Course: 12.4. 有效表格 | The Way To Learn

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有效表格
If an argument is valid and the premises are true, then the conclusion must be true. How then can you be sure that your argument is valid to start with? Are there some standard forms of valid arguments to refer to?
::如果争论是有效的,而且前提是真实的,那么结论必须是真实的。那么, 您如何能确定您的论点是正当的呢? 是否有一些标准的有效争论形式可以引用?

Valid Forms
::有效表格

An argument may be valid without being sound, but it cannot be sound without being valid. In addition, if a valid argument has true premises, then it must be sound. That means that one way to make sure that your arguments will be sound is to start by stating them in a particular form that you know to be valid. That way, you need only convince your audience that your premises are true in order to make your argument persuasive .
::争论可能没有合理性,但没有合理性则不能合理性。此外,如果一个有效的争论有真实的前提,那么它必须是合理的。这意味着确保你的论点正确性的一种方法就是首先以你所知道的某种特定形式来陈述。这样,你只需说服观众你的前提是真实的,才能使你的论点具有说服力。

In this lesson, we will practice some valid forms of argument. Don’t worry if the names of the forms seem odd, logical thinking and reasoning rules are sometimes literally thousands of years old, and so may have names based on ancient languages (primarily Latin).
::在这个教训中,我们将实践一些有效的论证形式。不要担心形式名称似乎很奇怪,逻辑思维和推理规则有时在字面上已经存在数千年了,因此名称可能基于古老语言(主要是拉丁语 ) 。

It is common when describing forms of argument to replace sentences or phrases with single letters, such as $\begin{aligned} P \end{aligned}$ and $\begin{aligned} Q \end{aligned}$ . By using letters to generalize an argument form, we can more easily evaluate a concrete argument for validity. It is a common, and useful, practice to replace $\begin{aligned} P \end{aligned}$ and $\begin{aligned} Q \end{aligned}$ with statements of your own in order to clarify the use of a particular form.
::在描述用P和Q等单字母取代句子或短语的论据形式时,这是很常见的。通过使用字母来概括一个参数格式,我们可以更容易地评估一个具体的有效性论据。以自己的声明取代P和Q是一种常见和有益的做法,以便澄清特定表格的使用。

Modus ponens (affirm by affirming): If $\begin{aligned} P \end{aligned}$ , then $\begin{aligned} Q \end{aligned}$ . $\begin{aligned} P \end{aligned}$ , therefore $\begin{aligned} Q \end{aligned}$ .

If water is frozen, then it is below 32 degrees Fahrenheit. This water is frozen, therefore it is below 32 degrees Fahrenheit.
::如果水被冷冻,则低于32华氏度。这种水被冷冻,因此低于32华氏度。

::Modus ponens(以确认方式确认):如果是P,那么是Q.P,因此是Q.Q.。如果水被冷冻,则低于32华氏度。这种水被冷冻,因此低于32华氏度。

Modus tollens (denying the consequent): If $\begin{aligned} P \end{aligned}$ , then $\begin{aligned} Q \end{aligned}$ . Not $\begin{aligned} Q \end{aligned}$ , therefore not $\begin{aligned} P \end{aligned}$ .

If water is frozen, then it is below 32 degrees Fahrenheit. This water is not below 32 degrees Fahrenheit, therefore it is not frozen.
::如果水被冷冻,那么水位在华氏32度以下,水位不低于华氏32度,因此水位不冻结。

::Modus illens(否认由此产生的后果):如果P,那么Q.不是Q,因此不是P。如果水被冻结,那么水在法赫伦海特32度以下。这种水不低于法赫伦海特32度,因此它不会被冻结。

Hypothetical syllogism (the chain argument): If $\begin{aligned} P \end{aligned}$ , then $\begin{aligned} Q \end{aligned}$ . If $\begin{aligned} Q \end{aligned}$ , then $\begin{aligned} R \end{aligned}$ . Therefore, if $\begin{aligned} P \end{aligned}$ then $\begin{aligned} R \end{aligned}$ .

