牛津逻辑推理入门 - 5.论证评估.

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, here we are at week five. Now, this is going to be the most difficult week you’ll have done. We’re going to be looking at evaluating arguments again, this time deductive arguments, and in particular we’ve got to look at the notion of validity. And this is a difficult notion to wrap your mind around, so expect to have a hard slog, but if you keep at it, you’ll be fine. Right, just a recap as usual on last week. if you remember last week we evaluated inductive arguments remind me what an inductive argument is a percentage chance of being right I’m not sure that’s quite the way I put it more or less what’s more or less likely given the premises the conclusion is more or less likely exactly as opposed to a deduction where if the premises are true, the conclusion must be true. Okay, so we looked at inductive generalisations and causal generalisations, arguments from analogy and arguments from authority, all different types of inductive arguments. And if you remember, we looked at these things. Now, I realised at the end of last week that I hadn’t added that one on. So if you’ve got, you might want to go back to the handouts that you had from last week and just note that this week’s handouts will have that one on as well and it’s fairly obvious what that is andas well.

[译文 1]

好的，现在我们来到了第五周。这一周将是你们经历过的最难的一周。我们要再次讨论如何评估论证，这次是演绎论证，尤其要研究"有效性"这个概念。这是一个很难在头脑中理清的概念，所以要做好打硬仗的准备，但只要坚持下去，你就没问题。好，照例先回顾一下上周的内容。如果你还记得，上周我们评估了归纳论证——提醒我归纳论证是什么——有百分之多少的可能性是对的——我不确定我是不是这样表述的——大致上是在给定前提的情况下，结论或多或少更可能——没错，是或多或少更可能，与演绎相反，在演绎中如果前提为真，结论就必然为真。好的，我们看了归纳概括和因果概括、类比论证和权威论证，这些都是不同类型的归纳论证。如果你记得，我们看了这些东西。现在，我意识到上周结束时我没有把那个加上。所以如果你愿意，可以回去看看上周的讲义，注意一下这周的讲义也会带上那个，而且它是什么相当明显。

[段 2]

And it’s fairly obvious what that is. And if it isn’t, it will be by the end of today. Okay. So those were the tests for an inductive generalization. These were the tests for a causal generalization. These for the argument from analogy, and these for the arguments for authority. I won’t go over them again, because as we’ve started a bit late, I would rather get straight on to today. But if we have time left at the end of today for questions, if you want to go over any of the ones that we did last week and you can’t remember them or you’d just like a reminder, ask me then and we’ll certainly come back to those. Okay, but this week we’re going to be looking at the distinction between validity and truth and at why validity is important and we’re going to finish both this week and next week with evaluating deductive arguments. We’ve actually already mentioned the distinction between validity and truth. Would anyone like to Have a go at telling me what it is. It was about three weeks ago, so quite reasonable if you don’t remember, and quite reasonable if you get it wrong, because we only mentioned it glancingly. Good, yeah, okay. An argument can be valid but not true. Why is that the case? Right, okay, let’s not push it. No, you were doing very well then.

[译文 2]

它是什么相当明显。如果不明显，到今天结束时就会清楚了。好的。这些是归纳概括的检验标准。这些是因果概括的检验标准。这些是类比论证的，这些是权威论证的。我不会再讲一遍了，因为我们已经迟了一些，我更想直接进入今天的内容。但如果今天结束时还有时间提问，你们想复习上周讲过的任何内容但记不清了，或者只是想再听一遍提醒，到时候告诉我，我们一定会回头看。好的，但这周我们要研究有效性与真之间的区别，以及为什么有效性是重要的，我们这周和下周都将以评估演绎论证作为结尾。我们其实已经提到过有效性与真之间的区别。请问有谁能尝试告诉我它是什么？那是大约三周前提到的，所以如果你不记得是完全合理的，如果你说错了也完全合理，因为我们只是顺带提了一下。好的，没错。一个论证可以有效但不是真的。为什么是这样？好的，咱们先不勉强。不，你刚才说得很好。

[段 3]

You’re absolutely right. statements or sentencesYou’re absolutely right. Statements or sentences or propositions can be true or false. But arguments can’t be true or false. Arguments can only be valid or invalid. Do you remember that? We talked about that in the first week. And I said then that one of the things that will give you away every time to a philosopher or a logician is if you talk about arguments being true or false. or if you talk about sentences being valid or invalid because it’s like my talking about the table being loud. It makes it clear that I either don’t understand the meaning of loud or I don’t understand the meaning of table or I’m speaking metaphorically might also help. So sentences, statements can be true or false. So premises can be true or false. Conclusions can be true or false, but arguments can’t be. And arguments can be valid or invalid, but they can’t be either true or false. So we’ll be looking at why that is in a little more depth today. And we’ll be looking at why validity is important because one of the interesting things about valid arguments, as you’ll see, is that they can have false conclusions. And you might ask yourself, well, why should an argument that has a false conclusion be a useful argument, never mind a good argument?

[译文 3]

你完全正确。陈述或句子你完全正确。陈述、句子或命题可以为真也可以为假。但论证不能为真也不能为假。论证只可能是有效的或无效的。你还记得吗？我们在第一周讲过。我当时说过，每当你说论证是真或假的，或者句子是有效或无效的，就会立刻让哲学家或逻辑学家看出你的破绽。就好像我说这张桌子很吵一样。这要么说明我不理解"吵"的意思，要么我不理解"桌子"的意思，要么我在打比方。句子、陈述可以为真也可以为假。所以前提可以为真也可以为假。结论可以为真也可以为假，但论证不行。论证可以是有效的或无效的，但既不能是真也不能是假。所以今天我们会稍微深入一点地研究为什么是这样。我们还会研究为什么有效性是重要的，因为你会看到，有效论证有一个有趣之处，就是它们可以有假的结论。你可能会问，一个带有假结论的论证，怎么会有用呢，更别说是一个好的论证了？

[段 4]

But we’ll see why in this session. Okay, right, first we’re going to deal with the idea of soundness. And an argument, a good deductive argument is sound if and only if it’s both valid and it has true premises. So soundness is to do with both validity and the truth of the premises. So, okay, is this argument sound? Put up your hand rather than yell out. Put up your hand if you think this argument is sound. Do you see what I mean? This argument is valid and has false premises. Could this argument be sound? Put up your hand rather than shout out. Anyway, you’ve all done it now and you’re quite right. No, that can’t be sound, can it? Okay, what about this one? Put up your hand because some people think more quickly than others, so give everyone a chance to think. As soon as you’ve decided, put up your hand. okay that’s most of you what is it no it’s got to be unsound hasn’t it it couldn’t possibly be both what about this one okay what are you saying to this one no okay again this one can’t be valid and so what about this one yes you can yell out this time okay yes that’s right that’s got to be sound. Good. Okay, so there’s the same thing filled in. Okay, now so the two things that are both necessarySo the two things that are both necessary for a sound argument or a good argument insofar as soundness goes, truth of the premises and the validity of the argument.

[译文 4]

但我们在这节课里会明白为什么。好的，首先我们要处理可靠性这个概念。一个论证，或者说一个好的演绎论证，当且仅当它既有效又有真的前提时，才是可靠的。所以可靠性既涉及有效性，也涉及前提的真。好的，这个论证可靠吗？举手回答，不要喊出来。如果你认为这个论证可靠，请举手。你明白我的意思吗？这个论证有效，但前提是假的。这个论证能可靠吗？举手回答，不要喊出来。不管怎样，你们都已经做完了，而且你们是对的。不，那不可能可靠，对吧？好的，那这个呢？举手回答，因为有些人思考得比较快，所以给每个人一点思考的时间。一旦你决定了，就举手。好的，那是你们大多数人，它是什么？不，它一定是不可靠的，对吧？它不可能两者都是。那这个呢？好的，你对这个怎么说？不，好吧，再一次，这个不可能有效。那这个呢？是的，这次你可以喊出来。好的，对，没错，那一定是可靠的。好的。所以这里填的是同样的东西。好的，那么对于可靠论证或好的论证来说——就可靠性而言——两个必要条件，前提的真和论证的有效性。

[段 5]

Now, the truth of the premises, and I’ve mentioned this before, is not an interesting matter for logicians or for you, given that your interest is in critical reasoning. And the reason for that is that when we determine the truth or falsity of a premise, it’s not necessarily a logical matter. It’s not necessarily a philosophical matter at all. So if I say, is the chair blue, how are you going to determine the truth or falsehood of that? It’s dead easy. There’s no trick question here. You’re going to look at the chair. That’s right. Okay, if I say 2 plus 2 equals 4, is that true or not? Okay, yes it is. Okay, and how do you know? yeah I mean you all you all know your basic arithmetic okay um and you might say okay all swans are white how do you determine the truth of that answer inductively and so on so there are lots of different ways in which a premise would be determined to be true or false and my job in teaching critical reasoning is not to teach you how to look at a premise and decide whether it’s true or false my job is to teach you how to look at an argument and determine whether it’s valid Okay? Are you with me? So when two characteristics of a sound argument, one is transgressive.Characteristics of a sound argument.

[译文 5]

现在，前提的真，我之前提过，对逻辑学家或对你们来说不是一个有趣的问题，鉴于你们的兴趣是批判性推理。原因在于，当我们确定一个前提是真还是假时，这不一定是逻辑问题。甚至根本不一定是哲学问题。所以如果我说，椅子是蓝色的吗，你如何确定它的真假？这很简单。这里没有什么陷阱问题。你会去看那把椅子。没错。好的，如果我说2加2等于4，这是真的还是假的？好的，是真的。好的，你怎么知道的？我的意思是，你们都会基本算术。好的，你可能会说，好的，所有的天鹅都是白色的，你如何确定这个的真假？用归纳的方法回答，等等。所以有很多不同的方法来确定前提是真还是假，而我在教批判性推理时，我的任务不是教你们如何看一个前提并判断它是真的还是假的，我的任务是教你们如何看一个论证并判断它是否有效。明白吗？跟上了吗？所以可靠论证的两个特征，一个是跨学科的。可靠论证的特征。

[段 6]

One is true premises. One is validity. I’m leaving it to you to ask about true premises. All I can teach you is what validity looks like, what validity is. Okay, so, yeah. Okay, validity is of interest to logicians because validity preserves truth. If an argument is valid, then if its premises are true, we can be certain that its conclusion is true. So it’s the if here that’s important. If the premises are true, then the conclusion must be true. And so the validity of an argument preserves the truth of the premises. If there’s truth there, it will preserve it. If there isn’t truth there, it won’t say anything about the truth of the conclusion. So we’ll see more about that in a minute. Okay, so validity is truth-preserving. That’s why it’s useful. So validity is of interest to anyone who’s concerned with truth. It’s not just true premises that concern you if you’re interested in truth. It’s also the validity of arguments. And that’s because we often don’t know the truth of our premises, and we often test the truth of our premises by constructing valid arguments and testing the truth of the conclusion. So let me go through that again. Okay, if an argument…go through that again. Okay, if an argument is valid, then if the premises are true, the conclusion must be true. Okay, so we might have a premise that we don’t know whether the premise is true or not, but if we can use that premise as the premise of a valid argument and then test the conclusion of that argument to see whether that’s true or false, then if we can show that the conclusion of a valid argument is false, what do we know?

