Transcript for:
Lecture on Deduction and Induction

so we are on to deduction i have here deduction dear pupils of course i'm making reference to whom deduction dear who says who says deduction all the time sherlock holmes does that's correct because he's a brilliant man and he uses he uses deductive reasoning all the time is that why he says it all the time why does he say deduction all the time what is the difference we're going to see between deduction and induction what is the argument that we can give this is just i'd like to throw a meme in every once in a while that's the philosoraptor as you can see but lord that's loud sorry the question to be or not to be in logic that's always true of course it's a question so questions don't have truth value but what's basically saying here is to exist or not to exist one exists or one does not i am or i am not that's a tautology in logic and that's referenced in one of the suggested readings tall oh g is the opposite of a contradiction in many ways and we'll look at both of these but mostly at the second one contradiction contradictions always false and the tautology is always true either it will rain tomorrow or it will not that is always true regardless of what the world happens to be like in a contradiction it is raining and it is not raining at the same time in the same place and so forth is always going to be false in our arguments we want to avoid in particular the contradictions and contradiction means to speak against specifically contradiction is something we look for in determining whether or not we've got what's known as a deductively valid argument what constitutes a deductively valid argument well let's look at sherlock holmes here's a little story about sherlock holmes and his good friend dr watson camping in the woods holmes and watson decide to go on a trip camping after dinner and a bottle of wine they lay down for the night and go to sleep some hours later holmes awoke and nudged his faithful friend watson look up this guy and tell me what you see watson replied i see millions of stars what does that tell you holmes asks and then watson goes into a lot of possibilities for what it means to be able to see the sky astronomically tells me excuse me astronomically it tells me that there are millions of galaxies and potentially billions of planets astrologically i observe that saturn is in leo horologically i deduce interesting use of the term deduce there oh where's my laser i've lost my laser oh my we can't go on what the hell it worked just last class okay uh i deduce that the time is approximately a quarter past three theologically i can see that god is all-powerful and that we are small and insignificant meteorologically i suspect we'll have a beautiful day tomorrow what does it tell you holmes he was signing for a minute then he spoke watson you idiot someone has stolen our intent now there's a couple of questions one is what form of reasoning did sherlock holmes just use to establish the conclusion that someone has stolen the tent did he use deduction induction and why either way yep let's say deduction because he's like well we can see right now so what does that mean yes so good reconstruct the argument adding premises that you might not normally think in an everyday conversation you would not state but go ahead two of you together even can combine i'm just gonna add on um the very last sentence because if someone has stolen intent not someone who might have store intent um very good in the suggested reading from herrick paul carrick there is a a useful guide on and again this is suggested if you don't have time don't read it but if you do have time i suggest doing it that's why i suggest suggested page 76 of the hair greeting it talks about deductive and inductive indicator words i'm going to talk more about that later but be cautious and i think herrick is too [Music] uh optimistic about human nature when he assumes that if somebody says my conclusion necessarily follows that they actually have a deductive argument and that's i'm jumping a little bit ahead here but it's you raise a good question someone has stolen our tent or it is necessarily true that someone has stolen our tent he's not saying maybe somebody stole our intent there the indicator word maybe does very likely indicate ah they intend this to be merely probabilistic they intend this to be inductive and i'm jumping ahead here for a moment i'll come back to all this shortly whereas if somebody says ah this conclusion necessarily follows they probably intend it to be deductive now that's not the same thing as it actually being deductive and we can be charitable for their sake and assume you don't really mean this to be deductive because if you did it would be a bad argument and i'll come i want to come back to that so be cautious in relying on indicator words they're a good help but don't over rely upon them similar to when we look at indicator words with premises and conclusions from last time just because there's an indicator word that doesn't necessitate that you've got say a premise you may not have an argument at all the premise word because could entail excuse me could uh simply indicate that you have an explanation as opposed to an argument and i apologize i'm going to remain seated again for most of the class my ankle is still hurt i don't know why this is just what happens when you age and you deteriorate to start you know on a kind of shitty note for the week i apologize but i'll be complaining about my physical ailments throughout the semester just because i feel good about it it kind of makes me feel good to complain it's deductive you say premise one we went to bed in the tent premise two we've awoken and can see the sky premise three the only way we can see this guy is if there's a giant hole in our tent or the tent is gone premise four or five i forgot which one now the tent is gone premise six the only way the tent could be gone is if it were stolen conclusion the tent was stolen now that way i framed it was as close to deduction deductive as possible the only way the tent could be gone is if it were stolen now if that's true and all the other ones are true the conclusion seems to follow with necessity ah it was stolen that's not a very good argument is it because what premise did i just mention seemed flawed the only way i don't think it necessarily proves it was stolen more so the tent is gone yes well even that's problematic because in philosophy we get the skepticism somebody can say well you're relying upon your vision and haven't you gotten things wrong based on sight before haven't your senses deceived you you look in the distance is that a is that a oasis is that water in the distance no that's that's a mirage is that stick bent no it's just in water is that is that my old friend go up to him slap on the ass oh it's not my old friend i thought you were somebody your vision and that's that's just a random example that didn't happen to me but you're you can be mistaken about it that's what we're looking for is it possible that the conclusion in this case the tent was stolen could be false even though all the premises are true if it's possible the conclusion could be false even though we accept the truth of all the premises you've either got a deductive argument that is invalid not truth preserving or perhaps better you've got an inductive argument and sometimes and you may have some this is where you're going to have to interpret what is this person intending do they intend this to be a deductive argument a deductive proof where they necessitate the truth of their conclusion are they trying to show with certainty their conclusion is true or are they merely trying to and i say merely that weakens it more than it should or are they giving us an argument that's a degrees of probability if it's probability probabilistic you're dealing with induction if it's certain dealing uncertainties necessities absolutes you're probably dealing in deduction let me give you another example oh this is from plato and a platypus walk into a bar uh introduction to philosophy through jokes it's a very good text and strangely i'll have more to say about the platypus later today i don't know why i've forgotten but it comes up there's holmes and watson looking over the dead body i assume it's amazing if you watch sherlock holmes or read the stories how he can come up with the conclusions that he does based upon little snippets of information how does he do this how does he deduce that somebody is or is not guilty question well he starts by asking himself a lot of questions to creating patterns