If you wear sunscreen, you won’t get sunburn. If you don’t get sunburn, you will not get skin cancer. Therefore, if you wear sunscreen, you won’t get skin cancer.
::如果你戴防晒霜,你就不会晒伤。如果你不晒伤,你就不会得皮肤癌。因此,如果你戴防晒霜,你就不会得皮肤癌。

::假设的体系主义(连锁论):如果是P,那么是Q。如果是Q,那么是R。因此,如果是P,那么是R。如果是P,那么是R。如果你戴防晒霜,你就不会晒太阳。如果你不晒太阳,你就不会得皮肤癌。因此,如果你戴防晒霜,你就不会得皮肤癌。

Disjunctive syllogism : $\begin{aligned} P \end{aligned}$ or $\begin{aligned} Q \end{aligned}$ . Not $\begin{aligned} P \end{aligned}$ . Therefore $\begin{aligned} Q \end{aligned}$ . (also works in reverse)

You are either dead or alive. You are not dead. Therefore you are alive.
::你要么死要么活,你没有死,所以你还活着

You are either dead or alive. You are not alive. Therefore you are dead.

::你要么死要么活,你不是活,你不是活,所以你死定了

::分辨的星系主义:P或Q。不是P。不是P。所以Q(也倒着工作)是死的或活的。你不是死的,就是活的。你没有死,所以你是活的。你生的或死,或活的,你活的,或活的,或活的。你生的,或活的。所以你已死。

Identifying Valid Forms
::识别有效表格

1. Is the following a valid form of argument? If so which form is it?
::1. 以下论点是否有效?如果有效,其形式是什么?

If you overeat, you will get a bellyache. You do not have a bellyache. Therefore you did not overeat.
::如果你吃过东西,你就会肚子痛,你没有肚子痛,所以你没有吃过。

This is a valid form. It is an example of modus tollens , denying the consequent. Because the initial premise is that every time you overeat, you get a bellyache, not having a bellyache must mean that you did not overeat.
::这是一种有效的形式。它是一个工作方式收费的例子, 否认由此产生的结果。因为最初的假设是每次你吃过头, 你都会肚子痛, 没有肚子痛, 必然意味着你没有吃过头。

Note that this does not necessarily mean that this is a sound argument . Since it is entirely possible to overeat without getting a bellyache, you might indeed have overeaten and felt fine. The important thing is that the form of the argument is valid, so that the only question is the truth of the premises.
::请注意,这并不一定意味着这是一个合理的论据。由于完全有可能在不吃腹痛的情况下过度吃饱,你确实可能吃饱了,感觉很好。重要的是,论据的形式是有效的,因此唯一的问题是前提的真实性。

2. Is the following argument stated in a valid form? If so, which form is it?
::2. 下列论点是否以有效形式陈述?如果是,采取何种形式?

If you are a teenager with a smartphone, you send text messages. You are a teenager with a smartphone. Therefore you send text messages.
::如果您是拥有智能手机的青少年, 发短信给您。您是拥有智能手机的青少年。因此您会发送短信。

This is a valid form, an example of modus ponens , affirm by affirming. Since the initial premise is that every teenager who owns a smartphone sends texts, if you are a teenager with a smartphone, you must send texts.
::这是一个有效的形式,一个以肯定方式肯定的“临时写字”的例子。因为最初的前提是拥有智能手机的每个青少年都发送短信,如果你是拥有智能手机的青少年,你就必须发送短信。

3. Is the following a valid form of argument? If so, which form?
::3. 以下论点是否有效?如果有效,采取何种形式?

If you wear a helmet, you won’t hurt your head in a crash. If you don’t hurt your head in a crash, you won’t get a headache. Therefore, if you wear a helmet, you won’t get a headache.
::如果你戴头盔,就不会在坠机时伤到头。如果你在坠机时不伤到头,就不会头痛。因此,如果你戴头盔,就不会头痛。

This is an example of the valid form known as hypothetical syllogism , the chain argument. The premise about not getting a headache if you don’t hurt your head is chained to the premise that you won’t hurt your head if you wear a helmet.
::这是一个有效的形式的例子,它被称为假设的丝绸主义,即连锁辩论。如果不伤害头部,不头痛的前提就被锁在以下前提上:如果你戴头盔,头部就不会受伤。