[译文 6]

一个是前提为真。一个是有效性。前提是否为真，我留给你们自己去问。我能教你们的只是有效性看起来是什么样的，有效性是什么。好的，所以，是的。好的，有效性之所以引起逻辑学家的兴趣，是因为有效性保持真。如果一个论证是有效的，那么如果它的前提为真，我们就可以确信它的结论为真。所以这里重要的是"如果"。如果前提为真，那么结论就必然为真。因此，一个论证的有效性保持了前提的真。如果那里有真，它就会保持它。如果那里没有真，它对结论的真假也什么都不会说。我们一会儿会更详细地看到这一点。好的，所以有效性是保持真的。这就是它有用的原因。所以对于任何关心真的人来说，有效性都是有意义的。如果你关心真，让你关心的不仅仅是前提是否为真。还有论证的有效性。这是因为我们常常并不知道我们前提的真假，我们常常通过构建有效论证并检验结论的真假来测试前提的真假。让我再讲一遍。好的，如果一个论证……再讲一遍。好的，如果一个论证是有效的，那么如果前提为真，结论就必然为真。好的，我们可能有一个前提，不知道它是真是假，但如果我们能把这个前提作为一个有效论证的前提，然后检验那个论证的结论，看它是真的还是假的，那么如果我们能证明一个有效论证的结论是假的，我们能知道什么？

[段 7]

If we can show that the conclusion of a valid, put your hand up, if we can show that the conclusion of a valid argument is false, what do we know? Let me remind you again of the argument is valid if and only if, if the premises are true, the conclusion must be true. So if we see that the conclusion of a valid argument is false, what do we know? Put your hands up when you’ve got the answer. A little bit longer. It’s quite difficult to play with these concepts in your mind if you’re not used to. So, okay, right. What do we know? Who wants to give me the answer? Do you want to have a go? Yep. Right. At least one of the premises must be false. That’s right. They might all be false, or it might be just one of them is false but we know that at leastit might be just one of them is false, but we know that at least one of them must be false. So if an argument is valid and the conclusion is false, then we know that at least one of the premises must be false. And here’s a couple of examples. Okay, smoking causes cancer. That’s a hypothesis. We’ve based that. Okay, where do we get that from? What sort of argument might that be the conclusion of an inductive argument.

[译文 7]

如果我们能够证明一个有效论证的结论是假的，举起手来，如果我们能够证明一个有效论证的结论是假的，我们能知道什么？让我再提醒大家一下，论证有效当且仅当，如果前提为真，结论必然为真。所以如果我们看到一个有效论证的结论是假的，我们能知道什么？知道答案了就举手。再等一会儿。如果你不太习惯的话，在脑中玩转这些概念是相当困难的。所以，好吧。没错。我们能知道什么？谁愿意告诉我答案？你想试试吗？好的。至少有一个前提一定是假的。没错。它们可能全是假的，也可能只有一个是假的，但我们知道至少有一个前提一定是假的。所以如果一个论证是有效的，而且结论是假的，那么我们就知道至少有一个前提一定是假的。我来举几个例子。好的，吸烟会导致癌症。这是一个假设。我们已经以此为基础了。那么我们是怎么得出这个结论的呢？这可能是某种论证的结论。

[段 8]

Good. So we see that this smoker’s got cancer, this smoker’s got cancer, this smoker’s got cancer, etc. And we form the hypothesis smoking causes cancer. Okay, that generates a prediction, doesn’t it? If we put that hypothesis as starkly as that, smoking causes cancer, it generates a prediction. If smoking causes cancer, then every smoker will get cancer, doesn’t it? Oh, yes, it does. No, remember I said if we put the conclusion as starkly as that, sorry, the premise as starkly as that, that’s the prediction it generates. Okay, the test or the conclusion of this argument is each smoker gets cancer. Now, if we look at smokers, we see that some of them get cancer and some of them don’t, don’t we? Okay, so what do we know? This is a valid argument, isn’t it? Yeah? Okay. but we’ve seen that the conclusion is false, so what do we know? It’s just one of the premises…So what do we know? That one of the premises is… Now, it might be that it’s not the case that smoking causes cancer, or it might be the case that smoking could cause cancer without it being the case that every smoker would cause cancer. So what do we do if we’re researchers at this point? What might be the case? We’ve got a correlation between smoking and cancer, haven’t we?

[译文 8]

好的。所以我们看到这个吸烟者得了癌症，这个吸烟者得了癌症，这个吸烟者得了癌症，等等。于是我们形成了"吸烟会导致癌症"这个假设。好的，这会产生一个预测，不是吗？如果我们把假设表述得这么直白，吸烟会导致癌症，它就会产生一个预测。如果吸烟会导致癌症，那么每个吸烟者都会得癌症，不是吗？哦，是的。当然是这样。不，记住我说的，如果我们把结论表述得这么直白，抱歉，是把前提表述得这么直白，这就是它所产生的预测。好的，这个论证的检验或结论就是每个吸烟者都得癌症。现在，如果我们观察吸烟者，我们看到有些人得了癌症，有些人没有，不是吗？好的，那我们能知道什么？这是一个有效论证，不是吗？是吗？好的。但我们已经看到结论是假的，那我们能知道什么？这只是其中一个前提……那我们能知道什么？其中一个前提是……现在的情况可能是，吸烟并不导致癌症，也可能是吸烟可以导致癌症，但并不意味着每个吸烟者都会得癌。所以在这个节点上，如果我们是研究者，我们会怎么做？情况可能是怎样的？我们已经有了吸烟与癌症之间的相关性，不是吗？

[段 9]

Otherwise, we wouldn’t have that first premise. but it was not going to be an exceptionless correlation is it? We’ve seen that so we could say we could decide to jettison the idea that causation is sufficient so we might want to say well okay it’s possible for A to cause B without it being the case that A is sufficient for B see what I mean? So we could jettison premise 2 so possibly A can cause B without it being the case that you always get B if you get A. Actually, we probably wouldn’t want to jettison that, would we? Why not? Okay, I think I’m going about this looking at your faces. I’m getting a bit wrong. Okay, let’s say that we decide to jettison that. Does that mean we’re going to say that’s false? What are we going to say instead? we could say that or we could say that smoking plus something else we could say we we know theplus something else. We could say we know the hypothesis is going in the right direction, but it’s smoking plus. I mean, maybe there’s some genetic characteristic of people who smoke and get cancer that’s different from those who smoke and don’t get cancer or something along those lines. Do you see what I mean?

[译文 9]

否则我们就不会有那个第一个前提。但这不会是一个没有例外的相关性，不是吗？我们已经看到了这一点，所以我们可以说我们可以决定抛弃因果关系是充分条件这种想法，我们可能会想说，好吧，A 可以在不是 A 对 B 充分的情况下导致 B，明白我的意思吗？所以我们可以抛弃前提 2，所以 A 也许可以在你有了 A 不一定总会得到 B 的情况下导致 B。事实上，我们可能不会想抛弃那个，对吧？为什么不呢？好吧，我觉得我在看着你们的脸来讲这些。我有点讲岔了。好吧，假设我们决定抛弃那个。那是不是意味着我们会说那是假的呢？我们又会怎么说呢？我们可以那样说，也可以说吸烟加上其他什么，我们可以说我们知道那个"加上其他什么"。我们可以说我们知道假设的方向是对的，但是它是"吸烟加上……"。我的意思是，也许吸烟并得癌症的人有一些基因特征不同于吸烟但不得癌症的人，或类似这样的说法。你明白我的意思吗？

[段 10]

So we’ve got something for which we’ve got reason to believe it’s true, but we’re not sure, or actually, I mean, given what we know, we’re pretty sure it isn’t entirely true but if we put these together in a valid argument we get that which we know to be false so we know that either one of those has got to be false we could play around with something that’s the business of philosophers to play around with namely our concept of causation and say well okay there can be causes that don’t always have their effects that don’t necessitate their effects or we could stick to being empirical and say there’s something in addition to smoking that causes cancer. You with me? If smoking always caused cancer, you couldn’t have a smoker that didn’t get cancer. So that would be true, wouldn’t it? So because that’s false, we know that one or the other of these is true. And if you’re a philosopher, you might want to say, well, maybe causes don’t necessitate their effects could premise to be true, sorry false. If you’re a scientist you’re a much moreIf you’re a scientist, you’re much more likely to say actually causes do necessitate their effects, therefore it’s not smoking on its own that causes cancer. There must be something in addition to smoking that goes to causing cancer.

[译文 10]

所以我们得到了一个我们有理由相信是真的东西，但我们不确定，或者实际上，我的意思是，鉴于我们所知道的，我们相当确定它并非完全为真，但如果我们把这些放进一个有效论证中，我们就得到了一个我们知道是假的东西，因此我们知道其中必有一个是假的，我们可以玩味一下，那是哲学家所玩味的，也就是我们的因果概念，可以说，好吧，可能存在这样的原因，它不总是产生效果，不必然产生效果，或者我们可以坚持经验主义的说法，说除了吸烟之外，还有其他什么东西导致癌症。你们跟上了吗？如果吸烟总是导致癌症，你就不可能有一个不患癌症的吸烟者。所以那本来应该是真的，不是吗？因为那是假的，我们知道这两个里面必有一个是真的。如果你是哲学家，你可能会说，好吧，也许原因不必然产生效果，前提二可以为真，抱歉，是假。如果你是科学家，你更倾向于——如果你是一位科学家，你更可能说，实际上原因确实必然产生效果，因此并不是单独的吸烟导致癌症。一定是除了吸烟之外，还有别的东西在导致癌症。

[段 11]

Surely by definition, cause creates an effect. Necessitates its effect, you mean. Well, you say by definition, but of course part of the job of a philosopher is to say, well, is it true that that’s the correct definition of cause? Could there be… If it doesn’t cause it, then it’s not a cause. No, if it doesn’t cause it, it’s not a cause, but if it doesn’t necessitate it, might it cause it? I mean, if we look at quantum mechanics, for example, here are some ideas that there may be causation that doesn’t necessitate. And one of the big questions of philosophy, and if you ever do an introduction to philosophy as opposed to an introduction to critical reasoning course, You might look at questions of could there be backwards causation, for example? Could the effect come before a cause? Could there be non-necessitating causes? What actually is the causal relation? These are all philosophical questions that are… Obviously philosophers have a different concept of cause. No, no, they don’t have a different concept of cause. What they do is they unpack the concept of cause that we think we have. And I quite agree that the common concept of cause is that cause is necessitating. Yeah, absolutely. Well, then what’s the cause? What do you mean by random here? Well, then you’re suggesting that a cause isn’t necessitating, which is what…

[译文 11]

