牛津逻辑推理入门 - 2.论证的不同型态.

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

由 Groq Whisper 转录 → M3 B 方案整文标点 + 分段 → M3 段号保留翻译 → 逐段对照。

[段 1]

Okay, and now we’re on week two, and this week we’re going to look at different types of arguments, and in particular we’re going to look at deduction and induction. These are the two basic types of arguments, and we’ll be looking at different examples of each type. Welcome back everyone. So it didn’t put you off entirely last week then. Difficult though it was, I’m sure it was difficult. Let’s do a quick recap on last week so we can remember where we were. if you remember I said that arguments are sets of sentences such that one of them the conclusion if you remember is being said to be true and the others called the premises are being offered as reasons for believing the truth of the one or reasons for believing the one okay so that’s what an argument is and I said it was important to distinguish arguments from two things firstly sets of sentences that aren’t arguments. And if you remember, I gave there two sorts of sets of sentences that are not arguments. Can anyone remember what they are? No, an assertion isn’t an argument. An assertion is the second thing from which you should distinguish arguments. So I said that there are two sets. I think you misunderstood my question slightly, whoever it was then. So there are two things from which you distinguish arguments.

[译文 1]

好的，现在我们进入第二周，这一周我们要看不同类型的论证，特别是演绎和归纳。这是两种最基本的论证类型，我们将会看每种类型不同的例子。欢迎大家回来。看来上周的内容并没有把你们完全吓跑。虽然很难，我相信确实很难。我们快速回顾一下上周的内容，这样我们可以记得讲到哪里了。如果你们记得，我说过论证是若干句子组成的集合，其中一个，也就是结论，如果你记得的话，被声称为真，而其他被称为前提的句子，则被提供作为相信它为真的理由，或者说是相信这个结论的理由，这就是论证的含义。我说过重要的是要把论证和两样东西区分开来，首先是与不是论证的句子集合。如果你记得，我给出了两类不是论证的句子集合。有人能记得它们是什么吗？不是，一个断言不是论证。第二个需要与论证区分开的是断言本身。所以我说有两类集合。我想你误解了我的问题，不管当时是谁。所以有两样东西需要与论证区分开。

[段 2]

But the first one is sets of sentences. And I said that there are two things, two types of sets of sentences.things, two types of sets of sentence that you need to distinguish from an argument. Can anyone remember what those two types of sets of sentences were? Sorry? No? No? No? Okay, maybe that’s not a fair question. Okay, the first one is sets of sentences that aren’t related at all. Do you Remember, I talked about sea as salt and melbons in Australia. Well, until you add therefore and a bit of context, that’s not an argument, is it? It’s just two unrelated sentences. And the second type of sets of sentence you should distinguish from arguments are those that are related, but not as an argument is related, not as the sets of sentences that constitute an argument are related. so in order for a set of sentences to be an argument it’s got to be related in the sense that the conclusion is being said to follow from the premises that’s what an argument is that one of the sentences of the set is being said to follow from the others if that relation isn’t being said to be there then it’s not an argument the second thing from which you must distinguish an argument is a sentence and can anyone remember how you distinguish sentences from arguments or one way at least in which you would distinguish a sentence from an argument?

[译文 2]

但第一个是句子集合。我说过有两样东西，两种类型的句子集合，你需要把它们与论证区分开来。有人能记得这两种句子集合是什么吗？什么？不是？不是？不是？好吧，也许这个问题不公平。好的，第一种是完全不相关的句子集合。你们记得，我谈到了澳大利亚的海水和甜瓜。在你加上"因此"和一些语境之前，那不是论证，对吧？那只是两个不相关的句子。第二种你应该与论证区分开的句子集合，是那些相关，但不像论证那样相关的句子集合，不像构成论证的句子集合那样相关。所以为了使一个句子集合成为论证，它必须以这样的方式相关：结论被声称为从前提中推出，这就是论证的含义——集合中有一个句子被声称为从其他句子中推出。如果这种关系没有被声称存在，那它就不是论证。第二件你必须与论证区分开的事是句子，有人能记得你如何把句子与论证区分开来吗？或者至少一种你会用来把句子与论证区分开的方式？

[段 3]

What do you mean by premise there? A premise has a very particular definition. The definition is that a premise is a sentence that’s being offered as reason for believing the truth of the conclusion. So what the question is here is how do you distinguish a sentence or assertion from an argument? A sentence you could see as an incomplete argument, I suppose, but that’s not what I was thinking of. Certainly there’s no conclusion, nothing being, well there is something being postulated if the sentence is being asserted, isn’t there? There’s no relation, that’s right, but okay, let me, oh hang on, there’s one more at the back there. Say that again? That’s right, this is just a statement, and a statement isn’t an argument, is it? A statement isn’t good or bad, well it could be I suppose, couldn’t it? a statement is true or false and an argument is good or bad. Do you remember? Very important that you shouldn’t call arguments true or false because arguments can’t be true or false. The only thing that can be aArguments can’t be true or false. The only thing that can be a true or false is the sentences that make up the argument. What an argument is, is truth preserving. So if you have truth in the premises, and it’s a good argument, then the conclusion will be true.

[译文 3]

你所说的"前提"是什么意思？前提有一个非常特别的定义。其定义是：前提是一个被提供作为相信结论为真的理由的句子。所以这里的问题是，你如何把一个句子或断言与一个论证区分开来？句子你可以看作是一个不完整的论证，我猜，但那不是我所想的。当然没有结论，没有什么被，嗯，如果这个句子被断言的话，确实有什么东西被假定，是吗？没有关联，对，但好的，让我说，哦等等，后面还有一位。重新说一下？对了，这只是一个陈述，而陈述不是论证，对吧？陈述不是好的或坏的，嗯，我想它也可以是好的或坏的，不是吗？陈述是真或假的，而论证是好的或坏的。你们记得吗？非常重要的一点是你们不应该说论证是真或假的，因为论证不能是真或假的。唯一能是真或假的是构成论证的句子。论证的本质是真值保持。所以如果前提为真，并且论证是好的，那么结论就为真。

[段 4]

But notice it’s the premises that are true and the conclusion that’s true, not the argument itself. The most the argument can be is truth preserving. Okay, so that’s distinguishing arguments from sets of sentences and from sentences themselves. What we’re going to do today is consider different types of argument. And we’re going to start using some of the concepts that you’ve already mentioned this morning. So, there are two basic types of argument. There are deductive arguments and there are inductive arguments. This is a very basic type of argument because you’ll see later there are lots of other types of arguments in these categories. But these two categories are the most important. These are the ones you need to get a grip on. OK, let’s look at deductive arguments first. Now, these are such that the truth of their premises guarantees the truth of the conclusion. So if the premises are true, then the conclusion must be true. Because if it’s a good deductive argument, it’s truth guaranteeing. So here’s a deductive argument. You’ll be familiar with this one. We used it last week. It’s Friday. Marianne always wearsWe used it last week. It’s Friday. Marianne always wears jeans on a Friday. Therefore, Marianne is wearing jeans. Notice that the conclusion of this argument is true, but neither of the premises are. So that should give you an idea that the argument is a good one.

[译文 4]

但请注意，前提为真，结论为真，而不是论证本身为真。论证所能做到的最多是真值保持。好的，那就是把论证与句子集合以及句子本身区分开来。今天我们要做的是考虑不同类型的论证。我们将开始使用你们今早已经提到的一些概念。所以，有两种基本的论证类型。有演绎论证和归纳论证。这是一种非常基本的论证类型，因为你们稍后会看到在这些类别中还有许多其他类型的论证。但这两个类别是最重要的。这些是你需要掌握的。好的，我们先来看演绎论证。它们的特征是：前提的真保证结论的真。所以如果前提为真，那么结论必然为真。因为如果它是一个好的演绎论证，它是保证真的。这里有一个演绎论证。你们会熟悉这个例子。我们上周用过。现在是星期五。Marianne 在星期五总是穿牛仔裤。因此，Marianne 穿着牛仔裤。请注意，这个论证的结论为真，但没有哪个前提为真。这应该让你们意识到这个论证是好的。

[段 5]

The conclusion is true, but actually neither of the premises are true. So this will be something we’ll look at again when we look at what a good argument is next week relating to the real world. That’s right. It’s not Friday. Therefore, that premise is false. It’s not true. You’ll have to take it from me on authority that I don’t always wear jeans on a Friday. I do happen to be wearing jeans today. But of course, that’s irrelevant because it’s neither Friday nor is it the case that I always wear jeans on a Friday. But what’s important about this argument is that it’s deductive. It’s truth guaranteeing at least conditionally upon the truth of the premises. Can you think of any situation, I really try and use your ingenuity here, let’s see if we can get, in which that would be true, okay, it isn’t true, we know that, but we’re assuming for the sake of argument that it is true. So imagine a situation where that’s true and that’s true for some reason. I always wear jeans on a Friday. Could that be false? Can anyone think? You might have lost them in the intervening week. Stop.Well, wouldn’t that make that not true? No, no, it doesn’t. I may hate wearing jeans. That may mean nothing to do with it. I may wear jeans as a penance on a Friday because I once did something really ghastly and said to myself, right, okay, from now on I’m always going to wear jeans on a Friday.

[译文 5]

结论为真，但实际上没有哪个前提为真。所以这将是我们下周再看什么是好的论证时涉及的内容，与现实世界相关。是的。今天不是星期五。因此，那个前提是假的。它不为真。你们得相信我权威地说，我并不总是在星期五穿牛仔裤。我今天确实碰巧穿着牛仔裤。但当然，那是不相关的，因为今天既不是星期五，也不是我总在星期五穿牛仔裤的情况。但这个论证重要的是它是演绎的。至少在前提为真的条件下，它是保证真的。你们能想到任何情况吗，我真的要在这里用一下你们的聪明才智，让我们看看能不能找到，在哪种情况下那是真的，好吧，它不为真，我们知道，但我们为了论证的目的假设它为真。所以想象一个情况，那里为真，而那里由于某种原因为真。我总是在星期五穿牛仔裤。那可能为假吗？有人能想到吗？你们可能在这一周里弄丢了它们。停。嗯，那不会让那个不为真吗？不，不，它不会。我可能讨厌穿牛仔裤。那可能与此毫无关系。我可能在星期五穿牛仔裤作为一种忏悔，因为有一次我做了非常可怕的事，然后对自己说，好吧，从现在起，我总是在星期五穿牛仔裤。

[段 6]

So it doesn’t say that I want to. Can anyone think of a counterexample? Okay, so it’s true it would be Friday on that day, but would this be true? No, it wouldn’t, would it? So what we’ve given there is a falsification of that, not a counterexample to the argument. Okay, do you see where I’m getting at? What we’re doing is we’re distinguishing the truth of the premises from the truth-preservingness of the argument. Lots of us can think of situations where that’s false or where that’s false, but that’s not what I’m asking you to do. What I’m asking you to do is to think of a situation where that’s true and that’s true and that’s false. It’s impossible for that to be true. It is, isn’t it? Well, hang on, there are a couple of other examples here.Well, hang on, there are a couple of other examples here. Let’s try one. What do you think about Mary Elliot? So I’m on the moon or something like that. Very ingenious. I think what we’re talking about is a situation where all these are true. Sorry, these two are true together. Do you see what I mean? And what you’re giving me is one where it’s not Friday. Aren’t you? Really? You’re trying to make it not Friday somehow by shifting me out of a time zone in which it is Friday.

[译文 6]

所以它并没有说我想要穿。有人能想到一个反例吗？好的，所以那一天确实是星期五，但那会为真吗？不，它不会，对吧？所以我们给出的是对它的反驳，而不是对这个论证的反例。好的，你们明白我的意思了吗？我们在做的是把前提的真与论证的真值保持性区分开来。我们很多人可以想到那种情况不为真或那种情况不为真的场景，但那不是我要你们做的。我要你们做的是想出一种情况，使那个为真，那个为真，而那个为假。它不可能为真。它是，不是吗？嗯，等等，这里还有其他几个例子。等等，这里还有其他几个例子。我们试一个。你们怎么看 Mary Elliot？比如说我在月球上之类的。非常巧妙。我认为我们在说的是一种所有这些都为真的情况。抱歉，这两个一起为真。你们明白我的意思吗？而你们给我的是一种不是星期五的情况。不是吗？真的？你们试图通过把我移出处于星期五的时区来让它不是星期五。

[段 7]

No, it won’t do. But we don’t need to guarantee it because all we’re doing, we’re saying this is true if this is true and if this is true. We’re not saying this is true. I mean, this is another very important distinction. When you’re doing logic, you’re not talking about the actual truth value of a sentence. Okay, so the truth value of that could be either true or false. Do you see what I mean? So that’s the value of its truth. It’s either true or false. And we’re not saying it is true, but we’re saying if it’s true. And if this is true, this can’t be false. And as you rightly said, actually…and as you rightly said actually if these two are true it’s impossible for this to be false it really is isn’t it well if we’re looking at an argument we’re saying we’re asking ourselves two questions the questions are does the conclusion follow from the premises and in asking that what we’re asking is if the premises were true would the conclusion be true if the premises are true, would the conclusion be true? And if we look at these two premises and we ask that question, we’re not asking whether the premises are true, we’re saying if they’re true, would the conclusion be true? And the answer is yes. Can everyone see that?