that people base theories off of that's right patterns detective work is pattern recognition actually an argument can be made that all scientific endeavors are pattern recognition in fact even even broader the human brain is a pattern recognizing machine and those who are really good at recognizing patterns can make inferences from those patterns to conclude all sorts of things that normal humans couldn't do now detectives that's their field that's their job that's what they do and so intuitively they can figure out and intuitive here doesn't mean it's magical it's a sixth sense it means they're able to sense quickly immediately based upon years and years and years of prior experience what is relevant what is irrelevant what is uh connected possibly to a crime and what can i ignore what can i how can i reserve my mental resources and time by excluding what is not relevant that's a kind of wisdom in itself to ignore to figure out what should be ignored now imagine this i'm going to give you some evidence and i'm going to put it in terms of an argument the evidence constitutes premises and let's just say assume that you are being accused of murder so each of you put yourself in the place of a defendant who has charges brought up against you and here are the claims the premises used to lead to the conclusion the conclusions you're guilty of murder okay so you tell me what kind of argument we have here premise one your dna was found at the crime scene that's pretty big you're you're already in a little bit of trouble your dna was found at the crime scene promise to the victim's blood was found on your clothes your footprint from your rare fancy italian leather loafers does anyone have any leather loafers on now that'd be ironic are they loafers oh so you said you were confident initially that you did ah you know what i think so yeah i actually don't it's got to be a dress shoe though i'm sorry i didn't mean to put you on the spot nobody here has fancy leather loafers i don't think so that's fine but but notice a footprint from your rare fancy and detectives like holmes somehow know the fashion of the day why would you need to know that ah here's a case in which it's relevant to know this is a shoe that's not very common and that means it's narrowing the focus you see but not completely not as not down to a singular individual four testimony of a witness places you at the vicinity when the crime likely happened promise five testimony of a witness claims to have overheard you claim that you could just kill that person that is the victim promise six oh there's a video of you stabbing the victim what follows murder you're guilty of murder first question to you is uh what form of argument is this because we cannot evaluate it until we determine it's deductive or inductive because importantly essentially here deduction has a different mode of analysis than does induction go ahead is it deductive because it says therefore you are guilty so good uh therefore is an indicated word for a conclusion but not us a specific deductive or inductive conclusion that's just conclusion of any argument but even the further part there's no possibility you are guilty yeah so that's vague isn't it do you mean i necessarily am guilty do you mean i'm probably guilty that's left out so we can't really determine based on the indicator any words there they don't indicate enough i guess you could say right there's nothing there that says clearly that indicates clearly we intend deductive deduction well i guess it would be inductive then just because of the process of to start off with your dna was found in pieces of evidence and then it gets further down to narrow the point by them being guilty and what about that process makes it inductive as opposed to deducting because deductive reasoning starts with [Music] no the in everyday language we may state our conclusion and then give reasons for it the order of events there is not sufficient to determine whether it's deductive or independent or where we put the conclusion now it may be that you start with claims that are general and go to specific that's a common instance of deduction we'll see though that that's not the definition of deduction i thought that's maybe that's where you were going did you want to um i would say inductive because it doesn't necessarily i wouldn't think it necessitates the conclusion because for all you know you could have been framed like say the video was i don't know video shocked um a deep fake did we talk about deep fakes here last time yeah yeah it's a deep fake you'd have to prove that and you can with technology but unfortunately as we said last time and we'll see again with fake news and post-truth era and so forth the the the the video that you wanted to show your opponent or your political opponent doing something saying something ridiculous is already out there and it's already been shared a million times but there are such things as deep face and if that's a deep fake then actually that premise would be false what we want is an instance a a a logical possibility where the conclusion in this case you're guilty could be false that means you're actually innocent even though all the premises are true can you assume the truth of one through six and yet still the conclusion be false without contradiction without absurdity if so deductive and deductively valid if not it's either deductively invalid which means it's a bad argument or we can be charitable and assume it's probably not meant to be deductive because it could be a strong argument if it were interpreted as an inductive argument real quick okay i was gonna ask like what if the video is true like it's an old video like let's say i start the person a couple years ago and like but i wasn't like the crime that killed them like yeah like it's true like there is a bit of mistake in them but like it was a couple years ago yeah yeah your honor it's true i murdered somebody but not this dude so you can't there's a double jeopardy coming to play there or you could say something like yeah that is me stabbing somebody but that's me part of a play and uh i was playing hamlet no did anyone get stabbed and hamlet probably oh my gosh what happens in hamlet give me a shakespeare play where somebody's stabbed caesar i was doing caesar and that's that was just to play your honor guys fine uh that is a video of me stabbing somebody but it's in a play that would be one way of doing it appealing to a prior murder that you committed to get out of the second murder would be an odd move maybe it worked though i guess because you're not i'm not being tried for the murder of that guy which i did kill but it's this one which i didn't so i'm innocent that would be a weird move yeah so we don't know if the person that stabbed him actually kill them what if the person steps oh yeah just injure them that's another thing from someone else that's possible here's a video of you stabbing that person yeah i did but it was with a marker and i only hurt them somebody else came afterwards and murdered them i guess that's logic notice what we're doing here that's logically possible in fact do people get framed yes they do this is what you might have to defend imagine you know you didn't do it how do you explain the evidence if you've seen making of a murderer i think it's called is that what's called netflix special couple years ago that looks like pretty strong case for the dude was framed somebody was able to get into the evidence uh uh uh room of a police department and it looked like somebody took a syringe a needle pulled out some blood and then brought it to the crime scene so that his blood was found at the crimes is this logically possible yes does it happen a lot i hope not but notice all of this can be true and yet the conclusion still false which would make that a bad deductive argument but is that a bad argument when you first read it if you're a prosecutor you're like yeah we got him that's pretty tight case so you wouldn't want to say it's bad so don't interpret that as deductive being if you don't know who the person is you just see the argument you can't ask them did you mean this to be deductive or indicted you just have to look at and say that's dealing with a high degree of very high degree of probability it's possible the conclusion is false even though the premises are true but it's very unlikely and so if it's inductive it's a strong argument if it's deductive it's a crap argument because it's invalid because in deduction anytime there's the possibility of a false conclusion assuming all the premises true it is invalid that's the