Introduction to Logic 逻辑导论
Basic Definitions 基本定义
Logic is the study of the criteria used in evaluating inferences or
arguments.
逻辑是对用于评估推论或结论的标准的研究
争论。
An inference is a process of reasoning in which a new belief is formed
on the basis of or in virtue of evidence or proof supposedly
provided by other beliefs.
推理是形成新信念的推理过程
基于或凭借其他信念提供的证据或证据。
An argument is a collection of statements or propositions, some of
which are intended to provide support or evidence in favor of one
of the others.
论证是陈述或命题的集合，其中一些旨在为其中一个陈述或命题提供支持或证据。
A statement or proposition is something that can either be
true or false. We usually think of a statement as a declarative sentence,
or part of a sentence.
陈述或命题可以是真也可以是假。我们通常将陈述视为陈述句或句子的一部分。
How many statements are there in the example below?
下面的例子中有多少条语句？
I have two brothers, and I have
no sisters. (The answer is 3!)
我有两个兄弟，我有
没有姐妹。 （答案是3！ ）
The premises of an argument are those statements or propositions in it that
are intended to provide the support or evidence.
论证的前提是其中的那些陈述或命题
旨在提供支持或证据。
The conclusion of an argument is that statement or proposition for which
the premises are intended to provide support. (In short, it is the point
the argument is trying to make.)
论证的结论是这样的陈述或命题
该场所旨在提供支持。 （总而言之，重点是
论证正在试图进行。）
(Important note: premises are always intended to provide support or evidence
for the conclusion, but they donn't always succeed! It's still an argument,
and there are still premises and a conclusion, even if the premises don't
really provide any support at all.)
（重要提示：场所始终旨在提供支持或证据
得出结论，但他们并不总是成功！这仍然是一个争论
仍然有前提和结论，即使前提不存在
真正提供任何支持。）
Some Example Arguments 一些示例参数
God is defined as the most perfect being. A perfect being must have every
trait or property that it's better to have than not to have. It is better
to exist than not to exist. Therefore, God exists.
上帝被定义为最完美的存在。一个完美的人必须具备一切
拥有比没有更好的特质或财产。更好了
存在总比不存在好。因此，上帝存在。
Hillary Clinton must be a communist spy. She supports socialized health care,
and everyone who supports socialized health care is a communist spy.
希拉里·克林顿一定是共产主义间谍。她支持社会化医疗保健，
每个支持社会化医疗的人都是共产主义间谍。
It has rained more than 15 inches per year in Amherst every year for the
past 30 years. So you can safely bet it will rain more than 15 inches in
Amherst this year.
阿默斯特每年的降雨量都超过 15 英寸
过去30年。因此，您可以放心地打赌，降雨量将超过 15 英寸
今年阿默斯特。
Professor Chappell said that the ratio of female to male students in the
class was exactly 3:1. This means that there are 112 female students in the
class, because there are 148 students in the class total.
查佩尔教授表示，该校男女学生的比例
班级比例正好是3：1。这意味着全校共有 112 名女学生。
班级，因为全班共有148名学生。
The Encyclopaedia Britannica has an article on symbiosis. It stands to reason
that the Encyclopedia Americana has an article on symbiosis as well, since
the two reference works tend to cover the same topics.
大英百科全书有一篇关于共生的文章。这是有道理的
美国百科全书也有一篇关于共生的文章，因为
这两本参考书往往涵盖相同的主题。
1 is a prime number. 3 is a prime number. 5 is a prime number. 7 is a prime
number. Therefore, all odd integers between 0 and 8 are prime numbers.
1 是素数。 3 是质数。 5是质数。 7 是素数
数字。因此，0到8之间的所有奇数都是素数。
Jason isn't an NRA member. Almost 90% of NRA members are republicans, and
Jason isn't a republican.
杰森不是全国步枪协会成员。 NRA 近 90% 的成员是共和党人，并且
杰森不是共和党人。
Inductive Logic and Deductive Logic
归纳逻辑和演绎逻辑
This can be a tricky subject, because many people are taught the distinction
wrongly in high school. Many people think deduction is reasoning from the
general to the specific, and induction is reasoning from the specific to
general. This is NOT how these words are actually used by most logicians,
nor in this course.
