Aristotle 1: Logic and Rational Thought

okay so welcome to this lecture on Aristotle we're going to be spending two weeks on Aristotle but we're gonna start by talking about his logic and ways of determining arguments are valid and this is because Aristotle is the one who discovers deductive logic so before we launch into that I just want to go ahead and give you some basic brief info about Aristotle be talking a lot more about this in the coming lectures but Aristotle lived between 384 and 322 before the Common Era so before a year one and just to give you some reference points Socrates dies in 399 so you can see that Socrates is dead before Aristotle is born so 399 is later in time and that's just because we're on this side of the time line so we'll keep that in mind now what we've been saying so far is that philosophy is partially determined by excuse me something being philosophical is partially determined by the kind of method that one uses or adopts and answering certain kinds of questions so in particular we've said that the philosopher is the one who's interested in using reason and argument as a source of knowledge and we've left that fairly intuitive up to this point we haven't really said what we mean by reason or argument but Aristotle's the first want to sort of realize that what we need is some to some determining criteria for what an argument is good or bad it's especially important if you think that that's the method that's you're gonna be using for getting to the truth and in the course of doing this he discovers what we call deductive logic and so that's where we're gonna be spending just some time talking about not very much it's gonna be a very kiddy pool level introduction to logic we will not go very deep into these things but we will say briefly what deduction is and how its contrasted with induction okay so get a little bit more technical hear arguments consists of two parts on the one hand there are the premises of the argument and on the other hand there are the conclusions of the argument and an argument can have anywhere from zero to infinite number of premises and same for the conclusions now there's a relationship between the premises and is in the conclusions of an argument and in particular the premises are offered in support of the conclusion such that the conclusion is said to follow from the premises and to translate this into epistemic talk we can say that the premises of an argument are supposed to be reasons to believe the conclusion so the an argument is not yourself random set of sentences thrown together and there are set of sentences where there's some kind of relationship between the sentences which are premises and the sentences which are conclusions and in particular the premises are supposed to give us some reason to believe that the conclusion is true now using this allows us a way to talk about the differences between inductive and deductive arguments because they're gonna have different kinds of relationships of support between the premise and the conclusion and we're gonna turn to that in just a second but before we do that we I want to just briefly mention the way that Aristotle thought about these things because he's the one who comes up with this terminology so for Aristotle deductive argument was generally one that moved from a general premise to a specific conclusion as for example if I said that all dogs are animals and then concluded that my particular dog was an animal so I've started with this general fact all dogs are animals and I've concluded something particular namely that my dog is an animal now induction can can be seen to move in the opposite direction and that is moving from a specific plus to a general conclusion so if you wanted to if you met my dog and my dog was a pitbull and the dog bit you and was very vicious you might say how that pitbull is vicious and then reason from that particular premise to the conclusion that all pitbulls are vicious now this is not a hard and fast rule people over the centuries have wondered and shown that some deductive arguments don't have general conclusions excuse me general premises and don't move to general conclusion so it's not hard and fast but it's a kind of way of understanding the difference and you can see that one of these would be more suited to the mathematical sciences starting from a universal fact and then all triangles have three sides and then concluding something about this particular triangle whereas in the other case we have something which looks like it's more suited to the biological sciences namely I'm starting from particular things and then trying to build up general facts about those things so that's a rough way that Aristotle thought about deduction and induction but we modern people think of these things in slightly different terms so here's the way we think about them in terms of the support between the premise and the conclusion so for an inductive argument if the premises of that argument are true then the conclusion is more likely to be true but could be false so suppose that you wanted to prove that all swans are white how would you do this well one obvious way of doing this is to go around looking at all the swans that there are and then trying to see what colors they are so you might give an inductive argument I've seen a lot of swans and they have all been white or put it this way every Swan I have seen so far has been white so the next one I see will be white and in fact in the early history of this area people did think that all swans were white based on massive induction people who are biologists had seen many many swans and every Swan that had been chronicled up to that point have been white and so people felt safe concluding that every Swan was white but of course if you ask the question is it really true that all swans are white it turns out that it's not true because there are in fact black swans black swans exist in Australia which is why they were relatively unknown to the West for some time and a group of people went to Australia and saw these birds off in the distance walking around said hey don't those things over there look like swans but they're black so they