definition of invalidity an argument in which it's possible to have false conclusion and yet all true premises right is there any premises that could be added to make that conclusion certain uh you could but you may make it then unsound so i might say premise seven in all cases there are there's video evidence of a murder the person is guilty since six tells us there is video evidence it concludes necessarily that the conclusion follows that you're guilty now that's valid because if we assume those claims are true that conclusion has to be true that's a very good question but now what have you done you've made a valid argument but an unsound one because clearly the premise all times and that's in be cautious of these absolute categorical terms frames uh claims all times there's video evidence is instances of guilt that's just false right so that claim is not true and that makes it valid truth preserving but testing validity is not about actual truth value it's about what are the logical possibilities and that's that's one of the weirdest things today and next class are going to be the kind of counter-intuitive specifically about deductive arguments and validity uh and uh more so than most of the rest of the class even though deduction is kind of appealing because it's either or and the conclusion is necessary and there's a kind of positive you know joy getting an answer that is the answer it's not a matter of well maybe it's valid maybe it's not no it either is or it isn't and the conclusion follows the necessity people like that and some people don't like that as we'll see oh yeah how can you even win an argument with a very small low logical possibility say again so i'm asking you you're talking about logical possibility in this case there's still a little bit of logical possibility yeah this person didn't kill them how would you well if i'm supporting that small chance if i'm the defense i want to show look there's a degree of doubt uh that you cannot prove beyond notice the phrase beyond a reasonable doubt it isn't you need to prove my guilt 100 nobody thinks that's that's i don't know that that's ever possible but beyond a reasonable doubt is itself a vague phrase and if i'm a defense attorney my goal is to show first of all that my client gets a fair trial and secondly that there's doubt that there are alternative possibilities that are in competition with the prosecutor's position now the prosecutor needs to show look at all this data it may be that your dna was found at the crime scene and that could be explained away you cut yourself and happened to be in that area the day before and that's why your blood is there fine but notice the evidence accumulates it's a cumulative case why is there victim's blood on you that's hard to explain why is your footprint there how do you know it's your footprint well look you're the only one in this city with these italian loafers or something all of that accumulates and makes it much much much harder to defend uh as as the defense in this case and that increases the strength of the argument which is key inductive arguments can get better or worse by adding premises there's a point at which you can't do anything more to make an argument valid or invalid by adding more premises we'll see how different they are why is it important as i just noted you need to first establish what kind of argument you have before you evaluate you cannot evaluate an inductive argument for example via the mode of evaluating deductive arguments because they're different kinds of reasoning technically as we'll see next class uh in a week from now all inductive arguments are invalid every single one of them including the one i just gave you this is invalid because it's logically possible that the conclusion is false even if we accept all the premises as true that's the definition of invalidity and so instead of saying that's a bad argument which is what you're saying when you call it invalid interpret it as inductive and you then interpret it as actually a strong argument whether it's cogent or not a term that applies to induction that's dependent upon whether the premises in reality are true but it is always logically possible to have a false conclusion and true premises in inductive arguments always every single one of them as we'll see so instead of saying they're all invalid which is kind of saying they're all terrible we say there's degrees the conclusion follows with degrees of strength degrees of probability there's the key to defining the difference between the two kinds of arguments does the arguer intend the conclusion to follow with necessity or does the arguer intend to have the conclusion follow with degrees of probability that's the essence of deduction versus induction it isn't just reasoning from general claims to specific claims that's a kind of deduction that's a type that's an example of deduction but not the definition that's not the essence of deduction as aristotle will tell us that's kind of what we're looking for and he gets this from socrates and plato before him now who is this fellow i'm not going to go into the history of a lot of a lot of logic here but aristotle's important figure to mention especially when we look at syllogisms as we will today he basically invented logic how do we know well he he tells us when it comes to this subject logic it is not the case that part had been worked out before in advance and part had not instead nothing existed at all until i came on the scene so it was aristotle who tells us this and i think we can forgive him as arrogance because it is accurate much of logic is still in place since aristotle which is incredible think of any discipline that is basically very very similar to its origins which tells you either we haven't done much at all with logic which is not the case uh or aristotle was pretty damn brilliant uh in developing this field this branch of philosophy that is the science of argumentation yes in my history class we're just learning about um francis bacon arguing with aristotle's logic um i want to see what you thought of that aristotle using his or i'll argue with it um it's saying using the science of big-time data yes yes so bacon comes along he's a philosopher as well and we get a lot of the philosophy of science that we have today because of francis bacon um and we'll look at that when we get to the end of the semester uh but aristotle was the philosopher up into the medieval period and it's bacon and descartes and others who are looking at logic from aristotle's lens and seeing those limitations to it there actually seem to be limitations to aristotelian logic as early as a couple centuries after him excuse with the stoic philosophers who expand on his categorical reasoning we'll talk about categorical logic in a moment and give us hypothetical arguments hypothetical syllogisms that expand to become prominent around the medieval period and the renaissance period that we see with bacon i think bacon is probably correct that there are flaws and he is correct there are flaws in aristotle's logic i would rather say there are elements of it that are undeveloped which is not surprising since he invented it that's going to it didn't exist in form before him so there's going to be things that need to be filled in and i think bacon and then and medieval scholars like aquinas and then especially in the uh when you get to the 18th 19th 20th century uh kant and hegel and logicians like gottlob fraga who will look at a little bit bertrand russell and ludwig wickenstein massively change how contemporary logic is done but it all is based on aristotelian reasoning um what do we mean by deduction well aristotle tells us and he doesn't do so in very clear language here what we have from aristotle are his lecture notes that his students compiled after his death so they're kind of dry we have on the contrary all of the uh dialogues of plato aristotle's teacher so a lot of people like plato's readings better because their dialogues their conversations whereas aristotle's papers books are his lecture notes which are very dense and oftentimes very dry and the writing is like this a syllogism is a deduction in a discourse in which certain things being supposed something different from the things supposed results of necessity because these things are so end quote from his prior analytics we will not be reading that text you'll be happy to know that basically is getting at what deduction is conclusions that follow with necessity and avoiding [Music] contradiction as he tells us in another text called the topics the purpose of this text is to discover a