As in prior examples, the validity of the argument does not necessarily lead to the soundness of it. Obviously you might get a headache for some reason other than hitting your head, and wearing a helmet won’t prevent that.
::与前几个例子一样,论据的有效性并不一定导致其合理性。显然,除了打头部之外,你还可能因为某种原因头痛,而戴头盔也阻止不了这一点。

Earlier Problem Revisited
::重审先前的问题

If an argument is valid and the premises are true, then the conclusion must be true. How then can you be sure that your argument is valid to start with? Are there some standard forms of valid arguments to refer to?
::如果争论是有效的,而且前提是真实的,那么结论必须是真实的。那么, 您如何能确定您的论点是正当的呢? 是否有一些标准的有效争论形式可以引用?

By making sure your own premises follow valid forms of reasoning, you will know that your conclusions are true as long as your premises are. There are many standard valid forms of argumentation, including modus ponens, disjunctive syllogism, hypothetical syllogism, modus tollens, and others.
::通过确保自己的前提遵循有效的推理形式,你就会知道,只要你的前提是真实的,你的结论就是真实的。有许多标准的有效论证形式,包括手法的推理、截然相反的丝状、假想的丝状、通法的推理等等。

Examples
::实例

Describe the form of the logical arguments in Examples 1-4.
::在例1-4中说明逻辑论点的形式。

Example 1
::例1

If a bull has been gelded, it is a steer. Ferdinand is not a steer. Therefore, Ferdinand is not a gelded bull.
::公牛被凝胶的、就是公牛 . 费迪南不是公牛 . 因此、费迪南不是凝胶的公牛

This argument is in the form: If $\begin{aligned} P \end{aligned}$ , then $\begin{aligned} Q \end{aligned}$ . Not $\begin{aligned} Q \end{aligned}$ , therefore not $\begin{aligned} P \end{aligned}$ . It is an example of the form Modus Tollens or denying the consequent.
::这一论点的形式是:如果是P,那么是Q,而不是Q,因此不是P。这是Modus Tollens或否认其后果的表象的例子。

Example 2
::例2

Ignoring problems makes them go away. I ignore my problems. My problems go away.
::我忽视我的问题,我的问题就消失。

This argument is in the form: If $\begin{aligned} P \end{aligned}$ , then $\begin{aligned} Q \end{aligned}$ . $\begin{aligned} P \end{aligned}$ , therefore $\begin{aligned} Q \end{aligned}$ . It is an example of Modus ponens or affirm by affirming.
::这一论点的形式是:如果是P,那么是Q.P,因此是Q.Q.。这是莫杜斯的担保人或通过确认而确认的例子。

Example 3
::例3

Arguments must be valid or invalid. This argument is not valid. This argument is invalid.
::参数必须有效或无效。此参数无效。此参数无效。此参数无效。

This argument is in the form: $\begin{aligned} P \end{aligned}$ or $\begin{aligned} Q \end{aligned}$ , not $\begin{aligned} P \end{aligned}$ , therefore $\begin{aligned} Q \end{aligned}$ . It is an example of Dijunctive syllogism.
::这一论点的形式是:P或Q,而不是P,因此是Q。这是二元性立体主义的一个例子。

Example 4
::例4

If you study Reason, you will better understand Logic. If you better understand Logic, you will make better use of Statistics. Therefore if you study Reason, you will make better use of Statistics.
::如果你学习理性,你会更好地理解逻辑。如果你更好地理解逻辑,你会更好地利用统计。如果你学习理性,你会更好地利用统计。因此,如果你学习理性,你会更好地利用统计。

This argument is in the form: If $\begin{aligned} P \end{aligned}$ , then $\begin{aligned} Q \end{aligned}$ . If $\begin{aligned} Q \end{aligned}$ , then $\begin{aligned} R \end{aligned}$ . Therefore, if $\begin{aligned} P \end{aligned}$ , then $\begin{aligned} R \end{aligned}$ . It is an example of: Hypothetical syllogism , also known as The Chain Argument .
::这一论点的形式是:如果是P,那么是Q。如果是Q,那么是R。如果是P,那么是R。举例来说:假设的星系主义,也称为“链条争论”。