这可能是一个棘手的话题，因为很多人都被教导区分
高中的时候就错了。许多人认为演绎是从
概括到具体，归纳是从具体到具体的推理
一般的。这并不是大多数逻辑学家实际使用这些词的方式，
也不在本课程中。
The distinction actually has to do with how strong the author of an argument
intends the evidence or support to be.
这种区别实际上与论证的作者有多强有关
打算提供证据或支持。
An argument is deductive if the author intends it to be so strong that it
is impossible for the premises to be true and the conclusion to be false,
or in other words, that the conclusion follows necessarily from the premises.
A deductive argument attempts (successfully or unsuccessfully) to provide
full proof of the conclusion.
如果作者希望论证的强度如此之大，那么该论证就是演绎性的
不可能前提为真而结论为假，
或者换句话说，结论必然是从前提得出的。
演绎论证试图（成功或不成功）提供
结论的充分证明。
An argument is inductive if the author intends it only to be so strong that
it is improbable that the premises could be true and the conclusion false,
or in other words, that the conclusion is likely if the premises are true.
An inductive argument only attempts (successfully or unsuccessfully) to provide
evidence for the likely truth of the conclusion, rather than
outright proof.
如果作者只是想让论证变得如此强烈，那么它就是归纳论证
前提为真而结论为假的可能性不大，
或者换句话说，如果前提为真，则结论是可能的。
归纳论证仅尝试（成功或不成功）提供
结论的可能真实性的证据，而不是直接的证据。
From now on, I'm going to focus only on deductive logic.
从现在开始，我将只关注演绎逻辑。
Validity and Soundness 有效性和合理性
A deductive argument is valid if it has a form that would make it
impossible for the premises to be true and the conclusion false, or if the
conclusion follows necessarily from the premises.
如果演绎论证的形式使前提不可能为真而结论为假，或者结论必然从前提得出，则演绎论证是有效的。
To test whether an argument is valid, you should first imagine that the premises
are true—whether or not they actually are—and then ask yourself,
without appealing to any other knowledge you have, could you still
imagine the conclusion being false? If you can, the argument is invalid.
If you can't, then the argument is valid.
要测试一个论证是否有效，你应该首先想象前提
是真的——无论它们是否真的是——然后问自己，
在不求助于您所拥有的任何其他知识的情况下，您还能想象结论是错误的吗？如果可以，则该论证无效。如果你不能，那么这个论点是有效的。
Note that validity does not have to do with the actual truth or falsity of
the premises. It only has to do with what would follow from them if they
were true. A valid argument can have false premises. For example:
请注意，有效性与事实的真实性或虚假性无关。
该处所。它只与如果他们这样做的话会发生什么有关
是真的。有效的论证可能有错误的前提。例如：
All toasters are items made of gold.
所有烤面包机都是金制成的。
All items made of gold are time-travel devices.
所有由黄金制成的物品都是时间旅行装置。
Therefore, all toasters are time-travel devices.
因此，所有的烤面包机都是时间旅行设备。
It may be hard to imagine these premises as true, but it is not hard to recognize
that if they were true, the conclusion would also be true.
可能很难想象这些前提是真实的，但也不难认识到
如果它们是真的，那么结论也将是真的。
So there's more to an argument's being a good one than validity. To be a
good argument, an argument must also have true premises. An argument with
true premises is called factually correct.
因此，一个论点的好坏不仅仅取决于其有效性。成为一个
好的论证，论证也必须有正确的前提。与的争论
真实的前提称为事实正确。
A sound argument is an argument that is both valid and factually correct.
合理的论证是既有效又事实上正确的论证。
An invalid argument may have true or false premises, and a true or false
conclusion. A valid argument may have false premises with either a true or
a false conclusion. The only combination that is ruled out is a valid argument
with true premises and a false conclusion. Sound arguments always have true
conclusions.
