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So I. Right, then I think we ought to sort.

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Um, so welcome to everyone here. Welcome to everyone on the podcast.

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Um. Um, anyone who didn't get the, um, thing I sent out last week about the, um, argument that we tried to do.

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Can you email me on that address and I'll bounce it on to you?

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Um, and I'll make sure that the thing that I sent out to everybody here is also available online for the people looking at the podcast later on.

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Right? Um, well, this week we're going to do different types of arguments.

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Um, so versus last week we learnt how to set out arguments, logic, book style.

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Do you remember how set done. What is it for an argument to be set out?

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Logic books. Style. Come on.

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We've got to get you warmed up, haven't I? Previous time to conclusion.

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That's right. You. So you identify the premise and the second premise if there is one, and the third premise if there is one.

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And then the conclusion. That's right. And the way I did it was just to label then premise one, premise two.

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Conclusion. But you could just put the premise one, premise two and then align and then the conclusion.

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There are different ways of doing it. Um, okay.

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We dealt with ambiguities. Hold on one second.

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How much did you miss? Okay. Uh, right.

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We we dealt with ambiguities. Remember, there were different sorts of ambiguity.

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What is ambiguous? Can anyone tell me? Start off with what is an ambiguity?

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Two or more. It's a word or phrase that has two or more meanings.

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That's right. So it starts in the context where it is.

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It could mean two different things, which is very confusing.

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And there are different types of ambiguities. Can anyone remember a couple of these types?

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No. I was so sorry. Linguistic.

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Um. No. What do you mean by linguistic?

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You might have different meanings for. For example, is. Right.

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Okay. That's lexical. A lexical ambiguous is one word which could mean different things.

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So rum could mean the drink or, um, this is strange or something like that.

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Or we use the example of bank, um, which could be all sorts of things that it could be a verb was, was a noun, all sorts of different things.

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And then it also structural ambiguities where you have every particular love to say that, um,

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does it mean there is a sailor such that every girl loves him or every particular love some sailor?

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Um, so there are different sailors who loved by themselves or just one.

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Um, and then there's ambiguity. Cross-reference. Does anyone remember what that is?

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Or anaphora? You might have been taught in school and, um, before it references, when, um, you have a pronoun that links back to a name.

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So, um, just subject comes to party because she doesn't like, uh, do you remember that?

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She becomes ambiguous and the hook becomes ambiguous.

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Okay. And then there are ambiguities of of just of sounds.

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So the picture of water that you remember could be a picture or a picture with a title of other difficulty,

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something that's a picture of water or a picture drawing of water.

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Um, we then uh, to identify conclusions and premises.

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Um, we learnt there that although that sometimes there are a conclusion on premise indicators,

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what's the only foolproof way of identifying the conclusion of an argument.

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Okay. So role innocence.

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The role is it plays within the arguments from within a sentence.

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Because of course a conclusion will be a sentence. That's exactly right.

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So, um, what role does play by the conclusion? It's the census that is.

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That's being asserted. Exactly. So. And the premises, which you can also tell in a foolproof way, only by rule that they are wards.

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Three the reasons being given. So the conclusion that you said okay.

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And we then we went to eliminate relevant seats. And that's where we got into a bit of hot water, isn't it.

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Because you were all accusing me of throwing things out, uh, just for fun.

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Um, but I hope that those of you who got the thing that I sent around see that actually, what make something relevant or irrelevant is the conclusion.

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Because once you've identified the conclusion that you have the arguments because the premises are the reasons for that conclusion,

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and anything that isn't the reason for that conclusion is irrelevant, isn't it?

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So even if it seems very important, like God, I mean, what could be more important than God, perhaps?

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Um, I'm afraid he gets left out. If what ever said about God is not a reason for believing that conclusion.

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Um, we identified suppressed premises, and we saw that sometimes you have to put a suppressed punch in, and sometimes you don't.

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When do you have to put it in its context?

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Well it's controversial. Good. That's right. Because you can't leave it out as an argument.

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If it's controversial, it would weaken the argument to have it in because it's controversial.

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Um, when can you leave the premises out? But it's understood from the general context,

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and it's obvious when it's blindingly obvious when all you'll be doing is sort of eking out the argument.

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So I'm going to take my umbrella, you know, do I have to say,

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because it's raining and if I don't take an umbrella, I'll get wet and I don't want to get wet.

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Um, no, of course I don't. You mean you understand immediately when I say I'm going to take my umbrella?

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Um. And finally, we learned how to make terms consistent.

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What did that involve? Going to rain.

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Uh. That's right. We had something like two words that meant the same thing.

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Or two phrases that meant the same thing. So it's raining and it's pouring.

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We could just choose one of them and get rid of the other, because that's all it does is confuse us.

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Um. And we did the same thing with the cat is innocent.

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Um, and the cat hasn't since, um, I said, in the context of this argument, there's no difference between them.

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Um, okay. So that's that's what we did last week. Um, bit of revision for us.

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Um, so now we know what arguments are, and we can distinguish arguments from other sets of sentences to remember,

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we can distinguish them from, um, conditional sentences.

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For example, um, we can analyse arguments and set them out.

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Logic book solve. Um, okay.

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So, so if you're not too badly, I'm for lecture three.

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Uh, but we haven't yet asked on how to evaluate arguments.

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And that's important because some of you last week were having trouble with the analysis of an argument because as you were analysing it,

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you were trying to evaluate it as well. So you were saying this premises isn't true.

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Well, maybe it's not. Um, but all we're interested in at the moment is whether it's a premise or not.

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We're not interested in whether it's true or not at the moment, but we will be.

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Um, so we're not even going to be able to start on analysis this week.

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What we're going to start on this week is looking at two different types of argument.

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And it's very important to to be able to identify the two different types of arguments.

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So we're going to the first the normativity of critical reasoning.

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Uh um uh of course I'll explain what normativity means.

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We're going to look at the relation of following from uh, we're going to look at the two main types of arguments.

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Um, and we're going to learn how to distinguish these two types from each other.

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Deductive arguments from inductive. Um, so in critical reasoning we're concerned with whether or not an argument is good.

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So importantly, it isn't a purely descriptive discipline.

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A purely descriptive discipline is one that tries to say what the world is like.

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So zoology, for example, will attempt to describe a different species.

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So it will tend to categorise living things into species, uh, and into geniuses and so on.

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And then it will try and describe each species and so on. But it doesn't really get into shoulds.

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Um, in, um, biology, I mean, you might get into a situation where all you mean by should is you'll talk about normal,

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um, some things being normal, you'll say you're really talking statistics.

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So cats, uh, cats should have four legs.

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You might say, well, yes, indeed they should. Statistically, most cats do have four legs, but this isn't a moral should.

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Um, and so whereas with critical reasoning, uh, we've got a what's called a rational should, it's normative.

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It lays down standards for us to follow. A good argument is an argument we want, and we want it because it is good.

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So critical reasoning is a normative discipline.

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Um, we're interested in when a conclusion follows from a set of premises and when it follows recessive premises, it's good.

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Okay. So we're interested in arguments that are good. Um, and that's what an argument follows from a set of premises.

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And we're also interested in which arguments are bad. Um, I mean, you need to be able to identify bad arguments as important.

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These are doing good ones. So following from is a very important relation between premises and conclusion.

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And there are broadly two varieties of following from um that's what we're going to learn to distinguish from each other today.

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Um both deduction and induction. Uh varieties of following from.

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So conclusion may follow deductively from a set of premises.

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Or it may follow inductively from a set of premises.

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And really these two types of arguments exhaust the types of arguments.

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There are there are arguments within each type. But but deduction an argument is either deductive or it's in.

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Up to um, and there are three questions you can ask to determine whether an argument is deductive or inductive.

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Um, here are the three arguments. I'll let you. Sorry. Three questions that you need to ask.

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And of course I'm going to look at each and explain them. Okay.

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Anyone have any questions so far? Nope.

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Okay, let's, um, write. The first property that distinguishes deduction from induction is the fact that a good deductive argument is truth preserving.

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Unbiased deductive arguments aren't truth preserving, and inductive arguments are not truth preserving at all.

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So if an argument preserves the truth, it is a good deductive arguments.

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If it doesn't, it may still be a detective argument, but it's a bad one, and no inductive argument ever preserves the truth.

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So what do I mean by an argument? Speaking truth preserving?

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Well, an argument is truth preserving if and only if, and that I double f is not me misspelling if.

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By the way, whenever you see I double f, I suppose it could be an error, but it usually means if and only if.

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Um. So uh um, you get the f going in both directions if p than q and if q, then p.

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So an argument is truth preserving if and only if it's not logically possible for its premises to be true.

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Well, its conclusion is false. Okay. So it's a very strong relation.

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Uh, this is the relation of entailment. So premises entail the conclusions when it's not logically possible for a set of premises to be true.

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And a conclusion is false.

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Um, and just before we look more closely at that, you've got to be able to distinguish logical impossibility from physical impossibility.

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This is actually crucial for a lot of philosophy, but it's particularly crucial for critical reasoning because it's slower and slower.

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I'm not going too fast. Okay, okay.

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Um, so okay, let me go back to this one.

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An argument is truth preserving if and only if it's not logically possible.

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So this is why you've got to know the difference between logical impossibility and, um,

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physical impossibility if it's not logically possible for its premises to be true and its conclusion false.

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Um, so we've got to be able to distinguish logical impossibility and physical impossibility.

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Uh, by the same token, logical and physical possibility.

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Something is physically impossible if it's inconsistent with the laws of nature,

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and it's logically impossible if it's inconsistent with the laws of logic.

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Um, um, something's inconsistent. Two things are inconsistent if they can't both be true together.

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Okay, so, um, if the laws of nature are as they are, um,

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something is physically impossible if it can't be the case consistently with the way the laws of nature are and with physical,

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uh, logical impossibility. It's the laws of logic that matter.

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So it's physically impossible for a human being to swim three miles underwater without breathing apparatus.

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Do you see that? If somebody told you that done that, you would know that they were not speaking the truth because it simply can't be done?

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Um, it's also physically impossible for A to talking intelligently about cats.

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I mean, even even Oedipus. I talked to him about cancer.

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Yes. He still doesn't talk back intelligently about it, or even I'll intelligently to that.

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Um, but both these things are logically possible.

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Logic has nothing to say about with my cat discusses Kant,

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and it has nothing to say about whether you can swim under water for three miles without breathing apparatus.

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Um, it's logically impossible, on the other hand, for a square to be a circle.

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Um, so all those people, like my father talk about squaring the circle.

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It's nonsense. You cannot square a circle because if something's a square, it cannot be a circle.

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And you can tell that just from the very ideas involved.

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Uh, an a man can't be a married bachelor, because if he's a bachelor, he's not married.

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And if he's married, he's not a bachelor. Just like if something's a square, it's not a circle.

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And if it's not a circle, it's not a square. We know that.

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And we know that a person can't have exactly three and exactly four children.

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These things are ruled out by logic. Um, in other words, it's in the very nature of the concepts square and circle,

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marriage and bachelor and so on that we don't need to leave our own chair to know that there are no square circles.

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This is why it's so comfortable to be a philosopher. Um, so here's an exercise.

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Give me two examples of states of affairs that are logically possible but not physically possible.

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Can you do that? Can you give me two examples? Of states of affairs that are logically possible but not physically possible.

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So if you remember, one example was that my cats can't talk intelligently about cats.

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Uh, and another one is this a human being can't swim for three miles underwater without breathing apparatus?

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Another example like that. The sunset over froze to death.

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The sun so hot you froze to death. I'm not sure that isn't a logical impossibility.

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I mean, because you're working on the words freeze and hot, aren't you?

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And actually, they logically exclude each other. Don't like, um.

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Don't have a good pace. Comply. That's a very good one.

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This Pink Floyd pace, as far as logic is concerned.

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Fine. Pigs. All fine. But yes, there are no pigs that can fly.

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Um, okay. Uh, yes.

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You must be looking at the. Okay. And the other examples.

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Yes. You mean like it? I believe I believe that you believe you did it, but I didn't like you sort of see it.

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Yeah. Yeah, yeah. Hey, can anyone think of another example of something that's physically impossible but logically possible?