method by which we shall be able to reason from generally accepted opinions about any problems set before us and shall ourselves when sustaining an argument avoid saying anything self contradictory now notice there reason from generally accepted opinions there you start to get the presumed definition of deduction as going from a general broad categorical claim and reasoning toward the specific again that's not going to be the essence of a deduction that is an example of deduction and then this concept of contradictory is going to be important in a moment so what are we doing with deduction as opposed to inductive reasoning we are attempting to establish the necess the necessary truth of the conclusion that is to say it follows necessarily assuming the premises are all true are they all true don't care don't know don't worry about that yet you're looking at the logical inferential strength first is it valid or is it invalid do the conclusion do the premises support the conclusion absolutely or do they not and so we say of deductive arguments they are truth preserving whatever truth is in the premises gets carried over into the conclusion truth preserving and in contrast here's another there's a lot of distinctions and a lot of different ways of varying uh showing deduction and induction are different deductive arguments truth preserving think of them as self-sealing webs so to speak that are consistent one thing leads to another inductive arguments are truth producing whatever truth you have in the conclusion is extending information beyond what's in the premises you're going outside of the truth of the premises the premises lead to a conclusion that increases our store of knowledge the conclusion isn't already in a sense embedded within the premises in an inductive argument and more examples uh we'll make this clear as we go that's the key distinction between induction and deduction go ahead i just had a question about the slide from last week um the very last slide of the ducks in the pond we said like the duct shape is pretty duck oh that was yeah that was it no that was a meme and joked me i forgot what it was now the definition of deduction is removing the act of removing ducts and induction is the act of putting ducks in i can't remember the meme but that's not true i forgot i did say we'll learn how accurate that is it's it's inaccurate that's not what deduction is although it could be it's ambiguous what'd you just do i took that duck out of the pond ah deduction dear watson that'd be a good meme right there i want to work on that one you all can work on your own means and send them to me if you wish if you can get me a a duck being removed from a pond and then say ah and then watson and sherlock homes are there deduction they're watching that's actually quite good i like that idea somebody worked that out i don't give extra credit but i was about to turn that into a meme i don't always give extra credit but when i do i drink dos equis okay uh quick distinction here um i have already mentioned this you'll find this in your la in your in your math textbooks still i don't know why it's just incorrect unless deduction means something different in mathematics than it does in logic which it doesn't and you'll see it online as well it is incorrect because what they're trying to tell you is this is the definition of deduction reasoning from general to particular that is false that is an example of deduction just as i can say that is a desk but when i say and point to that i'm not saying that is the definition of a desk i'm in fact giving you an example of a desk of desk hood you see the difference an example of something isn't the definition in fact the fact that you can point out an exemplar an example already presupposes you know what the general definition is under which that term applies we'll say a lot more about that with deduction with definitions where we'll look for necessary and sufficient conditions but let me give you a counter example and a counter example is where look here's your definition i'm going to give an example that doesn't fit your definition of in this case deduction yet is clearly an instance of deduction [Music] it's a lot of buses a counter example here's your definition and here's an example in which your definition does not apply in other words your definition is too broad it includes too much or it's too narrow it doesn't include enough so here's an example that shows reasoning from broad or general to specific or narrow is not the essence of deduction here's the counter example premise one and notice the kind of premise this is milo kramer is totally cool he's an individual he's a specific person and notice the language there species specific general genus that's not coincidental we'll see how that relates with specific kind of definitional technique by the way milo's my son milo kramer totally cool uh lola kramer she's also totally cool she's my daughter lynn kramer also totally cool she's one of my wives ah scared i'm just kidding she's my only wife chris kramer that's me totally cool you need this other premise though there are only four kramers what follows necessarily if those premises are all true all cramers are totally cool dude totally cool now you might quibble with what cool means and totally cool and people might mean different things that term cool is obviously ambiguous it could mean temperature wise i am cool i'm below 98 degrees all the time we have to do our temperature every day lola's always about 98 point something anyway that's we mean something different we mean uh what do we mean what does cool mean do people still use this term that dude's really cool which you mean hip hip people say that anymore i hope not i hip not this is a deductive argument because the conclusion follows with necessity assuming the truth of the premises has nothing to do with going from general to particular because this case goes from particular particular particular to general do you see and yet it's still deductive because of the logical strength that's what we're looking for that's the key uh determining factor and there are other counter examples we can look at uh just to give you a quick sense of what a counterexample is vaughn has this 82 to 83 for more details let's imagine this argument no mammals lay eggs assume that's true right all mammals are non-egg layers or no mammals lay eggs as a better way putting it that creature over there is a mammal what follows about that creature what must be true um [Music] it's not laying any eggs it does not lay eggs now we might refute that by finding a counter example and i did and it's this i told you that platypus would come back the platypus is a real thing you know that uh i'm so fascinated by it i printed something up that i'm going to read to you it's totally irrelevant to the class but it's incredible that this is a thing it is a duck-billed platypus semi-aquatic egg-laying mammal it senses prey through electrolocation i'm not entirely sure what that is sounds dangerous it's one of the few species of venomous mammals as the male platypus has a spur on the hind foot that delivers a venom capable of causing superior pain to humans the unusual appearance of this egg-laying duck-billed beaver-tailed otter-footed mammal baffled european naturalist when they first encountered it and the first scientists to examine a preserved platypus body 1799 they judged a fake made of several animals sewn together that's what they thought it was which if you look at it that's a pretty clear assessment that's what i would have thought this is a made-up animal this frankenstein of the sea or frankenstein's monster of the sea let me clarify that i know that upset some people um but it's a real thing my probably my favorite animal behind the narwhal also a magical creature of the sea as well i've i've stuff to say within our walls too so look forward to that i saw a question over there about the platypus no oh why don't you carry the bottom post instead uh well this one shows you the beaver tail duck-billed otter-footed part uh harry the platypus from obviously phineas and ferb uh doesn't show you the details that i wanted but believe you me what the hell that means i know who harry the platypus is you had a question about the logic no there's another animal that um people taxing everything together that's like so common i can't remember what it is it's like a jackrabbit or gap or something like that it's a it's a rabbit with the antlers from a deer a what yeah that's not a what that's a bang like a jackalope is that a thing we're spending too much time on that