[译文 7]

不行，这样不行。但我们并不需要保证它为真，因为我们所做的事情只是说：如果这是真的，并且如果这是真的，那么这个就是真的。我们并没有说这个本身是真的。我的意思是，这是另一个非常重要的区别。当你进行逻辑推理时，你说的并不是一个句子的实际真值。好，所以它的真值可能是真的，也可能是假的。你明白我的意思吗？所以那是它的真值，要么真要么假。我们并没有说它是真的，我们说的是如果它是真的。并且如果这是真的，那这个就不可能是假的。正如你正确指出的那样……正如你正确指出的那样，如果这两者为真，那这个就不可能是假的，确实是这样，对吧？好，如果我们在看一个论证，我们是在问自己两个问题：问题是结论是否由前提得出？在问这个问题时，我们其实在问的是：如果前提为真，结论会为真吗？如果前提为真，结论会为真吗？如果我们看这两个前提并问这个问题，我们并不是在问前提是否为真，我们是在说如果它们为真，结论会为真吗？答案是会的。大家都能看出来吗？

[段 8]

This is a deductively valid argument. It’s truth preserving and therefore it’s very, very useful because we know that if the premises are true, the conclusion must be true. Now, in this particular case, this is not very useful because it’s all hypothetical. But can you imagine if this was something that we didn’t know, but we were wanting to test, then we could say, okay, it’s Friday. Marianne always wears jeans on a Friday. Therefore, Marianne is wearing jeans. Then if you see that I’m not wearing jeans, What do you know? One or other of these isn’t true, exactly.one or other of these isn’t true exactly. So if you see that Marianne isn’t wearing jeans, you know either that it’s not Friday, that that one’s false, or that Marianne always wears jeans on a Friday is itself false. So you know either your hypothesis is false or your observation is false. Or both. Sorry, you’re quite right. Or both. That’s right. So if you have a valid argument, a deductively valid argument, the conclusion to which is false you know that one of the premises must be false and that’s why truth preserving this is useful whatever the situation is even if it turns out that the conclusion is false anyway again that’s something we’ll talk about more next week the only thing that’s important for now is that you understand what a deductively valid argument is you understand that it’s truth preserving that if the premises are true, the conclusion must be true.

[译文 8]

这是一个演绎有效的论证。它是保真的，因此非常非常有用，因为我们知道如果前提为真，结论必然为真。现在，在这个具体的情况下，这并不是非常有用，因为全部都是假设性的。但是你能想象吗，如果这是我们不知道但想要检验的某件事情，那么我们可以说：好，今天是星期五。Marianne 在星期五总是穿牛仔裤。因此，Marianne 正在穿牛仔裤。然后如果你看到我没有穿牛仔裤，你会怎么想？你会知道其中一个前提不为真，正是如此。其中一个前提不为真，确实如此。所以如果你看到 Marianne 没有穿牛仔裤，你就知道要么今天不是星期五，也就是那个前提为假；要么"Marianne 在星期五总是穿牛仔裤"这个前提本身就是假的。所以你要么知道你的假设是假的，要么知道你的观察是假的。或者两者都是假。抱歉，你说得对。或者两者都是假。没错。所以如果你有一个有效的论证，一个演绎有效的论证，而它的结论是假的，那么你就知道其中必然有一个前提是假的，这就是为什么"保真"无论在什么情况下都是有用的，即使结论最终是假的——不过这也是我们下周会进一步讨论的内容。现在唯一重要的是，你们要理解什么是演绎有效的论证，理解它是保真的，也就是说如果前提为真，结论必然为真。

[段 9]

Okay, everyone happy with that? Let’s move on. Okay, you should note, incidentally, that deduction is an either-or thing. Either an argument is deductively valid or it’s not. Okay, there’s no in-between there. It’s one or the other. A good deductive argument gives us conditional certainty. Certainty conditional upon? The truth of the premises. The truth of the premises. Well done. I can feel you’re getting it now.premises, well done, I can feel you’re getting it now. Okay, a bad one tells us nothing, because if the argument isn’t a good one, if it isn’t truth-preserving, then the conclusion could be either true or false, and we really don’t know. Okay, so that’s deduction. Let’s move to induction. Inductive arguments are such that the truth of their premises makes the conclusion either more or less probable. Okay? It doesn’t give us certainty makes the conclusion more or less probable. Now, this means that inductive arguments can be either weak or strong. Okay? So here’s an example of a strong inductive argument. The sun has risen every day in the history of the universe. Therefore, the sun will rise tomorrow. Okay? That’s a strong inductive argument. Why isn’t that a deductive argument? sorry what may not be true because arguments can’t be true of course can they this may not be true okay but but we’re saying if this is true then this will be true so why is that not deductively certain okay so this could be true and yet this false and yet this isAnd yet this false.

[译文 9]

好，大家对这个都满意了吗？我们继续。好，顺便你应该注意到，演绎是一种非此即彼的事情。一个论证要么是演绎有效的，要么不是。没有中间状态。二者必居其一。一个好的演绎论证给我们带来有条件的确定性。条件性的确定性基于什么？基于前提的真值。前提的真值。答得好。我能感觉到你们正在掌握它。前提，答得好，我能感觉到你们正在掌握它。好，一个坏的演绎论证什么也告诉不了我们，因为如果这个论证不是一个好的论证，如果它不是保真的，那么结论可能为真也可能为假，我们真的无从知晓。好，所以这就是演绎。让我们转到归纳。归纳论证是这样的：其前提的真使得结论或更加可能或更不可能。明白吗？它并不给我们确定性，而是使结论更加可能或更不可能。这意味着归纳论证可以是弱的也可以是强的。明白吗？这里有一个强归纳论证的例子。太阳在宇宙历史上的每一天都升起了。因此，太阳明天也会升起。明白吗？为什么这不是一个演绎论证？抱歉，这个可能不为真，因为论证本身当然不可能为真，对吧？这个可能不为真，好，但我们说的是如果这是真的，那么那个就会为真，那为什么这不是演绎确定的？好，所以这个可能为真，但那个却可能为假。然而那个却可能为假。

[段 10]

And yet this is a good argument. Yeah, good. Well done. That’s exactly right. The hallmark of a strong inductive argument is even though you’ve got a very strong argument, I mean, if the sun has risen every single day in the history of the universe so far, I have no idea how old the universe is, but it’s old, right? If the sun has risen every day in the history of the universe, then it’s hugely likely that the sun is going to rise tomorrow, isn’t it? And then you say, but we can’t be 100% certain because who knows, the sun may explode tomorrow. Or maybe the law that ensures that the sun rises every morning actually has a bit of a dogleg in it. so it’s saying okay what the law is is every morning the sun will rise except on the 7th of October 2009 it’s suddenly going to miss a day and from then on it’s only going to rise every other day okay for the rest of the history of time do we know that that isn’t what the law is? do we know that the sun that the law that ensures that the sun has risen every morning in the history of the universe so far won’t tomorrow miss a day. So how could it be a long-term change?well it makes it weaker but it means that we haven’t got certainty this could be true and this false but it’s a different type of argument you mustn’t think that because deductive arguments are certain and inductive arguments aren’t that therefore inductive arguments are somehow inferior because actually they’re dealing with different things.

[译文 10]

然而这是一个好的论证。对，好的。答得对。正是如此。一个强归纳论证的标志性特征是：即使你有了一个非常强的论证，我的意思是，如果太阳在宇宙迄今为止的整个历史中每天都升起，我完全不知道宇宙有多大年龄，但确实很老了，对吧？如果太阳在宇宙历史上的每一天都升起，那么太阳明天极有可能会升起，对吧？然后你会说，但我们无法百分之百确定，因为谁知道呢，太阳也许明天就会爆炸。或者也许保证太阳每天早晨升起的规律中其实带有一个弯曲之处。也就是说规律是这样的：每天早晨太阳都会升起，除了 2009 年 10 月 7 日会突然跳过一天，然后从那以后每隔一天才升起一次。好，在余下的全部时间历史中都是如此。我们能知道规律不是这样吗？我们能知道保证太阳在宇宙迄今为止的历史中每天早晨升起的规律明天不会跳过一天吗？所以它怎么可能是一种长期的变化呢？嗯，这会使它变弱，但这意味着我们并没有获得确定性，这个可能为真而那个可能为假，但这是一种不同类型的论证。你绝不能因为演绎论证是确定的而归纳论证不是，就认为归纳论证在某种程度上是劣等的，因为实际上它们处理的是不同的事情。

[段 11]

This is the sort of argument that science deals with, isn’t it? You observe that nature has been like this all the times before and then you extrapolate into the future to assume it’s going to be like that in the future. So every daffodil you’ve ever seen in your life so far has been yellow. You’re going to assume that the next daffodil you see will be yellow. There’s another bad example, you see. But you see what I mean, I hope. Why are Marianne’s dreams different in that case? Just because she’s worn them every Friday up till now, why are we saying that she will therefore tomorrow wear them as well? Let’s say tomorrow was Friday. Because there’s a… Whoops, sorry, I’m going the wrong way. This is the argument, right? An argument is a set of sentences. There are three sentences in this argument. The argument claim that’s being made by this sentence is that if this is true and this is true, then this will be true.and this is true, then this will be true. This will be true. Okay? And this one, the inductive argument, is saying if this is true, this will be true. Okay? Now, in this case, we can say, but there could be a counterexample to this. The counterexample might be that the sun explodes tomorrow or that the law of nature has had written into it from the history of time that it will change tomorrow of all days.

[译文 11]

这就是科学所处理的那种论证，不是吗？你观察到自然在以前的所有时候都是这样的，然后你据此外推到未来，假设它在未来也会如此。所以你迄今为止一生中见过的每一朵水仙花都是黄色的。你就会假设你见到的下一朵水仙花也是黄色的。你看，这是另一个不太好的例子。但我希望你能明白我的意思。在这种情况下，为什么 Marianne 的梦会有所不同呢？就因为她直到现在每个星期五都穿牛仔裤，为什么我们就会说因此她明天也会穿呢？假设明天是星期五。因为这里有一个……哎呀，抱歉，我方向反了。这就是这个论证，对吧？一个论证就是一组句子。这个论证中有三个句子。这个句子所作出的论证主张是：如果这是真的并且这是真的，那么那个就会为真。如果这是真的，那个就会为真。那个会为真。明白吗？而这个，归纳论证，说的是如果这是真的，那个就会为真。明白吗？现在，在这种情况下，我们可以说，但可能存在一个反例来反驳这个。反例可能是太阳明天爆炸，或者自然规律从时间历史的开端就注定会在所有日子中偏偏在明天发生改变。

[段 12]

We know that this doesn’t give us certainty, but it gives us a jolly good reason for thinking that this is true, doesn’t it? I mean, I could give you an inductive argument that goes like this. In fact, let me give you one. Every time I’ve seen Marianne, she’s been wearing earrings. Therefore, next time I see Marianne, she’ll be wearing earrings. Okay? Now, is that a strong inductive argument? No. Well, it’s not very strong, is it? I mean, the next time you see me, you might have come knocking on my door at 7 o’clock in the morning and I’ve just got up and I don’t wear earrings in bed. So the next, you know, we know too much about the world, about people, about earrings and things like that to know that that’s a good inductive argument. Could you put in another assertion that would make that deductive rather than inductive? Well, let’s go back to this one and notice that hereLet’s go back to this one and notice that here we’re arguing from this, not to it. This is a premise in our argument, not a conclusion. Whereas if we’re looking here, now I’m going the wrong way the other way. No, actually what I was just about to tell you there isn’t going to work. how did we get to this? We’ve seen the sunrise every single day.