captured the birds did a bunch of tests chopped them up checked out their DNA etc and came to the conclusion ah they are indeed swans and so it's therefore false that all swans are white now notice that what we just showed was that it's perfectly possible to have a good inductive argument if you've seen a hundred million swans and every one of them have been white then you have a solid base to conclude that every Swan is white and so it can be true that every someone that you had seen so far was white but then when you see your Black Swan it's false that all swans are white so knowing that the premises of that argument are true that every Swan you have seen is why doesn't guarantee that the conclusion will be true if you see a Black Swan then it's not the case that all swans are white and there's nothing you can do about it you certainly can't protest and say ah but I've seen almost an ape in white well that's just the way that induction works it doesn't guarantee certainty now given what you know about ancient philosophy up to this point that automatically indicates that it's going to be generally less interesting to people like Aristotle and Plato who are concerned with knowledge and who have also linked knowledge with certainty so if knowledge requires certainty and if induction never gives you certainty then inductive arguments will never give you know they're not just another kind of way of saying that you can't get knowledge from experience now on the other hand deductive arguments have a very different property a different level of support between premise and conclusion and if a deductive argument is valid if it's a good argument then when the premises are true the conclusion has to be true it must be true it can't fail to be true so that's a very different kind of level of support between conclusion and premises so we're going to come back to inductive arguments when we talk about Hume in the modern period because a problem similar to the Black Swan problem really starts to plague the modern sciences as developed by Newton and company so we'll spend a lot of time talking about what's called the problem of induction and a few weeks but now we'll turn our attention to deductive logic okay so I've already introduced the term valid and validity but let's go for it go ahead and more formally define these an argument is valid when it meets the following requirements first of all it's a deductive argument inductive arguments are never valid because they never give you this level of support but a deductive argument is valid when it meets the following condition if the premises are true then the conclusion must be true an argument a deductive argument is invalid that fails to meet this condition or in other words that it has the property that if the premises are true then the conclusion can be false so here we have our definition of validity and let's look at an example of a valid argument so here we have a very famous argument a premise one says that all men are immortal premise 2 says Socrates is a man premise 3 excuse me is a conclusion then line 3 would be therefore Socrates is immortal and you can sort of look at this and start thinking about the property of validity and see intuitively that this argument is a valid argument if it is really true that all men are mortal and if it is really true that Socrates is in fact a man then it can't fail to be true that Socrates is immortal so those two premises force the conclusion to be true there's no way to accept those premises as true and yet reject the conclusion imagine someone who said to you yes I agree with you that every man is going to die or mortal and I agree with you that Socrates was in fact a man but I don't think Socrates died he's still alive you can't rationally hold that position given that you do truly accept the first two premises as true so if those premises are true then the conclusion must be true now we can see intuitively now we can see intuitively that this argument is valid or in other words that it meets the criterion that we've outlined above whereby that if the premises are true then the conclusion must be true and you might be tempted to think that the reason is valid is because of something that the argument is talking about there's some conceptual relationship between being a man and being immortal or something like that but what Aristotle noticed is that this is not the case in fact what makes the argument valid is not what it's about at all but rather what Aristotle calls the form of the argument which is our way of talking about the way that the terms are distributed throughout the argument so let's go ahead and take a closer look at this argument and you can see that there are repeating terms so in the first premise all men are mortal and in the second premise Socrates is a man we see the term men or mankind distributed in the physician in the first premise and in the second position in a second premise and you can see again that the category are termed mortal is distributed at the end of the first premise and the conclusion and the third term Socrates of the category of those things which are Socrates which consists of one the namely Socrates is again distributed in a certain pattern whereby occupies the first position in the second conclusion the second premise in the conclusion so what Aristotle noticed was that it's because of this arrangement of the words in these sentences that guarantees that the argument is valid and so if we replace these terms with a letter that we designate to stand for those what's called our key then we'll come up with the logical structure of this argument so let's go ahead and do that so we replace the repeating terms with letters leaving everything else the same and then we get the argue it's form so let's assign a to the category of being a man or a human being and be to the category of being mortal or something which will die and see for the category of things which are Socrates or just Socrates and then we can rewrite the argument using those letters and we come up with the following thing all A's are B's all C's are ace therefore all C's are B's now this is what we call the form of the argument