基本概念
區(qū)分真與偽
命題一定存在真假，斷定任何東西才能被稱(chēng)為命題
命題：命題是陳述性的語(yǔ)句，可以被判斷為真或假。例如：“今天是星期天”、“人類(lèi)需要水才能生存”等等都是命題。命題可以被用來(lái)構(gòu)建論證，進(jìn)行推理和討論。
論證：論證是通過(guò)一系列的推理步驟來(lái)支持或證明一個(gè)觀點(diǎn)或結(jié)論的過(guò)程。論證由前提和結(jié)論組成，前提是用來(lái)支持結(jié)論的陳述或假設(shè)，而結(jié)論則是根據(jù)前提得出的推理結(jié)果。論證的目的是通過(guò)邏輯推理來(lái)證明某個(gè)觀點(diǎn)的正確性或合理性。
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
邏輯學(xué)四大基本定律
同一律，事物只能是其本身。例如貓就是貓 狗就是狗
矛盾律，在某一時(shí)刻，某個(gè)事物同一方面，不可能即使這樣又是那樣 例如李是個(gè)男人又是個(gè)女人
排中律，對(duì)任何事物在一定條件（即一定前提）下的判斷都要有明確的“是”或“非”，不存在中間狀態(tài)。
充分理由律(因果原理)，任何事物都有其存在的充足理由。
單個(gè)句子不能構(gòu)成論證，例如上帝不存在只是你的觀點(diǎn)不是論證argument
sentence也不一定是論證，它可能是在陳述事實(shí)，比如報(bào)紙，論文
because is a premise indicator
deductive argument(推演論證) includes valid argument and invalid argument
valid argument: if all the premises are true, then the conclusion is true.
inductive argument(歸納論證) 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(謬論), is mistaken reasoning, to draw a conclusion from weak and irrelevant evidences. insufficient evidences and grounds.
people commit fallacies intentionally or non-intentionally.
常見(jiàn)謬論：subjectivism(主觀主義),eg. I believe a is true, so a is true.
majority(訴諸多數(shù)),many people believe a is true, so a is true.
appeal to emotions(訴諸情感), 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(訴諸武力), try to threat(physically or psychologically)someone to accept propositions.
appeal to authority(訴諸權(quán)威), appeal to appropriate authority is not a fallacy.
it is a fallacy when you appeal to wrong and inappropriate authority.
ad hominem(人身攻擊), 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(假兩難推理), falling to consider all relevant alternatives.?
例子：If you are not with us, you are against us. But you may neutral.
Post Hoc(后此謬論), A occurred before B/ ?Therefore, A caused B.
Hasty generalization(輕率歸納 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(構(gòu)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(丐題)
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(復(fù)合問(wèn)題): 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(一詞多義), when a word switches its meaning in the middle of an argument.
Appeal to ignorance(訴諸無(wú)知), nobody has proved P is true, it does not follow that p is false.
Diversion(偷換話題), 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.(論證分析)
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(直言三段論), an argument with two premises and a conclusion, all of which are categorical propositions.
Disjunctive syllogism(析取三段論),?
Hypothetical proposition(假言命題),?
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, ?(前置條件)
P therefore Q?
?not Q then not P
invalid argument,
if P, then Q, (前置條件)
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(命題邏輯語(yǔ)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
結(jié)論指示詞：
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