don't start looking don't start looking up mythical creatures i'm not saying the jackalope is that it's it's really funny though because like they sell tens of thousands of them sell them yeah oh they're breeding them no no they taxidermy them and they take like oh that's different i see i thought okay when they taxed it there i missed that part that means they're not alive they're stuck but people don't realize that that's not real i see that that was the key point that i missed the taxidermy yeah the taxidermists have gone out of business though with uber and lyft lately no i don't let it let it come over you taxidermists ah yeah see okay it wasn't very good but it got you to say ah on we go categorical syllogism all men are mortal this is a common form there's a lot more of these and in your formal logic classes you go into this in more detail i'm just going to give you a number of them and i apologize for the rather tediousness of this element of the class where i'm giving you just a list of argument forms these are deductive forms reductive patterns such that anything you plug into them and i'll give you variables too that just shows you this form is what makes the argument deductive it makes it truth preserving whatever truth may be in the premises it gets preserved at the conclusion it's like a machine that churns out truth and that's where you get formal logic it's the form not the content that determines the inferential strength here so here's a literally textbook case uh all men or morals goes back to aristotle he used this example all men are mortal socrates is a man what must follow if those two claims are true socrates is mortal if you don't see that propositionally that is to say just the sentences in front of you some of these you can put into circles you can use what's known as a a variation of a euler diagram and that's just overlapping circles you'll see variations of this with then diagrams from the logician john venn those are a lot more complex in use in establishing validity they require at least a whole separate session on how to use venn diagrams and logic to test for validity we're not going to do that here that's not my focus but you can do a quick visual representation of the argument to see whether it is valid or invalid to whether it's intending a deductive inference or merely inductor and you can represent it this way if something is a man all men are part of that category anything that's a human you can expand on this and it tells us they're mortal that means every single human is part of the category mortal ah just occurred to me why one of the characters in my kid's story called zombies in love one of the characters names is mortimer you see he says zombie mort means death it's actually quite clever now well it was always clever i just got it anything that's a man is the thing that's mortal or all men are mortal what does premise two say socrates is a man where does socrates go assuming it's true the premise here yes what if i put him there that would just be misrepresenting the premise if i put him here also misrepresenting the premise because that's the category of men so you've already shown the conclusions embedded within the premises we haven't really extended our knowledge we've not gone beyond the truth that's in the premises it's a truth preserving argument if the first two claims are true it would be a contradiction an absurdity in the logical sense to deny the truth of the premise to deny the truth of the conclusion that came out wrong if you accept the truth of the premises assume they were true but deny that the conclusion is true that would be a contradiction you'd basically be saying all men are mortal and also some men are not mortal that's a contradiction you have spoken against yourself that means it's logically impossible you cannot conceive using a in in philosophy we call them thought experiments from the german ge duncan steele can you speak german a little bit of german duncan spiel spiel means we're playing with thought testing ideas in the laboratories of our mind what was i going to write i got tea fill in the bank was it of course yes thought experiment we we looked at that a little bit last time with the the good place a thought experiment engage in a thought experiment where you test the logical possibility where you can come up with true premises but the conclusion's false can you do that here it's true all men or more assume that it's true socrates is a man okay if those are both true is it still logically possible for the conclusion to be false if so it's invalid or it's possibly an inductive argument but we're only looking at deductive forms here so it would be invalid i don't think there's a way of assuming i don't think there's a way of getting a false conclusion assuming the true premises you can deny that one of the premises is true but that's just to say it's a valid but unsound argument maybe it's not true that all men are mortal maybe socrates wasn't man maybe he was a narwhal yes so on that circle diagram would the s go in the circle man that's right okay so that was wrong that was incorrect over there it has to be here that's what the premise says and you want to diagram the sentence the premise as clearly as possible and once you've stated that you see that this has to be true that socrates can't be anything but mortal he has to be well that's a wrong way of putting it he's more things than just mortal he's a philosopher for one uh but this premise shows that he has to be inside the category of mortal entities more told b what is the contradiction uh this says no left turn and this arrow says turn left so that's a contradiction it's fun there's a lot of examples of this this one says we can repair anything this is a sign on their maintenance shop then it says please not hard on the door the bell doesn't work that's not technically a contradiction because we can imagine them saying no no we can fix anything we just haven't gotten to that one yet so not not not technically a contradiction it's just funny what is the contradiction is to speak against that the hyperlink from the i think uh stanford encyclopedia philosophy to get more into contradiction it's a fascinating concept literally contra against speak uh speak against the contradiction the law of non-contradiction sometimes called the law of contradiction which is very confusing aristotle sees the law of non-contradiction as a basic law of thought that does not itself need to be defended if i say a i assert that a is the case a is a statement that uh can plug in anything it's a claim this or that whatever a is true well if a is true then it cannot be the case that not a is true they can't in other words be both true at the same time to say a and not a at the same time in the same way is to speak against yourself it is to engage in a contradiction and why is that a problem what's wrong with contradiction it is the telltale sign of flawed reasoning if your argument contradicts itself if your theory has a contradiction within it if your argument has premises that contradict each other or if your conclusion is contradicted by one of the premises it fails miserably that's been the view since aristotle not everyone agrees with this law of non-contradiction some think there are exceptions to it guiding graham priest is a contemporary terror consistent logician or dialecticism as he calls it we're not going to talk about that there's different logics involved and he thinks that there are exceptions to help address things like paradoxes like the liar paradox everything i say is a lie well if that's true then it's false how can we make sense of that paradox well maybe para-consistent logic that shows maybe the law of non-contradiction in fact doesn't always hold there are exceptions aristotle thinks that's absurd there are other philosophers buddhist philosophers jain philosophers from jainism who argue that there could be multiple truth values claims can be true and false at the same time uh both false at the same time uh one true one false at the same time and there's a variation of it but for aristotle which we're focusing on here classicological view to deny the law of non-contradiction is to deny a basic law of thinking and so he doesn't use argument to defend the principle law of non-contradiction he uses the law not contradiction as an axiom from which to build logical arguments to think at all that's what he means by a law of thought and he even says look if you deny the long cut if you deny the law of non-contradiction you are basically a vegetable and what do you say to that no i'm not aha what