基本概念

区分真与伪

命题一定存在真假，断定任何东西才能被称为命题

命题：命题是陈述性的语句，可以被判断为真或假。例如：“今天是星期天”、“人类需要水才能生存”等等都是命题。命题可以被用来构建论证，进行推理和讨论。

论证：论证是通过一系列的推理步骤来支持或证明一个观点或结论的过程。论证由前提和结论组成，前提是用来支持结论的陈述或假设，而结论则是根据前提得出的推理结果。论证的目的是通过逻辑推理来证明某个观点的正确性或合理性。

Logic = Evaluating Arguments

An argument  = a set of sentences that consists of the premise part and the conclusion part

At least 2 sentences to make an argument, every argument must have 2 parts of it

Premises are the reasons or the ground or the evidences you take to support the conclusion  of the argument.

The conclusion is your belief or the claim

逻辑学四大基本定律

同一律，事物只能是其本身。例如猫就是猫 狗就是狗

矛盾律，在某一时刻，某个事物同一方面，不可能即使这样又是那样 例如李是个男人又是个女人

排中律，对任何事物在一定条件（即一定前提）下的判断都要有明确的“是”或“非”，不存在中间状态。

充分理由律(因果原理)，任何事物都有其存在的充足理由。

单个句子不能构成论证，例如上帝不存在只是你的观点不是论证argument

sentence也不一定是论证，它可能是在陈述事实，比如报纸，论文

because is a premise indicator

deductive argument(推演论证) includes valid argument and invalid argument

valid argument: if all the premises are true, then the conclusion is true.

inductive argument(归纳论证) includes strong argument and weak argument

strong argument: if all the premises are true, then the conclusion is likely to be true.

weak argument: not strong

implicit premises, is consider that everyone knows that, it's obvious .

fallacy(谬论), is mistaken reasoning, to draw a conclusion from weak and irrelevant evidences. insufficient evidences and grounds.

people commit fallacies intentionally or non-intentionally.

常见谬论：subjectivism(主观主义),eg. I believe a is true, so a is true.

majority(诉诸多数),many people believe a is true, so a is true.

appeal to emotions(诉诸情感), when you try to persuade someone of a conclusion, not by presenting evidences, but by causing emotions such as pity, fear, guilty or whatever.

appeal to force(诉诸武力), try to threat(physically or psychologically)someone to accept propositions.

appeal to authority(诉诸权威), appeal to appropriate authority is not a fallacy.

it is a fallacy when you appeal to wrong and inappropriate authority.

ad hominem(人身攻击), attack a argument by attacking the person who made it.

例子：how can you tell me I should stop smoking when you still smoke yourself.

you are supporting Julie for the class president because she's your friend.

false alternative(假两难推理), falling to consider all relevant alternatives. 

例子：If you are not with us, you are against us. But you may neutral.

Post Hoc(后此谬论), A occurred before B/  Therefore, A caused B.

Hasty generalization(轻率归纳 以偏概全), Draw a conclusion on the basis of insufficient evidence.

例子：The tour guides were so kind. Thus, people in that country are kind.

composition/division(构成/分割)

Composition: Parts -> Whole

Every part of the car is cheap, So the car is cheap.

Division: Whole ->Parts

The apple is red. Thus all atoms that make up the apple are red.

Begging the question(丐题)

When you assume C in the process of proving C.

God exists - Bible says so - Bible is trustworthy - Bible is the words of God(That means God exists)

Complex question(复合问题): Presupposes something that has not been proved

例子：Have you stopped beating your wife? This question presupposes that you have been beating your wife, which has not be proved.

Equivocation(一词多义), when a word switches its meaning in the middle of an argument.

Appeal to ignorance(诉诸无知), nobody has proved P is true, it does not follow that p is false.

Diversion(偷换话题), changing the issue in the middle of an argument.

Red herring

straw man, attack someone's conclusion by attacking an oversimplified version of it.

Argument analysis and advanced argument analysis.(论证分析)

distill an argument:

Before we can evaluate an argument, we must first recognize that a given piece of writing contains an argument.

What's the conclusion?

what's the author's main claim?

The conclusion states your belief.

 Diagramming debates

A sound argument = valid + all true premises

We can criticize an argument in 2 different ways.

1, Not all premises are true.

2, Even if all the premises are true, the conclusion doesn't follow.

Categorical propositions, 

four basic types of categorical proposition

A-type, All S are P

E-type, No S is P

I-type,Some S are P

O-type, Some S are not P

the logical relation among 4 types:

A-I: All S are P -> Some S are P 

A&O are contradictory, A is true then O is false, A is false then O is true.

 E&I are contradictory, E is true then I is false, E is false then I is true.

categorical syllogisms(直言三段论), an argument with two premises and a conclusion, all of which are categorical propositions.

Disjunctive syllogism(析取三段论), 

Hypothetical proposition(假言命题), 

if P, then Q

P is a sufficient condition for Q

Q is a necessary condition for P

P is the antecedent of the conditional

Q is the consequent of the conditional

P only if Q = if P then Q

P unless Q = P if not Q

No P, no Q = if Q then P

valid arguments, 

if P, then Q,  (前置条件)

P therefore Q 

 not Q then not P

invalid argument,

if P, then Q, (前置条件)

Q, Therefore P,  affirming the consequent

Not P, therefore not Q, denying the antecedent

if P, then Q, if Q, then R, therefore, if P, then R

The language of propositional logic(命题逻辑语言)

primitive symbols: P, Q, R, S, ....

~ negation, not

. conjunction, and

V disjunction(wedge), or

> conditional( horseshoe), if - then

= biconditional(triple ban), if and only if 

complex propositions

combing simple propositions with connectives, we can generate more complex propositions

examples P,Q,R,S

P.Q, RVS, (P.Q)>(RVS)

Truth values 

True, T False, F

结论指示词：

therefore, for these reasons, hence,it follows that, so, I conclude that, accordingly, which shows that, in consequence, which means that,  consequently, which entails that, proves that, which implies that, as a result, which allows us to infer that, for this reason, which points to the conclusion that, thus, we may infer, since, as indicated by, because,  the reason is that, for, for the reason is that, as, may be inferred from, follows from, may be derived from, inasmuch as, In view of the fact that