当然，按照定义，原因产生效果。必然产生效果，你的意思是。好，你说按照定义，但当然，哲学家的工作之一就是说，好吧，那是不是正确的因果定义呢？会不会有……如果它没有导致，那它就不是原因。不，如果它没有导致，它就不是原因，但如果它没有必然导致，它会不会导致？我的意思是，如果我们看量子力学，举例来说，有一些观点认为可能存在不必然的因果关系。还有哲学的重大问题之一，如果你以后上哲学导论而不是批判性推理导论，你可能会研究这样的问题：会不会有反向因果？例如，结果会不会先于原因出现？会不会有非必然的原因？因果关系到底是什么？这些全都是哲学问题……显然哲学家对原因有不同的概念。不，不，他们并没有对原因有不同的概念。他们所做的是拆解我们自以为了解的原因概念。我完全同意，常见的原因概念就是原因是必然的。是的，完全对。那原因到底是什么？你这里说的随机是什么意思？好，那你就是在暗示原因不是必然的，这恰恰就是……

[段 12]

I’ve forgotten your name, sorry. Brian is questioning. Well… You can have random causes, I believe. so you disagree on the meaning of the word cause you can have that conversation later in the common room but I tell you now that if you want to find out what the answer to that is you should come to a philosophy weekend on the nature of causation because it’s a big issue that one very big one you had a question well that would lead you That’s why you know that each smoker doesn’t, but if you’re evaluating the inductive argument that leads to that, you might want to deal with percentages and so on exactly. But what I’m pointing out here is that you form a hypothesis, you generate a prediction, which is going to be based on your understanding of causation and so on, and then you test that prediction, and look, what you’ve done is you’ve constructed a deductive argument and as long as it’s valid and you testAnd as long as it’s valid and you test the conclusion, if the conclusion comes out false, then you know that at least one of your premises is false. Either your hypothesis is false or there’s something fishy about causation. And you’re almost certainly not going to go for that one unless you’re a philosopher. OK, here’s another one. All women are passive.

[译文 12]

我忘了你的名字，抱歉。Brian 在提问。好……你可以有随机的原因，我相信。所以你不同意"原因"这个词的含义，这个你可以以后在公共休息室再讨论，但我现在告诉你，如果你想知道那个问题的答案，你应该来参加一个关于因果本质的哲学周末活动，因为那是一个大问题，非常大的问题。你有一个问题，嗯，那会引导你。这就是为什么你知道每个吸烟者都不会得癌症，但如果你在评估那个归纳论证，你可能会想处理百分比等等，确实如此。但我在这里想指出的是，你形成一个假设，你生成一个预测，这个预测会基于你对因果关系等的理解，然后你检验那个预测，你看，你所做的是你构造了一个演绎论证，只要它是有效的，你就检验——只要它是有效的，你就检验结论，如果结论被证明是假的，那么你就知道至少有一个前提是假的。要么你的假设是假的，要么因果关系那里有点问题。而你几乎肯定不会选那个，除非你是一位哲学家。好的，再来一个。所有的女人都是被动的。

[段 13]

Mrs. Thatcher is a woman. Therefore, Mrs. Thatcher is passive. OK, you’ve got a hypothesis here. OK, you’ve generated that on what grounds? None at all. None at all, he says. Okay. The grounds of prejudice or something like that. Say inductive grounds as well. This is observation, isn’t it? And do we have a valid argument here? Yes. Yeah. If these premises are true, this conclusion must be true. Okay. The conclusion isn’t true. I think you’d probably agree with me. Therefore, one or other of these must be false. And as we know, an awful lot of people talked about Mrs Thatcher as being the best man in the cabinet. In effect, they were relying on this argument and suggesting that instead of that one being false, it’s this one that’s false. And here’s another one. Tony Blair is sorry. All Labour Party members are left or all socialists are left wing. Tony Blair is a socialist. Therefore, Tony Blair’s left wing. and if you think Tony Blair is far too right wing to be a socialist you’re going to say that Tony Blair isn’tsocialist, you’re going to say that Tony Blair isn’t a socialist rather than that not all socialists, da-da-da-da. That came off the top of my head. I may have got bits of that wrong, but I hope you can see the general thrust of it.

[译文 13]

撒切尔夫人是女性。因此，撒切尔夫人是被动的。好的，你在这里有一个假设。好的，你是根据什么理由得出这个结论的？完全没有理由。完全没有理由，他说。好吧。基于偏见或类似东西的理由。也可以说是归纳理由。这是观察，对吧？而且我们这里有一个有效的论证吗？是的。是的。如果这些前提为真，那么这个结论必然为真。好吧。这个结论不是真的。我想你大概会同意我。因此，其中一个前提一定是假的。我们知道，很多人说撒切尔夫人是内阁里最优秀的男人。事实上，他们就是在依赖这个论证，并暗示与其说第一个前提是假的，不如说第二个前提是假的。再看一个例子。Tony Blair 表示歉意。所有工党党员都是左派，或者说所有社会主义者都是左翼。Tony Blair 是社会主义者。因此，Tony Blair 是左翼。如果你认为 Tony Blair 太偏右而不像社会主义者，你就会说 Tony Blair 不是社会主义者，而不是说并非所有社会主义者都是左翼，之类的。这是我临时想出来的。其中有些地方可能说得不太准确，但我希望你们能看出大意。

[段 14]

As we’re going to see in a minute, you can have a valid argument, the conclusion of which is false. So you might ask, well, then what’s the point of a valid argument? Why should we be interested in validity if it can generate arguments, the conclusion to which is false. And I’m saying, well, actually, the discovery of a valid argument that its conclusion is false can be hugely important. And the reason it can be important is that we often test our premises by constructing a valid argument and testing the conclusion. I understand that. Okay, so I just, well, I just made it clear, just to make it clear that we were testing a hypothesis by constructing a valid argument showing the conclusion was false and then seeing that we can question either or both of the premises. Okay, so you can just substitute premise, premise, conclusion, no problem, exactly the same. So it’s just that we use premises in different ways, don’t we? Sometimes we use premises as hypotheses, sometimes we use them as predictions, and so on. Okay. So, I hope I’veOkay, so I hope I’ve convinced you that the relation of validity is important to you if you’re concerned about truth. And what makes it important is that validity preserves truth. If there’s truth in the premises, there will be truth in the conclusion.

[译文 14]

正如我们一会儿将要看到的，你可以有一个前提为真但结论为假的有效论证。所以你可能会问，那么有效论证的意义何在呢？如果它能够得出结论为假的论证，我们为什么还要关心有效性？我要说的是，实际上，发现一个结论为假的有效论证可能非常重要。它之所以重要，是因为我们常常通过构造一个有效论证并检验其结论来检验我们的前提。我明白了。好，我只是，我刚刚说清楚了，只是为了说清楚我们是在通过构造一个显示结论为假的有效论证来检验假设，然后看到我们可以质疑其中一个或两个前提。好，你可以直接替换前提、前提、结论，没问题，完全一样。所以我们只是以不同方式使用前提，不是吗？有时我们把前提当作假设，有时我们把它们当作预测，等等。好吧。我希望我已经……好吧，我希望我已经说服你，如果你关心真理，那么有效性关系对你来说是很重要的。它之所以重要，是因为有效性保留真值。如果前提中有真，那么结论中必有真。

[段 15]

If there isn’t truth in the premises, there won’t necessarily be truth in the conclusion. And that might tell you that the premises are not true, which might be very useful information. In fact, it is often very useful information because, of course, the whole of science involves testing hypotheses and hoping, some would say, to falsify them. Okay, so why is this relationship of validity so important? What exactly is it? Well, there are different theories of the nature of validity, and there are some problems, as we’ll see later on, with the notion of validity. but what I’m going to give you now is the best theory that we can come up with. An argument is valid if and only if, and notice this logical phrase here, if and only if there is no possible situation in which all its premises are true, remember it must be all of them, and its conclusion false. Okay, that’s a claim about a valid argument. Okay, let’s move on. Okay, two things to beware of. Firstly, it’s the possibility ofto beware of. Firstly, it’s the possibility of the combination of true premises and false conclusion that’s ruled out by an argument being valid. Okay, so it’s not that it must have true premises or it must have a true conclusion.

[译文 15]

如果前提中没有真，那么结论中不一定有真。这可能会告诉你前提不为真，这可能是非常有用的信息。事实上，它通常是非常有用的信息，因为，当然，整个科学都涉及检验假设，并且一些人会说，希望证伪它们。好吧，那么为什么这种有效性关系如此重要呢？它到底是什么？关于有效性的本质，有不同的理论，而且正如我们稍后会看到的，有效性这个概念存在一些问题。但我现在要给你们的是我们能想到的最好的理论。一个论证是有效的，当且仅当，注意这里的逻辑短语"当且仅当"，不存在一种可能的情况，使得它的所有前提都为真，记住必须是所有前提都为真，而它的结论为假。好吧，这是关于有效论证的一个断言。好吧，我们继续。好吧，有两件事要注意。第一，要注意的，是要注意的是有效论证所排除的是真前提与假结论组合的可能性。好吧，所以并不是说它必须有真前提或者必须有真结论。

[段 16]

What it must have in order to be valid is true premises, sorry, what it must not have in order to be valid is the combination of true premises and false conclusion that’s completely ruled out by an arguments being valid and we’re going to do some exercise in a minute um also the second thing to note and second thing to be aware of and this is going to trip you up boy are you going to go leave today having felt you’ve really had a mental gymnastics because you’re all going to get this wrong, probably. Maybe you won’t. I mean, maybe you’re cleverer than most people are. But every class I’ve ever taught this to starts off by getting it wrong in almost every aspect. So don’t be worried if you do. It’s the possibility of the combination of true premises and false conclusions that’s ruled out, not just the actuality of that combination. so it’s not just that the premises as a matter of fact are true and the conclusion as a matter of fact is false that’s ruled out it’s the very possibilityIt’s the very possibility of the premises being true and the conclusion false that’s ruled out. Big difference between actuality and possibility. Marianne is actually wearing a skirt today, but she might have been wearing jeans. So there is a possible world in which Marianne’s wearing jeans, even though in the actual world she’s wearing a skirt.

[译文 16]

它必须具有的才是有效的，对不起，它在有效情况下所不能具有的，是真前提与假结论的组合，这被论证的有效性完全排除。我们一会儿要做一些练习。嗯，还要注意的第二件事，以及要意识到的第二件事，这一点会让你们搞砸的，孩子们，今天下课时你们一定会觉得经历了一场头脑体操，因为你们几乎都会答错。可能不会。我的意思是，也许你们比大多数人更聪明。但我教过的每一个班级，在几乎所有方面一开始都会答错。所以如果你们答错了，不要担心。有效论证所排除的是真前提与假结论组合的可能性，而不仅仅是这种组合的现实性。所以排除的不仅仅是前提事实上为真、结论事实上为假这种情况，而是排除前提为真且结论为假这种可能性。这是前提为真且结论为假这种可能性。现实性与可能性之间有很大区别。Marianne 今天实际上穿的是裙子，但她本来可能穿的是牛仔裤。所以在一个可能的世界里 Marianne 穿的是牛仔裤，即使在现实世界里她穿的是裙子。

[段 17]

OK. So faced with an argument whose validity we’re trying to determine, we’ve got to ask not just are the premises true and the conclusion false together in actuality, but could the premises be true and the conclusion false together in some situation? Okay, do you see the difference? You’re all looking very worried. Okay, let’s try a few, let’s test a few. Okay, I’m going to leave that with you. You have a look, put your hands up when you think, well actually let’s do the first one. Do you think an argument could be valid if all its premises are false? Put your hand up if you think you’ve got the answer. Don’t yell out. And don’t worry if you’re a bit slower. Everyone thinks at different speeds. Okay, if the premises of an argument are false, could the argument be valid? Could the argument be valid if…Could the argument be valid if the premises are false? Okay, those who said yes are right. Okay, you could have a valid argument in which the premises are false. The only thing that’s ruled out by an argument being valid is the possibility of the combination of the premises being true and the conclusion false. Okay? So the only thing that’s ruled out by an argument being valid is the possibility, not the actuality, of the combination of the premises being true and the conclusion false.