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I can jump to the meat. Uh, good. It's logically possible for you to jump to the moon.

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But it's physically impossible, isn't it? Yes. Good. Okay.

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I think you're getting the idea. Anyone else want to have a go? I saw through the wall.

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You saw through the wall? Good. Yeah, that. That's physically impossible, but logically it's fine.

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Um, so there are lots of things like this that are physically impossible, ruled out by the laws of nature, but not ruled out by the laws of logic.

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That's false. And of course, there may be worlds out there that have different laws of nature.

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Um, and so when we want to know what's going on in those worlds,

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it's to logic that we look not to the laws of nature, because they're not going to tell us what these worlds like.

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Uh, can I only get two examples of state, some things that are logically impossible?

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Okay, so you might see it being frozen by a hot sun might be a logical impossibility.

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Anyone think of another logical impossibility? So it's, uh, it's raining cats and dogs.

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Uh, funnily enough, that's that's a physical impossibility is not a logical impossibility.

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Actually, it does rain frogs occasionally, I understand, but it actually does.

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Burnt by ice. Um, being burnt by ice ash.

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It's just. I know what you mean by burnt, doesn't it? But actually, if you put your tongue on the ice, the, um, in the Antarctic, you will.

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You are in trouble. Um, and it's actually called a burn, isn't it?

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Um, yeah. A female born, a female boy.

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Yes. That's a good example of a logical impossibility.

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Yeah. Okay. Any anything else?

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It's quite difficult just thinking of examples. But I hope you're getting the idea of the difference between physical and logical impossibility.

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Logical impossibility is inconsistent with the laws of logic.

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It's actually ruled out by the very concepts involved and physically possibilities ruled out by the laws of nature.

199
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So whereas, um, the logical impossibility can be determined a priori.

200
00:20:09,130 --> 00:20:16,780
In other words, we don't need experience of the world to determine what a logical possibility is is all you need is two concepts.

201
00:20:17,230 --> 00:20:21,040
Um, with physical impossibility, you need to know what the world is like.

202
00:20:21,370 --> 00:20:24,880
Science tells us what's physically possible and impossible.

203
00:20:25,390 --> 00:20:31,240
Um, so what about these? By means of genetic manipulation, we can produce pigs that are able to fly.

204
00:20:31,480 --> 00:20:37,240
Is that physically impossible? Logically impossible? Or are we unable to tell physically?

205
00:20:37,240 --> 00:20:45,490
Is it it's physically impossible? That's right. I mean, actually, maybe by genetic manipulation, we will produce pigs in five days.

206
00:20:45,940 --> 00:20:51,879
Um, we think we want some. Um, Joe has exactly twice as many siblings as Janet.

207
00:20:51,880 --> 00:20:55,750
He has Susan and the twins do that.

208
00:20:55,750 --> 00:21:00,340
Do you see how that's logically impossible? If somebody told you that, you would.

209
00:21:01,630 --> 00:21:05,290
You think for a minute, but then you think, no, that can't be right.

210
00:21:05,290 --> 00:21:12,399
And the reason it can't be right is if he's got three siblings, then he cannot have exactly twice as many as Janet has.

211
00:21:12,400 --> 00:21:16,570
However many Janet has. Um, muon neutrinos can travel faster.

212
00:21:16,570 --> 00:21:20,860
The speed of light in a vacuum. Physically possible.

213
00:21:20,860 --> 00:21:25,510
Logically impossible to physically just wait.

214
00:21:25,690 --> 00:21:31,960
Yes, for a moment. That might be not, uh, logically possible and physically possible.

215
00:21:32,290 --> 00:21:38,110
Um, but some of this, uh, microscope is shaking or something.

216
00:21:38,620 --> 00:21:42,070
Um, okay. Physicists succeeded in building a time machine.

217
00:21:42,850 --> 00:21:48,730
Is that physically impossible? Logically impossible or such that we can't tell physically?

218
00:21:50,470 --> 00:21:57,070
Um, so we can't tell on that one because it looks as if time machine time travel is logically impossible.

219
00:21:57,070 --> 00:22:05,440
Because if you could travel back and kill one of your parents before you were born, then the.

220
00:22:05,440 --> 00:22:08,770
Do you see the logical inconsistency that we get there?

221
00:22:09,220 --> 00:22:14,440
Um, well, if it's logically inconsistent, it shouldn't be physical, physically possible.

222
00:22:14,440 --> 00:22:21,550
But there are physicists who argue that it's not only not logically impossible, it's physically possible.

223
00:22:21,970 --> 00:22:29,350
Um, and I actually, I if you look on YouTube, if you put in time travel physically possible,

224
00:22:29,470 --> 00:22:32,980
you'll get us a physicist who believes that it is physically possible.

225
00:22:33,220 --> 00:22:38,230
So I'm not going to say I think I'm inclined to think it's logically impossible.

226
00:22:38,980 --> 00:22:47,020
Whereas, uh, sort of is our point about all of this in the sense of you have to almost as a caveat or that says,

227
00:22:48,400 --> 00:22:53,830
given what we know today with physical impossibility, that's exactly what we have to say.

228
00:22:53,830 --> 00:23:01,720
Yes. Because, um, the laws of nature, we may be able to work with them to produce a peak that can fly.

229
00:23:02,230 --> 00:23:08,590
I mean, obviously we can't work against them, but that's things. Currently, sons flying pigs are, uh, against nature.

230
00:23:08,800 --> 00:23:11,800
But logical impossibility, no.

231
00:23:12,010 --> 00:23:16,390
Logical impossibility seems more fixed because the laws of logic seem more fixed.

232
00:23:16,420 --> 00:23:25,750
But actually, um, quantum mechanics, for example, has called into question, um, a couple of the laws of classical logic.

233
00:23:26,320 --> 00:23:31,149
So, um, where it says a distinction between the laws of nature,

234
00:23:31,150 --> 00:23:40,629
i.e. the natural uniformity that govern our worlds and the laws of nature that we put together, i.e., uh, descriptions of the natural uniformity.

235
00:23:40,630 --> 00:23:49,720
So you see the difference. So there's the laws, uh, laws, if you'd like, and the natural uniformity that we describe in the same way,

236
00:23:49,720 --> 00:23:54,910
the laws of logic, there's all a description of these laws, and there are the laws themselves.

237
00:23:55,270 --> 00:23:59,460
Um, we. They have the wrong description and they need to tighten it up at some point.

238
00:23:59,970 --> 00:24:04,410
So we can't be sure we've got the right understanding of either type of law.

239
00:24:04,950 --> 00:24:12,030
But it's certainly true with physical possibility that it's, um, malleable according to often physical knowledge.

240
00:24:13,320 --> 00:24:20,300
So. Well, let me just ask other any other questions about physical and logical impossibility before I move on,

241
00:24:20,310 --> 00:24:27,300
because that is it's quite an important distinction. Chris Quine produced an argument against logical certainty.

242
00:24:28,410 --> 00:24:33,930
Um. So no challenge is that what he does?

243
00:24:33,930 --> 00:24:39,390
Is he he's, um, he what he challenges is the existence of analytic truths.

244
00:24:40,740 --> 00:24:45,120
Um, so he doesn't think that there are truths.

245
00:24:45,120 --> 00:24:49,830
This is not realisable. Okay.

246
00:24:50,490 --> 00:24:59,780
Um, okay. So an argument is truth preserving if and only if it's not logically possible for its premises to be true and its conclusion false.

247
00:24:59,830 --> 00:25:01,830
That's the definition we had up there before.

248
00:25:02,650 --> 00:25:13,590
Um, and it's important to notice that the actual truth value of the premises is irrelevant, uh, to determining whether an argument preserves truth.

249
00:25:13,620 --> 00:25:18,720
So have a look at this argument. All heavenly bodies revolve around the earth.

250
00:25:18,990 --> 00:25:23,280
The sun is a heavenly body. Therefore, the sun revolves around the earth.

251
00:25:23,850 --> 00:25:29,040
Do you see that if those premises are true, the conclusion must be true.

252
00:25:29,270 --> 00:25:37,560
Yeah, yeah. Do you see that? But the conclusion is false, as is at least one of the premises.

253
00:25:38,940 --> 00:25:45,600
Okay. Do you see that? So we have an argument that preserves truth but doesn't generate truth.

254
00:25:46,500 --> 00:25:55,170
Um, so that's the importance of the distinction. You've got to distinguish between an argument's preserving truth and generating truth.

255
00:25:55,380 --> 00:26:02,580
And if it preserves truth, what you're saying is if there is truth in the premises, there will be truth in the conclusion.

256
00:26:03,000 --> 00:26:12,660
And that suits this argument very well. So if if these premises were true, the conclusion would be true would have to be true, wouldn't it?

257
00:26:13,080 --> 00:26:20,010
Couldn't possibly be false. It's logically impossible, in fact, for that purpose to be that conclusion to be false.

258
00:26:20,220 --> 00:26:25,860
If those premises are true, and that's what it is for an argument to be truth preserving.

259
00:26:26,490 --> 00:26:30,630
So if an argument has that property, then it's called valid.

260
00:26:30,660 --> 00:26:35,700
As we'll discover next week. And the premises entail the conclusion.

261
00:26:36,480 --> 00:26:39,510
Um, this is a good deductive argument.

262
00:26:39,870 --> 00:26:43,680
And that's so even though the conclusion is false.

263
00:26:44,220 --> 00:26:54,150
Um, can anyone tell me why? We'll look at this a bit next week, but can anyone tell me why the property of being truth preserving is useful,

264
00:26:54,390 --> 00:26:57,360
even though you can end up with a false conclusion?

265
00:26:58,680 --> 00:27:06,570
Why should we care that our argument should be truth preserving, even though you could end up with an argument with a false conclusion?

266
00:27:06,960 --> 00:27:10,050
Because you can trace back to find the false premise.

267
00:27:10,780 --> 00:27:18,450
Good. If an argument is truth preserving, you know either that it's argued that its conclusion is true if its premise is true,

268
00:27:18,450 --> 00:27:24,660
or you know that if the conclusion is false, at least one of the premises must be false.

269
00:27:25,140 --> 00:27:29,610
And of course, you can look back to find which premise is false.

270
00:27:29,920 --> 00:27:37,620
And of course, this is all swans are white. The thing is, in Swan River in Australia, if it's a swan will be white.

271
00:27:38,100 --> 00:27:43,740
Um, but it's black. Um, you know that one of your premises is false.

272
00:27:44,430 --> 00:27:50,790
Um, so it can be empirically very useful to have the property of truth preserving.

273
00:27:50,790 --> 00:27:59,880
This is an argument. So we can be certain of an argument that preserves the truth, that it's a good deductive argument.

274
00:28:00,210 --> 00:28:03,710
So it's not just deductive. It's also good deductive argument.

275
00:28:03,720 --> 00:28:11,250
If it preserves the truth. Um, we can be just as if the second argument doesn't preserve the truth.

276
00:28:11,760 --> 00:28:17,310
Then it's either a bad deductive argument or it's an inductive argument.

277
00:28:18,000 --> 00:28:23,730
Okay, so it could be one or the other, but it's it's certainly not a good deductive argument.

278
00:28:24,030 --> 00:28:29,150
So let's do this exercise which is following arguments is truth preserving.

279
00:28:29,160 --> 00:28:32,250
In other words is a good deductive argument.

280
00:28:32,370 --> 00:28:37,310
Have a look at them yourself and put your hands up when you think you've got the answer to one.

281
00:28:37,320 --> 00:28:44,650
Let's say. Hands up when you think you've got the answer to one.

282
00:28:46,210 --> 00:28:50,590
Tom is a banker. All bankers are rich. Therefore Tom is rich.

283
00:28:52,360 --> 00:28:56,100
Okay, ladies. Earn. It.

284
00:28:56,410 --> 00:28:59,770
That's a good. That's a good to Touch Bar. Does everyone agree?

285
00:29:00,340 --> 00:29:08,200
Yep. Okay. You are absolutely right. If Tom is a banker, and if all bankers are rich, then Tom must be rich.

286
00:29:08,200 --> 00:29:13,000
Mustn't eat. There's no question about it. So that's a truth preserving arguments.

