 I'm here at the San Antonio Botanical Gardens. It's actually one of my favorite places to go So in the last section we saw something that Russell is pushing is that All of our good not all of our but a good chunk of our knowledge, especially knowledge about Anything that dealing with the laws of nature anything deal with the physical science is anything we're dealing with what we expect to happen tomorrow or the next minute relies upon the principle of induction Now the principle of induction cannot be proven using experience So the question is whether anything can justify the principle of induction now In this section Russell notes that the predict that the principle of induction is not alone He gives what he you know he gives in the text something that we can might be a generic that called the principle of inference Whatever follows from a true statement must also be true Whatever follows from a true statement must also be true. Here's something. That's true. I am a human being You know what follows from that I am a mammal Now since it's true that I'm a human being it's also true that I'm a mammal So that's just a general principle of inference I hear something that Russell notes look the principle of adduction It's not justified right at least not by experience If we're going to justify the principle of adduction using Using experience that we have to rely upon the principle of adduction Well, the principle induction is not alone in this suppose. I just gave a principle right there principle for inference Whatever follows from a true statement is also true. Okay Well, suppose I want to construct some kind of argument proving that principle of inference What would it look like well Suppose you just list a thousand reasons Right a thousand reasons for why the principle of inference is true Unless you have some kind of statement that says for all these reasons for all these true reasons The principle of inference follows you cannot justify the principle of inference But having that statement is an instance of the principle of inference So the principle of inference itself Must be Cannot be proven in that way right there is no proof for it The principle of induction is in this is in this trap. So is the principle of inference a Question then is well, how do we know these things? Do we know these things? How do we come about to have these kinds of universals these general principles as knowledge? well So there's lots of issues here, right? We kind of went through real fast while we can't prove these things and You know we can even you still ask the question. Well, okay So you given this reason why we can't prove a bike prove any of this by experience well Let's suppose we can prove a bike experience What would be required to prove these things by experience when we're dealing with something like the principle of induction? We would have to be familiar directly acquainted right or at least You know have some kind of acquaintance with everything If we're going to have the principle of induction and it's going to be justified by experiences You know talk about gravity Yeah, sorry. Yeah, talk about gravity each time I throw something in the air. So let's hear here. We go here My keys right so by experience I know that Those two times three times I throw my keys in the air. They're going to come back down, right? So the principle of induction says that the past Also, the future will resemble the past. Okay now if I'm going to justify by experience The this law of gravity I Have to experience every single time that gravity affects Objects and not just in the past but in the future and not just here but everywhere That is an incredibly large number of things to experience, which I can't do and this is the failing of empiricism, you know Russell's talking about is there is simply too much out there to justify By experience alone. You have to have general principles. You have the principle of induction We say well, you know my knowledge that this will come back down as nearing certainty never fights get there because I don't know What the future is and everything else but as nearing certainty, right? Well, the same thing is true for a lot of other kinds of truth I don't have to deal with the experience or you deal with your objects necessarily so you'll deal with mathematics, right? Here's a number 5,268 here's another number 3392 Okay Now you multiply those two numbers together and you get another number Well, you know how to do this you can sit down and do the calculations of this thing But the reason why you know how to do this is because of that principle inference that I mentioned earlier You understand what what the two numbers mean when a multiplication and a quality mean to get a further number But you simply haven't experienced all calculations that is literally infinite There is an infinite number of calculations, right? Even if you're stealing with the number one and Adding it to every other number. That's an infinite number of calculations if you deal with the number two and adding it to every other number That's an infinite number of calculations. It's huge So experience Can't get us this kind of knowledge So if we have this knowledge at all Russell says we have this knowledge of a priori and This is knowledge that is proven Independent of experience and this is knowledge that's proven independent of experience This is where he compares empiricism to rationalism and pierces say all knowledge is known through experience That means every last bit of your beliefs that our knowledge are also proven through experience This is compared to the rationalists the rationalists say some of your knowledge is not known through experience And what they mean by this and this is a subtle distinction that Russell is making here as that some knowledge is Not proven through experience So this is kind of a distinction between how we know something Or whether they have knowledge through experience. I have knowledge Independent