[译文 12]

我们知道这并不能给我们确定性，但它给我们一个非常好的理由去相信这是真的，不是吗？我的意思是，我可以给你一个这样的归纳论证。事实上，让我给你一个。我每次见到 Marianne 时，她都戴着耳环。因此，下次我见到 Marianne 时，她会戴着耳环。明白吗？现在，这是一个强归纳论证吗？不是。好吧，它并不很强，对吧？我的意思是，下次你见到我时，你可能是在早上七点来敲我的门，我刚刚起床，而且我睡觉时不戴耳环。所以下一次，你知道，我们对世界、对人、对耳环等等了解得太多了，我们知道那不是一个好的归纳论证。你们能不能再加入一个断言，使它变成演绎的而不是归纳的？好，让我们回到这一个并且注意到这里。让我们回到这一个并且注意到这里，我们是从这个开始论证，而不是论证到那个。这是我们论证中的一个前提，而不是一个结论。而如果我们现在看这里，我现在方向又反了。不，实际上我刚才正要告诉你们的那个说法是行不通的。我们怎么得到这个结论的呢？我们每天都看到日出。

[段 13]

We’ve seen lots of observations, and therefore we naturally extrapolate to a generalisation like this. This is a different form of reasoning. This is inductive reasoning. And it’s the same reasoning that causes us to say something like this. But in this case, the same reasoning isn’t as strong. Here’s another one. Who takes a lucky rabbit’s foot into an exam, if they ever go into exam, who used to take a lucky rabbit’s foot into exam, who has a lucky red jumper or something like that. We’ve all had the experience of something’s really nice happening to us and we were wearing something or carrying something and we think, you know, maybe I’ll wear that again and I’ll be lucky again because we extrapolate from what’s happened in the past to what’s going to happen in the future. I’ve lost you, I can see. I’m looking at your faces and you’ve gone. right the only thing you need to remember is thatthe only thing you need to remember is that a deductive argument you’ve got certainty because if the premises are true the conclusion must be true in an inductive argument you haven’t got certainty you’ve only got probability this premise gives you probable reason to believe this if this premise is true this conclusion is probably true but it’s not certainly true And if this premise is true, then this conclusion is not even probably true, is it?

[译文 13]

我们已经看到了大量的观察，因此我们自然地把它推广到像这样的一个普遍化。这是一种不同形式的推理。这就是归纳推理。也是同一种推理让我们说出这样的话。但在这种情况下，同样的推理就没有那么强有力了。再举一个例子。谁会把一只幸运兔脚带进考场，如果他们去考场的话，谁过去会带幸运兔脚进考场，谁有一件幸运的红色套头衫之类的东西。我们都曾有过这样的经历：某件好事发生在我们身上，而我们当时正穿着某件衣服或带着某样东西，于是我们就想，你知道，也许我下次再穿上它，就会再次交好运，因为我们从过去发生的事情推断未来将要发生的事情。我看你们走神了，我能看出来。我正看着你们的脸，你们已经走神了。好的，你们唯一需要记住的就是，你们唯一需要记住的就是，演绎论证中你能得到确定性，因为如果前提为真，结论必然为真，而在归纳论证中你得不到确定性，你只有概率性。这个前提给你一个可能相信它的理由：如果这个前提为真，那么这个结论可能为真，但它并非一定为真。而如果这个前提为真，那么这个结论甚至可能都不为真，对吧？

[段 14]

This is a very weak inductive argument. This gives you some reason for believing this, but not very much. Have a look at these. I’m going to give you a couple of minutes to do them on your own, so you really try and work this out for yourself. Decide which of those are deductive arguments and which of those are inductive arguments. and then we’ll have a look at them together. So the sun is coming out. Well, actually, let’s do them together. I think that’s probably easier at this point. Let’s have a look. The sun is coming out, so the rain should stop soon. Which is the conclusion of that argument? Oh, okay. Well, let’s do it the canonical way, shall we, just so we’ve all got it. Which is the conclusion of this argument? The rain should stop soon. That’s what we’re claiming. And the reason we’re giving for that claim is theis? The sun is coming out. So the premise is the sun is coming out, therefore the rain should stop soon. Now does the truth of that premise make the truth of the conclusion certain? No, you can’t have more or less certain, sorry. More or less probable but not more or less certain. Okay, so is it inductive or deductive? Put up your hands if you think it’s inductive. Yay! You see, I knew you got it really.

[译文 14]

这是一个相当弱的归纳论证。它给你一些相信这个结论的理由，但并不多。看一下这些题目。我给你们几分钟时间自己做一下，所以你们真的试着为自己解决这个。判断其中哪些是演绎论证，哪些是归纳论证。然后我们一起来看一下。太阳出来了，嗯，其实我们还是一起做吧。我觉得这个时候这样做可能更容易一些。我们来看一下。太阳出来了，所以雨应该很快就会停。这个论证的结论是什么？哦，好吧。那我们就用规范的方式来做，好吗，这样我们大家就都掌握了。这个论证的结论是什么？雨应该很快就会停。这就是我们所要主张的。而我们为这个主张给出的理由是什么？是太阳出来了。所以前提是太阳出来了，因此雨应该很快就会停。现在，那个前提为真是否使结论为真成为必然？不行，你不能说或多或少必然，对不起，只能说或多或少可能，但不能说或多或少必然。好的，所以它是归纳的还是演绎的？认为它是归纳的请举手。太棒了！看吧，我就知道你们真的掌握了。

[段 15]

Okay, good, that’s an inductive argument. What about this one? Let’s do it the canonical way. What’s the conclusion? Right, I’m going to make you do the things that I make undergraduate or used to make undergraduates do. Notice there’s, can you make that a proper sentence? John won’t be at the party, That’s right. It’s obvious what the sentence should be, isn’t it? So, OK, the conclusion is John won’t be at the party. And the premises are? Good. There are two premises here. One is Jane is at the party and the other is if Jane is at the party, John won’t be at the party. Notice that that’s a complex sentence that’s constituted of two sentences within the sentence. but you don’t separate those two to make them two different premises because this sentence being asserted is if Jane is at theBecause this sentence being asserted is, if Jane is at the party, John won’t be. That’s the premise. Good. Okay. So we’ve got an argument that goes, if Jane is at the party, John won’t be at the party. Jane is at the party. Therefore, John won’t be at the party. Is that deductive or inductive? Put up your hand if you think it’s inductive. Okay. Put up your hand if you think it’s deductive. Well done. Okay. So you are getting this. Okay. It’s just a sign up.

[译文 15]

好的，不错，这是一个归纳论证。那这个呢？我们用规范的方式来做。结论是什么？好的，我要让你们做我让本科生做的或者我过去让本科生做的那些事情。注意这里有，你能把它变成一个完整的句子吗？John won’t be at the party，对了。句子应该是什么，这很明显，对吧？所以，好，结论是 John won’t be at the party。那前提是什么？很好。这里有两个前提。一个是 Jane is at the party，另一个是 if Jane is at the party, John won’t be at the party。注意这是一个复合句子，由句子中包含的两个句子组成。但你不能把这两个分开作为两个不同的前提，因为这个被断言的句子是 if Jane is at the party, John won’t be。那就是前提。好的。好吧。所以我们得到一个论证是这样的：如果 Jane 在派对上，John 就不在派对上。Jane 在派对上。所以 John 不在派对上。这是演绎还是归纳？认为它是归纳的请举手。好。认为它是演绎的请举手。干得好。好的。所以你们已经掌握了这个。好的。这只是举手而已。

[段 16]

The house is a mess, therefore Lucy must be at home. What’s the conclusion? Just Lucy must be at home. The therefore just marks the conclusion rather than being the conclusion. Okay, Lucy must be at home. Premise, the house is a mess. Inductive or deductive? Put up your hand if you think inductive. Well done. Can you give me a counterexample to that argument? Yes, that’s right. Okay, so the house is a mess, but Lucy isn’t at home. You’ve had burglars instead. Good, okay. Either he’s in the bathroom or the bedroom. He’s not in the bathroom, so he must be in the bedroom. Conclusion’s obvious. He must be in the bedroom. And the two premises, either he’s in the bathroom or the bedroom, he’s not in the bathroom. Okay, deductive or inductive? Deductive. Well done. Okay, dog would have barked if it saw a stranger. it didn’t bark so it didn’t see a stranger it didn’tso it didn’t see a stranger. Deductive. Good. No one in Paris understands me, so my French must be rotten, or the Parisians are stupid. I got this from a book. Inductive. Okay, it’s difficult, that one, but it is inductive. You’re quite right, because what’s the conclusion? That’s right. It’s actually a complex conclusion, isn’t it? My French must be rotten, all the Parisians are stupid and the premise is no one in Paris understands me.

[译文 16]

屋子一团糟，所以 Lucy 一定在家。结论是什么？就是 Lucy 一定在家。因此这个词只是标示出结论，而不是结论本身。好的，Lucy 一定在家。前提是屋子一团糟。归纳还是演绎？认为归纳的请举手。干得好。你们能给这个论证举一个反例吗？是的，没错。好的，所以屋子一团糟，但 Lucy 不在家。倒是来了小偷。好的，不错。要么他在浴室，要么他在卧室。他不在浴室，所以他一定在卧室。结论很明显。他一定在卧室。两个前提是，要么他在浴室，要么他在卧室，他不在浴室。好的，演绎还是归纳？演绎。干得好。好的，狗如果看到陌生人就会叫。它没有叫，所以它没有看到陌生人。演绎。很好。巴黎没有人听得懂我说话，所以我的法语一定很差，或者巴黎人都很蠢。我是从一本书上看到的这个例子。归纳。好的，那个有点难，但它的确是归纳的。你们答得对，因为结论是什么？没错。它其实是一个复合结论，对吧？我的法语一定很差，所有巴黎人都很蠢，而前提是巴黎没有人听得懂我说话。

[段 17]

So it may be the case that if that’s true, these are true, but there are other reasons for nobody understanding me, aren’t there, as well? Okay, good. So you have actually got it, even if we got tied up in a few knots there. No, I’m not going to say all that. Right, logicians study deduction by studying valid argument forms. now here it’s very important to distinguish form from content okay arguments are deductively valid in virtue of their forms rather than their contents now that’s not true of all deduction but it’s true of most deduction so let’s have a look what I mean here all men are mortal Socrates is a man therefore Socrates is mortal okay all actions that produce the greatest happiness to the greatest number I got very bored writing it out so the greatestnumber, I got very bored writing it out, so the greatest happiness of the greatest number, all actions that produce the greatest happiness of the greatest number are right, morally right, that is. That action produced the greatest happiness of the greatest number, therefore that action was right. Okay, can you see that the form of those two arguments is exactly the same? Can you see that? So the content of the two arguments is quite different. This is an argument about Socrates and mortality, and this is an argument about morality and the greatest happiness of the greatest number.

[译文 17]

所以有可能的情况是，如果那个为真，这些就为真，但也可能有其他原因导致没有人听得懂我说话，对吧？好的，很好。所以你们其实已经掌握了，即使我们刚才在某些地方绕晕了。不，我并不打算把所有那些都说完。好的，逻辑学家通过研究有效的论证形式来研究演绎。现在这里非常重要的一点是要把形式和内容区分开。好的，论证之所以是演绎有效的，是凭借它们的形式而不是它们的内容。现在这并不是对所有演绎都成立，但对大多数演绎来说是成立的。所以我们来看看我这是什么意思。所有人都会死。苏格拉底是人。所以苏格拉底会死。好的，所有能产生最大多数人的最大幸福的行为，我在抄写的时候觉得很烦，所以最大多数人的最大幸福，所有能产生最大多数人的最大幸福的行为在道德上是正确的，那个行为产生了最大多数人的最大幸福，所以那个行为是正确的。好的，你们能不能看出这两个论证的形式是完全相同的？你们能看出来吗？所以这两个论证的内容是相当不同的。这是一个关于苏格拉底和死亡的论证，而这一个是关于道德和最大多数人的最大幸福的论证。

[段 18]

Completely different topics, completely different content, but each of the arguments has the same form. Can anyone try and write down the form? Tell me the form of that argument, the structure of it. Do you not know what I mean? No, okay. Let’s do it together. all A’s are B S is an A therefore S is a B did you get that? all A’s are B so A let’s do an interpretation here A equals let’s do it properly here X is a man X is mortal S is Socrates and the form of this is all A’s are B, S is an A, therefore S is a B. Are you with me? Let me do it again. Can you see on the side there? So if this is the interpretation, I’ve just changed the words for symbols here, and the symbols are only letters. So A of X says X is a man, X is mortal, is B, and S is Socrates. So all A’s are B. S is an A, therefore S is a B. You with me? So see if you can do that for the other argument. What would we have to say that A is there? Good. AX is A is an action. B, X is difficult. Go on. Produce, no, okay. All men are mortal. All actions that produce the greatest happiness, the greatest number are right.

