Argument Forms

Deductively VALID FORMS of argument • modus ponens (method of affirming) 1. If this is a plant, then it undergoes photosynthesis. 2. It is a plant. 3. Therefore, this undergoes photosynthesis. • modus tollens (method of denying) 1. If Spike is a racist, then he discriminates on the basis of race. 2. Spike does not discriminate on the basis of race. 3. Thus, Spike is not a racist. • disjunctive syllogism (an either-or argument) 1. Either God created humans or humans evolved from non-living matter by cosmic accident. 2. Humans did not evolve. 3. Therefore, humans were created by God. • 1. 2. 3. hypothetical syllogism (a conditional argument) If we successfully develop nuclear fusion power, then power will become cheap and plentiful. If power becomes cheap and plentiful, then the economy will flourish. Therefore, if we successfully develop nuclear fusion power, then the economy will flourish. Bad (formally INVALID) deductive arguments Erroneous because their conclusions do not follow from their premises. Even if their premises are true, these forms are not truth-preserving... Fallacy of affirming the consequent: "When you have a cold, your sinuses become congested, your eyes itch, and you have headaches. You are congested, your eyes itch and you have a headache. So you have a cold." Fallacy of denying the antecedent: "If abortion is murder, then it is wrong. But abortion is not murder. So abortion is not wrong." Fallacy of affirming a disjunct: "Jesus was the son of God or Jesus was a liar. Since Jesus was the son of God, Jesus was not a liar." Fallacy of undistributed middle: "All reptiles lay eggs, and all birds lay eggs. Therefore, all birds are reptiles." PRACTICE: Does each conclusion follow from the premises stated? Which of the following arguments is VALID? Are any SOUND? Where the form is invalid, describe how the premises could be true but the conclusion false... 1. If Spike is a racist, then he discriminates on the basis of race. Spike discriminates on the basis of race, therefore he is a racist. 2. If you study, you will pass the test. You do not study, so you will not pass the test. 3. If you don't let him buy a Hummer, then you don't love him. But you let him buy a Hummer, so you love him. 4. Unless she has a fever, she doesn't have the flu. She doesn't have the flu, so she doesn't have a fever. 5. If it is raining my car will get wet. But it is not raining. So my car will not get wet. 6. Every person should avoid keeping loaded guns around the house. People who have the capacity to kill should avoid keeping loaded guns around the house. Every person has the capacity to kill. 7. Liars mislead and deceive; Ollie is a liar because he gave misleading and deceiving testimony. 8. I should not diet, so I should jog. I want to get into shape. If I want to get into shape, either I should jog or I should diet. 9. Mice fed saccharin develop bladder cancer. It follows that humans who consume saccharin also develop bladder cancer, because substances that cause cancer in mice cause cancer in humans. 10. Nobody should be forced to risk their health against their will unless there is some greater benefit. Allowing cigarette smoking in public places provides no greater benefit. Cigarette smoking in public places should not be allowed because doing so forces the nearby non-smoker to risk her health against her will. 11. Capital punishment is an acceptable social policy only if it either deters murder or is justifiable revenge. Since capital punishment does not deter murders and is not justifiable revenge, capital punishment is not an acceptable social policy. 12. Time has neither a beginning nor an end, that is, time is eternal. If time had a beginning, then there would have been a time before time. If time had an end, then there would be a time after time. The idea of there being a time before time or a time after time is absurd since before and after mean before and after in time. Inductively Strong forms of argument Induction by enumeration "All ravens we have ever observed are black, so (we may conclude) that all ravens are black." Presumes: If all observed X are Y, then (probably) all X are Y. Induction by analogy 1. Person A has properties p, q, r, and s. 2. Person B has properties p, q, and r. 3. Therefore, (probably) person B has property s also. [p: has a backpack; q: has a class schedule; r: has this text; s: is a student] Presumes: If X and Y are very similar, then (probably) X and Y are similar in another respect. Statistical induction "On standard intelligence tests, asians consistently outscore whites and whites outscore blacks. Thus, whites have higher IQs than blacks and asians have higher IQs than both whites and blacks." Presumes: If the sample accurately represents the population from which it is drawn, then (probably) whatever is a property of the sample is also a property of the population. Causal induction "Many smokers are afflicted by chronic bronchitis, asthma, emphysema, heart disease, mouth and lung cancer. Heavy smokers suffer these problems even more so than do light smokers. Further, non-smokers living with smokers suffer these problems more than non-smokers who do not. Obviously smoking causes these problems." Presumes: If there is a strong correlation between X and Y, where X and Y do NOT accidentally coincide, X and Y do NOT have a common cause, and Y does NOT cause X, then (probably) X is a cause of Y.