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III. Some Basic Concepts of Logic Clarity § Definition -- lexical and stipulative -- ostensive -- definition by examples -- definition by a synonym -- genus and differentia genus = species differentia – has to be essential features. Examples § A mosque is a building, often with high towers and domes, where Muslims go to worship § § § Yellow is a color that resembles a ripe lemon. Yellow is the portion of the spectrum between green and orange. Yellow is radiant energy with a wavelength of 580 nanometers.
§ Extension (denotation) and intension (connotation) The extension of “chair” is this chair, that chair, … all the chairs that the word refers to. The intension of the word "chair" is (something like) "a piece of furniture designed to be sat upon by one person at a time. " -- Thin and thick. – this chair, four-legged chair, furniture, physical object, thing, being. -- Related to universalism vs. holism.
Arguments and Validity § Arguments - not verbal fighting - basic structure P premises C conclusion e. g. "I think she's in law school; she's always lugging around a pile of law books. " - Sometimes the conclusion or some premises are omitted.
§ Deductive Arguments and Validity - A (deductive) argument is valid if and only if it is impossible that simultaneously (a) all its premises are true and (b) its conclusion is false. - Not to be confused with truth value. - Propositions (e. g. premises and conclusions of arguments) are true or false. - Arguments are never true or false; they can however be valid or invalid. - Many invalid arguments have true conclusions. Example: Some human beings are mortal, and Socrates is a human being. Therefore, Socrates is mortal. (Can you see why this is an invalid argument? ) - Many valid arguments have false conclusions. Example: No human beings will ever die, and Socrates is a human being. Therefore, Socrates will never die. - Every valid argument with a false conclusion has at least one false premise.
§ Exercises P 1 All bananas are purple. P 2 All lettuce is orange. C All bananas and lettuce are either purple or orange. P 1 The Bible says God exists. C God exists. P 1 The Bible is the word of God. P 2 The word of God is always true. P 3 The Bible says that God exists. C God exists. P 1 My parents have taught me that God does not exist. P 2 Mom wouldn't lie. C God does not exist. War is the only way of stopping Saddam Hussein. After all, sanctions haven’t worked at all. Undemocratic societies kill the human spirit. The reason is clear: unless the people have the power in their society, the human spirit withers.
§ Inductive reasoning Induction is a form of reasoning that makes generalizations based on individual instances. P 1 In the past, when I've gone home, my house has still been there. C When I go back home this afternoon, my house will still be there. P Every day to date the law of gravity has held. C. Therefore: The law of gravity will hold tomorrow. - Statistic reasoning e. g. This year x number of people will die in auto accidents in HK. - Causal reasoning e. g. Two weeks after they put fluoride in St. John’s water I got sick. I had a fever and couldn’t keep solid food down. So, I switched to drinking bottled water and I recovered in a day or so. That fluoridated water is dangerous stuff. - Arguments from Analogy e. g. Children are like flower, they need tender loving care. - Arguments from authority
§ Daily One-minute Paper 1. What is the big point you learned in class today? 2. What is the main, unanswered question you leave class with today?