[译文 18]

完全不同的主题，完全不同的内容，但每个论证都有同样的形式。有没有人能试着把形式写下来？告诉我那个论证的形式，它的结构。你们不知道我是什么意思吗？不知道，好的。那我们一起来做。所有的 A 都是 B，S 是 A，所以 S 是 B。你们听懂了吗？所有的 A 都是 B，所以 A，我们来做一个解释吧。A 等于，我们这里正规地来做。X 是一个人，X 是会死的，S 是苏格拉底，这个论证的形式是所有的 A 都是 B，S 是 A，所以 S 是 B。你们跟上我了吗？我再讲一遍。你们能看到旁边写的内容吗？所以如果这是解释，我刚才把词换成了符号，而这些符号只是字母。所以 X 的 A 表示 X 是一个人，X 是会死的，是 B，S 是苏格拉底。所以所有的 A 都是 B。S 是一个 A，所以 S 是一个 B。你们跟上我了吗？所以看看你能不能为另一个论证也这样做。我们得说 A 在那里是什么？很好。X 的 A 表示 A 是一个行为。B，X 是……继续。产生，不，好吧。所有人都会死。所有能产生最大多数人的最大幸福的行为都是正确的。

[段 19]

Okay, so actually A isn’t actions, is it? It’s actions that produce, no, not right actions. Actions that produce the greatest happiness, the greatest number. so all men are mortal and all actions that produce the greatest happiness the greatestAnd all actions that produce the greatest happiness, the greatest number, are right. You with me? So all A’s, all men, are B’s, mortal. All A’s, actions that produce the greatest happiness, the greatest number, are right. Okay, and then the next one. That action produced the greatest happiness, the greatest number. You’ve got Socrates here is a particular thing, just as that action is a particular thing, okay? And you’re saying that particular thing is a man, i.e. falls into this class here, and therefore he falls into the other class too, okay? So both those arguments have the form all A is a B, S is an A, therefore S is a B. Now, the point of this is just to get you to distinguish form and content. Can you see that an argument can have different forms and yet the same content? Sorry, different contents and yet the same form. Okay, so these are two arguments of exactly the same form, different contents. What’s important about this is that logic is topic neutral. Once you’ve learnt how to do logic, it doesn’t matter what you’re doing it with or on, it’s always the same.

[译文 19]

好的，所以其实 A 不是 actions（行动），对吧？它是产生最大幸福的行动，不是，不是 right actions（正确的行动）。是产生最大幸福、最大多数的行动。所以 all men are mortal（所有人都会死）以及 all actions that produce the greatest happiness, the greatest number, are right（所有产生最大幸福、最大多数的行动都是正确的）。你们跟上我了吗？所以所有 A，即 actions that produce the greatest happiness, the greatest number（产生最大幸福、最大多数的行动），都是 right（正确的）。好，那下一个。That action produced the greatest happiness, the greatest number（那个行动产生了最大幸福、最大多数）。这里 Socrates（苏格拉底）是一个 particular thing（个别的事物），正如 that action（那个行动）也是一个个别的事物，对吧？而你是在说，那个个别的事物是一个 man（人），也就是说它属于这个 class（类），因此它也属于另一个 class（类），对吧？所以这两个论证的形式都是 all A is a B, S is an A, therefore S is a B（所有 A 是 B，S 是 A，因此 S 是 B）。现在，这样做的目的就是让你们区分 form（形式）和 content（内容）。你们能看到一个论证可以有不同的 content（内容）却具有相同的 form（形式）吗？抱歉，是不同的 contents（内容）却具有相同的 form（形式）。好，所以这两个论证是 exactly the same form（完全相同的形式），却有不同的 contents（内容）。这一点的重要性在于 logic is topic neutral（逻辑是主题中立的）。一旦你学会了怎么做 logic（逻辑），你用它在什么上面、做什么内容都没关系，它总是相同的。

[段 20]

Logic is the same whether you’re talking about the colour of chairs, whether you’re talking about biochemistry, whether you’re talking about biochemistry, whether you’re talking about the philosophy of time, it doesn’t matter what you’re talking about. If an argument is valid, it’ll be valid by virtue of its form, whatever the topic is you’re talking about. So logic is the ultimate transferable skill. If you’ve learnt logic, you can do it with whatever you happen to be talking about, whatever it is you’re interested in, whether it’s art history or fashion. right okay let’s have a look at a few argument forms here’s a valid argument form if p then q p therefore q what’s p standing in for here what type of thing is it standing in for can anyone tell me a good or a sentence i was going to say but a premise is even better yes well done. So this is one sentence, what’s this? No, no not even that, it’s a, oh actually I’ve, that’s a premise, actually that’s a premise, that’s only a sentence. Can you see why? That’s right, okay, so if p then q is one premise, p is the other premise and q is the conclusion. So all we’ve done there instead of thinking about actual sentenceswe’ve done there, instead of thinking about actual sentences, we’ve just put in what are called sentence letters.

[译文 20]

Logic（逻辑）是一样的，无论你谈论的是椅子的颜色、biochemistry（生物化学）、biochemistry（生物化学）、还是关于时间的哲学，你谈论什么都不重要。如果一个 argument（论证）是 valid（有效的），它将凭借它的 form（形式）而有效，无论你谈论的主题是什么。所以 logic（逻辑）是 ultimate transferable skill（终极的可迁移技能）。如果你学会了 logic（逻辑），你就可以用它来讨论你碰巧在谈的任何东西，你感兴趣的任何东西，无论是 art history（艺术史）还是 fashion（时尚）。好的，我们来看几个 argument forms（论证形式），这里有一个 valid argument form（有效的论证形式）：if P then Q, P, therefore Q（如果 P 那么 Q，P，因此 Q）。P 在这里代表什么？它代表哪种类型的东西？谁能告诉我一个 good 或者 a sentence（句子）？我本来要说，但 premise（前提）更好。是的，说得好。所以这是一个 sentence（句子），这是什么？不不，甚至不是那个，它是 a，哦其实我，那是 premise（前提），其实那是 premise（前提），那只是一个 sentence（句子）。你能看出为什么吗？对了，所以 if P then Q 是一个 premise（前提），P 是另一个 premise（前提），Q 是 conclusion（结论）。所以我们所做的不是去想实际的句子，我们只是放入了所谓的 sentence letters（句子字母）。

[段 21]

Any letter will do, it doesn’t matter, just so long as you get the form of the argument right. Can you think of an argument that fits that form? Okay, just think for yourself now of an argument that fits that form. You could use one that we’ve already used, you could use one to do with the colours of the chair in this room. Quite difficult, but see if you can think of one. go on try it if I’m happy then I can sleep I am happy therefore I will sleep give her a clap well done that’s exactly right can anyone think of another one all miracles no there’s no all there no just the impossible cannot happen If the impossible cannot happen, then? Miracles are impossible. No, you’re not quite getting the idea here. Now, this will be happening to lots of you. This is not just you. The form is if sentence, then sentence, sentence, therefore sentence. And these two have got to be the same sentence, and these two have got to be the same sentence. So the form of this has got to be if P, then Q, P, therefore Q. Think of another one. Think to yourselves first.Q. Think of another one. Think to yourselves first and then when you feel confident that you’ve got it, put your hands up and we’ll try.

[译文 21]

任何字母都可以，没关系，只要你把 argument（论证）的 form（形式）弄对就行。你能想出一个符合那个 form（形式）的 argument（论证）吗？好，现在自己想一个符合那个 form（形式）的 argument（论证）。你可以用一个我们已经用过的，你也可以用一个关于这个房间里椅子颜色的。挺难的，但看看你能不能想出一个。来试试。If I’m happy then I can sleep, I am happy, therefore I will sleep（如果我开心，那么我能睡着，我开心，因此我会睡着）。给她鼓掌。做得完全正确。还有谁能想到另一个？All miracles，no，没有 all 在那里，没有。只是 the impossible cannot happen（不可能的事不会发生）。If the impossible cannot happen, then?（如果不可能的事不会发生，那么？）Miracles are impossible（奇迹是不可能的）。不，你还没完全理解这个 idea（点子）。现在，这种事会发生在你们很多人身上。这不只是你一个人。The form（形式）是 if sentence, then sentence, sentence, therefore sentence（如果句子，那么句子，句子，因此句子）。这两个必须是同一个 sentence（句子），这两个也必须是同一个 sentence（句子）。所以这个的 form（形式）必须是 if P, then Q, P, therefore Q（如果 P，那么 Q，P，因此 Q）。再想一个。先自己想一想，然后当你觉得自己想好了，就举手，我们来试试。

[段 22]

This is really doing logic. If you’re finding it hard, that’s right, it’s in the nature of the beast. Are you? Well, sit down and think for yourself and then try again. No, you’ve just said, oh, no, you didn’t. No, it’s OK. Go on. You say one. If blue chairs are comfortable and the chairs are blue, then blue chairs are comfortable. No, that was an if P and Q, wasn’t it? And we’re looking for an if P then Q. These words that are left are the logical words. and it’s getting the logical words right, if, then, and, or, not, that’s hugely important. Have you got one? If he gets the bus, then he will be eco-friendly. He gets the bus, then he’s eco-friendly. Good, okay. If he gets a bus, then he’s eco-friendly. He does get a bus, therefore he’s eco-friendly. Good, well done. Paul? If it rains, I raise an umbrella. My umbrella is up, therefore it is ruined.Oh, there’s something wrong with that. What was wrong with it? Now, the sentences were great. Say it again, though. Okay, so P is it is raining. Okay, and Q is I raised an umbrella. Now, was P my umbrella is up? What was P? It’s raining. So what do you need there instead? It is raining. Then for your brother, do you see, what you were doing there is you were committing the fallacy of affirming the consequence.

[译文 22]

这就是在真正做 logic（逻辑）了。如果你觉得很难，那是对的，这是题中应有之义。你是吗？好，坐下来自己想想，然后再试。不，你刚才说的是，哦，不，你没有说。没关系。继续。你说一个。If blue chairs are comfortable and the chairs are blue, then blue chairs are comfortable（如果蓝色的椅子是舒服的，并且椅子是蓝色的，那么蓝色的椅子是舒服的）。不，那是 if P and Q（如果 P 且 Q），对吧？我们要找的是 if P then Q（如果 P 那么 Q）。剩下的这些 words（词）是 logical words（逻辑词）。把 logical words（逻辑词）弄对很重要——if（如果）、then（那么）、and（并且）、or（或者）、not（不是）——这非常重要。你想出来了吗？If he gets the bus, then he will be eco-friendly（如果他坐公交车，那么他将是环保的）。He gets the bus, then he’s eco-friendly（他坐公交车，因此他环保）。好，不错。If he gets a bus, then he’s eco-friendly（如果他坐公交车，那么他环保）。He does get a bus, therefore he’s eco-friendly（他确实坐了公交车，因此他环保）。好，做得好。Paul（保罗）？If it rains, I raise an umbrella（如果下雨，我撑伞）。My umbrella is up, therefore it is ruined（我的伞撑起来了，因此它坏了）。哦，这里有什么地方不对。哪里不对呢？现在，句子本身很好。再说一遍。好，所以 P 是 it is raining（正在下雨）。好，Q 是 I raised an umbrella（我撑了伞）。那么 P 是 my umbrella is up（我的伞撑起来了）吗？P 是什么？It is raining（正在下雨）。所以你那里需要换成什么？It is raining（正在下雨）。然后对你 brother（兄弟）来说，你看到了吧，你刚才做的事情是你犯了 affirming the consequence（肯定后件）的 fallacy（谬误）。

[段 23]

Very common fallacy. We’ll do fallacies next week, I think. But do you see, it has to be, you have to have the letters in the right order. Because what you gave me initially wasn’t a valid argument. but a valid argument could easily be made from it just by transposing those. Do you have another one? I do. I hope this is right. If it’s sunny, then I’ll take my dog for a walk. It’s sunny, so I’m taking my dog for a walk. Therefore, I’ll take my dog for a walk. Exactly. So P is, it is sunny. Q is, I’m taking my dog for a walk. And the argument is, if it’s sunny, then I’m taking my dog for a walk. It is sunny. Therefore, I’m taking my dog for a walk. Okay? Now, that has to be valid, doesn’t it? Sorry, thatNow that has to be valid, doesn’t it? Sorry, if those premises are true, that conclusion has to be true, because any argument of this form must be a good argument. It’s deductively valid. Anyone else want to try another one? If the postman is striking, then we will have no letters. Good, okay. If the postman is striking, then we will have no letters. The postman are striking, therefore we’ll have no letters. So P is the postman striking. No, not if, because the if, okay, the postman striking.