[译文 17]

好吧。所以面对一个我们试图判定其有效性的论证时，我们必须问的不仅是前提为真而结论为假在现实中是否同时存在，而且在某种情境中前提是否可能为真而结论是否可能为假。好吧，你们看出区别了吗？你们看起来都很紧张。好吧，我们试几个，我们检验几个。好吧，我把这个留给你们。你们看一看，想好了就举手，实际上我们来做第一题。你认为如果一个论证的所有前提都为假，这个论证还能是有效的吗？如果你有了答案就举手。不要喊出来。如果你慢一点也没关系。每个人思考的速度不同。好吧，如果一个论证的前提都为假，这个论证还能是有效的吗？前提为假的情况下……前提为假的情况下论证还能是有效的吗？好吧，那些说"能"的人是对的。好吧，你可以有一个前提都为假但有效的论证。论证有效性所排除的唯一情况就是前提为真而结论为假组合的可能性。好吧？所以论证有效性所排除的唯一情况，就是前提为真而结论为假组合的可能性，而不是现实性。

[段 18]

So you could have a valid argument, the premises of which are all false. If it’s Friday, Marianne’s wearing jeans, it is Friday, therefore Marianne is wearing jeans. Isn’t that an argument that has the two false premises but is valid? Okay, right, what about the following? The premises of the argument are true and the conclusion is true. Okay, remember the question. Do you think an argument of this sort could be valid? The premises are true and the conclusion is true. Okay, could it be valid or not? Well done. Well done. You’re getting there. Okay, that’s.Well done. You’re getting there. Okay, that’s pretty spectacular. Okay, good. What about the last one? The premises of the argument are true and the conclusion false. Put your hand up. Don’t yell out the answer. okay some of you say yes some of you say no the ones who say no in this case are right okay the only thing that’s ruled out by the definition of validity is an argument that’s valid where there’s a possibility and in this case there’s an actuality of the combination of premises that are true and conclusion false that’s the only one that’s ruled out and that is this one so an argument of this kind couldn’t be valid. The other two could. Okay, let’s, don’t worry, there’s plenty of time to practice. Okay, so let’s think again.

[译文 18]

所以你可以有一个前提都为假的有效论证。如果是星期五，Marianne 穿的是牛仔裤，今天是星期五，因此 Marianne 穿的是牛仔裤。这不是一个两个前提都为假但有效的论证吗？好吧，好的，接下来这个问题呢？论证的前提为真，结论为真。好吧，记住问题。你认为这类论证可能是有效的吗？前提为真，结论为真。好吧，它可能有效还是无效？做得好。做得好。你们开窍了。好吧，那真是。做得好。你们开窍了。好吧，这相当了不起。好吧，很好。最后一个问题呢？论证的前提为真，结论为假。举手。不要喊出答案。好吧，你们中有些说能，有些说不能。在这个题中说"不能"的同学是对的。好吧，定义有效性所排除的唯一情况就是一个论证是有效的并且存在一种可能性，在这个题中存在前提为真而结论为假的现实性，而这是被排除的唯一情况，就是这一种情况，所以这类论证不可能是有效的。另外两种可能是有效的。好吧，我们，别担心，有足够的时间练习。好吧，让我们再想一想。

[段 19]

If the premises could be true, together with, so do you remember I said two things you need to beware of, what are they? Two things I said you’ve got to beware of, what are they? Look back on your notes if you can’t remember, because I really meant it that you must be aware of these things. Two things you must be aware of. It’s the combination of true premises and false conclusion that’s ruled out, not either one or the other, but both together. So if the premises could be true together with the conclusions being false, okay, that’s one of the things you’re looking out for. What’s the other one? It’s the possibility of the combinationsone? It’s the possibility of the combination rather than the actuality. So if the conclusion could be false, together with the premises being true, if they could be the case, not just that if it is the case, if it could be the case, then the argument is valid. Is that right? Sorry, I lost track myself there. Yes, because it’s only deductive arguments that are truth-preserving, where the conclusion is guaranteed by the truth of the premises. Some people do talk about inductive validity and deductive validity, but if they do, they’re using valid in two different senses. I think it’s actually much better to stick to the idea of validity with deductive arguments and talk about inductive strength rather than inductive validity.

[译文 19]

如果前提可以为真，同时，记得我说过你要警惕的两件事，是什么？我说过有两件事你必须警惕，是什么？如果你想不起来，就回去看你的笔记，因为我说的是真的，你必须意识到这些事。两件你必须意识到的事。被排除的是真前提和假结论的组合，而不是单独其中之一，而是两者结合在一起。所以如果前提可以为真而结论为假，好，那是你要注意的事情之一。另一件是什么？那是组合的可能性而不是实际性。所以如果结论可能为假，前提为真，如果它们可能如此，不仅仅如果它是如此，如果它可能如此，那么这个论证就是有效的。对吗？抱歉，我自己有点跟不上了。是的，因为只有演绎论证是保真的，其中结论由前提的真来保证。有些人确实会谈论归纳有效性和演绎有效性，但如果他们这样做了，他们是在两种不同的意义上使用"有效"这个词。我认为坚持用"有效性"来谈论演绎论证、并用"归纳强度"而非"归纳有效性"来谈论要更好得多。

[段 20]

Because validity is an either-or thing, whereas strength is a matter of degree, and inductive arguments are more or less strong, whereas deductive arguments are either valid or invalid. What does an argument have to have to be sound? Can anyone tell me? Two things it needs in order to be sound. true premises and be valid that’s right so that’s soundness that’s fairly easy we can put that on one side we’re now looking atAnd that’s fairly easy. We can put that on one side. We’re now looking at validity, one of those characteristics. Okay. Last line, so it could be valid. Why don’t you say it is valid? Because, well, as I’m about to show you, it doesn’t mean it necessarily is valid. It could be valid. I thought valid was an either-or. Valid is an either-or thing for every argument. but if you have a situation where the premises have one truth value and the conclusion another truth value, that could encompass different arguments. I’ll show you exactly what I mean. Okay, so just keep this in mind. If the premises could be true together with the conclusions being false, then the argument is invalid, otherwise it could be valid. Okay, now this is a bit of a trick question. but, and I’ll explain why, actually it isn’t a trick question afterwards. Okay, here’s an argument. Now remember, I told you right at the very beginning that anything can be an argument depending on the context, okay?

[译文 20]

因为有效性是一个非此即彼的事情，而强度是一个程度问题，归纳论证或多或少是强的，而演绎论证要么有效要么无效。一个论证要成为可靠的，需要具备什么？有人能告诉我吗？它需要具备两样东西才能成为可靠的。真的前提并且有效，对了，那就是可靠性，那相当容易，我们可以把它放在一边，我们现在来看有效性，这是那些特征之一。好。最后一行，所以它可能是有效的。你为什么不说它是有效的？因为，好，我正要向你展示的，它并不一定意味着它就是有效的。它可能是有效的。我以为有效是一个非此即彼的。对于每个论证来说，有效是一个非此即彼的事情。但是如果你有一种情况，前提有一个真值，结论有另一个真值，那可以涵盖不同的论证。我会准确地向你展示我的意思。好，所以请记住这一点。如果前提可以为真而结论为假，那么论证就是无效的，否则它可能是有效的。好，现在这是一个有点刁钻的问题。但是，而且我之后会解释为什么，实际上它不是一个刁钻问题。好，这是一个论证。现在记住，我在最开始就告诉过你，根据上下文，任何东西都可以成为一个论证，好吗？

[段 21]

So you may not find this a very convincing argument, but believe me, it’s an argument. Because 2 plus 2 equals 5, therefore grass is green. Okay, that’s an argument. Could that be valid? Okay, now don’t try and be clever here.Now, don’t try and be clever here. Don’t try and be clever here. Work it out actually from the definition, which you can’t read there, but you can read in your notes. So have a look at that. Is there a situation in which the premises could be true and the conclusion false? Is there a situation, any situation in which that is true and that is false? Could it be that that is true and that false in any possible world? No. Okay. So is that argument valid? Who said yes? Somebody said yes, and if they would admit to it, I would then give them a clap. Well done. It is. That’s a valid argument. And what that shows you is that actually for an argument to be good, It needs more than validity. Okay, that is a perfectly valid argument because there’s no possible situation in which that premise is true and that conclusion false. And the reason for that is there’s no possible situation in which that premise is true, is there? That premise is a contradiction. And you may have heard the saying, anything follows from a contradiction. and the reason anything follows from a contradiction is that a contradiction must be false.

[译文 21]

所以你可能不会觉得这是一个很有说服力的论证，但请相信我，这是一个论证。因为2加2等于5，所以草是绿的。好，这是一个论证。那能是有效的吗？好，现在不要在这里耍小聪明。不要在这里耍小聪明。不要在这里耍小聪明。实际根据定义来推导它，你在那里读不到，但可以在你的笔记里读到。所以看看这个。是否存在一种情况，前提为真而结论为假？是否存在一种情况，任何情况，其中这个为真而那个为假？它可能在任何可能的世界中为真而那个为假吗？不。好。那么那个论证有效吗？谁说是的？有人说是的，如果他们愿意承认，我会给他们鼓个掌。答得好。它确实是。那是一个有效的论证。那向你表明的实际上是，要成为一个好的论证，它需要的不仅仅是有效性。好，那是一个完全有效的论证，因为不存在前提为真而结论为假的情况。而原因是，存在前提为真的情况，对吧？那个前提是一个矛盾。你可能听过这句话，矛盾可以推出任何东西。而矛盾可以推出任何东西的原因是，矛盾必定为假。

[段 22]

So there’s no possible situation in which the premise is true, therefore there couldn’t possibly be a situationtrue, therefore there couldn’t possibly be a situation in which the premise is true and the conclusion false, could there? So that satisfies the definition of validity. And that’s what I want you to go on. Because what, shall I tell you why you’re all sitting there looking so worried? I feel for you, I really feel for you, but I went through this. Honestly, I did that. I’ll tell you, When I was an undergraduate, we did logic in my first term. And I sat there looking a bit like some of you were looking there through the whole term, thinking, oh, what have I got myself in for? And then during the vacation, I sat there with my logic book, and I worked through it step by step by step. And I went over it again and again and again and again. And the thing that I had been missing all along was that I should have been taking more account of definitions than I had been. I was doing what you’re almost certainly doing now. True is a good thing, isn’t it? True sort of gives you a nice, warm feeling, all sort of warm and cuddly. And validity gives you that same sort of nice, warm feeling, doesn’t it?