287
00:29:13,330 --> 00:29:16,690
Um, and it's a good deductive argument.

288
00:29:16,690 --> 00:29:22,990
Therefore, um, what about Sue? And Tom leads similar lives, but Sue smokes and Tom doesn't.

289
00:29:23,440 --> 00:29:32,560
Therefore, Sue is more likely to die from heart disease than Tom puts up your hand when you think you know whether that's truth preserving or not.

290
00:29:40,360 --> 00:29:50,360
I'll let a few more put their hands up first. Okay, so tell us, do you think it's true, Sonny?

291
00:29:51,140 --> 00:29:55,070
No, because I think it's missing something. Yeah. Um, as it says.

292
00:29:55,070 --> 00:29:58,309
No. Okay. Stop there. Well, that's. It is.

293
00:29:58,310 --> 00:30:05,330
No. And that's because there is a possibility that the conclusion is false, even if the premise is true.

294
00:30:05,960 --> 00:30:13,280
Um, why is that? Because it doesn't make any link between smoking and what is it that needs an extra premise, right?

295
00:30:13,310 --> 00:30:18,290
And this is the premise, uh, I mean, it could be a premise that we just want to leave out, or it could be a controversial premise.

296
00:30:18,320 --> 00:30:21,890
What is the, um. Well, actually, no, don't ask for it.

297
00:30:22,310 --> 00:30:26,870
You're quite right. There is something left out. And that premise could be true.

298
00:30:27,050 --> 00:30:33,350
And that. And that conclusion is false. So we know that that argument doesn't preserve the truth.

299
00:30:33,620 --> 00:30:36,980
So there could be truth in the premises, but no truth in the conclusion.

300
00:30:37,100 --> 00:30:43,759
So it's not truth preserving. So either that's a bad deductible argument or it's an inductive argument.

301
00:30:43,760 --> 00:30:47,360
And we'll see later, which it is. What about all dogs are mortal?

302
00:30:47,570 --> 00:30:52,640
Lucy is mortal. Therefore Lucy is a dog. Which happens when you think you know.

303
00:30:54,860 --> 00:30:58,790
Okay, gentlemen. They're not. It's not truth preserving.

304
00:30:58,790 --> 00:31:03,019
That's right. Okay. It's actually a it's a bad deductive argument.

305
00:31:03,020 --> 00:31:06,739
This one, isn't it? Um, and we'll see why it is later on.

306
00:31:06,740 --> 00:31:10,309
But. Yes. Uh, so all dogs are lawful. Lucy is mortal.

307
00:31:10,310 --> 00:31:13,459
Therefore Lucy is a dog. Those two premises can be true.

308
00:31:13,460 --> 00:31:17,000
And yet that conclusion false quite easily, couldn't they?

309
00:31:17,000 --> 00:31:21,889
Lucy might be humans and mortal. Um, what about number four?

310
00:31:21,890 --> 00:31:26,390
Have a look at that and put your hands up when you think you know whether it's.

311
00:31:32,590 --> 00:31:39,490
Gentlemen that it's so good to have, um, everyone else agree.

312
00:31:40,030 --> 00:31:43,180
So, you know, before you. So I know before, uh. I'm sorry.

313
00:31:45,000 --> 00:31:48,819
I thought you were wrong, but actually, I think you're right. Can you guess wrong?

314
00:31:48,820 --> 00:31:52,680
So pretty clearly involves conceptual computer code. Yeah, exactly.

315
00:31:52,960 --> 00:32:01,360
So that's a good deductive argument. If that if it's true that killing is wrong and it's true that therapeutic cloning involves killing,

316
00:32:01,570 --> 00:32:05,470
then it must be true that therapeutic cloning is wrong. Okay.

317
00:32:05,730 --> 00:32:13,120
Uh, so if you want to deny that, you'd have to go back and deny one of the premises, wouldn't you have to say one of those premises is false?

318
00:32:13,780 --> 00:32:16,900
Okay, what about number five? Hands up when you think you've got.

319
00:32:17,920 --> 00:32:21,310
I'm giving this one away. Yes. All right, let's go.

320
00:32:21,370 --> 00:32:25,300
What it's about. Um, no.

321
00:32:25,510 --> 00:32:28,749
All you need at the moment is it's not a good deductive argument.

322
00:32:28,750 --> 00:32:33,820
It's not truth preserving. Um, actually, it's not a deductive argument, as we'll see later on.

323
00:32:34,540 --> 00:32:41,290
Um, every person with Huntington's disease who's been examined has had the HD gene on chromosome four.

324
00:32:41,590 --> 00:32:45,580
Therefore, everyone with HD has the gene on chromosome full.

325
00:32:45,850 --> 00:32:49,300
You see, that could be true. And that could be false.

326
00:32:49,810 --> 00:32:54,390
I mean, it's true that it's unlikely to be false, but it could be false, couldn't it?

327
00:32:54,400 --> 00:33:00,970
It could be that, um, we just haven't examined any of the HD people who have got the HD genome on prem.

328
00:33:00,980 --> 00:33:07,660
So five perhaps, or or whatever. Is there any biologists in the room who can, um.

329
00:33:07,870 --> 00:33:12,220
What about this one? If the liquid is acidic, it will turn this paper blue.

330
00:33:12,610 --> 00:33:19,660
This liquid does not turn litmus paper blue. Therefore, this liquid is not acidic and up.

331
00:33:21,790 --> 00:33:25,910
Um do that. Mhm. Yeah it is a good.

332
00:33:26,710 --> 00:33:33,310
Okay. Everyone agree. Good. Okay. So we've got a feel for when an argument is truth preserving or not.

333
00:33:33,580 --> 00:33:38,590
And we know that if it's true that it is a good deductive argument.

334
00:33:38,740 --> 00:33:44,650
And if it's not truth preserving it's either a bad deductive argument or it's an inductive argument.

335
00:33:45,460 --> 00:33:51,850
So that's the first question that we ask to distinguish deductive arguments from inductive.

336
00:33:52,180 --> 00:33:57,910
But it would be reasonable to ask at this point perhaps why is deduction useful?

337
00:33:58,540 --> 00:33:59,910
Um, um,

338
00:33:59,950 --> 00:34:08,470
and if we believe the premise is a good deductive arguments and it's logically impossible for the premises to be true and the conclusion false,

339
00:34:08,830 --> 00:34:12,520
then to believe the premises is to believe the conclusion, isn't it.

340
00:34:13,250 --> 00:34:20,530
Mhm. Do you see that in a, in a good deductive arguments the conclusion doesn't go any further than the premises.

341
00:34:21,170 --> 00:34:24,700
What is contained in the premises is contained in the conclusion.

342
00:34:25,270 --> 00:34:32,200
So you actually in a way you learn nothing from a deductive argument to good deductive arguments.

343
00:34:32,710 --> 00:34:40,740
Um, it doesn't tell us anything we don't already know. It's just it's it gives us the logical consequences of what we've already known.

344
00:34:41,230 --> 00:34:49,840
Well, if human beings were perfectly rational and believed all the logical consequences of all their beliefs, then deduction wouldn't be useful.

345
00:34:50,740 --> 00:34:55,090
The reason it is useful is because we're not perfectly rational.

346
00:34:55,510 --> 00:34:59,980
Um, we often need consequences of our belief spelled out to us.

347
00:35:00,430 --> 00:35:04,880
Um, and that's what deduction does. And I just dissolved this sentence.

348
00:35:04,960 --> 00:35:15,130
I put it in. I slightly changed it to make it even better, but it came from life savings, right?

349
00:35:16,060 --> 00:35:19,840
Okay. So, um. Uh. Deductive arguments.

350
00:35:20,560 --> 00:35:24,040
If the premises are true, then the conclusion must be true.

351
00:35:24,050 --> 00:35:29,560
There is no logically possible situation in which the premises are true and the conclusion false.

352
00:35:29,710 --> 00:35:32,820
That's a good deductive argument on purpose.

353
00:35:32,850 --> 00:35:38,440
So just back a little bit, um, on the on the need for the conclusion and not just the conclusion,

354
00:35:38,440 --> 00:35:43,270
not linked the two premises in a way that wouldn't have happened without the conclusion.

355
00:35:44,950 --> 00:35:51,130
Uh, yes. I mean, the conclusion is the logical consequence of the two premises table together links them.

356
00:35:51,580 --> 00:35:56,260
Well, it links and because it you've got to put them together in order to get the conclusion.

357
00:35:56,740 --> 00:36:07,140
I mean, so if you have, um, all heavenly bodies revolve around the earth, that would have, um, separable something.

358
00:36:08,020 --> 00:36:12,700
It wasn't possible. Uh, no, it's it's logical that this is truth, but, uh,

359
00:36:13,450 --> 00:36:20,380
but if you only have that premise without that one, then that one wouldn't logically follow, would it?

360
00:36:21,820 --> 00:36:27,930
No, but you would say didn't advance knowledge anymore, but it linked premises on premise.

361
00:36:27,940 --> 00:36:31,950
It links them and he can tell the lies. That's certainly true.

362
00:36:31,960 --> 00:36:38,200
I mean, the fact is that that that belief is a consequence of that, a logical consequence of that belief and that belief.

363
00:36:38,950 --> 00:36:42,610
So it links them because you need both of those beliefs to get that.

364
00:36:43,270 --> 00:36:46,420
Does that satisfy you? Yes. Good.

365
00:36:47,380 --> 00:36:52,870
Okay. Um, so, Beverly. Samberg.

366
00:36:54,910 --> 00:37:01,719
Okay. The second question we ask to distinguish deductive arguments from inductive arguments, um,

367
00:37:01,720 --> 00:37:10,690
is it's a matter of whether the conclusion follows from the premises an either or matter, or is it a matter of degree.

368
00:37:11,140 --> 00:37:14,170
So does this conclusion follow from the premises?

369
00:37:14,170 --> 00:37:21,910
Either definitely or definitely not. Or could you say, well, you know, maybe it does, maybe it doesn't.

370
00:37:22,720 --> 00:37:29,230
So let's have a look. It's an either or matter. The argument is deductive okay.

371
00:37:29,230 --> 00:37:34,210
So if it's either good or bad then it's a deductive argument.

372
00:37:34,540 --> 00:37:38,770
If it's a matter of degree. If it's not it's not bad.

373
00:37:39,520 --> 00:37:42,550
It's you know, it's better than the last one or something like that.

374
00:37:42,820 --> 00:37:44,980
Then it's an inductive argument.

375
00:37:45,670 --> 00:37:54,460
Let's so we know that the conclusion of a deductive argument follows from its premises if, if and only if the argument is truth preserving.

376
00:37:54,940 --> 00:38:01,690
So if a deductive argument is not truth preserving, its conclusion doesn't follow from its premises.

377
00:38:01,690 --> 00:38:06,640
It's either it does or it doesn't. It's either truth preserving or it's not.

378
00:38:07,000 --> 00:38:14,830
It's it can't be anything in between. Um, so the evaluation of a deductive argument is an either or matter.

379
00:38:14,920 --> 00:38:17,590
Either the conclusion follows from the premises or it doesn't.

380
00:38:17,590 --> 00:38:23,740
There's no maybe no degrees of following from at all when we're talking about deduction.

381
00:38:24,460 --> 00:38:30,970
Um, so okay, here's a good argument all by this a rich Deepak is a banker.

382
00:38:30,970 --> 00:38:36,460
Therefore Deepak is rich. Do you see that if those premises are true, the conclusion must be true.

383
00:38:38,050 --> 00:38:41,500
And here's the bad one. All by who's a rich? Deepak is rich.

384
00:38:41,500 --> 00:38:48,370
Therefore Deepak is a banker. Do you see that those two premises could be true without the conclusion is being true.

385
00:38:49,150 --> 00:38:52,750
And we can see that immediately. Can't wait to snoop on this.

386
00:38:52,750 --> 00:38:57,220
No. Maybe here. One is good, one is bad, and there's nothing in between.

387
00:38:57,400 --> 00:39:04,270
And that's always the case with deductive arguments. Question over here on the having one thing is can you see okay.

388
00:39:04,270 --> 00:39:12,580
Well therapeutic cloning. Yes, yes. It didn't say oh, uh, let me go back and see what it did.