Review
::回顾

Describe the form of the logical arguments in questions 1-13.
::描述问题1-13中逻辑论证的形式。

If $\begin{aligned} P \end{aligned}$ , then $\begin{aligned} Q \end{aligned}$ . $\begin{aligned} P \end{aligned}$ , therefore $\begin{aligned} Q \end{aligned}$ .
::如果是P,那么是QP,因此是Q。

If $\begin{aligned} P \end{aligned}$ , then $\begin{aligned} Q \end{aligned}$ . Not $\begin{aligned} Q \end{aligned}$ , therefore not $\begin{aligned} P \end{aligned}$ .
::如果是P,那么是Q,而不是Q,因此不是P。

If $\begin{aligned} P \end{aligned}$ , then $\begin{aligned} Q \end{aligned}$ . If $\begin{aligned} Q \end{aligned}$ , then $\begin{aligned} R \end{aligned}$ . Therefore, if $\begin{aligned} P \end{aligned}$ then $\begin{aligned} R \end{aligned}$ .
::如果是P,那么是Q。如果是Q,那么是R。如果是P,那么是R。

$\begin{aligned} P \end{aligned}$ or $\begin{aligned} Q \end{aligned}$ . Not $\begin{aligned} P \end{aligned}$ . Therefore $\begin{aligned} Q \end{aligned}$ .
::P或Q. 不是P. 因此Q.

If it is snowing, then it is below freezing. It is snowing, therefore it is below freezing.
::如果下雪了,那么它就冻在下面了, 下雪了, 因此它就冻在下面了。

If your homework is not done, you cannot go out. You are going out, therefore your homework is done.
::如果你的作业没有完成,你不能出去。你要出去,所以你的作业已经完成了。

If you wear drink too many energy drinks, you will not be able to sleep. If you aren’t able to sleep, you will be tired tomorrow. If you are tired tomorrow, you won’t do well on your exam. Therefore, if you drink too many energy drinks, you won’t do well on your exam.
::如果你喝太多能量饮料,你就睡不着。如果你睡不着,明天你就会疲劳。如果你明天累了,明天考试就不会有好成绩。因此,如果你喝太多能量饮料,那么考试就不会有好成绩。

You are productive or lazy. You are not lazy. Therefore you are productive.
::你确是有生产力的,或懒惰的,你不是懒惰的,所以你确是有生产力的。

The sky is either cloudy or clear. The sky is not clear. Therefore the sky is cloudy.
::天空是阴暗的,是清空的;天空是模糊的,所以天空是阴暗的。

Minivans get good gas mileage. Bob drives a minivan. Bob gets good gas mileage.
::迷你车的油气里程不错鲍勃开的是迷你车鲍勃的油气里程不错

Girls drive pink cars. Sam does not drive a pink car. Therefore Sam is not a girl.
::女孩驾驶粉色汽车 Sam不驾驶粉色汽车所以Sam不是女孩

If you eat too much candy, you will get cavities. If you get cavities, you will have to spend money on the dentist. If you spend money on the dentist, you cannot go to the movies. Therefore, if you eat too much candy, you cannot go to the movies.
::如果你吃太多糖果,你会得到洞穴。如果你得到洞穴,你不得不花钱买牙医。如果你花钱买牙医,你就不能去看电影。因此,如果你吃太多糖果,你就不能去看电影。

If you tell students to come in from recess, you are a teacher. You are not a teacher. You do not tell students to come in from recess.
::如果你让学生休课,你就是教师。你不是教师。你不应该让学生休课。

Review (Answers)
::回顾(答复)

Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键。

Section outline

General

有效表格

Valid Forms ::有效表格

Identifying Valid Forms ::识别有效表格

Earlier Problem Revisited ::重审先前的问题

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Review ::回顾

Review (Answers) ::回顾(答复)

Valid Forms
::有效表格

Identifying Valid Forms
::识别有效表格

Earlier Problem Revisited
::重审先前的问题

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Example 4
::例4

Review
::回顾

Review (Answers)
::回顾(答复)