[译文 22]

所以不存在前提为真的可能情况，因此不可能存在一种情况，前提为真而结论为假，对吧？所以那满足有效性的定义。而那正是我要你继续的地方。因为什么，要我告诉你们为什么你们都坐在那里看起来那么担忧吗？我同情你们，我真的同情你们，但我讲过这个了。说真的，我讲过。我告诉你，当我还在读本科的时候，我们在第一学期就学逻辑。我坐在那里的样子有点像你们有些人刚才看了一整个学期的样子，想着，哦，我给自己找了个什么差事？然后在假期里，我坐在那里抱着我的逻辑书，一步一步一步地钻研。我一遍又一遍又一遍又一遍地复习。我一直遗漏的事情是我本应更多地关注定义。我当时几乎肯定在做的就是你现在在做的事情。真是一件好事，对吧？真给你一种美好的、温暖的感觉，都很温暖很舒适。而有效性也给你同样的美好、温暖的感觉，不是吗？

[段 23]

You know, so therefore, anything that’s true is valid. And anything that’s valid is true. And all this business about false premises, you know, has nothing to do with… Is that… Do you think this might be behind what… Yeah. Yes. Okay. Does that help? So try and drop the fact that both truth and validity make you feel all warm inside.Truth and validity make you feel all warm inside. And just go for the definition. Does this argument satisfy the definition of validity or does it not? Could this argument satisfy the definition of validity or could it not? That’s what you answer on. Not on your nice, warm feelings of truth and validity going together. Because sadly, they don’t. Except in the one case of truth being preserved by true premises. okay does everyone see why this is a valid argument would you like me to go over it again yeah okay sorry okay um okay the definition of validity is there is no possible situation an argument is valid if and only if there’s no possible situation in which the premises are true and the conclusion false and what matters is that it’s a possible situation not an actual situation and that it’s the combination of true premises and false conclusion that’s ruled out. Okay, that’s the definition of validity. Now, here we have an argument. Okay, could this be valid?

[译文 23]

你知道的，所以，因此，任何真的东西都是有效的。任何有效的东西都是真的。所有关于假前提的事，你知道，都与……那是……你认为这可能是……在……的后面吗？是的。是的。好。那有帮助吗？所以试着抛开真和有效都让你内心温暖的事实。真和有效都让你内心温暖。直接去看定义。这个论证是否满足有效性的定义，还是不满足？这个论证可能满足有效性的定义还是不可能？这就是你要回答的依据。不是依据你对真和有效相伴而来的温暖感觉。因为遗憾的是，它们并不相伴。除了一种情况，真由真前提来保存。好，每个人都明白为什么这是一个有效论证了吗？要我再说一遍吗？好，抱歉，好，呃，好，有效性的定义是，不存在一种情况，一个论证是有效的，当且仅当不存在一种情况，其中前提为真而结论为假，而重要的是那是一个可能的情况而不是一个实际的情况，并且被排除的是真前提和假结论的组合。好，这就是有效性的定义。现在，我们这里有一个论证。好，这可能是有效的吗？

[段 24]

Well, is there a situation? Could it be the case, could it be the case, that’s what I’m asking, that this premise is true together with this premise being false? well you look at this and you see that there actually isn’t any situationand you see that there actually isn’t any situation ever anywhere in which this could be true. Is that true? So how could there ever be a situation in which that’s true and that’s false? Couldn’t be could there? With me? Yeah and I can see it’s getting there isn’t it? I can see understanding dawning on about 50% of faces. The other 50% are looking pretty sick. Okay. Okay, if I say that something’s P and Q, and then I say that, okay, is that true? You don’t know, do you? But if I then say not P, and say, is this true? What do you know? No, you don’t know not Q. But do you know the truth value of this? If P is false, what’s the truth value of P and Q? False. It must be, mustn’t it? Because a necessary condition for P and Q being true is that P and Q are true. Sorry. But it is, isn’t it? You all knew that immediately. In the same way, if I say there’s no possible situation where this is true and this is false, well if there’s no possible situation in which thiswell if there’s no possible situation in which this is true then how could there be a situation in which this is true and this is false?

[译文 24]

好吧，存在一种情况吗？它可能如此吗，它可能如此吗，我问的是，这个前提为真而这个前提为假？好吧，你看看这个，你会发现实际上在任何地方都根本不存在一种情况，它可能为真。是这样吗？那么怎么可能存在一种情况，其中那个为真而那个为假呢？不可能有，对吧？跟上我了吗？是的，我能看到它正在起作用，不是吗？我能看到理解在大概50%的人脸上浮现。另外50%看起来相当难受。好。好，如果我说某物是P和Q，然后我说，好，那是真的吗？你不知道，对吧？但是如果我接着说非P，然后说，这是真的吗？你知道什么？不，你不知道非Q。但是你知道这个的真值吗？如果P为假，P和Q的真值是什么？假。它必须是，对吧？因为P和Q为真的一个必要条件是P和Q都为真。抱歉。但确实是，对吧？你们都立刻知道这一点。同样地，如果我说不存在一种可能的情况，其中这个为真而这个为假，好，如果不存在一种可能的情况，其中这个为真，那么怎么可能存在一种情况，其中这个为真而这个为假呢？

[段 25]

Another couple of lights went on then. I’ll do another one. Let’s see another one. Could this argument be valid? Put your hands up when you’ve got the answer. Don’t yell it out. Don’t shell it out, just… Oh dear, nobody’s got it yet. Oh yeah, one hand’s up. Two. Well done. Well done. Okay, so you’re asking yourself, could there be a possible situation in which that is true and that’s false? Is there any possible situation in which that’s true and that’s false together? Is there any situation in which that’s true and that’s false together? put your hand up when you’ve got the answer yes IWhat’s worrying me is that I thought the valid argument was where the premises were true and the conclusion was true. No, you’re doing exactly what I’m warning against. Did you hear what the lady said? She said she thought a valid argument was where the premises were true and the conclusion true. Now, that’s a classic example of thinking that because validity is good and truth is good, therefore a valid argument must have true premises and true conclusion. Do you see how that works? But actually, a valid argument doesn’t have true premises and true conclusions. What is a valid argument? You give me the definition of a valid argument. Yeah. You’ve got it written down in front of you.

[译文 25]

然后又有几盏灯亮了。我再做一个。我再做一个。我们看看下一个。这个论证可能有效吗？想好答案就举手。别喊出来。别急着喊出来，只是……哎呀，还没有人想出来。哦，有了，一只手举起来了。两只。做得好。做得好。好吧，你们在问自己，有没有一种可能的情况，让这个为真而那个为假呢？有没有任何可能的情况，让这个为真而那个同时为假？有没有任何情况，让这个为真而那个同时为假？想好答案就举手，是的，我……让我担心的是，我原以为有效论证就是前提为真且结论为真的那种。不是的，你正在做的恰恰是我警告过的事情。你们听到那位女士说的了吗？她说她以为有效论证就是前提为真且结论为真的那种。这就是一个典型的例子，人们以为既然有效性是好的、真理是好的，因此有效论证就必须有真的前提和真的结论。你们明白这是怎么回事了吗？但实际上，有效论证并不一定有真的前提和真的结论。什么是有效论证？给我一个有效论证的定义。好的。你面前就写着呢。

[段 26]

Oh, no, you haven’t got it written there anymore. It’s on slide 19. I’m glad you asked me that question because you will be far from the only person in the room who’s thinking exactly what you’re thinking. And the two things that are important is that we’re looking at the combination of true premises and false conclusion, and we’re looking at the possibility of, not the actuality of. This is why the definition is important. And as soon as you understand that, as soon as you stop thinking of a valid argument as having true purpose,stop thinking of a valid argument as having true premises and true conclusion, you will see what’s going on here. I promise you. It’s a bit rash, isn’t it? Don’t give me the answer yet. Okay, put your hand up if you’ve got the answer to that. Is that, or could that argument be valid? Hand up if you’ve got it. Right up so I can see you. Okay, is it valid? Yes, it is valid. Those who said yes have got it right. Okay, now why is it valid? Okay, would anyone like to give me a crisp and clear account of why it’s valid, or should I do it? Would you like to have a go? That’s right. this can’t possibly be false, can it? So there’s no possible situation in which the conclusion is false.

[译文 26]

哎呀，你那里已经没有写着这个了。在第 19 张幻灯片上。我很高兴你问我这个问题，因为你绝对不会是这个房间里唯一正在这样想的人。重要的两点是，我们在看真前提与假结论的组合，而且我们看的是可能性，而不是现实性。这就是定义重要的原因。一旦你理解了这一点，一旦你不再把有效论证想成有真的前提……不再把有效论证想成有真的前提和真的结论，你就会明白这里在讲什么。我向你保证。这有点草率，不是吗？先别告诉我答案。好，想好答案了就举手。那个论证有效吗？想好答案了就举手。把手举高些，这样我能看见你。好，它是有效的吗？是的，它是有效的。说"是"的人都答对了。好，那为什么它是有效的呢？好，有没有人想给我一个简洁清晰的解释，来说明它为什么是有效的，还是要我来讲？你们想试一下吗？没错。这不可能是假的，对吧？所以不存在结论为假的可能情况。

[段 27]

So how could there be a possible situation in which the premise is true and the conclusion false? See what I mean? Could this argument be valid? Actually, as a matter of fact, this argument must be valid. Can anyone tell me why it must be valid rather than just could be valid? That can never be false. that’s necessarily true, isn’t it? Given that that’s necessary,necessarily true, isn’t it? Given that that’s necessarily true, how could there be a possible situation in which that’s true and that’s false, given that that cannot be false? Cannot be false. It’s not just that it is false, it’s that it can’t be false. And actually, the same is true of the other one, if you look at this. Given that that is a contradiction, it’s necessarily false. Again, there’s no possible situation in which that’s true, so how could it the case that that’s true and that’s false. It couldn’t be. So if we say, could this argument be valid in each of those cases, the answer is no, it could, sorry, yes. Not only is it valid, but it must be valid. And why is that? Because there’s no possible situation in which the premises are true and the conclusion false. So when you ask me, is the answer to those two questions different? They’re different questions. OK, let me just tell you that the two arguments I’ve given you here are called the paradoxes of entailment.