389
00:39:12,670 --> 00:39:17,889
I think it inspired all, but let me see. Wait a few Rocky whistle a little.

390
00:39:17,890 --> 00:39:21,850
Not when you say so. Killing is wrong. Therapeutic cloning involves killing.

391
00:39:21,850 --> 00:39:26,260
Therefore therapeutic cloning is wrong. You mean this doesn't say all killing is wrong?

392
00:39:26,680 --> 00:39:32,350
No, but it does imply it, doesn't it? I says, quite generally, killing is wrong, right?

393
00:39:32,440 --> 00:39:41,290
There's no degree that the. So we would I mean, the only way you could make that conclusion false is by making that not true.

394
00:39:41,290 --> 00:39:48,010
In other words, you'd have to say some killing is wrong. Most killing is wrong, but it's not the case that all killing is wrong.

395
00:39:48,340 --> 00:39:53,510
Okay, can I just say, I just thought that was a good objection.

396
00:39:53,620 --> 00:39:58,520
For what if you then. So there's a question of degree around the therapeutic cloning.

397
00:39:58,990 --> 00:40:03,880
Sometimes it involves killing. Well, then you would be falsifying that premise.

398
00:40:04,450 --> 00:40:07,000
Yeah. So with this argument's.

399
00:40:08,210 --> 00:40:17,210
It's a truth preserving argument in that if that premise is true and that premise is true, then that conclusion must be true.

400
00:40:17,420 --> 00:40:23,690
And if you don't think that conclusion is true, you've got to question either that premise or that premise,

401
00:40:23,690 --> 00:40:27,140
and you could question them in the way that you've just discussed.

402
00:40:27,650 --> 00:40:30,890
Yeah. Any questions about that?

403
00:40:32,900 --> 00:40:38,350
No. Let's go on to, um, I've got my maybe one, I assume.

404
00:40:38,360 --> 00:40:43,640
Okay. Um, so which one is good? One is bad, and that's always the way it's going to be.

405
00:40:44,030 --> 00:40:52,910
Um, so what did you tell us about. Which is good. Um, one is truth preserving, i.e. when its conclusion follows deductively from its premises,

406
00:40:53,240 --> 00:40:57,950
its premise is all conclusive reason for believing its conclusion.

407
00:40:58,610 --> 00:41:06,920
Okay, it's either good or it's bad. So if it's good, then it's premises are conclusive reason for believing the conclusion.

408
00:41:07,280 --> 00:41:11,210
And that's because deductive arguments. Uh, monotonic.

409
00:41:11,390 --> 00:41:14,510
Okay, so here's a new word for you. This time it's a new word.

410
00:41:14,510 --> 00:41:18,140
And if it's not, um, deduction is monotonic.

411
00:41:18,440 --> 00:41:26,060
And what that means is that we can add anything we like to a good deductive argument without making it bad.

412
00:41:26,180 --> 00:41:34,580
Good. Um. We cannot if if a good argument is good, if a good deductive argument is good, it's conclusively good.

413
00:41:34,880 --> 00:41:44,450
And if it's bad, it's conclusively bad. Um, so there's nothing we could learn that would change a good deductive argument to being a bad one.

414
00:41:44,450 --> 00:41:47,420
So let's have a look. Here's just good deductive argument.

415
00:41:47,730 --> 00:41:55,010
Do you would you like to have a go at giving me a premise that might change that from a good argument to a bad argument?

416
00:41:56,210 --> 00:42:02,070
Have a think about it. Some some bad guys.

417
00:42:02,100 --> 00:42:05,160
Oh, good. Sorry. Uh, sorry.

418
00:42:05,730 --> 00:42:09,900
Good. Thank you. So rich. Um.

419
00:42:13,860 --> 00:42:19,110
Well, that's also, I think, a premise that's changing one of the premises there, which is not playing the game.

420
00:42:19,260 --> 00:42:22,380
Sorry. Sorry.

421
00:42:23,970 --> 00:42:29,490
Um, okay. I did not say that. Um, I'll tell you what.

422
00:42:29,490 --> 00:42:32,490
Let me show you what I've got. What I thought you might come up with.

423
00:42:32,790 --> 00:42:38,150
Because I think that might be easier. Um, you can try putting in.

424
00:42:38,160 --> 00:42:45,410
What am I trying to put in there? I can't remember now. I know, it's not.

425
00:42:45,930 --> 00:42:49,200
So I tried to I. It's not the case that Deepak is a banker here.

426
00:42:49,530 --> 00:42:53,100
So there's the argument. First premise, second premise, some conclusion.

427
00:42:53,310 --> 00:42:57,420
And I'm adding that in, in the hope that that might make it a bad argument.

428
00:42:58,560 --> 00:43:02,310
Okay. Do you think it does make it a bad argument though?

429
00:43:03,120 --> 00:43:13,230
Okay. It doesn't, does it? It certainly doesn't change it from, um, if all these premises are true, this conclusion is true, does it?

430
00:43:13,990 --> 00:43:18,390
Which actually, if all these premises are true, anything follows from a contradiction.

431
00:43:18,780 --> 00:43:22,810
And we've got a contradiction in here, haven't we. Here. Do you see.

432
00:43:22,830 --> 00:43:26,370
So, so anything follows from it. And what about this one.

433
00:43:26,670 --> 00:43:32,670
What have I added here? No banker is rich, so I've actually contradicted that one.

434
00:43:33,060 --> 00:43:41,850
Um, but we've got exactly the same thing. We haven't we? It hasn't gone from being the case that all the premises are true without, uh,

435
00:43:41,850 --> 00:43:48,060
so it's being the case that if all the premises is true, the conclusion must be true again.

436
00:43:49,200 --> 00:43:52,660
So with deduction, you've got absolute comp.

437
00:43:52,950 --> 00:43:57,390
It's conclusive. Uh, it's either good or it's bad and there's nothing you can do.

438
00:43:57,750 --> 00:44:00,959
I'm not sure I understand that. Okay. Um.

439
00:44:00,960 --> 00:44:04,110
Let's see. Let me do the bad one and see if that helps.

440
00:44:04,110 --> 00:44:11,550
And if not, we'll go back. Okay, so by the same token, we can add anything we like to a bad deductive argument without making it good.

441
00:44:12,030 --> 00:44:17,310
Once again, there's nothing we can learn that would change it from a bad argument to a good argument.

442
00:44:17,700 --> 00:44:22,680
So, um, I think I've done that. Okay, here's a bad deductive argument.

443
00:44:22,890 --> 00:44:27,030
All bankers are rich. Deepak is rich, therefore deeper. Deepak is a banker.

444
00:44:27,570 --> 00:44:35,280
And I've asked again the same question. Is there any premise we could add to that that would change it from a bad argument to a good argument?

445
00:44:36,870 --> 00:44:42,240
I got a couple of that I'm going to try, but let me just say, if I put something in here that's false.

446
00:44:43,560 --> 00:44:48,070
Okay. Do you see that? I'm not changing it from a good argument to a bad argument.

447
00:44:48,090 --> 00:44:54,000
If something in there is false and it, um, it's not the case that all the premises are true.

448
00:44:55,080 --> 00:45:02,940
Therefore, the conclusion doesn't have to be true either. And if I put something in there that's true then.

449
00:45:03,720 --> 00:45:07,530
Or if all the premises are true, the conclusion will still have to be true.

450
00:45:08,190 --> 00:45:12,280
Let's let's try that. So I'm not convincing myself that.

451
00:45:14,010 --> 00:45:17,250
Um, okay. So I put in here.

452
00:45:17,280 --> 00:45:21,389
It's not the case that Deepak is a banker. So all bankers are rich.

453
00:45:21,390 --> 00:45:27,390
Deepak is rich. It's not the case that Deepak just banker. So I've contradicted the conclusion there.

454
00:45:27,760 --> 00:45:32,670
Yeah, yeah. Okay. Does that change it from a from a bad argument into a good argument?

455
00:45:33,550 --> 00:45:38,130
And has it become truth preserving? No it hasn't.

456
00:45:38,220 --> 00:45:44,510
Has this become truth preserving? No no, no.

457
00:45:45,000 --> 00:45:49,110
And you'll find that nothing you can add will change it from being.

458
00:45:49,110 --> 00:45:52,230
Not truth preserving to being truth preserving.

459
00:45:52,410 --> 00:45:54,660
And in exactly the same way with a good argument.

460
00:45:54,690 --> 00:46:00,570
Nothing you could add would change it from being, uh, truth preserving to being, not truth preserving.

461
00:46:01,380 --> 00:46:04,620
Let me, um, do one more thing. So I'm okay.

462
00:46:04,980 --> 00:46:09,959
You're okay. That's where I was confused as I thought that, um, you're actually making.

463
00:46:09,960 --> 00:46:13,710
You still think it's a good argument? And I wasn't saying that.

464
00:46:13,710 --> 00:46:21,540
I think it was a battle. What you're not doing is changing it from a good argument to evolve, or indeed, from a bad argument.

465
00:46:21,900 --> 00:46:27,000
But let's have a look at, um, induction. So okay, this is what I'm claiming.

466
00:46:27,390 --> 00:46:31,260
Um, either if a good if a deductive argument is good, it's premises,

467
00:46:31,260 --> 00:46:36,450
a conclusive reason to believe a conclusion, there's nothing we're going to learn is going to change that.

468
00:46:36,810 --> 00:46:43,410
And what is deductive argument is bad that its premises are new whatsoever to believe the conclusion.

469
00:46:43,560 --> 00:46:47,460
And again, nothing is going to change that. It's either good or it's bad.

470
00:46:47,640 --> 00:46:54,780
And that's the end of us. Um, and that doesn't mean that the conclusion of a bad deductive argument might not be true.

471
00:46:55,920 --> 00:47:00,330
Do you see that? It means only that it's premises and no reason to believe the conclusion?

472
00:47:00,460 --> 00:47:03,970
So I think I'm going to give you a, um.

473
00:47:04,150 --> 00:47:08,860
So it's a fine deductive argument. If it's Monday, Mario will be wearing jeans.

474
00:47:09,130 --> 00:47:12,400
Marianne is wearing jeans. Therefore it's Monday.

475
00:47:13,510 --> 00:47:17,920
Um, it is about to start developing today.

476
00:47:18,460 --> 00:47:22,090
Yes. Good. Thank you. I've got to the point where, um.

477
00:47:22,090 --> 00:47:26,140
Okay, but is that conclusion false? No, it isn't, is it?

478
00:47:26,170 --> 00:47:30,820
No, it is Monday. But it's not. Our reason for believing it's Monday.

479
00:47:30,910 --> 00:47:34,870
Doesn't depend on that argument, does it? At least I hope so.

480
00:47:35,230 --> 00:47:42,700
Because if it depended on that argument, too. But. So you can have a bad descriptive argument with a true conclusion in exactly

481
00:47:42,700 --> 00:47:46,330
the same way you can have a good deductive argument with a false conclusion.

482
00:47:46,960 --> 00:47:50,680
So if you have a good deductive argument with a false conclusion, you know what?

483
00:47:52,120 --> 00:47:57,670
What do you know? If the conclusion of a good deductive argument is false.

484
00:47:59,020 --> 00:48:03,520
One of the premises is false. Good. Well done. That's the question.

485
00:48:03,790 --> 00:48:10,510
You still have extra pence after the first if if you claim one, your double if it's not, change history, please.

486
00:48:10,660 --> 00:48:15,729
Good argument. No it would. Then you say if and only if it's Monday.

487
00:48:15,730 --> 00:48:19,540
Marianne will be wearing jeans. Marianne is wearing jeans.

488
00:48:19,990 --> 00:48:25,390
Therefore it's Monday. Um, you would change it from a, um.

489
00:48:26,410 --> 00:48:30,700
I think that would make it a good argument. Um.

490
00:48:31,810 --> 00:48:35,800
And you're changing. Yes. You know, but you'd be changing the premises.

491
00:48:36,160 --> 00:48:38,740
Just curious to know that if you just change quite a tiny bit. Bit?

492
00:48:39,130 --> 00:48:45,010
Well, yes, but you'd be actually making an if into an if and only if it's not making a tiny change.