this this underlies the original thing we had in English and is what actually makes the original thing valid so here a B and C stands for categories of things and this is why Aristotle's logic is called categorical logic because it relates groups of things or categories to one another and this is distinguished from contemporary logic which deals with sentences instead of single just categories so I will talk sweetly about that in just a little bit okay so this argument form is valid because no matter what you substitute for a B and C it is impossible to get a resulting argument where both premises are true and the conclusion is false so even if you put in something ridiculous into this argument in place of a B and C you still will end up with a valid argument so for instance let's let a stand for jellyfish and B stand for aliens and C stand for George so all jellyfish are aliens that's what we would get by replacing a and B in the first premise all jellyfish are aliens George is a jellyfish therefore George is an alien now that's a perfectly valid argument is they valid because the premises are true illusion has to be true so if it's really true that all jellyfish are aliens and if it's really true that George is a jellyfish then it has to be true that George is an alien now of course it's not true that all jellyfish are aliens and so we don't have to worry about having to believe the conclusion of this argument but the point of validity is not to ask whether the arguments premises are actually true but to stipulate look let's just count that they're true for the time being let's just say that they're true what could we tell about the conclusion a valid argument guarantees that the conclusion is true if the premises are true now don't become confused because it's perfectly normal to have valid arguments with false premises as the one with the jellyfish and aliens illustrates that's perfectly normal and it's also perfectly normal to have invalid arguments that in fact have true premises so you cannot just look at an argument and say the premises are true and the conclusion is true so the judgment is valid this could be an accident and have nothing to do with the way the argument is structure so what you first have to do in order to evaluate an argument for validity is figure out what kind of form the argument exemplifies so a valid argument form is one where it's impossible to find an example of it where there are two premises and false conclusions and so this is our first example of a valid argument form okay so errors those logic is called categorical logic because it deals with categorical statements and a categorical statement is simply statement about a category of objects so we've already looked at one kind of categorical syllogism and a syllogism here is an argument which is composed of two premises and a conclusion so categorical syllogisms are syllogisms composed of categorical statements and that was the kind of statement that Aristotle happened to be interested in and there are only four kinds of categorical statements that you can make you can either be claiming that all a zerbies you can be claiming that no Hayes or B's you can claim the some of the A's or B's or you can be claiming the some of the A's or not B's so for instance you can say all cats are mammals no snakes are reptiles excuse me no snakes are mammals some dogs have four legs some dogs do not have four legs so now a syllogism then is an argument which is composed of two premises and a conclusion each of which is one of these categorical statements so you could have a one that says all A's are bees all C's are a so all C's are B that's a categorical syllogism which is composed of all all statements you could have them composed of all no statements composed of all some statements composed of all some are not statements a mix two premises all no all no no you get the point there are many many different ways of combining these four different sentence types into three premise arguments and what Aristotle did is he went through and categorized the way that you could combine and determine which of these are invalid and which of these are valid and it turns out that the vast majority of categorical syllogisms are in fact invalid there's a handful of them which are valid and so it's important to be able to tell which are which and the method that he used was a method called counter examples and so that's what we're gonna be talking about the method of using counter examples so in order to do that let's look at another nother argument miss one all Republicans are vampires premise two some Republicans come out during the day premise conclusion excuse me conclusion so some vampires come out during the day all Republicans are vampires some Republicans come out during the day so some vampires come out during the day now let me ask you is this a valid argument give you a second to think about now well yes this is a valid argument we can see that if those premises were true then the conclusion would have to be true look at what the first premise says it says every republican is a vampire the second premise says some Republicans are things which come out during the day and the conclusion says so some vampires come out during the day well if it's true that all Republicans are vampires and some of those Republicans are coming out during the day then it has to be the case that some vampires are coming out during the day the ones which also are Republicans now of course it turns out that the first premise is false it's not the case that all of them Republicans are vampires perhaps just a couple of them are perhaps none of them are the point is that that argument is valid even though the premises are false now let me ask you another question what is the form of this argument and in particular is it the same form as our previous argument well again what you do you find the things which repeat assign them a letter replace those things with letters leaving everything else the same so in this case we'll assign the letter A to the category of things which are Republicans the letter B to the category of things which are vampires and the letter C to the category of things