[译文 27]

那么怎么可能存在前提为真而结论为假的情况呢？明白我的意思了吗？这个论证可能有效吗？事实上，这个论证必须是有效的。有人能告诉我为什么它必须是有效的，而不仅仅是可能有效吗？那永远不可能是假的。那是必然真的，不是吗？既然那是必然的……必然真的，不是吗？既然那是必然真的，怎么可能存在一种可能情况，让那个为真而这个为假呢，既然那个不可能为假？不可能为假。不仅仅是它为假，而是它不可能为假。事实上，另一个也一样，如果你看一下的话。既然那是一个矛盾，它就是必然假的。同样，不存在那个为真的任何可能情况，所以怎么可能那个为真而这个为假呢。不可能。所以如果我们问，这两个论证中每一个都可能有效吗，答案是……不，它可以，对不起，是的。它不仅有效，而且必须是有效的。为什么呢？因为不存在前提为真而结论为假的可能情况。所以当你问我，那两个问题的答案是否不同时，它们是不同的问法。好，让我直接告诉你们，我在这里给出的两个论证叫做"衍推悖论"。

[段 28]

The paradoxes of entailment. And a paradox is something that you cannot understand. It’s just something you can’t wrap your mind around. And the reason you want to look at these and tell me that they’re not arguments, OK, is because they couldn’t convince you of anything, could they? I mean, as arguments, they would be pretty lousy because theyarguments they would be pretty lousy because they wouldn’t be convincing but they’re still valid because they satisfy the definition of validity so in the same way we might say if if you think you know whales for example aren’t fish are they well they jolly well should be shouldn’t they i mean it seems to me they jolly well should be they they go swimming around and they’re you know they’re they’re fish aren’t they um but they’re not because they don’t satisfy the definition of fish, they satisfy the definition of mammal. Well, you might want to say, well, surely we should fiddle with our definitions so that whales come out fish, because they’re fish, obviously. But they’re not. And do you see what I mean? Sometimes things that are really rather irritating are thrown up by definitions that work for every other case. And therefore, you think, oh, Sonic will just put up with these anomalies. Well, these are the paradoxes of entailment, because we wish that our definition of validity didn’t generate these two arguments as valid, but they do.

[译文 28]

衍推悖论。悖论就是那种你无法理解的东西。就是那种你无法想通的东西。你们之所以想看看这些论证，然后告诉我它们不是论证，好，是因为它们没法说服你任何事情，对吧？我是说，作为论证，它们相当糟糕，因为它们……作为论证，它们相当糟糕，因为它们没有说服力，但它们仍然是有效的，因为它们满足有效性的定义。所以用同样的方式，我们也许会说，比如你认为你知道鲸鱼，它们不是鱼，对吧？它们理应是鱼，不是吗？我是说，在我看来它们理应是鱼，它们在水里游来游去，你知道，它们是鱼，不是吗？但它们不是鱼，因为它们不满足鱼类的定义，它们满足哺乳动物的定义。你也许会说，好吧，我们应该修改一下我们的定义，让鲸鱼也归为鱼类，因为它们显然是鱼。但它们不是。你明白我的意思了吗？有时候，定义在所有其他情况下都管用，却会抛出让一些相当令人烦恼的东西出来。因此你会想，哦，好吧，就容忍这些反常吧。这就是衍推悖论，因为我们希望我们关于有效性的定义不会产生这两个有效论证，但它确实产生了。

[段 29]

And actually, think about everything follows from a contradiction. That makes sense, doesn’t it? Because if I say Marianne’s wearing a skirt and it’s not the case Marianne’s wearing a skirt, that leaves open every possibility, doesn’t it? Everything follows from a contradiction because a contradiction doesn’t rule out any possibility at all. Okay, so those are the paradoxes of entailment. Actually, these are aare the paradoxes of entailment. Actually these are a pretty good test of your understanding of validity because when you see that those two arguments, the paradoxes of entailment, must be valid then you’ll have understood validity. So that’s quite a good little way of testing your own understanding of validity. Are you actually saying that you can put anything you like, any sort of garbage where you’ve got grass and the argument will still be that. Yes, absolutely. That’s right. It really doesn’t matter. And actually that’s true anywhere because let me this is actually a theorem. If you have an argument I’ve just seen a can of worms opening up in front of me as I’m about to do this but let’s see if I can do it. Okay, if you have a premise here and a premise here, sorry, let’s do it this way. I’m going to draw a truth table. I haven’t actually introduced you to truth tables, but it doesn’t really matter because they’re very easy.

[译文 29]

实际上，想想矛盾蕴含一切。这说得通，不是吗？因为如果我说"玛丽安穿着裙子"并且"并非玛丽安穿着裙子"，那就开放了所有的可能性，不是吗？矛盾蕴含一切，因为矛盾根本不排除任何可能性。好，那些就是衍推悖论。实际上，这些是……是衍推悖论。实际上这些是检验你是否真正理解有效性的一种相当好的方式，因为当你看到那两个论证——衍推悖论——必然是有效的时候，你就理解了有效性。所以这是检验你自己对有效性的理解的一个相当不错的小方法。你是不是在说，你可以放任何你喜欢的、放任何垃圾进去，只要你拿到草，那论证就还是会那样。是的，完全正确。就是这样的。确实无关紧要。而且事实上，这在任何地方都对，因为让我……这其实是一个定理。如果你有一个论证，我刚刚看到我面前打开了一罐虫子，就在我要做这一步的时候，但让我们看看我能不能做到。好，如果你在这里有一个前提，这里有一个前提，对不起，让我们这样做。我要画一个真值表。其实我还没有向你们介绍真值表，但这并不重要，因为它们非常简单。

[段 30]

True, true, false, false. P and Q. Okay, I’ve got each of these structures is a different world. Okay, this…is a different world. Okay, this is the world in which Q is true and P is true. Okay, what’s the truth value of P and Q in this world? True, good, well done. Okay, this is the world in which Q is true and P is false. What’s the truth value of P and Q in this world? Brilliant. Okay, this is the world in which Q is false and P is true. Okay, what’s the truth value of P and Q in this world? And here’s the world where P and Q are both false. What’s the truth value? False again. Okay, so we had true, false, false, false, didn’t we? Remember that? Okay, now this is the world where Q is true and P is true. What’s the truth value of Q in this world? True. What about this world? True. What about this world? False. False. false that’s just Q so in the world where Q is false it’s got to be false hasn’t it okay what about P true false true false okay that’s just copying out that bit of the truth table now here’s an argument Q and P Q therefore P okay you with me now we can use this truth table to test whether this arguments valid.

[译文 30]

真，真，假，假。P 和 Q。好，这里的每一种结构都是一个不同的世界。好，这个……是一个不同的世界。好，这是 Q 为真且 P 为真的世界。好，在这个世界里 P 和 Q 的真值是什么？真，很好，做得好。好，这是 Q 为真且 P 为假的世界。在这个世界里 P 和 Q 的真值是什么？太棒了。好，这是 Q 为假且 P 为真的世界。好，在这个世界里 P 和 Q 的真值是什么？这是 P 和 Q 都为假的世界。真值是什么？又是假。好，我们得到的是真、假、假、假，对吧？记得吗？好，现在这是 Q 为真且 P 为真的世界。在这个世界里 Q 的真值是什么？真。这个世界呢？真。这个世界呢？假。假。假，那只是 Q，所以在 Q 为假的世界里它必定是假，不是吗？好，那 P 呢，真、假、真、假，好，那只是把真值表那一部分抄下来。现在这里有一个论证，Q 且 P，Q，因此 P。好，你们跟上我了吗？现在我们可以用这个真值表来检验这个论证是否有效。

[段 31]

Here the two premiseswhether this argument’s valid. Here, the two premises are true, and the conclusion is true. So that’s okay, that seems to be valid. Here, one premise is true, the other is false, and the conclusion’s false. So that seems to be valid as well. Is that reasonable? That’s not a possible situation in which the premises are both true and the conclusion false. Yeah? Is this a situation in which the premises are both true and the conclusion false? No. No, because the premises are both false and the conclusion true, the other way around. And what about this? The premises are both false and the conclusion false, so that could also be valid. So as you’d expect, that argument is valid. But notice, if I put in any other premise here, it’s going to stay valid. Any other premise. What would you like me to put in here in order to make the argument invalid? Not P. Yeah? Okay, if I put in not P. OK, this is the world in which P is true, so not P will be, no, this is the world in which P is true, so not P will be false. OK, this is the world where P is false, so not P will be true, good. This is the world where P is true, so not P will be, and it’s false here, so it’ll be true.

[译文 31]

这里我们看两个前提，这个论证是否有效。这里，两个前提为真，结论也为真。所以没问题，这看起来是有效的。这里，一个前提为真，另一个为假，结论为假。所以这也看起来是有效的。这合理吗？这不是一种前提都为真而结论为假的情况。对吧？这是前提都为真而结论为假的情况吗？不是。不是的，因为这里前提都为假，结论为真，正好相反。那么这个呢？前提都为假，结论为假，所以这也可能是有效的。正如你所预期的，这个论证是有效的。但是注意，如果我把任何其他前提放在这里，它仍然是有效的。任何其他前提。你想让我在这里放什么才能让论证无效？不是 P。是吗？好的，如果我放上不是 P。好，这是 P 为真的世界，所以不是 P 将是假的，不，这是 P 为真的世界，所以不是 P 将是假的。好，这是 P 为假的世界，所以不是 P 将是真的，不错。这是 P 为真的世界，所以不是 P 将是，而它在这里是假的，所以它在这里是真的。

[段 32]

So, let’s test for validity again, OK. Now this one, in this world, the premises are true.Now this one, in this world, the premises are true, true and false and the conclusion is true. Okay, is that alright or is that a counterexample? Is that still valid? So it’s not the case that all the premises are true. Okay, the conclusion is true but that’s okay, it’s still valid, isn’t it? What about false, true, true as the premises and the conclusion is false? Still okay, isn’t it? we haven’t yet found one where we’ve got true, true, true, and then false as the conclusion, which is what we’d be looking for. Here we’ve got false, false, false, true. Valid? Yep. And here we’ve got false, false, true, false. Valid? Yep. So you see, I could add in even a negation of the conclusion and it hasn’t changed the validity. Once you’ve got a valid argument, you can add anything you like and it’ll still be valid. I don’t know why I went into telling you all that. This is information you really didn’t need to know, but it’s so interesting, isn’t it? I think it’s interesting. Let’s move on. Okay, so let’s test you again. Okay, don’t shout out your answer. So is the argument valid if we’ve got true premises and a true conclusion? could it be valid is what I should have askedCould it be valid is what I should have asked.