493
00:48:45,010 --> 00:48:48,130
It's making a huge change logically. Yeah, yeah.

494
00:48:49,030 --> 00:48:53,439
Okay. So either department is good premises,

495
00:48:53,440 --> 00:48:57,999
a conclusive reason to believe the conclusion it's truth preserving or deductive

496
00:48:58,000 --> 00:49:02,710
argument is bad because it's premises and no reason at all to believe its conclusion.

497
00:49:02,950 --> 00:49:06,580
So with deduction is always an either or matter.

498
00:49:07,210 --> 00:49:10,540
Um, but no inductive argument preserves the truth.

499
00:49:11,050 --> 00:49:16,780
Um, so we can't evaluate inductive arguments by appeal to whether or not they preserve the truth.

500
00:49:17,170 --> 00:49:21,880
Um, the very strongest inductive argument still doesn't preserve the truth.

501
00:49:22,240 --> 00:49:25,750
So we evaluate them according to how strong they are.

502
00:49:26,320 --> 00:49:29,770
And of course, strength is a matter of degree, isn't it?

503
00:49:30,250 --> 00:49:39,850
So here an inductive argument is strong if and only if the truth of its premises make its conclusions significantly more likely to be true.

504
00:49:40,390 --> 00:49:48,580
And an inductive argument is weak if and only if the truth of its premises makes its conclusion only slightly more likely to be true.

505
00:49:48,790 --> 00:49:57,640
And here are some examples. Well, actually, I've asked you a question, but I think you who who think so on the right hand side is the strong one.

506
00:49:58,150 --> 00:50:03,340
I know right hand side. No, that's that's this one. Uh, but that one.

507
00:50:03,820 --> 00:50:07,660
Yes. Uh. Yes, ma'am. No you're right.

508
00:50:08,020 --> 00:50:17,980
Mhm. Yes. Okay. Who thinks the one on the left hand side is strongest. Is that some of the stuff?

509
00:50:18,100 --> 00:50:22,480
Yes. I think that's a very strong inductive argument, isn't it?

510
00:50:23,320 --> 00:50:31,360
Someone who's written every day in the history of the universe suggests it is highly likely it's going to rise again tomorrow, isn't it?

511
00:50:31,870 --> 00:50:35,490
Um, whereas every time I've seen Marianne, she's been wearing earrings.

512
00:50:35,500 --> 00:50:41,680
Next time I see Marianne, she'll be wearing earrings. Okay, it's probably true, isn't it, that every time you've seen me, I've been wearing earrings.

513
00:50:42,040 --> 00:50:45,879
Um, but you've only seen me three times. Some of you, um.

514
00:50:45,880 --> 00:50:49,720
It's not really enough. Maybe next time you come around to my house at 4:00 in the morning.

515
00:50:49,900 --> 00:50:52,780
Get out of bed. I promise you, I don't wear earrings in bed.

516
00:50:53,360 --> 00:50:59,620
Uh, so that's a that's a fairly weak inductive algorithm, but do you see, they both have the same form, if you like.

517
00:51:00,130 --> 00:51:07,210
Um, so in each case, you'll say all the things that I've seen like this have been this.

518
00:51:07,660 --> 00:51:12,010
Therefore, the next one, one I haven't seen will be like this. Um,

519
00:51:12,610 --> 00:51:16,839
inductive straight is a matter of degree because one of the premises of an

520
00:51:16,840 --> 00:51:22,540
argument make the conclusion more or less likely is itself a matter of degree.

521
00:51:23,200 --> 00:51:26,770
Um, and inductive strength is not monotonic.

522
00:51:27,190 --> 00:51:31,990
Okay, so I taught you that new word deduction is monotonic.

523
00:51:32,170 --> 00:51:35,680
What that means is you can add anything you'd like to a good argument.

524
00:51:35,680 --> 00:51:41,469
You can't change it from being good. You can't stop it being good. You can add anything you like to a bad deductive argument.

525
00:51:41,470 --> 00:51:45,820
Can't stop it being bad. But evidence of strength is not monotonic.

526
00:51:46,150 --> 00:51:52,860
The addition of a new premise to an inductively strong argument might make it inductively weak.

527
00:51:52,870 --> 00:52:02,589
And I've got some examples coming up. Um, and also, the addition of a new premise to an inductively weak argument might make it inductively strong.

528
00:52:02,590 --> 00:52:08,620
So let's have a look at how this works. Um, so take the relatively strong inductive argument.

529
00:52:08,620 --> 00:52:11,800
Jones confess therefore Jones is guilty.

530
00:52:12,040 --> 00:52:15,310
Oh you agree? Probably. That's a pretty strong inductive argument,

531
00:52:15,610 --> 00:52:23,410
but then adds ten independent witnesses testify to Jones being 100 miles away from the scene of the crime at the time it was committed.

532
00:52:23,950 --> 00:52:27,370
Suddenly it looks very weak, doesn't it? Um. Um.

533
00:52:27,370 --> 00:52:28,350
Um, do you see that?

534
00:52:28,600 --> 00:52:36,640
So what we've done is we've taken a strong inductive argument, we've added another piece of information, and we've weakened the argument completely.

535
00:52:37,180 --> 00:52:40,420
Um, wait, um, Jones is a twin.

536
00:52:41,260 --> 00:52:45,940
Well, uh uh, well, would you remember when I said about ambiguity,

537
00:52:45,940 --> 00:52:53,380
we've got to assume that the Jones is referring to the same person, um, in the in the same context.

538
00:52:53,890 --> 00:52:57,760
Okay. Or take the relatively weak inductive argument.

539
00:52:57,760 --> 00:53:02,290
Jones, whose presence at the site cream site sign proves.

540
00:53:03,880 --> 00:53:11,530
Therefore. Jones, just go to the cream. Okay. Um, and ask the which which I think you'll agree is weak inductive argument.

541
00:53:11,530 --> 00:53:19,300
Yes. Okay. And the extra premise, uh, Smith, the policeman who tried to stop Jones killed the man, saw Jones plunge the dagger.

542
00:53:20,680 --> 00:53:25,960
I was hopeful with that one. Um, suddenly a weak argument looks very much stronger, doesn't it?

543
00:53:26,650 --> 00:53:30,969
Um, so induction is not monotonic.

544
00:53:30,970 --> 00:53:37,090
You could you can strengthen and weaken inductive arguments by discovering new information.

545
00:53:37,210 --> 00:53:42,550
You can't do that with deduction. Deduction. If it's good, it's good, it's bad, it's bad.

546
00:53:42,610 --> 00:53:45,150
And that's the end of it all. You in danger?

547
00:53:45,160 --> 00:53:50,350
They're turning the doctor argument into a deductive argument by the addition of the additional statement.

548
00:53:51,340 --> 00:53:59,080
Um, it's very easy to turn inductive arguments into deductive arguments by adding the right premises.

549
00:53:59,440 --> 00:54:04,870
Uh, have I done that here? I would have thought you're in danger of doing that in the second statement.

550
00:54:05,980 --> 00:54:10,570
Well, no, not if Jones died of electrocution. Okay.

551
00:54:11,290 --> 00:54:21,550
And he might have done mine pretty consistently with that has been kind of a good I mean, I haven't actually said what the crime is here.

552
00:54:23,230 --> 00:54:28,630
Okay. Um. Yes.

553
00:54:28,710 --> 00:54:33,820
I may not be. You could come back to me on that one if you want to later on.

554
00:54:34,210 --> 00:54:40,690
Okay. So let's have a look at this. This is, uh, exercise three, which is very similar to exercise two.

555
00:54:41,050 --> 00:54:49,810
Um, what we want to know now is whether it's being good or bad as a matter of degree or a matter of, um, either or.

556
00:54:50,050 --> 00:54:55,870
Um, whereas last time you identify the good deductive arguments, um,

557
00:54:56,050 --> 00:55:02,140
now you could also identify the bad deductive arguments and distinguish them from arguments.

558
00:55:02,410 --> 00:55:05,950
So Tom is a banker. All bankers are rich, therefore Tom is rich.

559
00:55:05,950 --> 00:55:10,899
What's that? Let's go to deductive us as it was before.

560
00:55:10,900 --> 00:55:15,100
Yeah, it doesn't change. Um, Sue and Tom lead similar lives, but Sue smoke.

561
00:55:15,350 --> 00:55:19,910
And Tom doesn't. Therefore, Sue is more likely to die from heart disease than Tom.

562
00:55:20,060 --> 00:55:23,690
Stick your hand up when you've got the. When you think you've got the answer to that.

563
00:55:24,230 --> 00:55:29,450
And. So what we want to know.

564
00:55:29,810 --> 00:55:33,440
We know that it's not a good deductive argument from the last time.

565
00:55:33,710 --> 00:55:37,520
But is it a data? It is a bad deductive argument.

566
00:55:37,760 --> 00:55:43,840
Or is it an inductive argument? So it's inductive.

567
00:55:43,850 --> 00:55:50,630
Exactly. So we could what could we add to that to make the conclusion much less likely?

568
00:55:53,070 --> 00:55:57,580
Why would you want to make people suffer? Well, just because if we can.

569
00:55:57,600 --> 00:56:01,200
We know it's inductive. Oh, yeah. If we.

570
00:56:01,200 --> 00:56:04,560
If we can't, we know it's. So what? What could we add to that?

571
00:56:04,650 --> 00:56:12,180
You could have the Thomas go to that hall. Um, all the Thomas all all Thomas family died of heart disease.

572
00:56:12,180 --> 00:56:18,180
Died young of heart disease. Yes. That that would immediately change the strength of that argument, wouldn't it?

573
00:56:18,630 --> 00:56:27,300
So as it is, it looks pretty strong. Um, but we can weaken it immediately by giving it a bit of Thomas family history.

574
00:56:27,930 --> 00:56:32,820
So it's a question when it, um, when it suggests that. So, um, Tom Latimer lives.

575
00:56:33,120 --> 00:56:37,380
Um, probably if you leave the first statement out.

576
00:56:37,800 --> 00:56:43,200
Uh, it might be stronger because Sue smokes and then Tom doesn't.

577
00:56:43,200 --> 00:56:50,100
So obviously, Sue is more likely to die when it suggests that Sue and Tom lead similar lives.

578
00:56:50,400 --> 00:56:53,400
Uh, is not true because she smokes and he doesn't.

579
00:56:53,400 --> 00:56:57,880
It isn't it? Well, they could lead some lives apart from that.

580
00:56:57,970 --> 00:57:04,650
I mean, they could both exercise, both eat lots of fruit and vegetables, but not eat much animal fat.

581
00:57:05,430 --> 00:57:09,180
Um, okay. What about all dogs are mortal.

582
00:57:09,180 --> 00:57:17,430
Lucy is mortal. Therefore Lucy is a dog. Put your hand up. If you say you know whether that's a bad deductive argument or an inductive argument.

583
00:57:19,680 --> 00:57:23,370
Uh, deductive. It's bad inductive bias. How do you know that?

584
00:57:23,850 --> 00:57:28,490
Because the premises. Uh, tell me more. Well, you have, uh.

585
00:57:29,100 --> 00:57:32,730
It's not true. It's not true. Uh, true. So is it.

586
00:57:32,880 --> 00:57:39,360
It's not truth preserving. And in fact, the premises are no reason whatsoever for believing the conclusion all day.

587
00:57:39,780 --> 00:57:44,880
So whereas with the first one, the premise is a conclusive reason for believing the conclusion,

588
00:57:45,120 --> 00:57:50,490
with the third one, the premises are no reason whatsoever for believing the conclusion.

589
00:57:51,000 --> 00:57:54,330
Okay, that's a bad deductive argument. What about number four?

590
00:57:54,340 --> 00:57:57,870
Can we we know that's a good deductive argument, don't we?

591
00:57:58,110 --> 00:58:09,450
Okay. What about number five? Is that a bad deductive argument or an inductive argument to indicate that it's inductive?

592
00:58:09,480 --> 00:58:15,630
That's right. Okay. So every person with Huntington's disease who's been examined has had the genome chromosome full.

593
00:58:15,930 --> 00:58:20,130
Therefore everyone with HD has the HD gene on chromosome four.