which come out during the day in that case we would write the arguments form as follows premise one all A's are B's premise two sum A's are C's conclusion so some B's or C's that's the form of this argument and once you have the form it's easy to see that the argument must preserve truth no matter what you put in for a B and C if you assume the premises are true then the conclusion must be true so the first premise says that everything that is an a is all meat and if it is really true that some of the A's are C's as the premise two says and we're assuming that then it has to be the case that some of the B's are seized and namely that's because a and B are all the same thing right all of the A's are B's so the validity of the argument depends only on the form and not on what is being said another way to put that is that the validity of an argument is indignant of the truth of the arguments premises we have another logical property that we reserve for talking about the truth of an arguments premises and that's the property of being sound a sound argument is by definition a valid argument with true premises now as a side note only valid arguments can be sound or unsound an invalid argument is never sound and you can see why if an argument is invalid then what that me at the finition you could have those arguments premises be true and the conclusion nonetheless turn out to be false well if that's the case then who cares if the premises are in fact true they can be true and the conclusion could still be false so knowing that those premises are true doesn't mean anything so no one cares about the soundness of an invalid argument only valid arguments our sounds are unsound so the way that you work these problems is you look at the argument figure out what for on the argument has figure out whether or not it's valid which means can it have two premises and a false conclusion and if it is valid then you go back and look at the arguments premises in the original and you ask yourself are those premises actually true and then you determine soundness now it's perfectly ordinary for a valid argument to be unsound or to have false premises as in our previous example the vampyre republican argument was a valid but unsound argument it's valid because the form guarantees that if the premises are true then the conclusion is true and it's unsound because it turns out that the premises are not in fact true so that's perfectly normal for valid arguments that happen to have false premises in fact a lot of what goes on in philosophy is people using valid arguments and then arguing about the soundness of those arguments here's a valid argument for the existence of God but are the premises true is it in fact sound so it's perfectly normal so it's very important for us to be able to sting guaa Sh between the validity of an argument and the soundness of an argument okay so now let's turn to our test for validity and we're gonna be using a very simple test the method which is known as the method of counter examples so to determine if a valid we need to know the form of the argument and whether it's possible for the form to have true premises and a false conclusion and that's what's called a counter example to the argument now it's important to note here that only invalid arguments allow counter examples it's impossible to find a counter example to a valid argument so a counter example is an argument with the same structure or form as the original but where the premises are true and the conclusion is false if the argument form is valid you cannot find a counter example if the argument form is in ballade it's very easy to find a counterexample although it does take a bit of creativity so let's go ahead and explore this a little bit more deeply okay if you can produce a counter example to an argument form then you've shown that every argument with that form is invalid so if you have some argument you find the form of it you show that that form is invalid then you now know forever and for always that any argument that has that feature is a bad argument where by bad we mean the premises could be true in the conclusion can still be false so what you've shown is that the conclusion does not follow from those premises another way of putting that the premises I'm an invalid argument whether true or not giving no reason to believe the conclusion you just have no reason whatsoever to believe the conclusion is true based on those premises there may be other reasons to believe that the conclusion is true but if the argument is invalid then the reasons given in the premises aren't the ones that actually support the conclusion now if a sound argument excuse me if an argument is sound which means that is valid and the premises are true then it rationally compels you to believe the conclusion it's irrational by definition and usually when these philosophers are talking about rationality this is the kind of thing they mean at least in this period what they mean is accept those things as true so if you say that's a sound argument then you are rationally compelled to believe the conclusion so let's use some of these tools here's another argument all men are mortal Socrates isn't a man so Socrates isn't immortal here again we have a syllogism two premises all men are mortal Socrates isn't a man and a conclusion so Socrates is immortal now we want to know if this argument is valid so first thing that we have to do is fund my form of the argument we find the form of the argument by finding the repeating terms assigning them a letter that's called your key and then you rewrite the argument with those letters so let's go ahead and assign a to the category of being a man or a human be to the category of being immortal or a thing which will die and we'll use s for Socrates you can use C you can use whatever you want now we leave everything else the same translating that then we would get the following argument form all a are B no s is an a so no s is a B now here I've done a little finagling here because I've put it into its actual categorical form notice that Socrates isn't a man isn't technically one of the four sentences of categorical variety that Socrates excuse