[译文 23]

非常常见的 fallacy（谬误）。我们下周会讲 fallacies（谬误），我想。但你看到了，它必须，你必须把字母按正确的 order（顺序）排列。因为你一开始给我的不是一个 valid argument（有效的论证）。但只要把那些 transposing（调换）一下，就可以很容易地使它成为一个 valid argument（有效的论证）。你有另一个吗？我有。我希望这是对的。If it’s sunny, then I’ll take my dog for a walk（如果是晴天，我会带我的狗去散步）。It’s sunny, so I’m taking my dog for a walk（是晴天，所以我带我的狗去散步）。Therefore, I’ll take my dog for a walk（因此，我会带我的狗去散步）。正是如此。所以 P 是 it is sunny（是晴天）。Q 是 I’m taking my dog for a walk（我在带我的狗去散步）。这个 argument（论证）是，if it’s sunny, then I’m taking my dog for a walk（如果是晴天，那么我在带我的狗去散步）。It is sunny（是晴天）。Therefore, I’m taking my dog for a walk（因此，我在带我的狗去散步）。对吧？现在，那必须是 valid（有效的），不是吗？抱歉，那现在那必须是 valid（有效的），不是吗？抱歉，如果那些 premises（前提）是真的，那个 conclusion（结论）必须是真的，因为任何这种 form（形式）的 argument（论证）都一定是一个 good argument（好的论证）。它是 deductively valid（演绎有效的）。还有谁想再试一个？If the postman is striking, then we will have no letters（如果邮递员在罢工，那么我们将没有信件）。好，不错。If the postman is striking, then we will have no letters（如果邮递员在罢工，那么我们将没有信件）。The postman are striking, therefore we’ll have no letters（邮递员在罢工，因此我们将没有信件）。所以 P 是 the postman striking（邮递员罢工）。不，不是 if，因为 if，好的，the postman striking（邮递员罢工）。

[段 24]

And Q is we will have no letters. So if the postman is striking, then we’ll have no letters. The postman are striking, therefore we’ll have no letters. Good. Okay, one more, and then we’ll move on. If he’s breathing, he’s alive. This is looking good. That’s right. If he’s breathing, then he’s alive. He is breathing, therefore he’s alive. Okay? Yeah, good. Okay, it’s dead easy, isn’t it, once you get the idea of it? And here’s the… Sorry, say that again. Like the third parrot. Oh, the dead parrot. Yes, I’m sure we could make one there. Here we are. If there are no chance factors in chess, then chess is a game of skill.chance factors in chess, then chess is a game of skill. There are no chance factors in chess, therefore chess is a game of skill. What’s P here? No chance factors in chess. Good. What’s Q? Chess is a game of skill. Good. Well done. Here’s another argument. Okay, that was modus ponens, by the way. So you now have to do modus ponens. Here’s modus tollens, the mode of denial. if P then Q not Q therefore not P if P then Q not Q therefore not P so this is saying in effect that P is sufficient for Q sorry have I got it the wrong way round No, I have got it the right way round.

[译文 24]

Q 是 we will have no letters（我们将没有信件）。所以 if the postman is striking, then we’ll have no letters（如果邮递员在罢工，那么我们将没有信件）。The postman are striking, therefore we’ll have no letters（邮递员在罢工，因此我们将没有信件）。好。再来一个，然后我们就继续。If he’s breathing, he’s alive（如果他在呼吸，他是活着的）。这看起来很好。对的。If he’s breathing, then he’s alive（如果他在呼吸，那么他是活着的）。He is breathing, therefore he’s alive（他在呼吸，因此他是活着的）。对吧？嗯，好。一旦你 get the idea of it（掌握了它的要点），是不是 dead easy（简单得要死）？这里是……抱歉，再说一遍。像 the third parrot（第三只鹦鹉）。哦，the dead parrot（死了的鹦鹉）。是的，我确信我们能在那里做一个。在这里。If there are no chance factors in chess, then chess is a game of skill（如果 chess（国际象棋）中没有 chance factors（偶然因素），那么 chess（国际象棋）是一个 game of skill（技巧游戏））。There are no chance factors in chess（chess（国际象棋）中没有 chance factors（偶然因素）），therefore chess is a game of skill（因此 chess（国际象棋）是一个 game of skill（技巧游戏））。P 是什么？No chance factors in chess（chess（国际象棋）中没有偶然因素）。好。Q 是什么？Chess is a game of skill（国际象棋是一个技巧游戏）。好。做得好。这里是另一个 argument（论证）。好，by the way（顺便说一下），那是 modus ponens（肯定前件式）。所以你们现在要做 modus ponens（肯定前件式）。这里是 modus tollens（否定后件式），the mode of denial（否定的方式）。if P then Q, not Q, therefore not P（如果 P 那么 Q，不是 Q，因此不是 P）。If P then Q, not Q, therefore not P（如果 P 那么 Q，不是 Q，因此不是 P）。所以这实际上是在说 P is sufficient for Q（P 是 Q 的充分条件）。抱歉，我是不是写反了？不，我写的是对的。

[段 25]

It’s, what we’re saying is here is that Q is necessary for P, and so if Q isn’t the case, then P isn’t the case either. Well, let’s have a look at the example, and then you can come up with your own. Actually, this example is wrong, because that shouldn’t be in there. But let’s do it. If the dog didn’t know the visitor well, the dog would have barked.didn’t know the visitor well, the dog would have barked. Okay? The dog didn’t bark, therefore the dog did know the visitor. That shouldn’t be in there. That’s the one that I was saying I’d got wrong before we started. So if you take that knot out, I won’t draw on the screen there. So on your handouts, make sure that you take that knot out on slide 16. Write that down now. I think it’s 16. Yep. Because that’s incorrect. But do you see how that argument is valid? if it’s true that if the dog didn’t know the visitor well the dog would have barked, it’s a good guide dog guard dog, not guide dog it didn’t bark, therefore it must have known the visitor well, mustn’t it so see if you can come up with something of that form now I’ll take the example out so it’s not confusing you, have you come up with one already?

[译文 25]

我们在这里要说的是，Q 是 P 成立的必要条件，所以如果 Q 不成立，那么 P 也不成立。好，我们来看一下这个例子，然后你们可以自己想一个。其实，这个例子是错的，因为那个不应该出现在里面。但我们还是来做一下。如果这只狗不太熟悉来访者，它就会叫。如果这只狗不太熟悉来访者，它就会叫。好吗？这只狗没有叫，所以这只狗是认识这位来访者的。那个不该出现在那里。那就是我刚才在课开始前提到的我弄错的那个。所以如果你把那个结去掉，我就不会在屏幕上画了。所以你们的讲义上，务必在第 16 张幻灯片上把那个结去掉。现在记下来。我想应该是第 16 张。是的。因为那个是错的。但是你们能看出来这个论证是怎么有效的吗？如果"如果狗不太熟悉来访者，狗就会叫"是真的，这是一只很好的看门狗，不是导盲犬，它没有叫，所以它一定是认识这位来访者的，对吧？现在你们能不能想出一个那种形式的我把那个例子去掉，这样就不会让你们困惑了，你们已经想出来了吗？

[段 26]

Yeah, if I have money, I’ll go to the pub. I’m not in the pub, therefore I have no money. Well done. Fantastic. Absolutely right. So P is I have money. Q is I would be in the pub. Is that right? I’m not in the pub, therefore I have no money. If I had money, so having money would be sufficient for you to be in the pub, okay? but you’re not in the pub therefore you haven’t got any money. Okay, anyone else want to have a go? Gentleman there. Good, you’ve got it I think. Does anyone else want to have a go or does everyone feel that they’ve got that? What was it? Sorry, say it again. If the sun is out, I will take my dog for a walk. Okay, so P is the sun is out, and Q is I’ll take my dog for a walk. The sun is not out. Ah, I’m sorry. Those of you who saw the error, that’s quite right. Okay, what should be here? I’m not taking my dog for a walk. I’m not taking my dog out for a walk. Therefore, the sun is not out. Yep, that’s right. Good. Okay, try one more then as we got that, as I got that wrong. Yes, okay. No, we had not in the wrong place there, didn’t we? How did it go again?

[译文 26]

好，如果我有钱，我就去酒吧。我不在酒吧，所以我没钱。答得好。非常棒。完全正确。所以 P 是"我有钱"，Q 是"我在酒吧"。对吗？我不在酒吧，所以我没钱。如果我有钱，有钱是你去酒吧的充分条件，对吧？但是你不在酒吧，所以你没有钱。好，还有谁想试试？那边的那位先生。很好，我觉得你答对了。还有其他人想试试吗，或者大家都觉得自己已经掌握了？是什么？抱歉，再说一遍。如果太阳出来了，我就带我的狗去散步。好，所以 P 是"太阳出来了"，Q 是"我会带我的狗去散步"。太阳没有出来。啊，抱歉，你们当中看出错误的人，说得完全对。好，这里应该是什么？我没有带我的狗去散步。我没有带我的狗出去散步。所以，太阳没有出来。是的，没错。好，既然我搞错了，我们再试一个吧。好。我们刚才把 not 放错位置了，不是吗？那个例子是怎么说的来着？

[段 27]

If I’m hungry, then I won’t concentrate. I’m not concentrating. I can’t concentrate. I’m hungry. it would be hang on we’ll write this one down becauseHang on, we’ll write this one down because there are knots in there that we need to get right. Okay, so P is I am hungry. Q is I can’t concentrate. Okay, notice that we’ve changed Q. Q is actually a negative here. That’s where it’s very easy to get tied up. So be very careful of this. Negatives immediately make things quite difficult. But never mind, we can do it. Okay, so Q is I can’t concentrate. Now, not Q, therefore, is I can concentrate. Therefore, I’m not hungry. Are you with me? Do you see how that works? So you had the right sentences. You were just not using the negatives in the right way. I’ve forgotten who said this, so I’m looking at all the wrong people. Okay, one more on this one because it’s quite difficult. Paul. Oh, actually, we’ve had you, Paul. So did we have you before? Okay. Good. Okay, if I catch my train. No, sorry, start again. If I miss my train, I’ll be late. I’m not late. therefore I haven’t missed my trainTherefore, I haven’t missed my train. Can you say, well, I’ve caught my train, but you have to use the same… You don’t have to use the same words as long as you…

[译文 27]

如果我饿了，我就无法集中注意力。我无法集中注意力。我无法集中注意力。我饿了。等一下，我们把这个写下来因为这里有需要理清楚的结。好，所以 P 是"我饿了"。Q 是"我无法集中注意力"。好，注意我们把 Q 改了。Q 这里实际上是一个否定。这就是很容易被绕进去的地方。所以一定要非常小心。否定会让事情立刻变得相当困难。但没关系，我们可以做出来。好，所以 Q 是"我无法集中注意力"。那么非 Q 就是"我可以集中注意力"。所以我不是饿了。你们跟上我了吗？你们能看到这是怎么运作的吗？你们给出的句子是对的。你们只是没有正确使用否定。我已经忘了这是谁说的了，所以我看错了人。好，关于这个再做一个，因为这挺难的。Paul。哦，其实我们已经点过你了，Paul。那我们之前点过你吗？好。很好。好，如果我赶上火车。不，抱歉，重新开始。如果我误了火车，我就会迟到。我没有迟到。所以我没有误火车。所以我没有误火车。你可以说，好吧，我赶上了火车，但是你必须使用相同的……你不必使用相同的词，只要这些词……

[段 28]

Now, this is actually an important point. You don’t have to use the same words as long as the words have the same meaning. Or, do you see what I mean? But it’s a very… When you’re learning logic, it’s a very good idea to use the same words because it cuts out one area of complication. Do you see that? Why change your language when what it’s going to do is confuse you? Keep things as simple as possible. This is quite hard enough without adding layers of complication in. Okay, good, you did that well. So what have I got? Oh, well, we’ve already tried that. Good, let’s try another one. This is a disjunctive syllogism. P or Q, not P, therefore Q. Okay, have a go at that one. P or Q not P therefore Q okay oh good look at you hands going up immediately now It’s either raining or it’sBrilliant. Okay, it’s either raining or it’s sunny. It’s not raining, therefore it’s sunny. Good, well done. One at the back there. Good, well done. Anyone else? Good, okay. I think you’ve got it one. Good, well done. OK, you’ve got notice that that works if you’ve got an exclusive or because or is actually an ambiguous word in English. It can mean either or or it can mean not both. And if this was either, this has got to be either or, hasn’t it?