of experience now what he means here and Russell is very clear about this He sides with the rationalists in the sense that some of our knowledge is Proven a priori meaning it's proven independent of experience Now you still have to learn about these things through experience Most of you learn about these things through mathematics right through your math class or through school You learn about 2 plus 2 equaling for E and school But learning about it is not the proof Okay, learning about it is not the proof So here's what Russell makes an interesting distinction With this knowledge between the rationalists and the pierces he kind of sort of sides with the empiricists and saying that everything that we learn We learn through experience But he also sides with the rationalists is saying Not everything that's justified or proven is proven through experience So when we're talking about proof Russell is a rationalist where we're talking about Acquiring knowledge Russell is an empiricist. It's an interesting little distinction. He's trying to Keep the best of both worlds there remember. Remember. This is what we said We talked about this that you know, he says that all knowledge Right all knowledge is based upon acquaintance and acquaintances this direct experience with these things Okay So that's how Russell falls between the rationalist and the empiricist and what he says are things like he says that Not that some of our knowledge is proven independent of experience Okay, so Russell's written a big check There are these other there's some a priori knowledge is proven independent of experience We know about it We learn about it through experience simply because we're experiential creatures But the proof for them is not in the experience the proof it lies elsewhere So maybe to get an idea of what he's talking about. Let's look at some of the things that that he thinks are priori Truths right so all logical truths All logical truths and the supplement that I gave you to read philosophy all the truth relations True makes true false makes false True makes false false makes true all those truth relations and how they Result in the different truths the logic that we have the different inference rules. That's all our priori knowledge The laws of thought that he provides okay the law of identity whatever is is and that just means that whatever exists is Identical to itself and and not identical to anything else. So I am identical to me That tree is identical to that tree, but we're not identical to each other The law of non-contradiction What there is nothing that both is and is not There is nothing you know that both is and is not you're looking me and I exist well That means that it's false that I don't exist Hey You're looking me and I am human well then it's false that I am not a human all right That's all that the law of non-contradiction means and the law exclude a middle is Whatever is either is or is not So yeah, so we're dealing with whatever either it is or it is not all right So, you know either I am human or I am not human It is false that I'm not human so I am human Okay, so laws of thought A lot of people argue that you could take the laws of thought and derive all of the laws of logic This is what Aristotle tried to do so laws of logic. That's our prior mathematical truth That's also our prior 2 plus 2 equals 4 4 plus 4 equals 8 8 plus 8 equals 16 16 plus 16 equals 32 so on and so forth the mathematical truths give us the entire system of mathematics that we have today The last one is rather interesting the Russell D is and they talked about truths of value This has to be a priori what is actually value valuable That's an interesting thing to say. I mean it's interesting because he says virtues are empirical, but what's valuable is not Virtues I think what he means this is you know virtuous what's virtuous is what helps us get what's valuable, right? And we can we can observe this right when we talk about health health is valuable, right? The health a healthy body is a valuable thing But we can't just simply intuit What is healthy? We have to go out and observe behavior to find out what constitutes health so eating right in exercise We've learned this through experience. Okay But health itself is not learned You know that that health is valuable is not learned as a matter of experience. That's just nerve. That's just known a priori Now he gives there. These are the examples of some of the opera or truths Now he he says something kind of interesting before he goes into these examples. He says the reason why These are opera are the reason why these are known Independent of experience as he uses his phrase. They are self evidence self evidence Now That's an interesting claim. They're self evidence. What does that mean? If I was feeling sufficiently poetic I'll make make some kind of crack about Philosopher coming out of the midst of obscurity to reveal the truth. I Think we're all glad that I'm not feeling poetic okay self evidence Well to understand self evidence let's contrast it with evidence. All right One of things that Russell says is that our you know knowledge of what exists It's not no not priori If we have knowledge of what exists, we always have to have some evidence of it So I have some knowledge. I have knowledge that At least one in waterfall exists All right And what's my evidence? Well, I go out you know, so I have this knowledge of what a waterfall is So I go out and I look for it now look for this evidence My evidence is I look for water falling for something That's kind of straightforward. Uh, I listen I have listened for sound of waterfall Uh, I listen for a certain touch for a waterfall right all this is evidence Now how it impacts my senses and everything else right we do a knowledge by quints All this is evidence plus some knowledge of truth is gonna say the principle of induction That together gives me the knowledge that Waterfall exists So I look for evidence other than the other