hello everyone welcome back today we are going to be talking about inductive versus deductive reasoning we'll also be talking about the law of syllogism and the Law of Detachment so let's get into it okay so first of all what is the difference between inductive reasoning versus deductive reasoning so inductive reasoning is when we look at several examples and we predict what is going to happen in the future so for example my teacher's been drinking coffee every morning the last five mornings therefore she will drink coffee tomorrow morning so it's not a definitive proof right because we never know what else might happen maybe the teacher will be sick tomorrow maybe the teacher will sleep in and so she won't have enough time to get coffee in the morning tomorrow and we'll just skip it and grab some water in the teacher's lounge before class maybe the teacher will have something else to do that morning or decide to switch it up to Hot Chocolate last minute who knows right but it does seem pretty probable that this will happen again because it continues to happen when we see a pattern that doesn't necessarily automatically mean that that pattern will continue but there's a good chance right there's a pretty good chance in general that a a pattern will continue now deductive reasoning on the other hand uses laws of logic to develop a conclusion with verifiable fact and we'll get into that later because the main types of deductive reasoning that we care about in this course are law of syllogism and Law of Detachment which we will get into later today so an example of this is if a person lives in San Francisco then they live in California you know for those of you who aren't uh familiar San Francisco is a big city in California those of you in California probably think that's very obvious and you know that since you were two uh Rachel lives in San Francisco therefore Rachel must live in California right so assuming that it's true that Rachel lives in San Francisco assuming that that's true and of course we know that if a person lives in San Francisco then they live in in California and we assume that it's also true that Rachel lives in San Francisco we can conclude that she must live in California right it's not possible for someone to live in San Francisco but not live in California right that's not really possible it's possible to live in California without living in San Francisco there's other parts of California too like Los Angeles and Sunnyvale and I forget where else but there's there's lots of other places in California it's a big state for sure uh but we know automatically that if someone lives in one of the cities in a state they must be part of that state they must live there right so we used verifiable facts to come to a conclusion made with logical details as opposed to inductive reasoning where we just saw that a pattern was happening and assume that the pattern will likely continue uh so here are some other examples of inductive reasoning let's say Lana has been going out for lunch every day for the past 30 days our conclusion might be that she will go out for lunch tomorrow now again this isn't guaranteed but it is pretty probable inductive reasoning can be wrong but you know generally is correct generally patterns do continue uh let's say for example that uh we are we didn't look at the label in a popcorn um bag and we just open the bag we started eating the popcorn and let's say the first five popcorn kernels were caramel pieces our conclusion might be that the rest of the bag will be caramel pieces now this is probably true we probably have a caramel bag of popcorn if the first five kernels were all caramel however um that's not necessarily the case maybe it was one of those ones that has like cheese and caramel like those those mixed ones I forget what they're called but there's some that have cheese and caramel in the same bag however that is not too likely given that the first five were all caramel we didn't get any cheese if that was the case but it is still possible technically maybe we just got five caramel by coincidence and it's actually a different type of popcorn bag but that said it seems pretty probable that if the first five kernels of popcorn were caramel the rest likely will be too it's not too too likely that it'll be anything else okay next let's talk about the law of syllogism the law of syllogism says that given that these are true that if P then Q is true and if Q then R is true then if P then R would also be true as well so for example if I stay up too late then I will sleep in if I sleep in then I will be late for school therefore if I stay up too late then I will be late for school so if we assume that the first two statements are true then it must also be true that if I stay up too late I will be late for school all right and this makes sense right if if we assume that it's true that if I stay up too late I will sleep in right that that's a conclusion we can make then that's the hypothesis for the next one of if I sleep in then I will be late for school we can conclude that really it's the staying up late that led to us being late for school in that scenario right we can take out the middle one you know the middle thing which in this case is q and just go straight to well if P happens then R will happen right because if P happens then Q happens you know if Q happens and R happens so therefore p is really in a way the cause of R right so we can take out the middle um the the middle statement there uh let's think of some other things for law of syllogism as well so so let's say for example if a quadrilateral is a rectangle then it is a parallelogram if it is a parallelogram then the area is base time height therefore the area of a rectangle