[译文 32]

好，让我们再检验一次有效性，好。现在这个，在这个世界里，前提为真。现在这个，在这个世界里，前提为真，真和假，而结论为真。好的，这样行得通，还是说这构成了一个反例？这还是有效的吗？前提并非全为真。好的，结论为真但那没关系，它仍然是有效的，对吧？那么前提为假、真、真，而结论为假呢？也仍然没问题，对吧？我们还没有找到一种情况是前提为真、真、真，而结论却是假，而这正是我们要寻找的。这里是假、假、假、真。有效？是的。这里是假、假、真、假。有效？是的。所以你看，即使我加入结论的否定，有效性也没有改变。一旦你有一个有效的论证，你可以随便加入任何东西，它仍然会有效。我不知道为什么我要跟你们说这些。这些信息你们其实真的不需要知道，但它真的很有趣，不是吗？我觉得很有趣。我们继续吧。好，我们再来考考你们。好的，不要喊出你的答案。如果前提为真且结论为真，这个论证有效吗？我本应该问的是——它可能有效吗，这才是我本应该问的。

[段 33]

Yeah, hand up if you think yes. Yeah, okay, you’re quite right. False premises, true conclusion. Hand up. Okay, premises are false, the conclusion’s true. Could it still be valid? Yep, good, well done. What about false conclusion, false premises? Could it still be valid? Yes, yes. and true premises, false conclusion, could it be valid? No. Some of you are getting there. Some of you I thought had got there have gotten themselves lost in the meantime. Okay, I’m going to look at this another way of looking at it just because you’re already probably exhausted. I’m already exhausted. We’re going to look at Venn diagrams. And we’re actually going to run out of time in this session. Okay, here’s an example. Here we have two arguments. In both cases, the premises are actually true and the conclusion is actually true. Okay, but one of them is valid and the other one isn’t valid. And I’m going to show that to you by means of Venn diagrams, if I can find my pen. So, all cats meow. Okay, here’s the class of meowers, right? All cats…all cats are meows, so where should I draw the class of all cats? Inside, outside, or overlapping? Inside. If all cats meow, then all cats must be inside the class of things that meow. Is that right? Okay. Bo, incidentally, I hope you noticed my topical reference to the dog of the United States of America. unless he’s died since I…

[译文 33]

是的，认为可以的人举手。是的，好，你完全正确。前提为假，结论为真。举手。好的，前提为假，结论为真。它仍然可能有效吗？是的，很好，做得不错。那么结论为假、前提为假呢？它仍然可能有效吗？是的，是的。那么前提为真、结论为假呢，它可能有效吗？不能。你们中的一些人快想到了。我以为你们中一些人已经想到了，但中间又绕进去了。好的，我要换一种方式来讲解，因为你们可能已经很累了。我已经很累了。我们要来看韦恩图。而且我们实际上这节课时间要不够了。好的，这里有一个例子。这里有两个论证。在这两种情况下，前提实际上为真，结论实际上也为真。但是其中一个是有效的，另一个不是有效的。我要用韦恩图来向你说明这一点，如果我能找到我的笔。好的，所有的猫都会喵。好，这里是喵喵叫的动物的类，对吧？所有的猫……所有的猫都喵，所以所有的猫这个类我应该画在哪里？里面、外面，还是重叠？里面。如果所有的猫都喵，那么所有的猫必须在喵喵叫的事物这个类的里面。对不对？好的。顺便提一下，我希望你注意到我对美利坚合众国之犬 Bo 的应景引用。除非他在我之后已经……

[段 34]

OK, Bo does not meow. So where do I draw Bo? Here. OK. Bo is not a cat. Well, is that true? Yeah, OK, that’s true. So if all cats meow and Bo does not meow, then Bo is not a cat. There’s no possibility, is there, in which those are true and that’s not true. If those are true, that’s got to be true. Okay, so that’s a valid argument. Accept it? Okay, and yes, the truth value of that is true. Yes? Truth value of that is true? I assume the dog doesn’t meow. And that’s true as well. Okay, so you accept my claim about the truth values, and you accept my claim about the validity. Okay, let’s have a look at this one. All cats meow. So, here’s the meowers. Well,meowers. Where do I draw the thing of cats? Okay, cats. Okay, second premise, dogs are not cats. They’re outside the class of cats, aren’t they? But they could be either inside or outside or overlapping the class of meowers, couldn’t they? So there is a possible situation in which that’s true and that’s true but that isn’t true and that’s the possible situation in which cats meow now we know that cats don’t actually meow glad you’re all with me um but you see dogs could meow couldn’t they as far as that i mean these do not guarantee that do they in the way that these guarantee that is that right And yet, would you agree with me that that’s true?

[译文 34]

好，Bo 不喵。那么我应该把 Bo 画在哪里？这里。好。Bo 不是猫。嗯，这是真的吗？是的，好，这是真的。所以如果所有的猫都喵，而 Bo 不喵，那么 Bo 不是猫。在任何可能的情况下，那些为真而这个不为真，对不对？如果那些为真，这个就必须为真。好的，所以这是一个有效的论证。接受吗？好的，是的，它的真值为真。是吗？它的真值为真？我假设这只狗不喵。而那个也是真的。好的，所以你们接受我关于真值的说法，也接受我关于有效性的说法。好的，我们来看这个。所有的猫都喵。所以，这里是喵喵叫的动物。嗯，喵喵叫的动物。我应该把猫这个事物画在哪里？好的，猫。好的，第二个前提，狗不是猫。它们在猫这个类的外面，对吧？但是它们可以在喵喵叫的动物这个类的里面、外面，或者与之重叠，不是吗？所以有一种可能的情况，那个为真，那个也为真，而这个不为真，这就是猫喵喵叫的那种可能情况——现在我们知道猫其实不会喵，我很高兴你们都跟上我，嗯，但你看，狗是可能会喵的不是吗，就这个论证而言，我的意思是这些并不能保证那个成立，对吧？就像那些能保证这个成立一样，对不对？然而，你会同意我说的那个是真的吗？

[段 35]

Yeah? That’s true? Is that true? Oh, come on. Is it true? Is it actually true? Yes, it is. Dogs do not meow. But that’s not a necessary truth, is it? Dogs could meow. So there is a possible situation. And this does not rule out that possible situation. So here we have premises where the actual truth values, the premises are all true, the conclusion is true, but here’s one of an argument exactly like that that’s valid, and here’s an argument exactly like that that’s not valid. What’s the difference between them? Answer, in this case, if the premises are true, the conclusion couldn’t be false. Okay? Whereas here, if the premises are true, the conclusion could still be false. Okay? If we didn’t know, I’m talking about dogs here, but what if I was talking about, name an animal you wouldn’t know anything about, griffins. Actually, you’ve all watched your Harry Potter, so that’s a bad example too. Okay, I’m talking about a mythological animal or an animal we’ve only just discovered. I can tell you, unicorns are not cats, but unicorns don’t meow. You actually wouldn’t know the truth value of that, would you? And you’d have to recognize that the truth of those two leaves that one open. Okay? That’s the importance of validity. Here’s the next one. Okay, I’ve got two arguments again. The premises are actually false, I hope, and the conclusion is actually true.

[译文 35]

是吗？那个是真的吗？那个是真的吗？噢，拜托。是不是真的？是不是真的？是的，是真的。狗不会喵。但这不是一个必然真理，对吧？狗是可能会喵的。所以这里有一种可能的情况。而这并没有排除那种可能的情况。所以这里我们有一个前提的实际真值都为真、结论为真的论证，但这里有一个与之完全一样但有效的论证，这里有一个与之完全一样但无效的论证。它们之间的区别是什么？答案是，在这种情况下，如果前提为真，结论不可能为假。好的？而这里，如果前提为真，结论仍然可能为假。好的？如果我们不知道，我这里说的是狗，但假如我说的是一种你一无所知的动物，比如 griffin（狮鹫）。其实你们都看过《哈利·波特》，所以这也是个不好的例子。好，我在说一种神话中的动物，或者一种我们刚刚发现的动物。我可以告诉你，独角兽不是猫，但独角兽不会喵。你其实不知道那个的真值，对吧？你必须认识到，那两个为真使这一个的真值悬而未决。好的？这就是有效性的重要性。这里是下一个。好的，我又有两个论证。前提实际上为假，我希望如此，而结论实际上为真。

[段 36]

Okay, do you accept that that’s false? Is that false? Is that true? It is. Is that false? Yes, there are fish without scales.There are fish without scales. I looked it up. And Jewish people either can or can’t eat them. I can’t remember which it is. But there’s a whole table of which fish have scales and which don’t. Whales have scales. Is that false? Good. Whales are not fish. True or false? True. Okay, good. So you agree with me that the truth values, the actual truth values are like that. Yes? Okay, as I described. Now let’s look at the validity of these arguments. All fish have lungs. This is the class of lunged things. Where do I draw the class of fish? Inside, here’s fish. If whales have lungs, where have I got to draw the… In the box. Hang on, all fish have lungs. Whales are fish. It’s got to be there, hasn’t it? Okay, so it’s got to be there. And if it’s there, what’s got to be the case? It’s got to have lungs, hasn’t it? So if those two are true, that’s got to be true. Accept that?

[译文 36]

好的，你接受那是假的吗？那是假的吗？那是真的吗？是的，是真的。那是假的吗？是的，有些鱼是没有鳞片的。有些鱼是没有鳞片的。我查过了。而犹太人要么能吃、要么不能吃它们。我记不清是哪一种了。但有一整张表列出哪些鱼有鳞片、哪些没有。鲸鱼有鳞片。这是假的吗？很好。鲸鱼不是鱼。真还是假？真。好的，很好。所以你同意我的看法，实际的真值是这样的。对吧？好的，就像我所说的。现在我们来看看这些论证的有效性。所有的鱼都有肺。这里是有肺的东西的类。我应该把鱼这个类画在哪里？里面，这里是鱼。如果鲸鱼有肺，我应该把……画在盒子里。等等，所有的鱼都有肺。鲸鱼是鱼。它必须在那里，对吧？好的，所以它必须在那里。如果它在那里，那么什么必须成立？它必须有肺，对吧？所以如果那两个为真，这个就必须为真。接受吗？

[段 37]

Now let’s have a look at the final one. sorry not the fine one all fish have scales this is the class of scaled things class of fish in there okay whales have scales so where do I draw whales it’s got to be within there has it got to be here or here it could be in either couldn’t it and whales are not fish okay that tells us that it is there but it could be either couldn’t it again, the truth of these two if they were true doesn’t guarantee the truth of that because you can have scales without being a fish so again, if you look at the explanation underneath in both cases the premises are actually false and the conclusion is actually true but in the first place, if the premises were true the truth of the conclusion I should have said there Can you see? Scrub it out on your copy. That should be conclusion. The truth of the conclusion would be guaranteed. In the second case, even if the premises were true, the conclusion could still be false. Okay, it isn’t false, but it could be. Are you beginning to follow? And here, I’ll actually, I’ll skip over these. Would you like me to do these with you as I’ve done the others? You would? Okay. You’re gluttons for punishment, aren’t you?You would.

