 Well, I have been alive for about 15,212 days. I know I counted Now in those 15,212 days, I have never known a day without the Sun I mean it's been some of these days have been cloudy like this But the Sun has always been there There's never been a time in which at 12 noon. I've seen the moon or There's never been a time at 12 noon. The Sun has just not been in the sky It was you know in the sky one day and then not in the next and those 15,212 days the Sun has always been there. Well, that's really great information, but Just with the knowledge is with the evidence that the Sun has been in the sky 15,212 days That doesn't tell us very much About whether the Sun will be there tomorrow All on its own It's great evidence for the fact that there's 15,212 days of Sun, but the question is will there be a 15,213th day or 214th day In order for me for me to make that inference. I need a general principle. I need a conditional I need something that says since I have seen the Sun for 15,212 days. I will see the Sun on the 15,213th That general principle is called the principle of induction and that's what Russell talks about in this section Well, so I have seen the Sun 15,212 days and from that I infer Oh from using that and something else I infer that I'm going to see in the 15,213th and the what I'm going to use to infer that is what we call the uniformity in nature the uniformity in nature is is so natural to Claim so easy to roll off the tongue that we take it for granted We don't think of it as something that needs to be proven to be true or anything like that And the uniformity in nature is basically this that you know the future will resemble the past So in the past I've seen the Sun rise right I got 15,212 days of that So it's really good evidence that in the 15,213th day that I will see the Sun rise We'd you know if what if for only 12,500 of those days I saw the Sun rise and in the other 12,500 and some change whatever There wasn't a Sun right it was daytime, but there wasn't a Sun well then I would conclude from that that well But you know there's a 50-50 chance that the Sun would rise tomorrow But since I've seen it rise 15,212 days The probability is really high that the Sun will rise and Again because of this presumption that the future will resemble the past You know in addition to the future or resemble a past we think that you know one area of the universe is Like all other relevantly similar areas of the universe, right? So I wouldn't expect to see this on Venus, right? But that's because this is not relevantly similar to Venus Venus has much more carbon dioxide is much hotter and As far as as far as we know it doesn't have any plant life Yeah, I would expect to see this on the surface of the moon and there's no atmosphere on the surface of the moon There's no soil that can be farmed on the surface of the moon. It's also too cold now because of That because the moon is not relevantly similar to this area. I don't expect to see this on the moon Now suppose the moon were different suppose that had an atmosphere and suppose I had soil things like this I would expect to see something like this maybe maybe maybe on the surface of the moon If there are enough of the conditions from that like this on the moon Now the principle that is uniformity of nature Me is what we use to form the principle of induction, which I'll get to in just a second But the something really important to remember here, you know the uniformity of nature is You know comes so naturally to us that we don't think that it needs a proof But the question very quickly becomes well, you know, we don't like to just assume things to be true We would like things to be justified. We'd like to have reasons or evidence for our claims Well, what proof can we give for the principle uniformity of nature? Well, you know like we said it we've used the uniformity of nature for such a long time as the basis for the principle Induction which we'll get to a second, which is the basis behind the scientific investigation, right? You know since we Don't see a place like this on the moon We don't expect there to be things like this on the moon, right? If we did find something like some if that we thought the moon was relevant to the earth We would expect to find things like this on the earth You know, but you know we use the principle uniformity nature so much and its work so often we say hey It has been working all this time. Why not think that it's going to work in the future since it has worked it will work But notice in order to make that inference in order to make the inference that the print that this uniformity in nature Will always be the case since it always has been the case is To use the uniformity of nature So right up front it looks like We've got to say if I'm going to prove The uniformity of nature. I've got to assume the uniformity of nature and you don't prove anything by assuming it's true Okay, so we talked about the uniformity of nature and this justifies what's called the principle of induction And the principle of induction is an inference rule for probability. Okay? so this kind of Complicated your rustic is kind of a complicated definition for the principle of induction and it comes into two parts the first part is that if we see events a correlated with events B All the time in the past Then we would expect that if we see an event of a kind a we can predict That an event of a kind B will follow and this is roughly what we get from causation So this is what we try to do You know the I think I think I forgot to mention that the uniformity of nature Presumes that there are these general laws right that governs all of What happens in the natural world and you know these causal laws, right? And this is used to inform the principle of induction. So we're trying to determine these causal laws And what we do is I mean this is the basis for scientific experiments We try to find those events a Correlate with those events B and we try to find okay Well, what would interfere with that what would maybe add to it what is also necessary for it? So maybe it's not just a that leads to B, but it's a C and D which leads to be we just you know we have to figure out what C and D are or Maybe you'll be doing kind of an event of a kind a we haven't seen B But maybe a different event called a G has been interfering with a to cause B things like that You know that that's a little bit more what's happening in the text, but this is this is the idea that We're trying to find thought that those correlations of events events of a type a along with the type B So that's the first part that we would expect to see you know If we have seen a and B all the time in the past we would expect to see be a company a in the future The second part has to deal with what kind of probability we can draw from this now You know, it's might seem a little confusing but what Russell says is we can We can draw a greater and greater probability without limit, right? So what he means by that is you know with more and more evidence we could have a 99 percent chance the 99.1 percent chance And 99.1 1 percent chance 99.1 1 percent chance to keep moving closer and closer to certainty We don't get 100 percent Right, we don't get 100 percent because of the nature of induction, right induction deals with Near certainties, but not absolute certainties if you deal with absolute certainties you deal with deductive inference Which we you know, we're talking about what we can't be doubted And we discuss what can't be doubted earlier from the earlier sections I can't doubt my own existence and I can't doubt the fact that I'm having sense experience Everything else has an error for doubt right has this little room this margin for error and that's where the probability comes in So here's what Russell says, you know through induction I Can get a greater and greater degree of certainty, but never quite reach it So we you know we talked earlier in that in the chapter dealing with the nature of matter When Russell said we can never know the nature of matter we can only know how it affects us Well, this is the effect We can know with greater and great uncertainty how matter is going to affect us in the future Now I said in the last scene that the print that the uniformity nature can't be proven it can only be a sin to be true Well, the same thing is true with the principle of adduction so what I mean by that well if Let's let's say we can prove the principle of adduction. Well, if we're gonna do that Then remember the only thing that can be that that can't be doubted is my existence in the end my sense data That can't be doubted So the other principle of adduction is not something that I that is just known with any with with certainty So what am I going to use to prove the principle of adduction to justify? Well, I'm going to use experience Well, if I use experience to prove the principle of adduction and let's say hey, it has always worked All right, the principle of adduction has always worked in the past. So The principle of adduction will work in the future But if he is that line of reasoning, I'm using the principle of induction to prove the principle of adduction well That that's false right you can't Use a principle to prove a principle because that's just assuming it's true. Just like we saw earlier with the uniformity of nature So the principle of adduction Doesn't look like at least at this point doesn't look like it has a proof now We don't have any evidence against it either, right? We don't have any proof against the principle of adduction We don't have any proof against the uniformity of nature, but We don't have proof for it either So this this leads us to the really interesting question. How are we going to justify the principle of induction? We use the principle of adduction all the time to make inferences about what's going to happen in the future Or what we're going to find in different parts of the earth that there aren't necessarily exactly the same what we find But pretty close to it. We use the principle of adduction all the time if it's not justified Right Russell says it's early on if I can't if I don't have the principle of adduction I don't have much knowledge at all namely any knowledge about the future Well, if it's not justified Why am I allowed to use the principle of induction?