594
00:58:20,640 --> 00:58:28,210
Um, what would we want to. I mean, could you add anything to that to make it a bad inductive argument?

595
00:58:28,230 --> 00:58:34,170
I mean, as it stands, it looks pretty strong. What might we do to change it into a weak one?

596
00:58:35,340 --> 00:58:42,660
We've been examined. Yeah. Yeah, exactly. If we've only examined five people, then it suddenly looks a lot less strong.

597
00:58:43,170 --> 00:58:46,830
Good. Okay. And the last one was a good inductive.

598
00:58:47,070 --> 00:58:56,130
Deductive good. Okay, so we now know that if an argument preserves the truth, it's a good deductive argument.

599
00:58:56,610 --> 00:59:02,550
If an argument doesn't preserve the truth, it's either a bad deductive argument or it's an inductive argument.

600
00:59:03,240 --> 00:59:12,990
And we know that if an argument is either good or bad, with no matter of degrees or no maybes, um, then it's a deductive argument.

601
00:59:13,320 --> 00:59:18,540
And if it's being good or bad, it's a matter of degree that it's an inductive argument.

602
00:59:18,750 --> 00:59:22,650
Okay. So that's we've looked at our first question and our second question.

603
00:59:22,920 --> 00:59:30,300
Now let's look at the third. So the third question was can we evaluate the argument a priori.

604
00:59:30,840 --> 00:59:39,540
Now to be able to evaluate something a priori is able to say whether it's good or bad or true or false or whatever, something normative.

605
00:59:40,050 --> 00:59:45,840
Um, without experience, without needing to go and look at the world.

606
00:59:45,840 --> 00:59:50,940
If you'd like, you can do it simply from, um, logic on its own.

607
00:59:51,540 --> 00:59:54,570
Um, um, the opposite is a posterior. All right.

608
00:59:54,600 --> 00:59:57,810
Which is when you have to actually go and look at the world.

609
00:59:58,140 --> 01:00:06,450
So let's have a look at this. To be able to evaluate, uh, an argument a priori is to be able to tell whether the argument is good or bad by

610
01:00:06,450 --> 01:00:12,600
appeal only to the structure of the argument and to the logical words used in it,

611
01:00:13,050 --> 01:00:16,530
um, without need of any information about the world.

612
01:00:16,770 --> 01:00:20,620
Now, you might as well say you need information about language, and that indeed is true.

613
01:00:20,640 --> 01:00:27,870
So you need some information about the world. Um, but you don't need more than information about language and meanings.

614
01:00:28,380 --> 01:00:30,900
Um, so these are the logical words.

615
01:00:30,900 --> 01:00:40,320
And if then not or and if and only if, um, there are other logical words, but we wouldn't worry about those at the moment.

616
01:00:40,830 --> 01:00:45,590
Um, and this gives you an indication of what's meant by the structure of an argument.

617
01:00:45,600 --> 01:00:50,580
So here's an argument we use last week. Um, if it's snow, the mail will be late.

618
01:00:50,760 --> 01:00:54,729
It is snowing. Therefore, the. Will be late. Can you see that?

619
01:00:54,730 --> 01:00:58,030
If you, um, want to take. It is snowing.

620
01:00:58,360 --> 01:01:07,089
He. Then you've got f p under the chair again and the male will be late.

621
01:01:07,090 --> 01:01:11,140
Becomes cu. So if P then cu p 30.

622
01:01:12,490 --> 01:01:20,350
Do you see the structure of the occupants? Um, can be brought out just by taking away the sentences in the argument.

623
01:01:20,350 --> 01:01:24,010
Leaving the logical words. Um, okay.

624
01:01:24,020 --> 01:01:29,170
Is this is good argument. Put your hands up when you've decided, rather than yelling out.

625
01:01:50,370 --> 01:01:53,180
Put your hand up when you've decided up. So I can see it. Because.

626
01:01:53,190 --> 01:01:58,740
Because I'll ask when there's a sort of critical mass of people who know, they'll think they know.

627
01:02:03,050 --> 01:02:07,070
Okay. What do you think? Is it a good argument? Yes. Yes it is.

628
01:02:07,100 --> 01:02:10,730
Isn't it good? Does anyone know what it means?

629
01:02:11,840 --> 01:02:15,320
Which it is or what it is for something to be possible?

630
01:02:16,310 --> 01:02:19,220
No. Okay, good. I'm not surprised because I made them up.

631
01:02:19,730 --> 01:02:26,660
Um, but you see that actually, the content is completely irrelevant to your ability to evaluate the arguments.

632
01:02:27,050 --> 01:02:33,320
Um, you really don't need to know anything about the subject matter in order to be able to say that that argument is good.

633
01:02:33,800 --> 01:02:40,700
And the reason for that is that what makes that argument good is the way the logical words itself combines.

634
01:02:40,970 --> 01:02:45,800
It's the structure of the arguments. It's nothing to do with the contents of the arguments.

635
01:02:45,980 --> 01:02:49,220
And that's true of all deductive arguments.

636
01:02:49,490 --> 01:02:52,760
All deductive arguments can be evaluated a priori.

637
01:02:53,270 --> 01:02:56,419
Um, so oh, here's another one. Okay.

638
01:02:56,420 --> 01:03:02,930
Is this a good argument? No no no it isn't.

639
01:03:03,440 --> 01:03:07,339
And you can tell that because this is actually a Bob's deductive argument.

640
01:03:07,340 --> 01:03:15,440
Whereas the last one was a good deductive argument. Um, and it's interesting to note that the facts deduction is a priori.

641
01:03:15,680 --> 01:03:24,440
Actually means that it's topic neutral. Um, this is what makes logic or deductive logic anyway such a useful transferable skill.

642
01:03:24,710 --> 01:03:28,580
Because it doesn't matter what you're talking about, what you're thinking about.

643
01:03:28,940 --> 01:03:34,550
Um, if you can recognise a deductive argument, you will be able to evaluate it.

644
01:03:34,760 --> 01:03:39,169
Even if you know nothing whatsoever about the subject matter.

645
01:03:39,170 --> 01:03:44,810
The subject matter is completely irrelevant to evaluating a deductive argument,

646
01:03:45,140 --> 01:03:52,490
because what matters is the logical words and the way that combined, excuse me in the first premise.

647
01:03:52,970 --> 01:04:06,320
Who's speaking? Um, okay. In the first press, um, of the last one of the nonsense words that, um, if which is a positive and I'm having a negative.

648
01:04:09,140 --> 01:04:13,969
Then the first premise in those terms stands up.

649
01:04:13,970 --> 01:04:19,430
But it's nonsense. Well, um.

650
01:04:21,710 --> 01:04:27,230
What you're doing is you're trying to put content in that's going to make it's nonsense.

651
01:04:27,230 --> 01:04:32,210
But it's already nonsense, isn't it? I mean, you don't need to do anything to make it not cold.

652
01:04:32,270 --> 01:04:35,930
It's nonsense already, but it's still a good argument for bad arguments or whatever is is.

653
01:04:38,330 --> 01:04:42,680
What was causing you always cold? Which is a positive then?

654
01:04:42,680 --> 01:04:47,360
Which is a negative. And that is a premise that cannot stand up in logic.

655
01:04:50,390 --> 01:04:54,190
Well. It's true. No, it's the contents.

656
01:04:54,530 --> 01:04:57,920
It's. The logic is what you're saying is it's false.

657
01:04:58,340 --> 01:05:03,410
Yes. Yeah, but. Well, actually, it's not even false because it is meaningless, isn't it?

658
01:05:05,180 --> 01:05:08,360
But if you if widgets are positive, then widgets are negative.

659
01:05:09,020 --> 01:05:12,800
Mm hmm. I mean that that's nonsensical. It doesn't have meaning.

660
01:05:13,160 --> 01:05:17,270
Yes, but you only know that from the content that you're putting in there.

661
01:05:17,630 --> 01:05:24,440
And my aim in using this is to show that you can decide whether something is a good argument or not.

662
01:05:24,560 --> 01:05:28,640
Without knowing what the content is like a is about.

663
01:05:30,440 --> 01:05:36,590
So wanting to put in some content that doesn't make sense is not changing my arguments at all.

664
01:05:38,930 --> 01:05:47,479
So you could use positive and negative if you said they were positive. And negative meant well, is what I mean.

665
01:05:47,480 --> 01:05:50,880
Why yes. I mean why would you? Okay.

666
01:05:51,200 --> 01:05:55,810
If my aim is to show you is that you can tell whether an argument is good or bad

667
01:05:55,820 --> 01:05:59,570
and deductive argument is good or bad without knowing what the content means.

668
01:05:59,780 --> 01:06:06,740
I take it that I because you were able to see that the first argument was good, and that the first second argument was bad.

669
01:06:06,890 --> 01:06:10,340
I take it that I've proved my point. Yes. Okay.

670
01:06:10,520 --> 01:06:15,799
Now I could go back and discuss, but I'm inclined not to,

671
01:06:15,800 --> 01:06:23,330
because I don't see why changing one nonsensical argument into another nonsensical argument is going to gain a something.

672
01:06:23,970 --> 01:06:29,480
Okay. May I move on? Yes. I'm not sure if I've dealt with your better.

673
01:06:29,570 --> 01:06:33,799
Perhaps we can talk afterwards. If you. If you replaced it with P's and Q's.

674
01:06:33,800 --> 01:06:38,060
And it's clear what is clear with all of these positives.

675
01:06:38,060 --> 01:06:41,210
But you say all soon. Well, yeah. Let me carry on.

676
01:06:41,880 --> 01:06:44,900
Now I'm going to, um, replace things with P's and Q's.

677
01:06:45,210 --> 01:06:52,040
Uh, all of these I could show you. How do you see these two arguments have exactly the same structure.

678
01:06:59,580 --> 01:07:05,490
Yeah, know. Not because anyone wants to deny that.

679
01:07:08,640 --> 01:07:11,790
Can you help me work out? Well, the structure is using P's and Q's.

680
01:07:11,790 --> 01:07:20,340
Let's use that one. Um, he is p and q, then q p p.

681
01:07:21,420 --> 01:07:24,450
Therefore. Therefore q q q.

682
01:07:24,930 --> 01:07:29,610
And so here means it is snowing and q means the mail is late.

683
01:07:30,510 --> 01:07:34,310
What's P in the second document. Yeah.

684
01:07:34,530 --> 01:07:40,649
Yeah. And I mean the the actual produces the greatest happiness is greatest.

685
01:07:40,650 --> 01:07:46,709
Um, but what's Q if he's right it's or the act is to remove the cross-reference the actors.

686
01:07:46,710 --> 01:07:50,910
Right. Yes. Exactly. So so we've got exactly the same structure.

687
01:07:50,910 --> 01:07:59,070
Does the basis arguments stuff into it? Why don't you use p q uh, instead of r an X or something?

688
01:07:59,100 --> 01:08:04,770
Uh, yes. It's just convention that. Yeah. Yeah, it's a convention to do with pigs and queens.

689
01:08:05,130 --> 01:08:10,140
No no no no no no I, I think so.

690
01:08:10,760 --> 01:08:20,310
And actually some people would use um s ends here just because saying begins with s and then the mail begins to say um,

691
01:08:20,760 --> 01:08:24,030
but it would be then less relevant to that one.

692
01:08:24,330 --> 01:08:28,379
Um, so it's convention that we use P and Q. Okay.

693
01:08:28,380 --> 01:08:35,070
So hang on here because not all widgets I've ever seen have been having, um, therefore all widgets are having to.

694
01:08:35,580 --> 01:08:42,209
Okay. Can we tell whether that's a good argument or not to the fact that we can't, can we.

695
01:08:42,210 --> 01:08:49,230
Why not? Doesn't she don't say in the world you don't know how many widgets you see.

696
01:08:49,230 --> 01:08:52,350
You don't know what widgets are and you don't know what it is.

697
01:08:52,350 --> 01:08:57,690
Do we have another? And you I mean, no, just you do need to know what the content is,

698
01:08:58,050 --> 01:09:03,540
and you need to know something about the contents in order to be able to evaluate that argument.