me that Aristotle was interested in so I've translated the English sentence socrates isn't a man into the category limits know things which are Socrates are things which are man or in other words no s is an A and you could write for our purposes C isn't an A and that's not technically correct but everybody knows what you mean and if you took a class on logic and went into a little more detail you would find out how you translate these kinds of things but don't worry about that overly much let's just focus on the form that we have here all a are B no s is an A so no se E and try to figure out is that form valid when I remember what do you have to do you have to come up with a counter example where you figure out some way of putting in the A's and the B's and the S is there where the premises come out true and the conclusion comes out false so this is something that you should be able to do try to think of a scenario where the premises are true and the conclusion is false in fact the original argument is itself a counter example Oh I'm sure you guys were thinking of Socrates as the name of a person at the name of a philosopher but of course I can name anything Socrates and suppose that I have a pet maybe a pig and I want to name my Pig Socrates so if Socrates is the name of my Pig then it could be true that all men are mortal that's a true statement and it could be true that Socrates isn't a man because Socrates is the name of my Pig but it would be false that Socrates immortal as all pigs painfully know they are in fact immortal they get killed all the time so here what we've shown now is that that argument structure can have true premises and a false conclusion and so we've proved that the argument is invalid so let's do another counter example because once you know in arguments invalid there's an infinite number of counter examples and they're easy to come by so let's see here all A's are B's no s is an a no S as a bean suppose we wrote that all dogs are mammals that's true no cat is a dog that's also true so therefore no cat is a mammal that's false so there again we have our true premises and false conclusion let's do another one all dogs are animals no cat is a dog so no cat is an animal another perfectly good counter example here's another one all women are able to give birth to live young no dog is a woman so no dog is able to give birth to live young here again we have true premises false conclusion now what if we said something like all basketball players are tall football player is a basketball player so no football player is tall now here's a bit of a complicated exponent because at first of all it's not really true then all basketball players are tall and nor is it really true that no football player is a basketball player but even if those things were true it wouldn't follow that no football players are tall so finding a counterexample is a bit of an art you have to play around with the structure of the argument substituting various things in and trying to see whether or not you can make the conclusion false while the premises are true and the best way to do that is to think of things where there's a nice connect between being a dog and being a mammal or being a dog of being an animal and those aren't the only kinds that work but they're probably the easiest for our level for things for our kinds of things that we want to do so now usually as we just Shaw saw an argument that is invalid will be a counter example to itself and that was the Socrates isn't a man Socrates isn't immortal but sometimes it's hard to tell and that's why you want to try and generate a new argument with the same form one that is easy to see that the premises are true other contestants false so every invalid argument as I've said already has an infinite number of counter examples all you have to do is find one of those so let's go ahead and do some practice together and before we quit so here 2 2 3 4 arguments no Republicans are liberals some liberals want to legalize marijuana so no Republicans want to legalize marijuana argument - if I study hard I'll get an A in philosophy but I haven't studied hard so I won't get an A in philosophy argument 3 all murderers kill people cancer kills people so cancer is a murderer argument for if I want an A in philosophy I need to study for the exam since I haven't studied for the exam that means that I don't want an A in philosophy so now if I were you I would pause this lecture and try to determine whether these arguments are valid by first finding the form of the argument and secondly determining whether or not you can generate a counterexample to that form so pause the lecture work on these assignments and then when you're finished come back and we'll go over the answers so go ahead possible ok so now that you've worked on these answers let's go ahead and get to some of them so our first argument no Republicans are liberals some liberals want to legalize marijuana so no Republicans want to legalize marijuana now remember what we do we first find the things which repeat we assign them a letter and then we rewrite the argument using the structure that is there replacing the terms with these letters so let's assign a to those things which are Republicans and B to those things which are liberals and C to those things want to legalize marijuana so we would get the argument structure then as no a czar B's some B's are C's therefore no A's are C's so that's the correct structure for that argument now we want to know is this structure valid or invalid well it turns out it's invalid so here's a counterexample no dogs are cats that's true I don't care what they say about cat dog there are no dogs which are cats premise to some cats like to eat chicken that's true conclusion therefore no dogs like to eat chicken that's false dogs love chicken so there we've shown that the argument is invalid because we've shown that there can be true premises and a false conclusion and again the original argument was also a counter example maybe it's true that no Republicans are liberals and maybe it's true that some liberals want to legalize marijuana but that doesn't mean that there are no Republicans who want to