Week 2: Critical Thinking

Critical Thinking How do we make progress on a philosophical issue? Critical Thinking involves thinking objectively without prejudice, emotion or bias Reasoning/giving arguments for one’s own views Raising objections to someone else’s reasons/arguments thinking clearly by defining one’s own concepts Critical thinking is the right way to think in any area of life: math, science, business and in philosophy

A Philosophical Debate Main Ways to Advance a Philosophical Issue Definition Define a central concept: e.g. moral right/wrong, Apply concepts to issue Arguments: any two (or more) statements where one is the reason for the other Deductive argument (e.g. mathematical proof) Inductive argument (e.g. scientific argument) Objections to Arguments

Propositions and Arguments 1 From Clear and Present Thinking, Chapter 3.1-3.3

Argument Form Ordinary Language to Argument Form Ordinary Language Three years after its handover from Britain to China, Hong Kong is unlearning English. The city's "ghost men" must go to ever greater lengths to catch the oldest taxi driver available to maximize their chances of comprehension. Hotel managers are complaining that they can no longer find enough English- speakers to act as receptionists. Departing tourists, polled at the airport, voice growing frustration at not being understood. The Economist 2001. Argument Form ………. ……….. 1-3 must be propositions 1, 2 are reasons for 3 We say one makes an inference from 1, 2 to 3 Premises Conclusion

Indicator Words Inferences are often embodied in certain indicator words, which show you which way the direction of the argument is flowing. Here are a few examples of indicator words: Because Since Given that... Which means that... We can conclude that... Hence It follows that...

A Philosophical Debate Person A gives an argument in ordinary English Convery A’s argument into precise form Identify Properties of A’s argument Evaluate A’s argument

Propositions (3.1) The premises and conclusion in an argument form must be propositions Proposition/Statement/Claim a sentence that is simple and has one meaning a sentence that asserts something IS the case or IS NOT the case

“The other day, I was really pissed off “The other day, I was really pissed off. I ordered this new computer from the Internet. And it took three weeks to get here, which was bad enough. Then when it arrived I got so mad again! Because the one I ordered was silver, but the one they sent me was black! Somebody in that company is asleep at the wheel.” “The other day, I was really pissed off. I ordered this new computer from the Internet. And it took three weeks to get here, which was bad enough. Then when it arrived I got so mad again! Because the one I ordered was silver, but the one they sent me was black! Somebody in that company is really asleep at the wheel.”

Part of Argument (3.3) Propositions are true or false an argument is valid if its inferences lead you properly from premises to conclusions. An argument is sound if it has true premises and valid inferences Two Kinds of Arguments a deductive argument is an argument that, if it begins with true premises, logically guarantees that the conclusion is also true. Logical connectives: ~ (NOT), & (AND), v (OR), → (IF), ↔ (IF and only IF) Simple statements are propositions without logical connectives

Types of Statements (3.3) Negation (~A) A = It is raining today ~A = It is not raining today The truth value of ~A depends entirely on the truth value of A If we know the truth value of A, we can calculate the truth value of ~A using a truth table Truth-Table for Negation A ~A T F

Types of Statements (3.3) Conjunctions: A & B Disjunctions: A V B Bill jogs and Ann walks. Ann dances, but Andres sings. Disjunctions: A V B Jones will get a truck or SUV The hoarder will either clean or be evicted. A B A & B T F A B A V B T F

Types of Statements (3.3) Conditional: A → B Biconditionals: A ↔ B A B Example If it is raining then it is cloudy If it is sunny then it is night Example: ~ P → C If you don’t give me that pony, then I’ll cry. I’ll cry only if you don’t give me that pony. When I don’t get my pony, I cry. Biconditionals: A ↔ B You can have cake if and only if you eat pasta. You can have cake just in case you eat pasta. A B A → B T F A B A ↔ B T F

Exercise: Statements Identify the following statements as a simple statement, negation, conjunction, disjunction, conditional, or biconditional (a) Lois is awesome. (b) If you don’t eat your meat, you can’t have any pudding. (c) You can go to the party if and only if your homework is done. (d) You said you would give me a pony, but you didn’t. (e) Either you’re going to the dentist, or I’ll rip that tooth out myself. (f) I’m a wussy little girl. (g) “Hoser” is not an acceptable Scrabble word.

From Clear and Present Thinking, Chapter 3.7 Deductive Arguments 3 From Clear and Present Thinking, Chapter 3.7

Deductive Arguments Deductive arguments: Valid deductive arguments: the conclusion follows necessarily if the premises are true The conclusion MUST be true assuming the premises are true Sound deductive arguments: the argument is valid and the premises are true The validity of a deductive argument is determined by its form only. Some argument forms show that an argument is valid; others show that it is invalid

Modus Ponens Argument Argument Form [Modus Ponens] (P1) If the dog is barking, then there’s an intruder in the house. (P2) The dog is barking! (C) Therefore, there’s an intruder in the house! Argument Form [Modus Ponens] (P1) If P, then Q P → Q (P2) P P (C) Q Q Any argument that has this form is deductively valid: ASSUMING P1, and P2 are true, C MUST be true (it cannot turn out to be false)

Affirming the Consequent Here is a similar argument form that is invalid Argument (P1) If it is raining, then I will need my umbrella. (P2) I will need my umbrella. (P3) Therefore, it is raining Argument Form (P1) If P then Q P → Q (P2) Q Q (P3) P P Invalid! Assuming that the premises are true, the conclusion is NOT necessarily true ( (P3) could turn out to be false)

Hypothetical Syllogism Argument (P1) If it gets below freezing outside, I can make ice out there (P2) If I can make ice, my soft drinks will be deliciously refreshing. (C) If it gets below freezing outside, my soft drinks will be deliciously refreshing Argument Form (P1) If P, then Q P → Q (P2) If Q, then R Q → R (C) If P, then R P → R Invalid! Assuming that the premises are true, the conclusion is NOT necessarily true ( (P3) could turn out to be false)

From Clear and Present Thinking, Chapter 3.7 Inductive Arguments 3 From Clear and Present Thinking, Chapter 3.7

Inductive Arguments Inductive Arguments An induction, or an inductive argument, is a type of argument that asserts the likelihood of the conclusion. In an inductive argument, if the premises are true, then the conclusion is probably true. An argument that show that a conclusion is probably true assuming the premises are true Inductive arguments are more common than deductive arguments; they appear everywhere in daily life and in science

Definitions 4

A Philosophical Debate Definitions Dictionary definitions: imprecise, misleading, circular Philosophical definitions: very precise, clear, no circularity A Philosophical definition Must be stated in proper form D: <defined term> : ……….. E.g. D: refrigerator: a storage device used for keeping food cool Must not be circular: (e.g. contain the defined term) Must have no counter-examples

Exercise: Definition A Philosophical Definition of a CAR

Two Kinds of Counter-Examples Counter-Example: definition is not necessary Dictionary definitions – not very precise, misleading, circular Philosophical definition: very precise, clear, no circularity Counter-Example: definition is not sufficient Must not be circular: (e.g. contain the defined term) Must have no counter-examples