699
01:09:03,870 --> 01:09:13,469
So with a deductive argument it can be evaluated a priori, i.e. on the basis only of its structure in the logical words um,

700
01:09:13,470 --> 01:09:24,240
if it can only be evaluated by appeal to some background information, some, um, information that you have, then it's an inductive argument.

701
01:09:26,070 --> 01:09:33,149
Okay. Um, so, um, inductive arguments can be evaluated only a posteriori.

702
01:09:33,150 --> 01:09:41,400
And in the light of an understanding of the content of the arguments, uh, and by bringing to bear background information about the world,

703
01:09:41,730 --> 01:09:48,690
so long as you can strip the content out of the deductive arguments and still determine whether it's a good or bad argument,

704
01:09:48,930 --> 01:09:55,140
there's no way you can stretch the content out with good inductive arguments and still hope to evaluate it.

705
01:09:56,670 --> 01:10:01,380
So can we evaluate these arguments a priori or not?

706
01:10:02,520 --> 01:10:06,059
Um, Jennifer is tall. Jennifer is the bank manager.

707
01:10:06,060 --> 01:10:14,370
Therefore the bank manager is tall. Put your hand up when you've decided whether it can be evaluated a priori.

708
01:10:20,460 --> 01:10:23,460
Okay. What do you think? Yes it can. Yes it can.

709
01:10:23,910 --> 01:10:31,080
Okay. So the it's the structure of that argument that tells us whether it's, um, a good argument or not.

710
01:10:31,080 --> 01:10:35,160
So is it good? Yes. Yes, it's a good argument, isn't it?

711
01:10:35,400 --> 01:10:38,700
What about crocodiles is dangerous. James's dog is dangerous.

712
01:10:38,700 --> 01:10:43,440
Therefore James's pet is crocodile. I think I was getting tired of this.

713
01:10:45,810 --> 01:10:50,130
Uh, can we evaluate that argument? Can't we?

714
01:10:50,430 --> 01:10:54,839
Yes. It's, uh. Uh, it's a bad job.

715
01:10:54,840 --> 01:10:58,230
Too long, doesn't it? We can see this is bad. We don't need to do anything.

716
01:10:58,890 --> 01:11:03,959
Um, it's wrong to tell a lie. Just tell your mum her hair looks good.

717
01:11:03,960 --> 01:11:07,560
Was a lie. Therefore, Jane's telling her mum her hair looked good, was wrong.

718
01:11:07,950 --> 01:11:12,150
Um, can we can we evaluate that argument a priori or not?

719
01:11:12,390 --> 01:11:15,420
Yes, I think we can. It's such a good one.

720
01:11:16,080 --> 01:11:20,280
Yeah, it's it's another good deductive argument.

721
01:11:20,700 --> 01:11:26,190
Tomato plants are to be fed well, kept warm and watered frequently, usually thrive.

722
01:11:26,670 --> 01:11:33,540
This tomato plants must be fed well and watered frequently. But it's dead that all this tomato plant hasn't been fed properly.

723
01:11:34,920 --> 01:11:38,850
That's interrupted. Yes. Um that's inductive.

724
01:11:39,270 --> 01:11:42,510
Um, might not be careful because you want to know why it's bad.

725
01:11:42,780 --> 01:11:46,770
Yeah. Why is it bad? I mean, is it just that I can just out of its pot?

726
01:11:47,550 --> 01:11:52,230
Um, okay. Yes. We need to know a little more about that situation.

727
01:11:52,230 --> 01:11:56,070
Wouldn't we would need to have some background information. Um, what about this one?

728
01:11:56,070 --> 01:11:59,760
This looks familiar. If this liquid is acidic, it will turn.

729
01:11:59,760 --> 01:12:03,510
It was paper blue. This liquid turns litmus paper blue.

730
01:12:03,510 --> 01:12:11,069
Therefore, this liquid is acidic. It's good for just about the last two springs.

731
01:12:11,070 --> 01:12:15,060
Well, hot and sunny. But the summers were awful. This spring was hot and sunny.

732
01:12:15,330 --> 01:12:18,420
Therefore, this summer will be awful. Yeah.

733
01:12:20,130 --> 01:12:26,340
Why? Do we need to bring to bear background information?

734
01:12:26,760 --> 01:12:30,780
What sort of background information will we need to bring to bear with the school counsellors?

735
01:12:31,260 --> 01:12:34,290
With the data? What we didn't know.

736
01:12:34,740 --> 01:12:38,280
We need more information. We need more to use with that information. Yes.

737
01:12:38,640 --> 01:12:44,310
We would want a lot more than two years, wouldn't we? In order to generate that scenario?

738
01:12:44,970 --> 01:12:48,720
Yes. Go back to five. Yes.

739
01:12:49,050 --> 01:12:53,640
If the liquid is something other than acidic, it like to paper through two.

740
01:12:54,780 --> 01:12:59,730
Um, what are you bringing to bear? To be honest, one analysis.

741
01:12:59,940 --> 01:13:06,000
Let me have a look at that. Um, so I think to the point where it's actually quite difficult to, to know.

742
01:13:06,630 --> 01:13:11,940
So if P then Q oh, that's a bad deductive argument.

743
01:13:12,120 --> 01:13:15,240
Yeah. Do you why did we say it was a good one? Yeah, yeah.

744
01:13:15,270 --> 01:13:18,630
That's because the last one that talked about newspaper in the city.

745
01:13:18,750 --> 01:13:31,710
No, that's a bad argument. Can you see that. It's um, it's P then q q therefore P, which is not if p that q p therefore q.

746
01:13:31,890 --> 01:13:34,920
Yes. Do you see. Yes. Got to be careful about that.

747
01:13:34,920 --> 01:13:40,380
So that's, that's um, a policy of affirming the consequence.

748
01:13:41,130 --> 01:13:50,610
Um, um, what would happen later on? I'm not sure that's me is good to talk to, but it's wrong to tell a lie.

749
01:13:50,640 --> 01:13:55,260
Jane's telling her mum her hair looked good was a lie. Therefore, Jane.

750
01:13:55,590 --> 01:14:00,240
Uh. It is. Well, it's just not why you say that is wrong.

751
01:14:00,270 --> 01:14:03,630
I think it so let me let me just, um, see if it is.

752
01:14:06,610 --> 01:14:13,690
Uh, so p is it's wrong to tell a lie.

753
01:14:14,890 --> 01:14:18,220
Um. Oh, actually, no. Uh, I'll have to do it.

754
01:14:18,310 --> 01:14:24,250
Um. I'm going to have to go into the predicate calculus.

755
01:14:24,260 --> 01:14:48,980
Excuse me a second. Um, sorry. Okay, here's my interpretation.

756
01:14:49,550 --> 01:14:54,800
F of x x is a lie. Okay of x x is wrong.

757
01:14:55,160 --> 01:14:58,400
An x, which is a, um, a thing.

758
01:14:58,520 --> 01:15:02,000
An action. In this case, Jane's telling her mom her hair looks good.

759
01:15:02,450 --> 01:15:09,229
So we've got, um. Uh, all x.

760
01:15:09,230 --> 01:15:12,740
If, uh, X is alive, then X is wrong.

761
01:15:13,490 --> 01:15:23,120
Okay, that's the first time. Is, um. L x x is a sorry, l s x is a lie.

762
01:15:24,170 --> 01:15:29,360
Do you see? We've got that. And therefore w x s rather.

763
01:15:32,700 --> 01:15:37,470
Both of those offices. So. Everything is such that if it's a lie, it's wrong.

764
01:15:38,130 --> 01:15:42,510
See, that's the first premise. Um, s is a lie.

765
01:15:42,840 --> 01:15:48,540
Jane's telling her mom her hair looks good, is lying. Therefore S is wrong.

766
01:15:48,960 --> 01:15:52,920
James telling her mom her hair looks good is wrong to be straight.

767
01:15:53,040 --> 01:15:56,400
Good deductive argument. Sorry to see the logic.

768
01:15:56,640 --> 01:16:01,710
Oh, good. But in reality, the premises are opening.

769
01:16:02,310 --> 01:16:08,370
Oh, well, but we're not evaluation purposes. Yeah, we're we're not evaluating the arguments at the moment.

770
01:16:08,640 --> 01:16:11,790
Uh, I'm not saying anything about whether the premises are true or false.

771
01:16:11,820 --> 01:16:15,300
I mean, if widget samplers. Yeah. Nonsense.

772
01:16:15,840 --> 01:16:26,430
Uh, what is positive? Can you go? Oh, sorry. So I wonder wonder, uh, would it make any difference to five if you put if and only if at the beginning,

773
01:16:27,420 --> 01:16:31,020
it would always make a difference to change it to a different.

774
01:16:31,020 --> 01:16:37,739
Only if always. I mean, I found that students, when they first start formalising something, um,

775
01:16:37,740 --> 01:16:43,170
will immediately reach for a double arrow, which you see if and only if, um,

776
01:16:43,350 --> 01:16:49,440
when actually all there is is an if or all the rest is an only if and actually

777
01:16:49,440 --> 01:16:55,710
if and only if it's very different to if and it's different also to only.

778
01:16:56,520 --> 01:17:02,400
Um so yes it would make a huge difference. Doesn't make it deductively valid or a good argument.

779
01:17:02,970 --> 01:17:09,900
Um, it's exactly the same as one we had earlier when somebody was talking about, if, you know.

780
01:17:10,320 --> 01:17:16,260
So if you have, if, if this liquid is acidic, it will turn litmus paper blue.

781
01:17:16,770 --> 01:17:20,220
This. Yes it would be. Yes. Yes. Good. Yeah.

782
01:17:21,330 --> 01:17:24,420
Uh, okay. So right. That's sort of the question asking for a right.

783
01:17:24,420 --> 01:17:27,570
That's good. Two for the price one. Yeah okay.

784
01:17:27,600 --> 01:17:30,720
Ooh exercise to do at home already. Right.

785
01:17:30,780 --> 01:17:35,400
Well we got in that case we can we can wait a bit for that because I'm sure there must be more questions.

786
01:17:35,970 --> 01:17:39,930
Okay. I usually summarise if I not done that this week.

787
01:17:39,990 --> 01:17:45,360
Yes. Here we go. Um, so there's your exercises to do at home.

788
01:17:45,360 --> 01:17:50,280
Um, and I will give you the answer sizes on your answer sheet next week.

789
01:17:50,790 --> 01:17:59,069
Um, so you can have a look at those at home. And so this week we've looked at critical reasoning is normative not descriptive.

790
01:17:59,070 --> 01:18:06,030
Do you remember that something's normative if it involves standards either moral standards or rational standards.

791
01:18:06,030 --> 01:18:11,490
So right and wrong in some sense it involves norms.

792
01:18:12,000 --> 01:18:20,850
Um, we've looked at the fact that there are two types just following from um, so deductive follow following from an inductive following from um,

793
01:18:20,850 --> 01:18:26,130
we've seen that deductive arguments are truth preserving, or at least they are when they're good.

794
01:18:26,640 --> 01:18:31,410
So I hadn't made that clear that. But that should be clear. The truth preserving if good.

795
01:18:32,310 --> 01:18:36,360
Um, there are also such that there being good is an either or matter.

796
01:18:36,810 --> 01:18:39,810
Uh, do you remember that they're monotonic?

797
01:18:40,260 --> 01:18:44,070
Um, once you once. It's good. It can't be changed to anything else.

798
01:18:44,640 --> 01:18:50,850
Um, um, deductive arguments are such that we can determine a priori whether they're good or not.

799
01:18:51,270 --> 01:18:55,679
An inductive arguments are necessary, serving no matter how good they are.

800
01:18:55,680 --> 01:19:01,650
They do preserve the truth in that very definite definition of truth preserving that I gave at the beginning.

801
01:19:02,130 --> 01:19:05,190
Um, there also is such that there being good is a matter of degree.

802
01:19:05,700 --> 01:19:09,570
Um, there's such that we can only determine whether they're good by bringing to bear,

803
01:19:09,840 --> 01:19:15,420
uh, experience of understanding of the contents and or background information.

804
01:19:16,200 --> 01:19:19,529
So that's it, folks, for today.