is base time height well assuming the first two are true the conclusion must also be true so let's see were the first two things true is it true that if something is a rectangle if a quadrilateral is a rectangle then it is a parallelogram that is true yes because all rectangles Les are also parallelograms now uh is it true that a parallelogram always has base times height as its area yes that is also true so therefore it must be true that a rectangle also would have base times height because a rectangle is a parallelogram all parallelograms have base times height as their area therefore base times height would also get us the rectangle area and that may be something we already knew as well perhaps but that's just another example of LOB syllogism working okay here's a couple more examples if I study for the test then I will get a higher score if I earn a higher score then I will get $20 therefore if I study for the test then I will get $20 so if we assume that it is true that studying will lead to a higher score earning a higher score will lead to us uh getting $20 then studying will lead to us getting $20 right because it will lead to a higher score and the higher score leads to$ $20 so studying is where it all starts that studying is where it will lead to will lead to us getting $20 uh here's another example if an angle is 305 degrees then it is an acute angle well that is true right we know that all angles that are between 0 and 90 not inclusive are going to be acute angles we also know if an angle is acute then it is not obtuse that's also true because acute angles are less than 90° obtuse angles are more than 90 degrees but less than 180 so it is not possible for an angle to be acute and obtuse an angle is either acute or it's obtuse or it's some other type of angle like straight right or reflex um therefore if an angle is 35° then it is not obtuse so we can verify this in two ways first of all of course we know that if an angle is 35 degrees then it's not obtuse just by the definition of it being you know 35 deges we know that obtuse angles are greater than 90 so that's not going to be the case however the other way we can verify this is true is because we verifi the other two are true and we can use a law of syllogism to say okay therefore it's not going to be obtuse in this case that it's 35 degrees if it's 35 degrees it can't be obtuse because the other statements were true and we know that if P then q and if Q then R if those are true then if P then R is also true right and so there's two ways we can verify it right the regular way and also with the law of syllogism as well okay let's talk about the Law of Detachment so if these are true if it is true that if P then Q is true and P is true then we can conclude that P is true so for example if Brenda lives in Orlando then she lives in Florida which for those of you who don't know Orlando is a place in Florida um so yeah so let's just take that for granted that we know that Orlando is a place in Florida so if Brenda lives in Orlando then she lives in Florida right which that is absolutely true we know that that's true if someone lives in Orlando they live in Florida um now then this next one says Brenda lives in Orlando now assuming that's not a lie assuming Brenda's not lying to us about where she lives assuming she really does live in Orlando then we can include okay then she lives in Florida because we know that all people who live in Orlando live in Florida right again we can't be part of a um a certain city that's within a state and not be part of the state that doesn't make sense right um so yeah so there we go there's an example of Law of Detachment so here's another um another couple of examples if someone works at the bar then they have a Smart Serve certification right so let's assume that that's true right that if someone works at a bar then they have a smart Sur certification okay great Alex works at a bar again let's assume that's true that she works at a bar therefore Alex has a Smart Serve certification is something we can conclude right however something I want to mention too is that just because the conclusion is true does not mean that the hypothesis is true so for example let's say they said if someone works at a bar they have a smart Ser certification Alex has a smart s certification does that necessarily mean she works at a bar no right just because someone has a smart Ser certification it sure it means they're certified to work at a bar it doesn't mean that they actually do right based on what what is being said here so we can't say the you know assume the conclusion is true and use that to say that the hypothesis is true it only goes one way right it only goes the way that if P then q p is true so then Q is true if we know that if P then q and we know that Q is true that does not necessarily make p true it means P could be true certainly but not always not always because it's not byond conditional here's another example if a shape is a quadrilateral then it has exactly four sides a parallelogram is a quadrilateral therefore a parallelogram has exactly four sides so again this is the same pattern where we are saying okay if a shapes a quadrilateral if this is true then it has four sides so then that's true right then we're saying okay the first one's true this this thing you know it's a quadrilateral well therefore we can come to that conclusion that it has four sides because we know that all quadrilaterals have four sides based on what was said in the beginning so yeah so that is all that is the Law of Detachment law of syllogism and just an overview on inductive and deductive reasoning and their differences as well so I hope everyone learned something and I will see everyone next day bye everyone