[译文 37]

现在我们来看最后一个。抱歉，不是"好的"那个。所有鱼都有鳞，这是有鳞事物的类，鱼的类在这里。好，鲸鱼有鳞，那么我应该把鲸鱼画在哪里呢？它应该在这里或这里，对吧，它可以在任意一处，不是吗？而且鲸鱼不是鱼。好，这告诉我们它应该在这里，但它也可以在任意一处，不是吗？同样，如果这两个前提为真，并不能保证结论为真，因为你可以有鳞但不是鱼。所以再次强调，如果你看一下下面的解释，在这两种情况下，前提实际上是假的，结论实际上是真的。但首先，如果前提为真，那么结论的真——我应该说——你看得出来吗？在你那份上擦掉。那里应该是"结论"。结论的真会得到保证。在第二种情况下，即使前提为真，结论仍然可能为假。好吧，它实际上不是假的，但它可以是假的。你开始跟上来了吗？这里呢，我其实会跳过这些。你们希望我像之前那样带你们一起做这些吗？你们想？好。你们真是自讨苦吃，对吧？你们想。

[段 38]

Okay. You’re gluttons for punishment, aren’t you? Okay. Firstly, do you agree with me that the truth values are as I say? Okay. I’ve said everything’s false. Is that false? All fish have wings. Yep. Whales are fish. Is that false? Whales have wings. False? False. Okay. All fish have scales. False. Whales have scales. False. Whales are fish. Okay, so all the premises and the conclusions are false here. But this argument is valid and this argument is invalid. Okay, why do I say that? Well, if I find my pen again. All fish have wings. Here’s the class of winged things. The class of fish is inside. Whales have wings. Oh, sorry, yes, thank you. I’m suddenly thinking, oh my God, it’s not valid. All fish have wings. Whales are fish. Okay, therefore they’ve got to have wings, haven’t they? That guarantees it. They’ve got to be inside the class of winged things. What have we got over here? We’ve got all fish have scales. So there’s the scales things. And there’s the fish. whales have scales wellWhales have scales? Well, they could be either or, couldn’t they? Whales are not fish. Well, okay, that tells us that whales are here. But is that guaranteed other than the fact that we’re saying that that’s true? You know, actually, it could be false, couldn’t it? Even though it is true, it could be false.

[译文 38]

好。你们真是自讨苦吃，对吧？好。首先，你们同意我说的真值如我所说的吗？好。我已经说了所有都是假的。这是假的吗？所有鱼都有翅膀。是的。鲸鱼是鱼。这是假的吗？鲸鱼有翅膀。假？假。好。所有鱼都有鳞。假。鲸鱼有鳞。假。鲸鱼是鱼。好，所以这里所有前提和结论都是假的。但这个论证是有效的，这个论证是无效的。好，我为什么这么说呢？嗯，如果我再找到我的笔的话。所有鱼都有翅膀。这是"有翅膀的事物"这个类。鱼的类在里面。鲸鱼有翅膀。哦，抱歉，是的，谢谢。我突然想到，哦天哪，这不是有效的。所有鱼都有翅膀。鲸鱼是鱼。好，所以它们必须有翅膀，对吧？这保证了这一点。它们必须处在"有翅膀的事物"这个类里面。我们这边有什么呢？所有鱼都有鳞。所以那是"有鳞的事物"。那是鱼。鲸鱼有鳞，唔，鲸鱼有鳞吗？嗯，它们可以在这里或这里，不是吗？鲸鱼不是鱼。好，这告诉我们鲸鱼在这里。但除了我们说这是真的之外，这一点是否得到保证？你知道，实际上，它可能是假的，不是吗？即使它是真的，它也可能是假的。

[段 39]

And it’s not guaranteed by those, is it? because as far as the fact that all fish are in the class of things that have scales, that doesn’t tell us whether whales are out here, so they have scales but are not fish, or whether they’re in here and they’re fish with scales. We don’t know that. Is this the structure where you were talking about confirming the antecedents or confirming the consequences? It happens that all the arguments I’m using are straightforward cases of modus polens. All P’s are Q, P, therefore Q. No, hang on. No, I’m sorry. I’ve gone past the stage where I’m thinking. Your homework this week is to go home and work out what the form of that argument is, because I’m using the same one for each one. What I’m trying to point out is that what matters is the pot of benefitstrying to point out is that what matters is the possibility, not the actuality. It’s the possible truth values, not the actual truth values that matter. Possible truth values, not the actual truth values. Okay, here’s another way. We’ve used Venn diagrams to have a look, but let’s have another look. Another way of determining validity is to create a counter example set and then determine consistency. Let’s have a look at what we mean by that. Firstly, to determine the counter-example set, we set out the argument logic book style, okay?

[译文 39]

而且这并没有被这些前提所保证，对吧？因为就"所有鱼都处在有鳞事物的类中"这一事实而言，这并不能告诉我们鲸鱼是在外面——即它们有鳞但不是鱼，还是在里面——即它们是带鳞的鱼。我们不知道。你说的那种结构是不是指"肯定前件"或"肯定后件"？我碰巧用到的所有论证都是 modus ponens 的简单情况。所有 P 都是 Q，P，所以 Q。不，等等。不，抱歉。我已经过了思考的阶段了。你们本周的作业是回家去弄清楚那个论证的形式是什么，因为我对每个论证用的都是同一个。我想要指出的是，重要的是……我想要指出的是，重要的是可能性，而不是现实性。重要的是可能的真值，而不是实际的真值。可能的真值，而不是实际的真值。好，这里是另一种方法。我们已经用文氏图看过了，但我们再看一下。另一种确定有效性的方法是创建一个反例集，然后确定其一致性。让我们看看这是什么意思。首先，为了确定反例集，我们以逻辑书的形式展开论证，好吗？

[段 40]

Here are two arguments set out logic book style. You’re familiar with these, you’ve seen them before, okay? Now, that’s the argument set out logic book style. Now, I’m going to negate the conclusion and thereby set out the counter example set. So we negate the conclusion by tacking it is not the case that in front of the conclusion. So here we are. This is the counter example set of the two arguments I gave you. And all I’ve given you is exactly the same arguments, but with the words it is not the case that tacked in front of them. The next thing we do is we need to consider whether the set consisting of the premises and the negation of the conclusion, in other words, the counter-example set, is consistent, i.e. could they all be true together? If the counterexample set is consistent, then the original argument is invalid. Can anyone see why that’s the case? Oh, this is really tough. Why am I doing this to you? If the counterexample set isn’t consistent, then the original argument isn’t valid. Now, again, let me warn you that consistency is a bit like truth. You think of it as a nice, good, warm thing. And so you tend to think that if it’s valid, it must be consistent. But what I’m suggesting here is if the counterexample set is consistent, in other words, if the counterexample set can’t all be true together, then the argument is invalid.

[译文 40]

这里是两个以逻辑书形式展开的论证。你们熟悉这些，你们之前见过，好吗？现在，那就是以逻辑书形式展开的论证。现在，我将否定结论，从而展开反例集。所以我们通过在结论前面加上"情况并非"来否定结论。所以我们在这里。这就是我给你们的两个论证的反例集。我给你们的正是完全相同的论证，只是在它们前面加上了"情况并非"这几个字。我们接下来要做的是，我们需要考虑由前提和结论的否定组成的集合，换句话说，反例集，是否一致，也就是说，它们是否可能同时为真？如果反例集是一致的，那么原论证就是无效的。有人能看出为什么是这样吗？哦，这真的很难。我为什么要这样折磨你们？如果反例集不是一致的，那么原论证就不是有效的。现在，再次提醒你们，一致性有点像真值。你把它看作一个美好、良好、温暖的东西。所以你倾向于认为如果它是有效的，它就一定是一致的。但我在这里要说的是，如果反例集是一致的，换句话说，如果反例集不能同时为真，那么论证就是无效的。

[段 41]

Let’s have a look why. okay this is the counter example set okay consisting of the premises plus the negation of the conclusion do you accept that are you with me on that now what I’m claiming is if this is consistent then the original argument must have been valid okay let’s have a look at here with you’ll agree with me that the original argument here is invalid isn’t it do you agree with that Okay, so if it’s snowing, the mail will be late. The mail will be late, therefore it’s snowing. That’s invalid, isn’t it? Because there is a possible situation where the mail will be late.it? Because there is a possible situation where the premises are true and the conclusion false. Well, what we’re doing here is we’re saying, well, let’s assume that the conclusion is false and let’s see if these can all be true together. Well, if they can, then it can’t be the case that the original argument was valid, could it? I think this is an argument too far frankly so if you’re not with me don’t but actually what you can do is you can because this bit is dead simple actually and if you go away yourself and you work out there’s several ways in which you can test your understanding of what I’ve said today the first one is if you understand why the paradoxes of entailment the two arguments I gave you and told you were the paradoxes of entailment.

[译文 41]

让我们看看为什么。好，这就是反例集，好，由前提加上结论的否定组成，你们接受这一点吗？你们跟上我了吗？现在我主张的是，如果这个是一致的，那么原论证一定曾是有效的。好，我们看这里，你会同意我这里的原论证是无效的，对吧？你同意吗？好，所以如果下雪，邮件就会晚到。邮件晚到了，所以下雪了。这是无效的，对吧？因为存在一种可能的情形，在那里邮件会晚到。存在一种可能的情形，在那里前提为真而结论为假。好，我们这里做的是，我们说，好，让我们假设结论为假，让我们看看这些是否可能同时为真。好，如果它们可以，那么原论证就不可能是有效的，对吧？坦白说，我认为这个论证讲得太远了，所以如果你们没跟上我，那就不跟了，但实际上你们可以，因为这部分其实非常简单，而且如果你们自己回去算出来，有几种方法可以检验你们对我今天讲的内容的理解。第一个是，如果你们理解为什么"蕴涵悖论"——我给你们的两个论证，并告诉你们它们是蕴涵悖论——

[段 42]

If you can work out why they are valid, you will have understood validity. Second thing is, if you understand why this is the case, why you can test the validity of an argument by appeal to a counterexample set, and you can understand why this is the case, in other words, if the counterexample set is consistent, then the original argument is invalid and if the counter example set isn’t consistent um ah oh ahAh! Oh! Oh! Oh! Sorry, you can still see it over my hands, can’t you? That’s terrible. Right, okay. You will all see that I’ve put a knot in where I shouldn’t have put a knot, which is the worst thing you can do when you’re teaching people logic. So will you please all note that that knot shouldn’t be there. And so the second test of whether you’ve understood today’s work is whether you can see how this works. Okay? So if you haven’t understood where you are now and if you’re feeling, I’m never going to understand another thing again, I don’t ever want to see that Talbot woman ever again, quite understand, but go home and have a look at it yourself and I promise you, if you work through it step by step and just think of the definitions, you will understand. And if you don’t, email me and we’ll go through it all again by email.

[译文 42]

如果你们能弄明白为什么它们是有效的，你们就理解了有效性。第二件事是，如果你们理解了为什么情况是这样，为什么你们可以通过诉诸反例集来检验一个论证的有效性，而且你们能理解为什么情况是这样，换句话说，如果反例集是一致的，那么原论证就是无效的，如果反例集不是一致的，唔，啊，哦，啊！啊！啊！啊！抱歉，你们仍然能透过我的手看到它，对吧？这太糟糕了。好，好。你们都会看到我在不该打结的地方打了一个结，这是教人逻辑时你能做的最糟糕的事。所以请大家注意那个结不应该在那里。所以检验你们是否理解了今天课程的第二个测试是，你们能否看出这是怎么运作的。好吗？所以如果你们现在不明白自己在哪里，如果你们觉得，我再也不会明白任何东西了，我再也不想见到那个 Talbot 女人了，我完全理解，但回家自己看一看，我向你们保证，如果你们一步一步地过一遍，并且仅仅想一下定义，你们会理解的。如果你们不理解，给我发邮件，我们会通过邮件再过一遍。

[段 43]

Okay, I’ll stop there, but there’s five minutes for questions if anyone has still got some energy.

[译文 43]

好的，我就讲到这里，如果大家还有精力的话，留 5 分钟时间回答提问。