[译文 28]

现在，这其实是一个重要的观点。你不必使用相同的词，只要这些词的意思相同就行。或者，你们明白我的意思吗？但这是非常……当你学习逻辑的时候，使用相同的词是一个非常好的主意，因为它省去了一层复杂性。你们看出来了吗？为什么要换一种说法，结果只会让你更困惑呢？把事情尽可能保持简单。这已经够难了，不用再增加一层复杂性。好，很好，你们做得不错。那我手里还有什么？哦，好吧，那个我们已经试过了。好，我们再试一个。这是析取三段论。P 或 Q，非 P，所以 Q。好，试一下这个。P 或 Q，非 P，所以 Q，好，哦，太棒了，看你们立刻都举手了现在是下雨还是……非常棒。好，要么在下雨，要么是晴天。没有下雨，所以是晴天。很好，做得好。后排那位。很好，做得好。还有其他人吗？好，好。我觉得你们已经掌握了。很好，做得好。好，你们已经注意到这能成立是因为你们用的是排斥性的"或"，因为"or"在英语中其实是个歧义词。它可以表示"二选一"，也可以表示"不能两者兼有"。而如果这里是"二选一"，那就必须是"二选一"，对吧？

[段 29]

Because if it were not both, you couldn’t get the conclusion, could you? so that’s where English can lead us astray a little bit because English is itself ambiguous okay here’s my example this is actually a Bertrand Russell example either we hope for progress through improving morals or we hope for progress through improving intelligence we can’t hope for progress through improving morals therefore we must hope for progress through improving intelligence what this should tell you incidentally we’ve been looking at very simple ones but actually these forms can be very complicated. One of the things I’m going to ask you to do this weekvery complicated. One of the things I’m going to ask you to do this week while you’re at home is when you read your newspaper, you listen to your television or argue with your friends in the pub or whatever you happen to do, I want you to try and identify arguments that come up. Whenever you hear the words if, then, and, or, not, if and only if, all these logical words, all is. Lovely, logical words. You’ve got to be sensitised to them this week because I want you to hear you. Every time you hear an if-then, I want you identifying the form of the argument in which you find it. Of course, it might not be in an argument, might it?

[译文 29]

因为如果不是"不能两者兼有"，你就得不出这个结论，对吧？所以这就是英语可能会把我们引入歧途的地方，因为英语本身是有歧义的，好，这是我的例子，这其实是罗素的一个例子要么我们希望通过改善道德来取得进步，要么我们希望通过改善智力来取得进步我们不能希望通过改善道德来取得进步所以我们必须希望通过改善智力来取得进步顺便说一下，这应该让你们明白我们一直在看的是非常简单的形式，但实际上这些形式可以非常复杂。本周我要让你们做的一件事之一是……非常复杂。本周我要让你们做的一件事之一是，当你们在家的时候，当你们看报纸、看电视或者在酒吧里和朋友争论，或者无论你们碰巧在做什么，我想让你们试着去识别出现的论证。每当你们听到"如果"“那么"“并且"“或者"“不是"“当且仅当”，所有这些逻辑词，全部都是。可爱的逻辑词。这一周你们必须对它们敏感起来，因为我想让你们听到。每当你们听到一个"如果—那么”，我都希望你们能识别出你们所找到的论证形式。当然了，它可能不是在一个论证里，对吧？

[段 30]

It might be just a freestanding assertion. But have a look, see if there is an argument there. I’m just getting a bit lost there, Marianne. The second paragraph, is that an assertion? Second sentence. Is that an assertion? Yes. Each of the premises is an asserted sentence, a sentence that’s being asserted, isn’t it? So Russell is saying, you know, it’s true that either we hope for progress this way or we hope for it this way. Okay, there’s no other option. We can’t hope for it this way, he’s asserting. Therefore, we must hope for it that way. Okay? what’s incorrect is that there’s a higherHang on, what’s false here? So is it the first premise? Let’s start to use the language now. Is it the first premise that’s false or the second? Well, improving intelligence isn’t a sentence. And it appears here and here. So what? So is that the false premise or that one? intelligence can improve moral progress. Right. I think I’m going to put this on one side because A, we’re not really looking at the truth of the premises and B, you’ve got to take the premises as they are here. This is what’s being asserted. So we’re not saying this is true or that this is true. What we’re saying is if this is true and this is true, then this must be true.

[译文 30]

它可能只是一个独立的断言。但可以看一看，看看那里是不是有一个论证。Marianne，我有点跟不上了。第二段，那是一个断言吗？第二句。那是一个断言吗？是的。每一个前提都是一个被断言的句子，一个正在被断言的句子，不是吗？所以罗素在说，你知道的，要么我们希望以这种方式取得进步，要么我们希望以那种方式取得进步，这是真的。好，没有其他选项了。他断言，我们不能以这种方式希望取得进步。所以，我们必须以那种方式希望取得进步。好吗？这里错误的是有一个更高……等一下，这里什么是假的？那这是第一个前提是假的吗？我们现在开始使用这套术语吧。是第一个前提是假的还是第二个前提是假的？嗯，“improving intelligence"不是一个句子。它在这里和这里出现了。所以呢？所以那是假的前提还是那个？智力的提升能推动道德进步。对。我想我暂时把这个放一边，因为第一，我们其实不是在考察前提的真假，第二，你们必须把这些前提就当作它们在这里写的那样来看。这才是正在被断言的内容。所以我们不是说这个是真的，或者说那个是真的。我们在说，如果这个是真的，而且这个是真的，那么这个就必须是真的。

[段 31]

Okay. These conditionals are very important. Where does presupposition and biases come from when we identify an argument? Presupposition of what? And biases. We’ll get on to that later on. So what I want to get us now, just sensitising us now to deduction and induction and to the form of an argument. That’s what we need to get today. Okay, let’s move on. Here’s another one, Leibniz law. A is F. A equals B. Therefore, B is F. I’ll giveB, therefore B is F. I’ll give you my example of that because it’s quite a difficult one. Jane is tall. Jane is the bank manager. Therefore, the bank manager is tall. If these are true, is that true? Has to be, doesn’t it? Can’t be anything else. Go on, think of a couple of examples of that one. Go for it. Dog’s bark. No. Don’t think it’s going to work. Why is that not going to work? Let’s see. Why is this not going to work? Because it’s too generic. Well, dog’s bark doesn’t have the form A is F. A is F is the chair is blue. Marianne is tall. The board duster is lost, et cetera. Not dog. You could say the dog is barking, but dog’s bark is saying of one class of things that they fit another class of things. And that’s not the form of that sentence, is it?

[译文 31]

好的。这些条件句非常重要。当我们识别一个论证时，前设和偏见从何而来？关于什么的前设？还有偏见。我们稍后会讲到这些。所以我现在想让我们做的，只是让我们对演绎和归纳以及论证的形式变得敏感。这就是我们今天需要掌握的内容。好的，我们继续。这里还有一个例子，莱布尼茨律。A 是 F。A 等于 B。因此，B 是 F。我给你们举个例子，因为这个相当难。简很高。简是银行经理。因此，银行经理很高。如果这些前提为真，那么结论为真吗？必然如此，不是吗？不可能是别的。继续，想几个这样的例子试试。开始吧。狗会叫。不行。我觉得这行不通。为什么行不通呢？我们来看看。为什么这个行不通？因为它太笼统了。嗯，狗会叫并不符合"A 是 F"这种形式。A 是 F 应该是"这把椅子是蓝色的”、“玛丽安很高”、“黑板擦不见了"等等。不是狗。你可以说"这只狗正在叫”，但"狗会叫"是在说某一类事物属于另一类事物。而这不是那个句子的形式，对吧？

[段 32]

I don’t know, but could you say chair is blue, this chair is comfortable, therefore this chair is… Go on. Not quite, no. So what we’ve got here, this is a very interesting ambiguity here. Is is a very slippery word in English. Is you can have the is of predication. Predication.and the is of identity. And your attempted argument there, and don’t worry about this at all, this is a perfectly reasonable mistake to make, you equivocated between these two ises. So you said this chair is blue, is that right? Then you said this chair is comfortable. okay, now this well actually those are both is of predication aren’t they whereas what we’re looking for here is of identity isn’t it A is B is the very same thing as B so here we’ve got a predication haven’t we, A is F A has a certain property and here we have and this thing A is the same thing as this thing B, therefore B is F. Do you see how that has to be true? It’s a law of logic, this one, isn’t it? This is Leibniz law. It is a law of logic. If A is F, if Marianne is tall, I’m just giving you the same example, so let me give it to you. If Jane is tall and Jane is the bank manager, here’s an is of predication so we’re predicating tallness of Jane aren’t we, are you with me? andJane, aren’t we?

[译文 32]

我不知道，但你能不能说"这把椅子是蓝色的，这把椅子很舒服，因此这把椅子是……"。继续。不太对，不是。所以我们这里有的是，这里有一个非常有趣的歧义。“是"在英语中是一个非常滑头的词。“是"可以是谓述性的"是”。谓述。和等同的"是”。你刚才尝试的那个论证，不用在意，这完全是一个合理的错误，你在这两种"是"之间产生了歧义。所以你说"这把椅子是蓝色的”，对吧？然后你说"这把椅子很舒服”。好的，现在这其实两者都是谓述性的"是”，对吧，而我们这里要找的是等同的"是"，不是吗？“A 是 B"就是说 B 与 A 是同一个东西。所以这里我们有一个谓述，对吧，A 是 F，A 具有某种属性，然后这里我们有，这个事物 A 与这个事物 B 是同一个，因此 B 是 F。你们看这为什么必然为真吗？这是一条逻辑规律，不是吗？这就是莱布尼茨律。它是一条逻辑规律。如果 A 是 F，如果玛丽安很高，我给你们同样的例子，让我再说一遍。如果简很高，而且简是银行经理，这里是一个谓述性的"是”，所以我们是把"高"这个属性归于简，对吧，你们跟上我了吗？以及……简，对吧？

[段 33]

Are you with me? And here we’ve got the is of identity, haven’t we? Jane is the bank manager. Okay? If that’s true and that’s true, that has to be true, doesn’t it? Because the bank manager is Jane, isn’t she? Yes, that’s exactly, that’s what we’re doing. We’re looking at examples of deductively valid arguments. Arguments that are valid by virtue of their form. Okay, good. One last one, I think. Here’s a syllogism. Now, this should be easy. All Fs are G. A is an F, therefore A is a G. All Fords are cars. Okay, A is a Ford, therefore A is a car. Yeah, well done. That’ll do. Anyone else want to give one more example and we’ll move on? Good. I see where you’re getting to. Yeah, the grammar got a bit mixed up, but yes, okay. So all my clothes are wet. That pair of jeans is one of my clothes, sort of. Therefore, it is wet. I see where you’re coming from. Okay. You’ve got one. Okay. All miracles are impossible. Resurrection is a miracle. Okay. It works, doesn’t it? Well done. We knew we’d get there somewhere. incidentally let me just give you a logical problem with that just because I think you might enjoy itgive you a logical problem with that just because I think you might enjoy it. You said the resurrection is a miracle therefore the resurrection is impossible.