have you just done what's that did you just denied it denied what the point you were making that you're a vegetable it could be either or you mean i'm not a better no i don't agree with that point which makes you a vegetable what if aristotle says look you want to deny the law of non-contradiction that basically will make you a vegetable yeah and if i say but i'm not a vegetable aha then you cannot deny the law of non-contradiction because the moment you say the moment you say anything the moment's words come out of your mouth to the extent that you mean them you mean what those words mean not the opposite not their contradictors when i tell you i'm not a vegetable that means the statement i am a vegetable is false right it's it's silly to talk this way here's a better example from avicenna a medieval arab philosopher muslim philosopher he says for those who deny the law of non-contradiction throw them into the fire because for them to be thrown into the fire is the same thing as not being thrown into the fire why because they've denied the lifetime contradiction which is absurd they can't actually do it no one actually does it the moment you start speaking you have presumed this basic law of thought that's the essence that aristotle wants to get at and he says as much in his metaphysics which i'm not going to go into now it's the most certain of all principles and again i told you there's some debate about this currently he says quote it is impossible that the same thing can at the same time both belong and not belong to the same object in the same respect and all other specifications that might be made let them be added to meet the local objections as you can see his writing is not fun so we won't be reading directly from much of aristotle except when we get to rhetoric okay so we have a little bit about contradiction we have a little bit about how arguments go together now about the formal aspect of it forget about the content forget about whether the claims are true or false in reality or what you think about them assume for the sake of argument that the premises are true let's imagine it's true premise one it is true all flubs are libels premise two she's a flub what must be true she's a lipple that's right all flubs are lipples fnl she's a flub she has to go where according props to inside that's where she goes it follows necessarily that she's also a little it doesn't matter what the content actually is you would be contradicting yourself if you said it's true well folks are liberals it's true she's a flub but it's false that she's a little you're basically saying she is and is not a liberal yes so the mortal argument the other chart that you make was like the mortal is the sausages or whatever was that also a categorical syllogism yes exactly right that was also a categorical syllogism think of categorical syllogisms as arguing with two premises all syllogisms syllogism means to argue together or to reckon facility being together two premises and a conclusion every syllogism has that they have a minor and a major premise a minor and a major term those are details that you get into in a formal logic class which we don't need to focus on here we'll look at a couple of syllogisms the categorical syllogism where you're saying here's a subject and it belongs to this predicate or it belongs to this group or this category and either all of this category belongs to this category or some from this category belongs to this category or none of these belong to these that's categorical logic and you can translate almost any sentence into standard categorical form which you would do in a deductive logic class we'll look at uh hypothetical syllogisms that are comprised of if then statements i'll get to that in a moment and then we'll look at disjunctive syllogisms which is an either or and then we'll look uh at arguments by definition briefly and if we have time an argument form known as the reductio ad absurdum which we kind of touched on a little bit already and it's pretty impressive that that's about it i mean there's variations of categorical syllogisms there's variations of hypothetical syllogisms but there aren't a whole lot of different forms and there you get again at the four it doesn't matter what the content is get into the habit of assuming the truth of the premises and if the premises were true would they necessitate the truth of the conclusion if so you've got a deductive argument and it is valid formal argument here's another one all cats are mammals there's a different structure though still categorical you can do it this one's very easy i think if you do it with just consecutive expanding circle premise one all cats are mammals assume that's true which is easy to assume because it is premise two all mammals are animals where what do you do there how do you represent premise two all mammals are animals so again another circle here ah yes animals yes and notice again i don't even have to do anything else what have i just showed ah whatever c is there it's part of m and if it's part of m it's part of a that has to be the case assuming the truth of the premises ah all cats are there for animals if all cats are mammals and all males are animals it follows at all cats or animals that's pretty straightforward as a deductive categorical syllogism you would be contradicting yourself there's no logical possibility in which this can be false while accepting those is true if so valid and here's the final pun of the day it's a categorical syllogism because i'm talking about cats it's not that great i apologize all cats are hunters chloe's part of the cattle oh there it is all cats are hunters chloe's a cat follows that chloe is a hunter is it true that all cats are hunters i don't think so i had a cat named hank i think you should i showed you a picture of him before grading papers he was chloe's brother there's chloe yeah she's cute until she rips your eyeballs out with her claws or brings a rabbit bleeding and wounded into your house which is terrible the rabbit escaped somehow but not without leaving a trail it was just terrible she's a cute cat but she's an absolute murderer to the extent that cats can murder they can torture i'll tell you that anyway let's move on that's categorical here's a hypothetical syllogist these are a little more complex these develop after aristotle and the history of it is not relevant here to us but it's it's interesting aristotle uses categorical syllogisms in a way that presumed with respect to let's say species static presumptions all mammals are warm-blooded or all mammals are non-leg egg layers or something like that as if there aren't possibilities for change or species uh uh evolving over time and so it wasn't specifically because of this development of evolution of course that wasn't many many many centuries later but the stoic philosophers develop what are known as hypothetical or conditional argumentation and you can translate categorical arguments into hypothetical ones and there's variations as to how and why you should do this but one that we'll look at that's very common most maybe the most common in deductive logic textbooks is the argument of affirming the antecedent or modus ponens the way of positing right affirming and you know it's a hypothetical because it's giving you an if that q is conditional or conditional state it's conditional upon p if then and what do you know about a singular if then statement can it be an argument by itself no no because no argument can be comprised of just one claim and a conditional as a reminder is merely one claim you need to link the chain so to speak conditional arguments are like chain arguments as they're sometimes referred to if p is the case then q is the case well is p the case if i assert that it is q follows necessarily modus ponens fill in the content you can fill in anything you want even if it's absurd it's going to be valid if you want you can come up with your own example of absurdities fill in what you want for p and q anything at all we'll see if it's valid okay you don't have to okay let's let's do an actual one if it is physical then it has a cause for its being you can put it another way into categorical logic all physical things are things that have a cause for their being the universe is a physical thing therefore it is a cause for its being this is a conditional if p then q p i'm asserting that the antecedent that which follows the if in conditional argumentation is true i've given a sufficient condition for the consequent the antecedent is the sufficient conditions for q the consequent and the q the consequent is the