legalize marijuana again we can also generate numerous other counter examples so they know snakes are mammals some some mammals are living so no snakes are living true true false and you can multiply this indefinitely so let's go ahead and turn our attention to the second argument now we haven't talked about this yet this would be an example of the more modern version of logic so here instead of talking about categories of things we've switched sentences so notice the first premise says if I study hard then I will get an A in philosophy so I study hard and I'll get an A in philosophy are the things which are repeating through this argument so let's just call I study hard a and I'll get an A and philosophy B then you would rewrite the argument as if a then B not a so not B and that just follows right if I study hard I'll get an and philosophy so if a then B but I haven't studied hard that's denying a so not a so I won't get an A in philosophy that's denying B so there's our structure of the argument now we want to know is this argument valid or invalid well it's invalid because we can generate a counter example so here's a counter example if it's raining then I'll bring my umbrella it's not raining so therefore I did not bring my umbrella well it could be true that if it's raining I'll bring my umbrella and it comes true that it's not raining and make it the case that I didn't bring my umbrella I may have brought my umbrella anyway in fact the original argument was a half ton for example as well it can be true that if you study hard then you'll get an A in philosophy and it could be true that you haven't studied at all but that doesn't mean that you won't get an A in philosophy because there are other ways to get a name you may be lucky may cheat so again numerous counter examples you should practice generating your own if you haven't already okay so let's turn our attention now to the third argument all murderers kill people cancer kills people so cancer is a murderer so remember the first thing that you want to do is identify the things which repeat substitute a letter for those things rewrite the argument structure leaving everything else the same so let's assign a to murderers B two things which kill people and C to cancer then when we get all A's or B's all C's are bees so all C's are a now is this argument valid or invalid well it's invalid it's very easy to generate a counter example just like we did earlier so let's say here's my counter example all dogs are mammals Socrates is a mammal so Socrates is a dog well it could be true that all dogs are mammals and also to the best Socrates is a mammal if he's a human being but that would mean that it's false that he's a dog so here's another way of doing it all birds have wings airplanes have wings so airplanes are birds true true false you can do this ad nauseam now of course which gear was to see that I can again premise cancer kills people is really a claim about not some particular cancer about about all now let's do our final example here which is if I want an A in philosophy I need to study for the exam since I haven't studied for the exam that means that I don't warm on an a so again identify the things which repeats play someone with a letter and rewrite the argument if I want an A in philosophy I need to study for the exam since I have a study that means I don't want to name SOCAN I want an A and philosophy we'll call that a I study for the exam B so then the argument says if a then B not B therefore teh notice closely related to the first argument we looked at of this kind but very different the first argument said not a therefore not be this one reverses that not B therefore not a well is this argument valid or invalid it turns out that is valid there is no way for you to make the premises true and the conclusion false it just can't happen you can see that just by looking at the argument the first premise says if a then B so assume that's true the second premise says not be assume that's true well if the first premise is true then if you have a then you're going to get B so you know that if you don't have B you couldn't have had a because if you did have a then you would have B that's what the first premise says so if those premises are true the conclusion not be must be true now this argument form actually named it's called modus tollens modus tollens is a Latin for I deny and it's basically named for the second premise here you're denying the antecedents excuse me you're denying the consequence which is the second position in the conditional statement if a then B you're denying the B part so don't get confused by the fancy Latin terminology here modus tollens is just a name for this valid argument form of course many people might have stumbled on this and thought but hey look you know just because I want an A doesn't mean I need to study that's what the first premise says but and then they might have then concluded well then the argument is invalid but that of course is a mistake what you just pointed out that hey look it's not really the case that if I want an A I need to study what you're saying is that the first premise could be false so that the argument might be unsound but that's not the same as saying that the argument is invalid so you want to make sure that you distinguish between soundness and validity and that's very different than the first kind of example where it says if you study hard and you'll get an A in philosophy you might say yeah well even if I study I'm not gonna get an A and that's a way of saying that the first premise is false as well but remember since that argument is invalid we don't really care if it's sound or not so you don't just start by looking at the premises and say well it sounds true to me what you do is you start by determining the arguments form and then determining whether that form can have a counter example which is having the same argument with two premises and a false conclusion okay so that concludes the discussion of logic

Channel: Richard Brown

Views: 83,131

Rating: 4.7531648 out of 5

Keywords: Aristotle, logic, syllogism

Id: hj7u3G_K6TA

Length: 45min 4sec (2704 seconds)

Published: Mon Oct 10 2011