[译文 33]

你们跟上我了吗？而且这里我们有一个等同的"是"，对吧？简是银行经理。好吗？如果这是真的，而且这是真的，那么这必然是真的，不是吗？因为银行经理就是简，不是吗？是的，正是如此，我们做的就是这些。我们在考察演绎有效论证的例子。这些论证是凭借其形式而有效的。好的，很好。最后一个，我认为。这是一个三段论。嗯，这应该很简单。所有 F 都是 G。A 是一个 F，因此 A 是一个 G。所有福特都是汽车。好，A 是一辆福特，因此 A 是一辆汽车。是的，干得好。够了。还有谁想再举一个例子？然后我们就继续。好的。我知道你想说什么了。是的，语法有点乱，但是的，好吧。那么我所有的衣服都湿了。那条牛仔裤是我的一件衣服，算是吧。因此，它是湿的。我明白你的意思了。好的。你有了一个。好的。所有奇迹都是不可能的。复活是一个奇迹。好的。它成立，不是吗？干得好。我们就知道我们能达到那里。顺便说一句，让我就那个给你们一个逻辑难题，因为我猜你们可能会喜欢。你们说复活是一个奇迹，因此复活是不可能的。

[段 34]

There’s something very logically fishy about negative true negative existential sentences isn’t there. If we say Pegasus doesn’t exist aren’t we picking out something by the word Pegasus in order to say of it that it doesn’t exist. In which case, how can a negative existential be true? See what I mean? Hamlet doesn’t exist. You’re picking out something, Hamlet, in order to say of him that he doesn’t exist. Well, how can you do that? You shouldn’t be able to do that. I’ll just leave you with a little conundrum because that’s philosophical logic and we’re not doing that here. We’re doing symbolic logic here. So now you know of two different types of logic. Okay, there’s the canonical example for that one, all men are mortal, da-da-da-da. Now, I said that some arguments are deductively valid, but not in virtue of their form. Here are just a couple that are valid in virtue of their content, apparently. Deontic logic, now this is cutting-edge stuff. We know very little about deontic logic. Logic, deontic logic is the logic of morality. Okay? What we’re trying to look at is,okay what we’re trying to look at is the area of discourse in which we talk about morality and say how does it work logically how can we get a valid argument form from a talk of morality now look at this argument lying is wrong therefore we shouldn’t lie now that looks like a deductively valid argument, doesn’t it?

[译文 34]

关于否定的真否定存在句，有一些非常奇怪的逻辑问题，不是吗？如果我们说"佩加索斯不存在"，我们不是在用"佩加索斯"这个词指称某物以便说它不存在吗？如果是这样，一个否定存在句怎么可能为真呢？明白我的意思吗？“哈姆雷特不存在”。你是在用"哈姆雷特"指称某物，以便说他不存在。可是，你怎么能这样做呢？你应该做不到这一点。我就把这个小难题留给你们，因为那是哲学逻辑，我们这里不讲那个。我们这里讲符号逻辑。所以现在你们知道了两种不同类型的逻辑。好的，这有一个这方面的经典例子，所有人都是会死的，嗒嗒嗒嗒。现在，我说过有些论证是演绎有效的，但不是凭借其形式而有效的。下面只是几个显然凭借其内容而有效的例子。义务逻辑，这是前沿的东西。我们对义务逻辑知之甚少。逻辑学，义务逻辑是关于道德的逻辑。明白吗？我们想考察的是，好，我们想考察的领域是，我们谈论道德的论域，我们说它在逻辑上是如何运作的，我们如何能从关于道德的谈论中得到一个有效的论证形式。现在看看这个论证：撒谎是错的，因此我们不应该撒谎。这看起来像一个演绎有效的论证，不是吗？

[段 35]

In other words, if that’s true, surely this must be true as well. But if so, it’s not true in virtue of its form, it’s true in virtue of its… Well, could you say lying is wrong, but I’m going to lie? Well, we all know that you could lie, but if you truly believe that lying is wrong, you’re also going to believe you shouldn’t lie. Now, that doesn’t mean you won’t lie, but you’ll feel guilty. Madam, that’s just what I said. I said if you believe lying is wrong then you’re going to believe you shouldn’t lie, aren’t you? Do you think you could possibly believe that lying, really believe that lying is wrong and yet not believe that you shouldn’t lie? Well, I think that if you find it, okay, if you lie, either you’re going to feel shame which manifests your belief that lying you do think lying is wrong or you don’t going to feel any shame at all which manifests the fact that you don’t believeat all which manifests the fact that you don’t believe that lying is always and everywhere wrong. Being wrong is relative, isn’t it? Oh, don’t get me on that. I’m not going to follow that one up at all. It’s very important, though, isn’t it? Oh, it’s very important, yes, but we’re not. But actually, we can safely leave it on one side here.

[译文 35]

换句话说，如果那是真的，那这个必然也是真的。但如果是这样的话，它就不是凭借其形式为真，而是凭借其……嗯，你能说"撒谎是错的，但我要撒谎"吗？嗯，我们都知道你可能会撒谎，但如果你真的相信撒谎是错的，你也会相信你不应该撒谎。那并不意味着你不会撒谎，但你会有负罪感。女士，那正是我说的。我说如果你相信撒谎是错的，那么你会相信你不应该撒谎，不是吗？你觉得你有可能真的相信撒谎，真的是相信撒谎是错的，却不相信你不应该撒谎吗？嗯，我想如果你……好吧，如果你撒谎，要么你会感到羞耻，这表明你的信念——你确实认为撒谎是错的；要么你完全不会感到羞耻，这表明你不相信……完全不会感到羞耻，这表明你不相信撒谎在一切时间一切地点都是错的。“错"是相对的，不是吗？噢，别让我扯到那个上面。我根本不打算跟进那个话题。不过，这很重要，不是吗？噢，是很重要，是的，但我们不。不过，其实，我们可以放心地把它放在一边。

[段 36]

If you’re a Kantian, you think that this entails that. Incidentally, you might want to put another premise in here, you might want to say we shouldn’t do things that are wrong. Someone wants to do that? Okay. Kant would say if you did that, you’re manifesting the fact that you think that you could believe that something’s wrong without believing you shouldn’t do it. And that just shows you don’t understand what wrongness is. To Kant, to have the proper moral concept, which is that, you know, lying is wrong or something like that, you cannot believe that something is wrong without also believing you shouldn’t do it. So it doesn’t mean you won’t do it, because we all know that we do things we believe to be wrong, but your belief that it’s wrong will manifest itself as guilt, and if it doesn’t, it manifests the fact you don’t believe the first thing, that lying is wrong. So anyway, we’re not going to get into morality, I just wanted to say there is a logic, a type of logic called deontic logic, and it looks at that sort of inference. And notice that that’s kind ofthought of inference. And notice that we can’t give you a form for that. That’s the very meaning of the word wrong. There’s something very special about the meaning of the word wrong logically.

[译文 36]

如果你是一个康德主义者，你会认为这蕴含着那个。顺便说一句，你可能想在这里加上另一个前提，你可能想说我们不应该做错事。有人想加吗？好的。康德会说，如果你那样做，你就是在表明这样一个事实：你可以相信某件事是错的，却不相信你不应该做它。而这恰恰说明你不理解"错"是什么。对康德来说，要拥有恰当的道德概念，也就是那个，你知道，“撒谎是错的"或者类似的东西，你不能相信某件事是错的，却不相信你不应该做它。所以这并不意味着你不会做，因为我们都知道我们会做我们认为是错的事，但你的"它是错的"这个信念会表现为内疚感，而如果没有这种表现，那就表明你不相信前一个命题，即撒谎是错的。所以无论如何，我们不打算深入道德问题，我只是想说，有一种逻辑，一种叫做义务逻辑的逻辑，它考察的就是那种推理。并且注意，那种推理……种推理。注意，我们无法为它给出一个形式。那就是"错"这个词的真正含义。“错"这个词的逻辑含义有一些非常特别之处。

[段 37]

Here’s another one, modal logic. Modal logic is the logic of necessity and possibility. It’s necessarily the case that there are no square circles. In other words, there’s no possible world in which there’s a square circle. If it’s square, it’s not circular, and so on. Therefore, it’s not possible that there are square circles. So if P is necessarily true, then not P is not possible. Can you hear that? Your capacity for reason would follow that quite quickly. If A is necessary, then not A is not possible. Got to be the case, hasn’t it? So again, we have a deductively valid argument, but it’s not deductively valid, at least. Actually, we’re a lot further on with modal logic than we are in deontic logic. We can do quite a lot with modal logic these days. And here’s a bit of temporal logic for you. it’s raining today therefore tomorrow it will have been raining yesterday is that true? if that’s true then that must be true mustn’t it? couldn’t not and that’s because of the attemptYeah, couldn’t not. And that’s because of temporal logic, the way the logic of time works. Okay, let’s move on. We’re a bit short of time here. We’ll move on to inductive arguments. Now, inductive arguments, remember, what’s the hallmark of an inductive argument? It’s if the premises are true, the conclusion might be true, probably is true.

[译文 37]

再来一个，模态逻辑。模态逻辑是关于必然性和可能性的逻辑。必然如此的情况是没有方形的圆。换句话说，不存在一个可能世界，其中存在一个方形的圆。如果是方的，它就不是圆的，以此类推。因此，不可能有方形的圆。所以如果 P 必然为真，那么非 P 就不可能。你听到了吗？你的理性能力会很快得出这个结论。如果 A 是必然的，那么非 A 就是不可能的。一定是这样，不是吗？所以同样，我们有一个演绎上有效的论证，但至少可以说它不是演绎上有效的。其实，模态逻辑的研究比道义逻辑要深入得多。现在我们可以用模态逻辑做很多事情了。下面是一些时态逻辑。今天在下雨，所以明天就是昨天在下雨，这是真的吗？如果这是真的，那么它必须是真的，不是吗？不能不是，这就是因为那种尝试。对，不能不是。这正是由于时态逻辑，即时间逻辑的运作方式。好的，我们继续。时间有点紧。我们继续讲归纳论证。归纳论证，记得吗，归纳论证的标志是什么？前提如果为真，结论可能为真，很可能是真的。

[段 38]

That’s right. OK. So the premises give us reason for believing the conclusion, but not in this case certainty. They don’t give us conclusive reason for believing the conclusion. And that’s because inductive arguments rely on the assumption of the uniformity of nature. That’s what Hume called it, David Hume. The idea that the future will be like the past. so if we’ve seen the sun rise every day in the history of the universe we expect it to rise tomorrow if every time we’ve come here for Marianne’s lecture on Monday at 2 o’clock and Marianne’s been lecturing at 2 o’clock we’ll carry on doing that and if we come on the 7th week we’ll be disappointed sadly it was quite a good reason for believing that Marianne would be lecturing on Monday at 2 that she has been lecturing at 2 every Monday for the last 6 weeks but it’s not conclusive and so on. So we are… One of the biggest problems of philosophy, in fact, is how do we justify…philosophy in fact is how do we justify, can we justify this assumption, the assumption that the future is going to be like the past. Why should we think that the future has been like the past? Can anyone give me a reason? Exactly, because it has always been the case that the future has been like the past in the past.

[译文 38]

对，就是这样。好的。所以前提给了我们相信结论的理由，但在这种情况下不是确定性。它们没有给我们相信结论的结论性理由。这是因为归纳论证依赖于自然齐一性的假设。这就是 Hume（休谟）所说的，David Hume（大卫·休谟）。其思想是未来会像过去一样。所以如果在整个宇宙的历史中我们每天都看到太阳升起，我们就会预期它明天也会升起；如果我们每次来听 Marianne（玛丽安）周一两点钟的课，而 Marianne 一直在两点钟讲课，我们就会继续这样做；如果我们第七周来的话就会失望，但相信 Marianne 会在周一两点钟讲课是相当合理的理由，因为她过去 6 周每个周一都在两点钟讲课，但这不是结论性的，以此类推。所以我们……事实上，哲学最大的问题之一就是如何证明……哲学事实上就是如何证明，我们能否证明这个假设，即未来会和过去一样。为什么我们应该认为未来会和过去一样？有人能给我一个理由吗？正是如此，因为在过去，未来一直和过去一样。

[段 39]

So that’s a circular. Yes, exactly. Every time you try and justify the belief that the future is going to be like the past, you’ll find yourself arguing in a circle. The only reason we think that that works is because it always has worked in the past. Therefore, we assume it will work that way in the future. But human beings just cannot not argue like that. It’s very interesting. I was playing with my cat the other day and I noticed that it doesn’t go in for inductive reasoning. If you do that with a cat, if you do it with a human being, the human being will keep going and expect you to keep going, but the cat doesn’t. If you stop it, it stops. You don’t catch it just slightly. It was interesting. Anyway, that’s what inductive arguments rely on. Okay, tell me why this one. Tell me what it is we’re assuming. actually this is a silly question in fact I don’t like this question I’m going to skip it you can see why the assumption here isYou can see why the assumption here is that because the sun has always done this, it’ll always continue doing that in the future. And the assumption here is that because in your experience, Marianne’s always done this, in the future Marianne will always do this. But our background knowledge comes in to say whether you think it’s a strong argument or a weak argument.