than the claim that waterfall exists So I have this claim the waterfall exists right or there is a waterfall There's a waterfall santerna botanical gardens, but I look for evidence other than the proposition That a waterfall exists and that evidence is what I see by the senses. Okay Now a self-evident knowledge claim right self-evidential knowledge, but Russell's getting up the top for our truth Is the claim itself Is its own knowledge? The claim itself is its own evidence So we got these mathematical truths, you know, let's deal with let's deal with the principle of inference that we dealt with earlier Whatever falls from a true statement must be true Why is that self-evident? well Suppose you were going to construct an argument for it if you're going to construct an argument for the claim That whatever is self-evident or whatever is true. Well, whatever falls for a true statement is true Suppose you get struck an argument for that you would have to use the principle Well, suppose you were wanting to construct an argument to reject it You would still have to use the principle Right, you know if your conclusion to that argument is the principle of inference Whatever falls for a true statement is true is not true Then you would lose reason To accept the principle That's because when you lose reason to reject the principle So any way you try to either prove or disprove the principle you have to use it has to be there And this is kind of what Russell means when he says it's impossible to doubt impossible to doubt Okay, that's great for the principle of inference What about the principle of deduction? Well, it's kind of the same thing If you're trying to doubt it How would you go about doing that? Well, you wouldn't use experience to doubt it Or excuse me if you let me back up if you are going to be able to doubt something you're going to have to use experience You have to use experience But anytime you use experience to either prove or disprove something You have to use the principle of induction Right because the principle of induction uses experience it draws inferences from experience So that's going to mean possible to doubt mathematical truth Is it possible to doubt the 2 plus 2 equals 2 plus 2 equals 4 say I want to say well 2 plus 2 equals 5 Well, how do you do that? You know what 2 means? Yes, I do. You know what addition means? Yes, I do You know what equals means? Yes, I do. You know what 4 means? Yes, I do So how is it possible that 2 plus 2 equals 5? Using the meaning to those terms well, it doesn't work So on for our truths are going to be self-evident in the sense that the truth itself is its own evidence And on top of that that it's impossible to doubt Impossible to doubt It's going to be a possible to doubt because anytime you try to construct an argument to doubt it you have to use it That's you know one reason okay So this gives us an interesting distinction between opera or truth and any other kind of truth opera is no independent experience Because anytime any way you try to reject it doesn't work Yeah, so for that reason it's the possible to doubt Well, it's least of some other consequences. All right opera truth Russell says opera truth is always hypothetical It's always in a situation where You know we're dealing with meaning Right or concepts, but not particular things So I can doubt the existence of waterfalls I can doubt the existence of waterfalls If I never experienced a waterfall I could doubt it's exist even if I have experienced You know phenomena that tell me there's a waterfall. I could be hallucinating I could be dreaming So we can we can go back to all that material from the earlier chapter Now so knowledge of existing things can be doubted So that means that knowledge of existing things can't be opera or our truths Because opera or truth can't be doubted So opera or truth never give us knowledge of existing things It's only when we take other knowledge by acquaintance. So said stata That we add that together with opera or a knowledge that then I get knowledge by description of waterfalls And badgers and honey and everything else So that's an interesting difference then between opera or truth And knowledge of existing things knowledge of existing things is not a priori This is the mistake that the rationalist made they thought that they could discern the existence Of of things simply by meanings of terms and for rustlers as it doesn't work another interesting difference Is that opera our knowledge only deals with deduction? Whereas induction is a different kind of inference Does not deal with opera our knowledge Now rustle gives the distinction between deductive and inductive Uh, and you should you should look at that from the book So we definitely have questions about what's deductive and inductive according to rustle So for rustle deductive knowledge deals with the general that you that they start with the general right you are there to do Uh, you start with the general and you refer what's general or you start with general and you refer with particular Whereas induction is you start with particular and you infer the general We'll talk about a class. It's not exactly going to work Uh, we'll talk but we'll talk about that in class. You should still know how rustle distinguishes between those two Um so Opera our knowledge deals only with what's deductive every all other knowledge deals with deals with what's inductive So rustle gives us Uh a distinction in knowledge right and this distinction is important We have opera our knowledge And that's knowledge proven independent of experience And we have Empirical knowledge Empirical knowledge relies either in whole or in part on experience Now even though rustle has given us this kind of preliminary Of uh, you know the different of uh some kind of a preliminary argument about What what justifies opera our knowledge? I'm still going to ask the question. How is opera our knowledge possible and it deals with that in the next section