necessary condition for the antecedent that's abstract and confusing i'll make sense of it with a concrete example whether or not this argument works we're not evaluating it yet we're just showing the different forms this is valid because it fits the valid form and that's all we're looking for it's truth preserving now if in a philosophy religion class we might expand on this what would be the cause of the universe's being the big bang and what caused the big bang yeah okay and what brought gravity into being and i was going to for god eventually but yes all of that maybe we can explain all that without god but that requires a whole semester we're not going to get to that now but you can make this conclusion the universe has a cause a premise in an extended argument how many buses come through here a day this is amazing this could become a premise the universe has a cause for its being the only cause that could be possible for such a for such a physical thing would have to be vast in its capacity or so forth and a bunch of other promises to get to the possibility of being a god yo go ahead so is pete always going to be the mission position and q going to be the necessary condition good if i were to say only if p then q the only if actually changes that and makes the thing immediately following it the consequent it makes it the s uh uh uh necessary condition but that's that's something we'll get to in a moment if we will and that's something that's more for a um a deductive logic formal logic class but that's a very good question um but yes everything after the if is going to provide you in this whole thing you have to see it comes prior is going to provide you with the uh sufficient condition for the the consequent the second part and then do i get to that now i will i'll get to it after this slide in fact so another hypothetical syllogism another mixed syllogism is called the way of removing or denying the uh the consequent what you're doing you're taking away you're saying the consequent isn't true which is to say you've removed a necessary condition for the antecedent if you take away the necessary condition for the antecedent not q here i deny that q is the case well then i've gotten rid of the possibility for p if i take away the necessary condition for p then p cannot be the case how do i mean premise one if i am a philosopher then i am wealthy that fits premise one motor's tolling's there with a variable if p than q premise two i am not wealthy i deny you i deny that the consequent is the case and once i've denied that i've taken away unnecessary condition and if you remove a necessary condition for something you cannot have p if i'm a philosopher then i'm wealthy i'm not wealthy i've taken away the possibility of me being a philosopher is this a is this a sound argument who cares not there yet what do you mean by wealthy and so on those questions would have to be raised but anything that fits this form this modus tollens form affirming but denying the consequent is going to be valid it's a deductive form we'll look at other examples that are very similar to this but are not truth-preserving that are not valid but that's for next time oh here we go conditional statements are set up in such a way that they have a relationship that's logical the antecedent produces or provides us with a certain kind of condition for the consequent and vice versa and here's where we get into necessary and sufficient conditions which we'll see again with uh definitions this is the kind of thing that socrates is looking for what is the definition of virtue of piety of justice and so forth don't give me an example of piety of justice of virtue give me the essence of it he didn't use necessary and sufficient he didn't use those two terms but that's basically what using language in contemporary philosophy with logic he's he's referring to what are the necessary and sufficient conditions so what do we mean in a conditional statement an if then hypothetical if p then q the antecedent after the if provides us with a sufficient condition i should have started with that that's the part that comes right after you but doesn't give us the necessary condition for the truth if it's consequent whereas the consequent is a necessary but not sufficient condition for the truth of the antecedent that's very abstract very kind of unclear perhaps as to what it means so to make sense of it we can look at a very concrete and simple simple example to look at the logical connections among those terms and it's very easy to use animals mammals cats things where the categories are clear to us there's not a lot of but fuzziness and we can actually see in testing validity for next time using counter examples like this will help in any case if it is a kent then it is an animal not an argument that's a singular claim it's a condition being an animal provides you with a specific condition for being a cat put another way being an animal is necessary to be a cat this is pretty straightforward so if you remove animal hood animalia you also get rid of katniss because if you take away it's being an animal if you say it's not true that it's an animal then it cannot be true that it's a cat being a cat is merely sufficient to be an animal it's enough it's all you need so the antecedent provides the sufficient condition such that if you affirm the antecedent you say basically ah here's enough it's enough for p to be true to get to q because p being true is sufficient for q to be true being a cat is enough to be an animal that's the logical connectedness between those claims and that will be essential in understanding why reasoning can go wrong just by switching the order of the terms in a hypothetical syllogism and where you can go from a modus tollens that looks obvious as modus tones and therefore valid into something called the fallacy of affirming the consequent as opposed to denying it but that's complex and needs some a bit more time on it and we'll do that next time so i i looked we've looked at categorical syllogisms uh hypothetical syllogism known as a mixed hypothetical and that means usually it's called that because like modus ponens modus tollens only one of the premises of the syllogism is a conditional or hypothetical one that is a pure hypothetical syllogism all of the claims all of the premises and the conclusion is itself a conditional it's a chain argument anything that fits the form of if p then q premise two if q then r conclusion so if p then r now all that variable talk is confusing it's kind of hard to keep track of what any of that means and yet we know that this is valid truth preserved the added content here would be something like if it's a cat then it is a mammal if it is a mammal then it is an animal it follows that if it's a cat it's an animal those variables apply here if p and q if q then r it follows necessarily if p is the case then r is the case a pure hypothetical syllogism and you can imagine stringing together a whole series of these to get to a very long argument i believe both the readings the suggested reading from eric uh and and the vaughan reading have examples of that my point these are deductive and anything that fits those forms is deductive we have like three more here uh a disjunctive syllogism probably the easiest to recognize you've got an either or a disjunct and we talked about this last time briefly there's two different senses of a disjunct you can have an inclusive or an exclusive disjunction but imagine i say premise one either p or q which is assuming it's not both it's not p therefore it has to be the case that q and it goes the other direction as well and this is very straightforward in fact maybe too easy because politicians are prone to use this kind of argument either we follow this procedure in which case it would lead to armageddon or we follow my procedure obviously we're not going to go armageddon wise therefore the only other rational option is mine therefore it must be mine that's a disjunctive syllogism it's valid assuming there are not actually alternative hypotheses beyond the two that are mentioned and that this can easily go wrong i tell my kids either you eat or you will die that's not a scare tactic and it's not a false dilemma which is the name of the fallacy where i set up a dichotomy a choice a disjunction and only one of them could be true it is the case if you do not eat you will die that is absolutely true and so i can set up a disjunctive syllogism that is valid and sound now to remind you of the distinction between a disjunctive exclusive sense versus inclusive either applicants must have