How does one produce a logical argument? (Handout)

Answer: Use deductively valid or inductively strong reasoning.

1. Follow these 5 steps to outline a cogent, logical argument

1. State the conclusion precisely. Make sure it is about one and only one specific issue/subject in question. Only assert your conclusion after thinking a lot about it, don't just state your opinion and look for evidence to support it. That is backwards - it is called rationalizing - it is rarely convincing and people don't trust it. Always consider evidence for and evidence against your view, then decide whether or not to argue for your conclusion. If you cannot find or imagine any evidence against your view, then do not argue for your conclusion. If you can't be wrong, why should people believe your view is correct? Evidence-based reasoning is superior to faith-based reasoning where people want more objective reasosn rather than purely subjective reasons for accepting a view.
   
   
2. Find information relevant to your conclusion. That is, present acceptable, objective data, facts, observations, definitions, values, etc. You need enough supporting material to make your argument compelling. One must justify each assumption of one's argument and present that data for all to see and evaluate.
   
   
3. State whatever supporting evidence you have for your conclusion. Inforamtion becomes evidence for a conclusion when you present it as if it supports your conclusion, but this does not make the evidence compelling. Your assumptions (or premises) which you present as evidence must be stated precisely. In the arguments above, which are sketches really, one needs to support with further evidence the allegedly factual assumptions, e.g., in each of the first three arguments above, claim (2) needs additional support. State your assumptions only after evaluating the information honestly, don't make a conclusion where the preponderance of evidence is against it. Respect your listener or reader by providing all relevant evidence and they are more likely to respect your point-of-view.
   
   
4. Produce a general, conditional or categorical principle which justifies your conclusion. Make its logical form look just like claim (1) in each of the above samples - and claim (2) in the fourth example. Do you see how those claims are general and, if true, supportive of each argument's conclusion. State each clearly, and in such as way that each can be tested against serious counter-examples. You need at least one powerful principle to make your argument logical. If you are constructing an ethical argument, then you will need to a use a relevant and justifiable ethical principle from an acceptable ethical theory. (For arguments about ethical issues, see my handout on how to frame issues, principles and judgments.)
   
   
5. Construct the entire argument exactly like one of the forms above, stating relevant facts, principles and your conclusion. Frame the argument so that others can check your facts, test your principles and objectively accept or reject your conclusion. At a minimum, your argument needs to have a precise, defensible conclusion supported by corroborating evidence, and at least one general, reasonable, defensible principle and one or more alleged fact(s).
   
   
   • In short, make your argument have the same pattern of reasoning in the logical forms exemplified above. The logical pattern plus the facts and rational principles together must justify your conclusion. You will usually need to draft and revise and draft and revise several times before you actually produce a compelling argument - but do persevere.
     
     
   • Example of a cogent, logical argument outline: At the top of this page here you will see an outline of my argument for banning laptop use in the classroom. Following this, on the same page, you will find supporting evidence. This also includes a consideration of counter-arguments, which I may or may not require you to do depending on the goals of the paper I assign. If you can't produce an outline of your argument and supporting evidence for your point-of-view just like this example, then you do not understand how to do this, and you must see me for help.
     
     
   • Also, review my Examples of moral principles and arguments (Handout 2) for more samples of moral arguments.
     
     

2. Some logical, deductively valid forms of argument

modus ponens (method of affirming)

1. If an activity in the classroom is unnecessary and an avoidable distraction, then it should not be permitted by the professor.
2. Student laptop-use in the classroom is unnecessary and an avoidable distraction.
3. Therefore, student laptop-use in the classroom should not be permitted by the professor.
   
   

modus tollens (method of denying)

1. If George is negligent, then George fails to protect people from foreseeable injuries.
2. George protects people from foreseeable injuries.
3. Thus, George is not negligent.
   
   

disjunctive syllogism (an either-or argument)

1. Either you should get her informed consent permission before you share her personal data or you should just ask her forgiveness after you share it.
2. You should not just ask her forgiveness after you share her personal data.
3. Therefore, you should get her informed consent permission before you share her personal data.
   
   

hypothetical syllogism (a conditional argument)

1. If killing another person is wrong, then killing is immoral.
2. If killing is immoral, then it should not be permitted.
3. Therefore, if killing another person is wrong, then it should not be permitted.
   

3. Avoid these 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."

4. 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.

5. Some logical, 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 B.

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 any 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 Y, then (probably) X is a cause of Y.