无效的论证可能有真或假的前提，以及真或假的前提
结论。一个有效的论点可能有错误的前提，或者是正确的或
一个错误的结论。唯一被排除的组合是有效的参数
具有正确的前提和错误的结论。合理的论点总是有道理的
结论。
Argument Form
The validity of a deductive argument is determined entirely by its form.
Consider these arguments.
演绎论证的有效性完全由其形式决定。
考虑这些论点。
1) All tigers are mammals.
1）所有老虎都是哺乳动物。
No mammals are creatures with scales.
哺乳动物都不是有鳞片的生物。
Therefore, no tigers are creatures with scales.
因此，老虎并不是有鳞的生物。
2) All spider monkeys are elephants.
2）所有蜘蛛猴都是大象。
No elephants are animals.
没有大象是动物。
Therefore, no spider monkeys are animals.
因此，蜘蛛猴都不是动物。
These arguments share the same form: All A are B, No B are C, Therefore,
No A are C. All arguments with this form are valid. So the examples above
are valid. (What is wrong with #2?) Now consider:
这些论点具有相同的形式：所有 A 都是 B，没有 B 都是 C，因此，
没有 A 是 C。这种形式的所有论证都是有效的。所以上面的例子
是有效的。 （#2有什么问题？）现在考虑：
3) All basketballs are round.
3）所有篮球都是圆的。
The Earth is round. 地球是圆的。
Therefore, the Earth is a basketball.
因此，地球是一个篮球。
4) All Jedis are one with the force.
4) 所有绝地武士都与原力合一。
Yoda is one with the force.
尤达是原力之一。
Therefore, Yoda is a Jedi.
因此，尤达是绝地武士。
These arguments also have the same form. All A are F. X is F. Therefore,
X is an A. All arguments with this form are invalid. #4 may seem like a good
argument because all the premises and the conclusion are true (at least in
fiction), but note that the conclusion isn't made true by the premises. It
could be possible for the premises to be true and the conclusion false. #4
is invalid, and all invalid arguments are unsound. #4 is not a good argument.
这些论证也具有相同的形式。所有 A 都是 F。X 是 F。因此，
X 是 A。所有具有这种形式的参数都是无效的。 #4 可能看起来不错
论证是因为所有前提和结论都是正确的（至少在
虚构），但请注意，前提并不能使结论成立。它
有可能前提为真而结论为假。 #4
是无效的，所有无效的论点都是不合理的。 #4 不是一个好的论点。
Evaluating Arguments Logically
Logic is very important in philosophy, because so much of what philosophers
do involves putting forth arguments, and assessing those of others. There
are two steps in evaluating an argument. First, ignore for the moment
whether or not the premises actually are true, and ask yourself whether or
not, if you imagine that they are, the conclusion follows from them.
If it does, that is, if the process of reasoning is a good one, then
the argument is valid. Next, ask yourself whether or not the premises
are true. If all of them are true (regardless of the conclusion), then
the argument is factually correct. These are the only two ways of
evaluating an argument that are important for the purposes of this class.
If the argument is both valid and factually correct, then the conclusion
must be true.
逻辑在哲学中非常重要，因为哲学家所做的很多事情都涉及提出论证并评估他人的论证。评估论证有两个步骤。首先，暂时忽略前提是否真的为真，并问问自己，如果你想象它们是真的，结论是否会从中得出。如果是的话，也就是说，如果推理过程是好的，那么这个论证就是有效的。接下来，问问自己这些前提是否正确。如果所有这些都是正确的（无论结论如何），那么该论证实际上是正确的。对于本课程来说，这是唯一两种重要的评估论证的方法。如果论证既有效又事实上正确，那么结论一定是正确的。
1) If God existed, then J. Lo and Puffy would still be dating. But J. Lo
and Puffy are not dating anymore. Therefore, God does not exist.
1）如果上帝存在，那么J. Lo和Puffy仍然会约会。但罗杰
和 Puffy 不再约会了。因此，上帝不存在。
2) If Minnie Driver has agreed to go on date with Kevin, then God exists.
