Critical Thinking

Critical Thinking

1. Common Rules

   • Mention : "............"
   • Bold and Red Type : Important Technical Terms
   • Underline = Emphasis

2. Expressions (>= 1 word)

   • Sentences : Grammartically Correct Sentences
     • Proposition (Have T/F)
       • 1 Proposition
         • Literally T/F
           • Kenneth Lee is a girl (Literally False)
         • Logically Possible / impossible
           • Kenneth Lee is a girl (Logically Possible)
           • Patent (直接矛盾) （e.g. Big Ben is a tower and not a tower
           • Latent (間接矛盾) (e.g. Big Ben is a tower and not a building)
       • 2 or more Propositions
         • Logically Consistent or not
           • Consistent
             • Some donkeys have attacked human. Some have not
             • The winning ticket is 240. Kelly holds 239. She holds the winning ticket
           • Inconsistent
             • Frank defeated all participants in the race
     • Questions
     • Different sentences can express the same Prop.
       • I hit Sam
       • Sam was hit by me
     • Different prop. can be expressed by the same sentence
       • Hedonist : Happiness is the end of life (Purpose of Life)
       • Ascetic : Happiness is the end of life (Finisihing of life)
     • Analytic Sentences (T/F merely in the virtue of its meaning)
       • True Analytic Sentence
         • Absolute Vaccuity
           • Use a true analytic sentence to provide empirical info.
           • How can you be the top of class ? Just by scoring the highest in class!
         • My mother is a woman
         • Definitions
           • Definiendum (被定義項)
           • Definiens (定義項)
             • Bad Definiens
               • Too Wide
               • Too Narrow
                 • Apple is a Red and Juicy Fruit
                 • Sexual Harrassment : Making a woman feel angry
             • Good Definiens
               • Not Too Wide / Narrow
               • No vicious Cycles
                 • Bachelor = Bachelor
               • Definiens not as obsure as the definiendum
                 • Supplementary absolute self = adjunct unconditional age
         • Implicatures
           • Conversational Implicature
             • Maxims
               • Quality / Quantity / Relevance / Manner
             • Cancellable
             • Can you be my girlfriend? I have a boyfriend already
           • Conventional Implicature
             • Non-Cancellable
             • Colored Expression (e.g. He is stubborn, but I dont have hard feelings on him)
           • Literal Meaning
             • Non-Cancellable
       • False Analytic Sentence
         • A boy is a girl
     • Synthetic Sentences (Informative + Need Add. info. to determine T/F)
       • True Synthetic Sentences
         • Some People has drawn triangles
         • Relative Vaccuity
           • Use a true synthetic sentence to convey a redundant empirical Info.
           • What do you think of the DSE exam ? I think all candidates want to get good grades and enter university
       • False Synthetic Sentences
         • No one has drawn triangles

3. Insufficient Clarity

   • Vague (e.g. Fat, Hot)
   • Meaning Incomplete (e.g. Tom's height is above average)
   • Ambiguous Expression
     • Semantic Ambiguity (Ambiguity due to meaning of the sentence)
       • Happiness is the end of life (Purpose / Ceasing of life)
     • Syntactic Ambiguity (Ambiguity due to the way of terms combined)
       • 兒子生性病母倍感安慰
     • Phonological Ambiguity (Ambiguity due to the pronunciation of the word)
       • there - their / here - hear / Plane - Plain

4. Dispute

   • Verbal Dispute
     • Disagreement due to the different uses of an expression
     • Vague, Meaning-incomplete and ambiguous expressions cause verbal disputes
       • Productive Scholar / Fat / Wait at the bank
   • Genuine Dispute
     • Disagreement due to different understandings of facts

5. Uses of Expressions

   • Cognitive Use
     • Informative Use (e.g. Synthetic Sentences
     • Non-Informative Use (e.g. Analytic Sentences)
   • Non-cognitive Use
     • Expressive Use (e.g. Fuck You)
     • Directive Use (e.g. Shut Up)
     • Other Uses
   • Mixed Use of Expressions
     • Your friends have all got married
       • Informative Use
       • Expressive Use : Impatience
       • Directive Use : Please get married ASAP

6. Logical Relations

   • Contrary (正對立) (Both True : NOT OK // Both False : OK
     • All donkeys are naughty. All donkeys are obedient
   • Subcontrary (次對立) (Both True : OK // Both False : NOT OK)
     • Kelly said that there are alients. Kelly said that there are not aliens
   • Contradictory (Both True / False : NO OK)
     • There are aliens. There are no aliens
   • Entailment
     • Logically Entail (If P is TRUE, Q must be TRUE)
       • P : Peter is Running Q : Peter is moving his body)
       • Exceptions (Implications)
         • Some dogs are black. Some dogs are not black
     • Logically Stronger (P entails Q, but Q does NOT entails P)
       • P : An astrologer proved that there are UFOs Q : There are UFOs
     • Logically Equivalent (P entails Q and Q entails P)
       • Peter and I are happy. Peter is happy and I am happy

7. Argument

   • Premise
     • Indicators : Since / for / In view of
     • Hidden Premises
       • Holding Hands Rule (Key terms in Premise must appear in conclusion)
         • Ronny is a politician. Politicians are selfish. Ronny is selfish
       • Rabbit Rule (Key Terms in Conclusion must appear in Premise)
         • An intruder entered the house. The dog hadn't barked. If the dog didn't know the intruder, then it would have barked. (Hidden Premise). The dog knew the intruder
   • Conclusion
     • Indicators : Therefore / Hence / As a Result
   • Supporting Relation
   • Non-Arguments
     • Reports
     • Explanation
       • I ate your apple since I'm hungry
     • Conditionals (If-then Propositions)
     • Unsupported Claims (e.g. 2 + 2 = 6)
   • Argument Mapping
     • Use arrows to unpack reasoning
     • Use Complete Sentences
     • Differentiate independent premise and co-premise
       • If X is False, the extent to Y supports the conclusion decreases >>> Co-premise
         • Bella is a husky. All huskies are dogs. So Bella is a dog
     • Make hidden conclusion and premises explicit
   • Deductive Arguments
     • Valid Arguments
       • When all Premises are TRUE, the conclusion must be true
       • Premises logically entials Argument
       • Sound Argument (The Premises are literally TRUE)
       • Non-defeasible
   • Inductive Arguments
     • Strong Arguments
       • If All Premises are TRUE, it's very probable that the argument is TRUE
       • Defeasible
         • Adding Premises will affect the strength of the argument
       • Cogent Arguments (Premises are TRUE as well)
   • Good Argument
     • Epistemic Condition (Reasonable Premises)
     • Logical Condition (Premises support the conclusion in a valid way)
       • NO Invalid Arguments
       • NO Weak Arguments
       • No Circular Arguments
       • NO Irrelevant Arguments
       • Not to be defeated