experience or a va degree of course if you have both then you're qualified that is an inclusive sense either a or b or both uh but you wouldn't say either a or b or both with this one premise one either you are immortal or you will eventually die those are the only two options unless no those are the only two options oh you have a counter oh no no what if this be there's types of disjunctive syllogism this would be an exclusive disjunctive syllogism correct correct that's exactly right so this is the exclusive sense not both you can't be mortal and also not die wait a minute is that true yes yes correct all right uh again we'll see the fallacy that's that applies to this when there is an error in reasoning is where you set up a dichotomy which you presume there's only two when there's actually a third or fourth or fifth rational option that you have purposely ignored right and then you've got an argument from definition uh here's where i assume and this is typically deductive i there may be exceptions to it but most times you see somebody arguing from a definition presumably they've defined that term or concept or idea a state of affairs and then under that heading of that definition derive a particular conclusion you can think of in terms of axioms followed in geometrical proofs so for instance premise one god is defined as an all-perfect being this is a variation from a philosopher named saint anselm who influenced a guy named rene descartes and this is basically descartes version of this what's known as ontological argument for the existence of god assume that's true which most atheists do except what is god well an all perfect day it's just that the atheist denies that such a being exists however if i add premise two necessarily existing is required for perfection and by necessary existing of course we'd have to define and just distinguish between mere contingent existing if i exist contingently that's like me and you something brought us into being our parents we didn't always exist we have not always been our existence is not necessary which in logic and and metaphysics just means it has always been there was never a time in which god was not that means god's existence is necessary it wouldn't be god if there was a time in which god did not exist because that would make god imperfect but the definition of god is a perfect being therefore god necessarily exists if the premises are true it seems the conclusion has to be if you don't like that argument or maybe you disagree with the conclusion it might be then you have to find a fault with one of the premises in fact as i've said again and again and i will continue to repeat always address the premises and assume that they're true when you're especially confronting somebody who's conclusion you disagree with because you're more inclined to not listen to any of their justification any of their premises start with the logical inferential strength do these premises if true lead to the conclusion that they clay all right we have five minutes that's enough time to introduce the reductio this is the last one uh herrick discusses this toward the end of his reading uh which was suggested and then there's a little bit on this uh from i think pawn as well you get a sense of what this is don't ever recall that don't call somebody out and say i'm going to apply a reduction absurdum to your k don't just don't use latin unless it's in this class then you know what it means and it's okay but a reduction absurdum is a method of reasoning it's similar to what you'd find in geometry when you do indirect proofs where you start with a contradictory you start with the opposite conclusion that you think is the case and try to reason toward a contradiction try to show where there's an absurdity or something that can't be true so if i'm saint anselm and i believe in god and saint anselm was a medieval scholar who argued that god exists and he uses a form of reduction absurdum i assert the opposite and show that if we accept the opposite claim look at what it leads to it leads to contradiction it leads to absurdity it leads to a repugnant conclusion or something like that so what are you doing with the reductio you reduce to absurdity and absurdity has a logical sense here like a contradiction and we know what a contradiction is now so you assert that your claim must be true because it's negation the not a the god does not exist that's negating my conclusion for ansel is obviously false it would be absurd to say that it is true and you do this all the time when you think when you say things like if that's true then pigs can fly or i'll be a monkey's uncle or whatever the other absurd phrase is that's a variation of a reduction absurdum if what you're saying were true here is what would have to be true as well and what this is you do not accept therefore your initial claim can't be true so your job is to show why and how the initial claim from your interlocutor or your opponent whatever you want to call them probably not a potent opponent leads to an absurdity and this is a very useful tactic when addressing conspiracy theorists if i'm alex jones no i forget i said that that's say alex jones says to you sandy hook was an inside job those kids were killed just to fight against the nra what you mean massive child murder happened just to undermine the nra which is actually one of the things he says uh what else would have to be true what would have to be true is that that was a setup such that people were willing to kill children so that they can make a mark against the nra and try to push gun control is that likely the case that sounds absurd therefore likely the initial claim that led to that absurdity is probably false and if it's contradictory it's necessarily false here's a final example to use ansem's example two minutes assume god does not exist which is the opposite contradictory of anselm's argument that god does notice that's contradictory they're not contraries there's not degrees it's not maybe god exists a little bit but not as much as anselm thinks no either god exists or god does not let's assume god doesn't exist the atheist hypothesis if that's the case then it follows the greatest conceivable being doesn't exist why well that goes back to the definition of god god is the greatest conceivable being perfect being so promised two the greatest conceivable being does exist because it couldn't be the greatest conceivable being if it failed to be i can imagine something better than that but how can you imagine something better than the greatest conceivable being you see the problem so god must exist and you can put the reductio out absurdum into modus tollens form assume p is true if p is true then so is q but notice q isn't true because it's obvious it's silly to assume q is true it would be ridiculous it would be like saying peaks comply that follows that not p that's the modus tollens form that we looked at previously and so we'll see reductive absurdums very common in fact and as i said potentially useful in responding to uh arguments that don't question presuppositions that don't go beyond what would have to also be true if what you're saying is true you think we faked the land mooning land mooning that's a spoonerism you think we faked the moon landing sorry no we're almost done uh what else would have to be true how many tens of thousands of people would have to be in on that to keep a secret to lie consistently that sounds absurd two people trying to lie consistency consistently good lord thank goodness we're almost done uh is very difficult it gets exponentially more difficult the more people you you bring in it's then to reduce to absurdity in that argument i'm not going to go over this now this is where we'll refer to again and again a couple of times the distinction between uh deductive and inductive arguments some criteria it's not always obvious but here are some helpful hints and we'll go through each of these again once we learn more about inductive arguments but for next time uh you've got a short reading and i apologize because cavender i need to fix that it comes out shaded like that so maybe don't print that it's going to waste a lot of ink i don't know why that happened so but it's only a short reading you should be able to have it on your computers we'll be looking at methods of evaluating deduction and deductive arguments specifically looking at validity and soundness it's strange validity is weird remember you're gauging in thought experiments could the conclusion be false even if the premises are true if so that's invalid okay if you didn't turn in your uh discussion