Minnie Driver has not agreed to go on a date with Kevin. Therefore, God does
not exist.
2）如果米妮·德赖弗同意和凯文约会，那么上帝就存在。
米妮·德赖弗尚未同意与凯文约会。因此，神
不存在。
3) Either materialism is false or all emotions are physical processes in
the brain. If all emotions are physical processes in the brain, then it is
possible to know what love feels like simply by studying brain chemistry.
It is not possible to know what love feels like simply by studying brain
chemistry. Therefore, materialism is false.
3）要么唯物主义是错误的，要么所有情感都是物理过程
大脑。如果所有情绪都是大脑中的物理过程，那么它就是
只需研究大脑化学物质就可以了解爱的感觉。
仅仅通过研究大脑是不可能知道爱的感觉的
化学。因此，唯物主义是错误的。
It is worth noting that an argument may still have a true conclusion
even if it is invalid or factually incorrect (or both). Consider:
值得注意的是，即使一个论证无效或事实上不正确（或两者兼而有之），它仍然可能有一个真实的结论。考虑：
Christina Aguilera loves all of Eminem's lyrics. The Eifel tower is made
of cheese. Therefore, Atlanta is the capital of Georgia.
克里斯蒂娜·阿奎莱拉喜欢阿姆的所有歌词。埃菲尔铁塔是用奶酪制成的。因此，亚特兰大是佐治亚州的首府。
The real upshot of this, however, is that just because you believe
a certain conclusion, you do not logically have to accept the soundness of
every argument for that conclusion.
然而，这样做的真正结果是，仅仅因为你相信某个结论，你就不必在逻辑上接受该结论的每个论证的合理性。
Some Logical Pitfalls
Begging the Question
An argument begs the question when it makes use of a premise
that no one who didn't already accept the conclusion would believe. Simply
put, an argument begs the question when it reasons in a circle or
presupposes the truth of the very thing it's trying to prove.
当一个论证使用了一个尚未接受结论的人不会相信的前提时，它就回避了问题。简而言之，当一个论证绕圈推理或预设它试图证明的事情的真实性时，它就回避了问题。
Example: God exists, because it says that God exists in the Bible, and everything
in the Bible is the true word of God.
例子：上帝存在，因为圣经说上帝存在，一切事物都存在
圣经中是神真实的话语。
The Appeal to Ignorance Fallacy
This fallacy is committed when something is concluded to be true simply because
it hasn't been proven to be false, or is concluded to be false just because
it hasn't been proven to be true. Reasoning in such a way is invalid. Something
can be true even if no one has succeeded in showing it to be true.
当仅仅因为某事被推断为正确时，就会犯这种谬误
它尚未被证明是错误的，或者仅仅因为它被断定是错误的
这还没有被证明是真的。这样的推理是无效的。某物
即使没有人成功地证明它是真实的，它也可能是真实的。
Example: No one has even proven that there is life after death. Therefore,
there is no life after death.
例子：甚至没有人证明死后还有生命。所以，
死后没有生命。
The Wishful Thinking Fallacy
This fallacy is committed when someone concludes that something must be true
in virtue of what he or she wants to be true (or doesn't want to be false)
instead of what the evidence suggests. Unfortunately, just because there
are better consequences to something's being true rather than false does
not provide evidence that it is true.
当有人得出结论某事一定是真的时，就会犯这种谬误
凭借他或她想要真实的（或不想虚假的）
而不是证据表明的那样。不幸的是，仅仅因为有
某事为真会产生比错误更好的后果
不提供证据证明其属实。
Example: The idea of life in a universe without God would be frightening
and depressing, and very difficult to accept. Therefore, God must exist.
例子：在没有上帝的宇宙中存在生命的想法将会令人恐惧
而且很压抑，很难接受。因此，上帝必定存在。
The "Ad Hominem" Fallacy
This fallacy is committed when an argument or position is rejected not
in virtue of its logical merits, but rather in virtue of the character, personality,
background or motivation of the person giving the argument or holding the
position. However, a position can be true, and an argument can be sound,
no matter how deplorable the person is. Who holds a belief has nothing
to do with whether or not it's true.
