny name two philbert&amp;#39;s taller than pistachio you do that what follows hazel&amp;#39;s taller than just yes she is this is an argument i got from the singer johnny cashew forgot i had that one in there you can write that down that might that might be on your test the johnny cashy one johnny all right any questions on why that&amp;#39;s valid that has to be true yes yes [Music] very good if hazel&amp;#39;s taller than filbert no no how would you phrase that into a hypothetical you could yeah you&amp;#39;d have to add something else if because you can do it into a categorical form all this is how you do it all people identical to hazel are people who are taller than people who are identical to fill them that&amp;#39;s how you would rephrase it but we&amp;#39;re not doing that uh so yeah it&amp;#39;ll be tough to i don&amp;#39;t know that would be tough it doesn&amp;#39;t quite fit the forms of categorical versus conditional and so forth how about this since the spanish-american war occurred before the civil war and the civil war happened after the korean war it follows that the spanish-american war occurred before the korean war oh and then i say that huh uh i don&amp;#39;t know what form this fits it&amp;#39;s not obvious we have a premise indicator with since it follows that there&amp;#39;s our conclusion the spanish american war occurred before the korea war must be the case that the spanish american war occurred before the korean war assuming the truth of those premises and again we&amp;#39;re assuming the truth of the premises whether or not they are true if you&amp;#39;re historians you might want to immediately point out they&amp;#39;re not or whatever ignore that what do we think valid or invalid and why and how do we even start testing this yeah i would say it&amp;#39;s valid because expansion did not work anymore but one of the premises is false oh you&amp;#39;re basing it upon truth value remember validity though we don&amp;#39;t want to get to there yet so i see we&amp;#39;re going to that yeah but hold off on that until we get to soundness and and only after we&amp;#39;ve determined that it&amp;#39;s vowel because you don&amp;#39;t test soundness unless it&amp;#39;s first established that it&amp;#39;s valid oh go ahead i would say that invalid because because there&amp;#39;s no premises that states how do you know that well doesn&amp;#39;t it how do i is there a way of visually representing this with time how do we do time can you assign them each a letter just like yes and put them on a timeline time&amp;#39;s going that way let&amp;#39;s assume and promise one says spanish-american war occurred before the u.s civil war that means before it&amp;#39;s over here in time civil war happens i don&amp;#39;t know there let&amp;#39;s say that represents accurately premise one spanish-american war occurred before the civil war and the civil war occurred after the korean war that means the korean war was before the civil war and that goes here here you could have been here at the same time as a spanish american in a terrible time notice what we have with three options there to your point we don&amp;#39;t know for sure whether or not the spanish-american war occurred before the korean war or not since there&amp;#39;s more than one option for that conclusion to to graph that so to speak it&amp;#39;s invalid because validity is about absoluteness the conclusion either does necessarily follow or it does not this one&amp;#39;s for fun if you can figure out what&amp;#39;s going on here good for you premise one if a if a deductive argument has all true premises and a false conclusion it is invalid premise two this deductive argument right here it&amp;#39;s representing itself does have all true prophecies at a false conclusion therefore it is invalid what&amp;#39;s cute about this it fits the valid form of if p then q p therefore q so it&amp;#39;s valid as any argument that fits modus ponens is valid but the conclusion tells us it&amp;#39;s invalid so the conclusion must be false but if the conclusion&amp;#39;s false and the true the premises are all true then it&amp;#39;s invalid and then the premise is true which makes it invalid but it&amp;#39;s valid because it&amp;#39;s p modus opponents think about it all right i know think about it and then review that this is the same slide i posted earlier we&amp;#39;re almost there and remember this what makes a good argument it depends if it&amp;#39;s deductive then we say it&amp;#39;s a valid and sound argument and we remember we don&amp;#39;t use the word valid to refer to particular claims we use valid to refer to entire arguments same thing with soundness same thing with as we&amp;#39;ll see next week strong encode refer to arguments as as a whole we say that the claims the premises are true or false and if you want to know what a good inductive argument is well you&amp;#39;ll have to come to class next time all right i will see you all thank you very much for your presence indeed

Transcript for:Lecture on Deductive Reasoning, Validity, and Soundness

Transcript for:
Lecture on Deductive Reasoning, Validity, and Soundness