805
01:19:19,530 --> 01:19:27,300
Uh, but we've got time for questions, which is so, um, um, um, let's see if I can turn this.

806
01:19:29,290 --> 01:19:32,409
Does that make it easier? It makes it easier. Sorry.

807
01:19:32,410 --> 01:19:36,430
Some of the other questions. I got a feeling that you mentioned earlier.

808
01:19:36,460 --> 01:19:40,420
They also say white business as being.

809
01:19:41,820 --> 01:19:55,820
Not the time to that. Um, black swans, but, uh, but then later you said that the premise don't have to be true, and the GOP said all sponsor wives.

810
01:19:56,220 --> 01:19:58,470
This is a sport and therefore it is wives.

811
01:20:01,580 --> 01:20:10,430
Even if swarms only showed you that student multitasking, creativity of swarms, animals or birds, let's pretend they're animals.

812
01:20:11,360 --> 01:20:16,180
They're birds or they both shoot.

813
01:20:16,490 --> 01:20:25,850
Yeah. Okay, here's an argument.

814
01:20:32,220 --> 01:20:49,140
And here's another argument. Okay.

815
01:20:49,150 --> 01:20:52,520
All sounds white. The animal in the next room is a swan.

816
01:20:52,540 --> 01:20:58,450
Therefore, the animal in the next room is white. Is that an inductive argument or deductive argument?

817
01:20:59,770 --> 01:21:05,590
It's deductive. Okay, so, um, um, what about every swan I've ever seen has been white.

818
01:21:05,860 --> 01:21:09,790
Therefore, all swans of white is inductive.

819
01:21:10,000 --> 01:21:16,600
So you see that? Um, I mean, I could say all swans I've seen have been white.

820
01:21:17,290 --> 01:21:23,460
Um, it would still be inductive, wouldn't it? Um, it's the first one.

821
01:21:23,470 --> 01:21:28,000
The top one. Deductive one is correct, even though it's not true.

822
01:21:29,200 --> 01:21:36,520
Um, in real life, it is truth preserving. That's all argument, even though one of its premises is false.

823
01:21:36,850 --> 01:21:41,739
It's that we'll be doing this more next week. And it's it's something that people are find very difficult.

824
01:21:41,740 --> 01:21:47,140
Um, I think there's a sort of argument that goes in some people's heads that validity is good.

825
01:21:47,710 --> 01:21:52,480
Truth is good. Therefore validity and truth are the same thing, but they're not.

826
01:21:53,500 --> 01:22:00,280
You can have a valid argument with a false conclusion, and you can have an invalid argument with a true conclusion.

827
01:22:00,850 --> 01:22:09,550
So the notion of truth preserving this, um, is very different from from truth, simplicity or truth generating.

828
01:22:10,540 --> 01:22:16,710
Because. Can I take you back to the argument to back stabbing through the heart, the plunging the dagger?

829
01:22:16,720 --> 01:22:25,480
Yes. Because I think I would argue you're turning that deductive argument with a hidden, uh, with the hidden premise.

830
01:22:26,020 --> 01:22:33,250
Do you remember what it was? Uh, it was what I was talking about.

831
01:22:33,920 --> 01:22:38,530
This and it. You were not honest since he wasn't right. But, uh.

832
01:22:39,250 --> 01:22:44,430
Okay. Um, I would say that's a hidden premise which turns into one.

833
01:22:44,710 --> 01:22:49,960
No, every inductive argument. You could find a hidden premise that turns it into a deductive argument.

834
01:22:50,920 --> 01:22:58,180
I mean, uh, taking that one, every soul that I've seen has been white.

835
01:22:58,810 --> 01:23:01,990
I have seen every swan.

836
01:23:04,240 --> 01:23:07,930
Immediately becomes a detective. I mean, there's no problem.

837
01:23:07,930 --> 01:23:11,739
We take your deductive argument, add to your premise to turn it into deductive.

838
01:23:11,740 --> 01:23:15,670
Um, we can always do that. I don't think I've done that here.

839
01:23:16,630 --> 01:23:21,880
Um, well, I would suggest the premises plunging daggers into heart are inevitably fatal.

840
01:23:24,250 --> 01:23:28,360
Uh, not if you've already killed a chap from. I mean.

841
01:23:28,690 --> 01:23:32,310
So you die with electric shock, and then I plunge a dagger into your heart.

842
01:23:32,350 --> 01:23:37,929
I'm not guilty of murder. I may have the intention to murder you, Christopher, but I didn't do it.

843
01:23:37,930 --> 01:23:42,579
It's already dead anyway. What's that was, anyway?

844
01:23:42,580 --> 01:23:47,040
Because you don't know who his referred to. Um.

845
01:23:47,250 --> 01:23:51,210
Um. John? Yes. You would have to assume that there's somebody.

846
01:23:51,400 --> 01:23:56,080
I mean, we always see somebody dead here. Uh, that's what Hilton was, exactly.

847
01:23:58,060 --> 01:24:04,690
But he's not dead because you're you're policing is trying to see. If I just like to listen to his own heart.

848
01:24:04,690 --> 01:24:07,750
Of course. Yeah, yeah, that's true.

849
01:24:08,410 --> 01:24:17,170
But we do sometimes have to take just take it for granted that there is a person here that was introduced to, I think, in talking about the cats.

850
01:24:17,170 --> 01:24:22,090
We talked about her, didn't we, without make it absolute clear who we meant.

851
01:24:22,090 --> 01:24:25,149
But you got three people. They got Smith. Smith.

852
01:24:25,150 --> 01:24:28,570
You've got John. Um. Hit him. Yes.

853
01:24:28,660 --> 01:24:35,350
That's what he is. Yes. You've got three people. It doesn't say whose heart it holds.

854
01:24:36,010 --> 01:24:39,820
No. It's true. So when you've got the man.

855
01:24:39,970 --> 01:24:43,250
Yes. Who is him? Clearly.

856
01:24:43,270 --> 01:24:46,690
But it's the one. It's the. His.

857
01:24:47,860 --> 01:24:52,540
Yes. Physical. Three members who tried to stop him.

858
01:24:53,140 --> 01:24:58,510
Jones killed a man. So Jones plunge the jacket into his pocket so he could be Jones.

859
01:24:59,380 --> 01:25:07,870
Smith. Uh, I think for any English person to be an US for a restroom reference.

860
01:25:07,990 --> 01:25:11,220
Back to the science. Yes, I really do. Yes, yes.

861
01:25:11,740 --> 01:25:14,950
And I know you're old English, but I think you're just saying it for fun.

862
01:25:16,120 --> 01:25:22,760
Okay. Uh, well, look, supposing that. You a bit electrocution.

863
01:25:22,780 --> 01:25:29,410
You said he could have been electrocuted, but he can because he's dealing with someone who's still alive.

864
01:25:30,130 --> 01:25:35,880
He's going to kill. I don't try to prove he's been tried to stop Jones killing the man and failed.

865
01:25:36,100 --> 01:25:40,690
His wife stated, sometimes you get daggers plunged into your hearts without killing you.

866
01:25:40,720 --> 01:25:44,520
Coming. What are we talking about?

867
01:25:44,540 --> 01:25:49,350
This is. It doesn't seem to be the slightest bit interesting.

868
01:25:51,780 --> 01:26:03,480
Are you sure you have. When we look as students, logic deductive inductive reasoning basically takes subject to the tragedy of the equation,

869
01:26:03,870 --> 01:26:12,180
not with deductive inductive argument, because you've got to bring to bear your background knowledge on the argument with deduction.

870
01:26:12,210 --> 01:26:17,160
Yes. Um, your background knowledge is can be just taking this completely out of the equation.

871
01:26:17,670 --> 01:26:21,300
Yep. That's just like deducting this computers use deduction.

872
01:26:21,900 --> 01:26:27,630
They do. And don't cut it subjective to know how well we talk about something.

873
01:26:28,110 --> 01:26:33,870
First you just have to be different is that we can make it problematic.

874
01:26:34,320 --> 01:26:39,570
Yes. There's a big difference between deduction and induction in that with deduction

875
01:26:39,990 --> 01:26:45,490
we have a very simple mechanical system that can be given to computers.

876
01:26:45,510 --> 01:26:53,970
I mean, computers embody the, uh mechanistic testing evaluation system for deductive arguments.

877
01:26:54,370 --> 01:27:09,060
Um, we can't do all deductive arguments that way. And we for example, if I say, um, uh, lying is wrong, therefore, you shouldn't lie.

878
01:27:11,000 --> 01:27:16,940
Now that looks like a deductive argument. It couldn't be the case that that's true without that's being true.

879
01:27:17,690 --> 01:27:25,640
Um, but we can't mechanistically test that because, um, it seems to depend on the meaning of the word role.

880
01:27:26,570 --> 01:27:32,809
Um, so deduction, we could we could do the propositional calculus as a predicate calculus.

881
01:27:32,810 --> 01:27:40,490
All very powerful systems, uh, that we can use to test deduction, but they don't test all deduction.

882
01:27:40,700 --> 01:27:45,290
They still we we don't like logic, which is the logic of morality.

883
01:27:45,620 --> 01:27:55,430
It's still very much in its infancy. And there are other um, there's also modal logic, which is less in its infancy by if it is possible.

884
01:27:56,090 --> 01:28:01,130
Um, that just means possible. Then it is not.

885
01:28:02,430 --> 01:28:06,520
Um. Yeah.

886
01:28:06,530 --> 01:28:09,440
I've seen you've tried to think of something more interesting, but, um.

887
01:28:09,980 --> 01:28:16,670
Yeah, I mean, you can see that's a deductive argument, but actually, again, that seems to dependable the meaning of the word possible there.

888
01:28:17,360 --> 01:28:22,700
Um, so we might think that wrong and possible are both themselves logically,

889
01:28:22,700 --> 01:28:28,790
but it's like and or if but if so, they act very differently and we don't know how they act.

890
01:28:29,090 --> 01:28:33,080
But what is we a very good system for the vast majority of deductive arguments.

891
01:28:33,680 --> 01:28:42,020
Um. If we can mechanise probability at all, it's only a very small part of it.

892
01:28:42,530 --> 01:28:50,090
Um, so, yes, there is a problem for mechanistic systems because you need to bring to bear all sorts of background knowledge.

893
01:28:50,390 --> 01:28:53,390
Yeah. Okay. One final question.

894
01:28:53,540 --> 01:28:59,090
Is it correct? The speaker mentioned that, um, it could be subjective.

895
01:29:00,080 --> 01:29:03,440
The inductive arguments could be subjective. Is that correct?

896
01:29:04,580 --> 01:29:09,620
I don't like do you, uh, I banned graduates from using the word subjective to learn the third year.

897
01:29:10,320 --> 01:29:19,250
Um, um, it's all you need to bring to bear some background information to that extent.

898
01:29:19,250 --> 01:29:21,590
You're bringing your beliefs to bear on it.

899
01:29:22,220 --> 01:29:30,590
Um, I'm still, you know, subjective is is a subjective state, is a state of a subject to, say, accessible to conscious awareness.

900
01:29:31,070 --> 01:29:41,840
Um, so, but some subjective is not quite the right word, but it's certainly true that the different people could be more or less inductively bold.

901
01:29:42,560 --> 01:29:46,549
So some of you here might say, every time I've seen my aunt, she's been wearing earrings.

902
01:29:46,550 --> 01:29:51,650
Therefore, next time I see you should be wearing earrings, even though you met me three times.

903
01:29:51,980 --> 01:29:55,670
But some of you might wait to meet me ten times before you prepared to say that.

904
01:29:56,270 --> 01:30:07,190
Or whatever. Do you see? Um, so some people are very inductively bold, so they'll draw a generalised conclusion from very little evidence.

905
01:30:07,370 --> 01:30:12,259
And other people wants quite a lot of evidence before they'll draw an inductive conclusion.

906
01:30:12,260 --> 01:30:18,739
So there's certainly an element of subjectivity in how inductively followed you.

907
01:30:18,740 --> 01:30:22,520
All right. We'd better stop there.

908
01:30:22,760 --> 01:30:26,380
Um, and the, uh, presentation for today.

909
01:30:26,390 --> 01:30:30,460
So here are some of the arguments. But at the end of last weekend and today.