当一个论点或立场被拒绝时，不是因为其逻辑优点，而是因为提出论点或持有立场的人的性格、个性、背景或动机，就犯了这种谬误。然而，无论这个人多么不幸，立场都可以是正确的，论点也可以是合理的。谁拥有一个信念与它是否真实无关。
Example: Former president Clinton has argued in favor of increasing restrictions
on the sale of guns. But President Clinton is a lecherous, adulterous, untrustworthy,
draft-dodging old pervert, so his views must surely be misguided.
示例：前总统克林顿主张加强限制
关于枪支销售。但克林顿总统是一个好色、通奸、不值得信任的人，
一个逃避兵役的老色狼，他的观点肯定是被误导了。
What I call the "who's to say" fallacy is an instance of ad hominem reasoning.
E.g.: "Descartes has argued that all persons consist of two distinct substances:
a material body and an immaterial mind. But who is Descartes to say what
is true of all persons?"
我所说的“谁该说”谬误是人身攻击推理的一个例子。
例如：“笛卡尔认为所有人都由两种不同的物质组成：
物质的身体和非物质的心灵。但笛卡尔是谁，能说什么
对所有人来说都是如此吗？”
Opinion and Fact
An opinion is something that someone believes to be true.
意见是某人认为正确的事情。
A fact is something that is true.
事实是真实的事情。
Sometimes people disagree about what the fact of the matter is with regard
to a certain question. In those cases, there are many opinions, but only
one fact. Those people whose opinion agrees with the facts are correct, those
who have other opinions are incorrect.
有时，人们对于事情的真相存在不同意见
对于某个问题。在这些情况下，有很多意见，但只有
一个事实。那些观点与事实相符的人就是正确的
如有其他意见，均不正确。
Some points to remember: 需要记住的一些要点：
1. Just because there is disagreement about what the facts are DOES NOT mean
that there is no fact of the matter.
1. 仅仅因为对事实存在分歧并不意味着
事实并非如此。
2. Something can be a fact even if no one, or even if very few people, believe
it. (Copernicus's opinion that the Earth revolved around the sun was a fact,
even before he managed to prove it and even before anyone else believed it.)
2. 即使没有人，或者即使很少人相信，某件事也可能是事实
它。 （哥白尼关于地球绕太阳转的观点是事实，
甚至在他设法证明这一点之前，甚至在其他人相信之前。）
3. Just because people disagree about something does NOT mean that the thing
in question is "true for for some people" but not "true for others".
3. 仅仅因为人们对某件事有不同意见并不意味着这件事
问题是“对某些人来说是正确的”，但不是“对另一些人来说是正确的”。
4. Most things we talk about in philosophy are not in any way relative or
subjective, in the same way that tastes is music or food are relative.
If God exists, God exists for everyone everywhere, and those people who
believe that there is no God are mistaken. This may not sound nice, but
it's the only coherent thing to say.
4. 我们在哲学中谈论的大多数事情都不是相对的或
主观的，就像音乐或食物的口味是相对的一样。
如果上帝存在，那么上帝就为每个地方的每个人而存在，并且为那些
相信没有上帝是错误的。这听起来可能不太好，但是
这是唯一可以说的连贯的话。
5. If you believe something is true, you cannot coherently NOT believe that
people who believe that it is not true are mistaken.
5. 如果你相信某件事是真的，你就无法连贯地不相信它
那些认为这不是真的的人是错误的。
6. It is not an objection to something to call it "just an opinion" or "just
a theory".
6. 称某事为“只是一种意见”或“只是
一个理论”。
Example: Sartre believes that human free will is incompatible with the existence
of God. But that's just his opinion about the relationship between God and
free will, not everyone's.
例子：萨特认为人类的自由意志与存在是不相容的
上帝的。但这只是他对上帝与上帝之间关系的看法。
自由意志，不是每个人的。
Is this an objection to Sartre?
这是对萨特的反对吗？
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