[译文 39]

所以这是循环论证。是的，确实如此。每当你试图证明未来会和过去一样的信念时，你会发现自己陷入了循环论证。我们认为这行得通的唯一原因是它在过去一直行得通。因此，我们假设它在未来也会这样行得通。但人类就是不能不那样推理。这非常有趣。几天前我在和我的猫玩，我注意到它不搞归纳推理。如果你和猫这样做，如果和一个人类这样做，人类会继续下去并期望你继续，但猫不会。如果你停下，它就停下。你不会刚好骗到它。这很有趣。总之，那就是归纳论证所依赖的。好的，告诉我为什么这个。告诉我我们在假设什么。事实上这是个愚蠢的问题，我不喜欢这个问题，我要跳过它，你可以看出这里的假设是什么，你可以看出这里的假设是，因为太阳一直这样做，所以它将来也会一直这样做。而这里的假设是，根据你的经验，Marianne 一直这样做，所以将来 Marianne 也会一直这样做。但我们的背景知识会影响你认为这是一个强论证还是一个弱论证。

[段 40]

And I think you’ll see that given what we know about physics, about astronomy, about the laws of nature, etc., that is a strong argument. Given what we know about people and what they wear, that’s a weak argument. But both of them rely on the assumption of the principle of the uniformity of nature. And there are subcategories within the category of inductive arguments. Here’s one, an argument from an analogy. A is like B, A is F, therefore B is F. Okay, A is like B. And notice these smaller lowercase letters stand in for particular things, whereas letters like this stand in for either properties or sometimes sentences. But I tend to use PQR for sentences and A for oh actually that should be smaller case now I’ve started explaining it that should be smaller case scrub that okay A is like B A is F therefore B is F you see how that works in heretherefore B is F. You see how that works? And here’s an example. The universe is like a pocket watch. A pocket watch has a designer, therefore the universe has a designer. You’ll be familiar with that, Pascal’s… No, it’s not Pascal’s… What is it? Paley, thank you. So the universe is like a pocket watch. A is the universe. B is a pocket watch. A is F. I’ve got this the wrong way around, haven’t I?

[译文 40]

我想你会看到，鉴于我们所知道的物理学、天文学、自然规律等等，这是一个强论证。鉴于我们关于人以及他们穿什么衣服的了解，那是一个弱论证。但它们都依赖于自然齐一性原理的假设。在归纳论证这一类下还有子类。这是一个，类比论证。A 像 B，A 是 F，所以 B 是 F。好的，A 像 B。注意这些小写字母代表具体的事物，而像这样的字母代表属性或有时是句子。但我倾向于用 PQR 代表句子，A 代表……哦其实应该是小写，现在我开始解释了，应该是小写，划掉那个，好的，A 像 B，A 是 F，所以 B 是 F，你明白这是怎么运作的吗？所以 B 是 F。你明白这是怎么运作的吗？这里有个例子。宇宙像一个怀表。怀表有设计者，所以宇宙有设计者。你会对这个熟悉，Pascal（帕斯卡）的……不，不是 Pascal（帕斯卡）的……那是什么？Paley（培里），谢谢。所以宇宙像一个怀表。A 是宇宙。B 是怀表。A 是 F。我把这个弄反了，是吧？

[段 41]

Here’s your homework. Take that argument and put it into proper canonical logical form. Come back and tell me where I’ve got that wrong because I’ve got several quite interesting little errors in there. Some of them are just in the logic that I’m using and some of them I’ve just transposed various things. it should be easy for you to see where I’ve gone wrong do it and if you want to come and check that with me next week I’m very happy to have a look at it do you want to come up with your own argument from analogy got time for one or two perhaps hang on there’s someone over here who hasn’t had a chance so far.over here who hasn’t had a chance so far? The universe is like a cabbage, a cabbage in green, therefore a universe. Yes, okay, that would do. One of your premises isn’t true. Well, actually no. Yes, one of your, well, I suppose a universe is like a cabbage, isn’t it, in a, roughly so, shape-wise. Okay, well, that would work, yeah. One more. Trish is like Sylvia. Sorry, say that again. Trish is like Sylvia. Trish is like Sylvia. Trish is blonde, therefore Sylvia is blonde. Good. Yep, absolutely. That’ll do. Good, we’ve got that. Let’s have a look at another inductive argument. Can you see how that’s inductive, by the way?

[译文 41]

这是你们的作业。把那个论证写成规范的标准逻辑形式。下次回来告诉我哪里我搞错了，因为里面有好几个相当有趣的小错误。其中一些只是在我使用的逻辑中，还有一些我把各种东西换位了。你应该很容易看出我错在哪里，去做吧，如果下周你们想来找我核对，我很乐意看一下。你们想自己想出一个类比论证吗，也许有时间来一两个，等一下，那边有人还没机会。还没机会？宇宙像一个卷心菜，绿色的卷心菜，所以一个宇宙。是的，可以。这样就可以了。你的一个前提不是真的。嗯，其实不是。是的，你的一个，嗯，我想一个宇宙像卷心菜，不是吗，大致上，从形状上，是的。好的，那也行，可以。再来一个。Trish 像 Sylvia。抱歉，再说一遍。Trish 像 Sylvia。Trish 像 Sylvia。Trish 是金发，所以 Sylvia 是金发。好的。是的，绝对可以。这样可以。好的，我们懂了。我们来看另一个归纳论证。顺便说一下，你能看出为什么这个是归纳的吗？

[段 42]

Why does that depend on the principle of the uniformity of nature? Again, we’re assuming if one thing is like another in some ways, then it’ll be like another in other ways. So we’re assuming the uniformity of nature, aren’t we? So if it’s like that in one way, it’ll be like that in another way as well. Here’s another argument, an argument from authority. Einstein is a brilliant physicist. Einstein says relativism is true, therefore relativism is true. Of course, we could put in a different thing here. Einstein says pacifism is the right creed, therefore pacifism is the right creed. What have we done there? we’ve changed a good argument to a bad argument. Why is one good and one bad? Because.argument. Why is one good and one bad? Because he is an authority on physics, that’s right, and he isn’t an authority on politics. But we’ll be looking at good and bad arguments from now on, after next week. Okay, causal arguments. We looked at causal arguments briefly last week. Every time an A occurs, a B occurs. Therefore, A’s cause B. Now, we have a huge tendency, and in fact, That tendency was manifested here last week in this very room, wasn’t it, where we assume that where there’s a correlation, there’s also a causal relation. Well, we know that that’s not true, is it? We know that there can be correlations without causal relations.

[译文 42]

为什么这依赖于自然齐一性原理？我们再次假设，如果一件事在某些方面像另一件事，那么它在其他方面也会像另一件事。所以我们假设了自然齐一性，不是吗？所以如果它在某方面像那样，它在另一方面也会像那样。这是另一个论证，诉诸权威的论证。Einstein（爱因斯坦）是一位杰出的物理学家。Einstein（爱因斯坦）说相对论是真的，所以相对论是真的。当然，我们可以在这里放一个不同的东西。Einstein（爱因斯坦）说和平主义是正确的信条，所以和平主义是正确的信条。我们在那里做了什么？我们把一个好论证变成了坏论证。为什么一个好一个坏？因为……论证。为什么一个好一个坏？因为他是物理学方面的权威，对了，而他在政治方面不是权威。但从下周开始我们会研究好的和坏的论证。好的，因果论证。我们上周简要看过因果论证。每次 A 发生，B 就发生。所以 A 导致 B。现在，我们有一种巨大的倾向，事实上，这种倾向上周就在这个教室里表现出来了，不是吗，我们假设只要有相关性，就也有因果关系。我们知道那不是真的，不是吗？我们知道可以有相关性而没有因果关系。

[段 43]

But even so, our evidence for causation tends to rest on a correlation. So if every time an A occurs, a B occurs, we’ll tend to think that A’s cause B’s. So we argue from observation of a correlation to an assertion about a causal relation. And just to say quickly that causal arguments can be deductive or inductive, depending on whether we’re arguing from a causal claim or to one. So A’s cause B, there was an A, therefore there will be a B. every time, every observed A has been followed by B, therefore A is cause B. Which of these is deductive? Left or right? My left or… That’s… Left. Deductive. Inductive. Yep, that’s right. We’re taking cause here. What we’re saying, we’re arguing to a causal claim, aren’t we, from observations of correlation. and here we’re arguing from a causal claim, indeed the conclusion of that one, to a particular claim. That’s deductive. Well, you should be able to do this. Okay, that’s deductive because if that’s true, if that’s true and that’s true, then that must be true. Okay, this might be true and yet this be false. But even so, that is reason to believe that, isn’t it? Okay, it’s just not conclusive reason. Whereas these are conclusive reason to believe that. Right. Your task for the week ahead. See if you can find in your newspaper, magazine, or a book, or wherever.

[译文 43]

但即便如此，我们关于因果关系的证据往往基于相关性。所以如果每次 A 发生，B 就会发生，我们往往会认为 A 导致 B。因此我们从观察到的相关性出发，得出关于因果关系的断言。简单说一下，因果论证既可以是演绎的，也可以是归纳的，这取决于我们是从一个因果主张出发论证，还是论证出一个因果主张。所以"A 导致 B，出现了一个 A，因此会有一个 B”，以及"每次观察到的 A 之后都跟着 B，因此 A 导致 B”。这两个哪个是演绎的？左边还是右边？我的左边还是……那是……左边。演绎的。归纳的。没错，对了。我们这里用的是"导致”。我们说的是，我们从相关性的观察中论证出一个因果主张，对吧？而这里我们是从一个因果主张——实际上就是前面那个的结论——论证出一个具体的命题。这是演绎的。好，你应该能理解这个。好的，那是演绎的，因为如果那是真的，如果那是真的并且那也是真的，那么那个必须是真的。好的，这可能为真但那个为假。但即便如此，这也是相信那个的理由，对吧？好的，只是这不是决定性的理由。而那些是相信这个的决定性理由。正确。你接下来这一周的任务。看能不能在你的报纸、杂志或书里，或者随便什么地方，找到这些模式相符合的论证。

[段 44]

I’ve said four, but that’s entirely arbitrary. just see if you can find some arguments that fit the patterns that we’ve been looking at today. And you might also notice in your own behaviour, as you’re talking to people, you’ll find yourself, and I’m hoping to sensitise you to these logical words, so that they can’t go past without your thinking, ooh. So when you find yourself saying, if, then, that’s a particularly good one, if, then, or therefore, or since, or things like that, catch yourself and try and work out what your argument was now some of your argument is going to be far too complicated to work out like that at the moment stick to simple ones see if you can find yourself offering a simple argument if you do I said if you don’t clean your room then this would happen you did not clean your room therefore you know this this sort of thing is what you’re trying to find out for and have a look and see if you can fit them into the forms that we’ve given here. Okay, and next week we’re going to look at actually identifying arguments and setting them out logic book style. We’ve been doing that today, but we’re going to do that with some rather more complicated arguments next week. We’re going to look at arguments that you might make in the pub or in a newspaper or something like that.

[译文 44]

我说了四个，但那完全是任意的。看看你能不能找到一些符合我们今天所讨论模式的论证。你也可能会在自己的行为中注意到，当你和别人交谈时，你会发现自己在使用这些词，我希望让你们对这些逻辑词汇变得敏感，这样它们就不会在你脑中轻易滑过，让你不去想"哦"。所以当你发现自己说"如果，那么"，这是一个特别好的例子，“如果，那么”，或者"因此"，或者"既然"，或者类似的东西时，停下来，试着弄清楚你的论证是什么。现在你的某些论证会太复杂而无法这样分析，先坚持简单的，看看能不能发现自己提出了一个简单的论证。如果你发现，我说"如果你不打扫你的房间，那么这件事就会发生"，“你没有打扫你的房间”，“因此你知道这件事”，这种类型的论证就是你要寻找的，看看能不能把它们套入我们这里给出的形式。好的，下周我们实际上要学习识别论证并以逻辑书的方式把它们列出来。今天我们已经做了一些，但下周我们会用一些更复杂的论证来做这件事。我们要看看你在酒吧里或报纸上可能提出的那些论证。

[段 45]

We’ll look at a few magazine leaders and things like that. Sorry, newspaper leaders. That’s it.

[译文 45]

我们会看几篇杂志社论之类的东西。抱歉，报纸社论。就这样。