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Lecture 2- different types of arguments 

by Marianne Talbot, university of Oxford 

Deduction VS. induction — 2 basic types of arguments 

Deductive argument—we are arguing from this premises

the truth of their premises guarantees the truth of their conclusion 

EX: 

it is Friday. —true
Marianne always wears jeans on Friday.— true 
Therefore, Marianne is wearing jeans.— definitely TRUE

If Marianne is not wearing jeans, that means either “it is not Friday” or “Marianne don’t always wears jeans on Friday." Or both not ( counterexample )

Deduction is an “either / or ” thing :

A good deductive argument gives us conditional certainty and the premises are true 

A bad one tell us nothing

Inductive arguments —we are arguing to this conclusion 

The true of their premises make the conclusion more or less possible — there is no certainty

Inductive argument could either “weak” or “strong” 

There must be some counterexamples existed. 

EX—strong :

The sun has risen everyday in the history of universe ( uniformity of nature )
Therefore, the sun will rise tomorrow 

EX—weak :

Every time I have seen Marianne, and she is wearing earrings.  
Therefore, next time I see Marianne, and she will be wearing earrings.

Exercise:

1. The sun is coming out so the rain should stop soon—Inductive..

    Conclusion : so the rain should stop soon

    Premises : The sun is coming out 

2. If Jane is at the party John won’t be. Jane is at the party. Therefore, John won’t be.—Deductive…

    Conclusion : Therefore, John won’t be.

    Premises : If Jane is at the party John won’t be. Jane is at the party.

3. The house is a mess. Therefore, Lucy must be home. — Inductive…

    Conclusion : Therefore, John won’t be.

    Premises : The house is a mess.    

4. Either he is in the bathroom or bedroom. He is not in the bathroom, so he must be in the bedroom. — Deductive…

    Conclusion : so he must be in the bedroom.

    Premises : Either he is in the bathroom or bedroom. He is not in the bathroom  

5. The dog would have barked if it saw a stranger. It didn’t bark, so it didn’t see a stranger. — Deductive…

    Conclusion : so it didn’t see a stranger    

    Premises : The dog would have barked if it saw a stranger. It didn’t bark

6. No one in Paris understand me, so my French must be rotten or Parisians are stupid.—Inductive… 

    Conclusion : so my French must be rotten or Parisians are stupid

    Premises : No one in Paris understand me

Logicians study deduction by studying valid argument forms….

….argument that are valid in virtue of their forms as opposed to their contents. 

Syllogism: (described below )

@: All men are mortal. (All As = B)
     Socrates is a man. (A= B)
     Socrates is mortal. (so, S=A)

@: All actions produce the GHGN are right. (greatest happiness greatest number)   
     That action produces the GHGN.
     That action was right.

These two have the same form but different content.

Modus ponens:

If P then Q, P therefore Q. ( deductive )

EX: if he get a bus, then he is eco-friendly. 
       He dose get a bus. 
       Therefore, he is eco-friendly.

EX: it is raining, then I raise an umbrella.
       My umbrellas is up. 
       Therefore, it is raining. —affirming consequent

EX: if postmen are striking, then we will have no letters. 
      The postmen are striking. 
      Therefore, we will have no letters.

Ex: if there are no chance factors in chess then chess is a game of skill.
      There are no chance factors in chess. 
      Therefore, chess is a good of skill. 

Modus tollens:

If P then Q, not Q therefore not P. ( deductive )

EX: if the dog did not know the visitor well, the dog would have barked.
       The dog did not bark.
       The dog know the visitor well.

EX: if I have money, I would be in the pub.
       I would not be in the pub.
      Therefore, I have no money.

Disjunctive syllogism:

P or Q, not P therefore Q ( deductive )

EX: it’s either rainy or sunny.
       It is not rainy. 
      Therefore it is sunny.

EX: either we hope for progress through improving morals or we hope for progress from improving intelligence.
       we cannot hope for progress through improving morals.
       Therefore, we hope for progress from improving intelligence.

Leibniz’s law:

A is F, a=b, therefore b is F

EX: Jane is tall.
       Jane is the bank manager.
       Therefore, the bank manager is tall.

Syllogism:

All Fs are G, a is an F, therefore a is a G

EX: all Mercedes are cars.
       It is a Mercedes.
      Therefore, it is a car. 

EX: all miracles are impossible.
       Resurrection is a miracle.
      Therefore, resurrection is impossible.

Right, but there is a negative existential problem.
If resurrection doesn’t exist, how do we know resurrection is a miracle?

EX: All men are mortal. (All As = B)
      Socrates is a man. (S= B)
      Socrates is mortal. (so, S=A)

Deontic logic: ( about moral )

EX: Lying is wrong. 
       Therefore, we should not lie.

This means that we know lying is wrong, but we still do that. And you may feel guilty. 
They can be deductive because the special meaning of “wrong ”

Model logic:

( If A is necessary then not A id not possible )

It is necessarily the case that there are no square circles.
Therefore, it is not possible that there are square circles.

Temporal logic:

It is raining today.
Therefore, tomorrow it will have been raining yesterday.

the logic that time works.

All Inductive arguments rely on the assumption of 『 the uniformity of nature 』.

The idea that the future will be like the past.

sun rise for example : sun rise every day then you will see the sun again tomorrow.

Considering the uniformity of nature: 

because you can find the circular regulation described from the premises. 

Like you judge the conclusion by the past.

EX: Every day in the history of universe, the sun has risen. 
       Therefore the sun will rise today.— induction and strong. 

EX: every time I have seen Marianne she has been wearing earrings.
       Therefore Marianne will wear earrings when I see her today.

Within the category of inductive argument, there are many different sub-types:

Argument from analogy 

A is like b, b is F, therefore A is F

EX: the universe is like a pocket watch  
       A pocket watch had a designer 
       Therefore the universe has a designer…

Argument from authority

 EX: Einstein is a brilliant physicist 
        Einstein says relativism is true.
        Therefore, relativism is true.

causal relation 

Every time an A occurs and a B occurs.
Therefore As cause Bs.

Causal arguments can be deductive or inductive, depending on whether we are arguing from a causal claim or to a causal claim.

recap:

deductive:

As cause Bs (certainty)

There was an A 

Therefore there will have been a B… definitely 

Inductive :

Every observed A has been followed by a B

Therefore As cause Bs…. More likely 

簡單來說第二講主題教大家怎麼分演繹法跟歸納法，我覺得這是講數學的邏輯運算，演繹法（deductive）就是類似『交集』的意思，而歸納法就是『聯集』的意思，在這裡之後還分一堆演繹法總類，這根若Ｐ則Ｑ那麼～Ｑ則～Ｐ是一樣的內容，『演繹法』所獲得的結論是由『前提』推出來的，然而『歸納法』可以找到反例去『破壞結論』的可能性，這個可能性是指他的結論可能出現的機率（slightly likely / likely / more likely ）他並不是讓結論變成不可能，舉個例子，每天旭日東昇，所以明天太陽從東邊升起的機率應該是接近100%了，所以是more likely, 那麼老媽每天都煮晚餐給我們吃，但其實常常會買便當回來，所以不一定每天開火，所以是likely...以此類推。

以上來自牛津大學教授上課筆記希望能幫上忙，喜歡，或是不喜歡還是有錯誤，歡迎留言指教，謝謝!!