Avoiding Flawed Logic

Induction…

Starts by examining particulars and arriving at a generalization that represents probability.

Whenever we observe something around us and then draw a conclusion about this, we are engaging in inductive reasoning.

We should always ask three questions of an inductive argument:

1. Is the evidence sufficient?2. Is it representative?3. Is it up-to-date?

Inductive Leap

When you jump from the observations you’ve made or the examples you’ve found and reason that the same is true of other things…

This reasoning is not necessarily faulty, but you have to be careful not to commit the fallacy of Hasty Generalization.

Difference between sound inductive reasoning and

Hasty Generalization:• An inference from a sample of a group to

a whole group is legitimate only if the sample is representative —that is, only if the sample is sufficiently large and every member of the group has an equal chance to be a part of the sample.

A Deductive Argument:

• Is intended to provide conclusive support for its conclusion.

• If it succeeds in providing conclusive support it is valid.

• If it fails to support its conclusion, it is invalid.

Valid Deductive Arguments:• If the premises are true, then the conclusion

MUST be true.• It is impossible for a deductively valid argument

to have true premises and a false conclusion.• Thus, we must distinguish whether or not the

premises are indeed true, since just because an argument is in valid form does not necessarily mean the conclusion is true; if the premises are false, then the conclusion may also be false.

Example of a valid deductive argument that is false:

Major premise: If you have scars on your body, then you have been abducted by space aliens.

Minor premise: You obviously do have scars on your body.

Conclusion: Therefore, you have been abducted by space aliens.

(This argument is valid, but it is not sound).

Example of a valid and sound deductive argument:

All minors are under the age of eighteen.My son is under the age of eighteen.

Therefore, my son is a minor.

Consider the following deductive argument…

Penelope claims that all her test scores have been good, and so her course grade should be good, too.

We can express this argument as a syllogism:

All those who receive good test scores receive good course grades.

Penelope’s received good test scores.Therefore, Penelope gets a good course grade.

Is it valid? Is it sound?

When a premise is omitted…

• Some deductive arguments might seem confusing or misleading because they are missing a premise (usually the major premise).

• We need to evaluate the truth of the unexpressed premise in order to decide if the logic is truly sound. (This is similar to examining the implicit warrants in an argument).

Enthymemes…

• Results when only two parts of the syllogism appear.

• Thus, if a deductive argument is missing a premise (if it is implied but not explicitly stated) then the resulting syllogism is called an enthymeme.

Example of an enthymeme:

Susan studies rhetoric, so I know she speaks eloquently.

What is left out here is the major premise that all those who study rhetoric speak eloquently.

Another enthymeme…

The gun has the defendant's fingerprints on the trigger. He is clearly guilty!

What is missing here, is the major premise that links the gun to the crime, such as it being found next to the murdered person's body or that bullets from the body match the gun.

What could go wrong with this enthymeme?

"If you have been healed or saved or blessed through TBN and have not contributed . . .

you are robbing God and will lose your reward in heaven."

(Paul Crouch, co-founder of the Trinity Broadcasting Network, quoted by William Lobdell, The Week, August 10, 2007)

What’s the missing premise?

It's morally wrong to treat human beings as mere objects.

So, genetically engineering human beings is morally wrong.

And these?

"Hungry? Grab a Snickers."(advertising slogan for Snickers chocolate bar)

"One of the Soviet Georgia's senior citizens thought Dannon was an excellent yogurt.

She ought to know. She's been eating yogurt for 137 years."

(1970s television advertisement for Dannon Yogurt)

Missing premise?

"I wanted to serve as President because I love this country and because I love

the people of this Nation." (Jimmy Carter, 1980 Concession Address)

Final thoughts on enthymemes…

When a part of the argument is missing, it is assumed not only to be true, but so obvious that it is not worth including.

This makes it very difficult to challenge, as questioning the obvious is an admission of ignorance, which puts oneself lower down the social order and opens oneself to attack.

It also uses and 'out of sight, out of mind' principle: when the unsafe part of the argument is missed out, then people may not realize that it has been omitted.

Advertisers and politicians thus make great use of enthymemes (as we’ve seen in some of the previous examples).

Let’s take apart some arguments and find some

fallacies…

It’s way better than fast food. It’s Wendy’s.

The Earth has air, water, and living organisms.

Mars has air and water.

Therefore Mars has living organisms.

Ever since I started wearing these crystals around my neck I haven’t caught a cold. I bought some crystals for all my family

members so that they will also stay healthy.

The following appeared in a letter from the principal of Allentown High School to the teachers in the school:

Backusville High School instituted a policy last year requiring all of its students to arrive at school half an

hour early to finish all their homework before attending classes. Since the inception of this policy,

15 percent more students have enrolled at Backusville. The Board of Education reminds us that

the more students we have enrolled at Allentown High School, the more federal funding we receive, so

it’s clear to improve the quality of education for all Allentown students we need to institute an early-

attendance policy similar to the one that Backusville has instituted.

Claim (Conclusion):Support (Premises):Warrant (Assumptions):Possible fallacies?

Name that fallacy…Q: Now, the United States government says that you are still funding military training

camps here in Afghanistan for militant, Islamic fighters and that you're a sponsor of international terrorism... Are these accusations true?

Osama Bin Laden: ...At the time that they condemn any Muslim who calls for his right, they receive the highest top official of the Irish Republican Army at the White House as a political leader, while woe, all woe is the Muslims if they cry out for their rights. Wherever we look, we find the US as the leader of terrorism and crime in the world. The US does not consider it a terrorist act to throw atomic bombs at nations thousands of miles away, when it would not be possible for those bombs to hit military troops only. These bombs were rather thrown at entire nations, including women, children and elderly people and up to this day the traces of those bombs remain in Japan. The US does not consider it terrorism when hundreds of thousands of our sons and brothers in Iraq died for lack of food or medicine. So, there is no base for what the US says and this saying does not affect us...

Source: "CNN March 1997 Interview with Osama bin Laden"

• Tu Quoque (two wrongs make a right) is a very common fallacy in which one attempts to defend oneself or another from criticism by turning the critique back against the accuser.

• This is a classic Red Herring since whether the accuser is guilty of the same, or a similar, wrong is irrelevant to the truth of the original charge. However, as a diversionary tactic, Tu Quoque can be very effective, since the accuser is put on the defensive, and frequently feels compelled to defend against the accusation.

Some of you may have seen the 90-minute ABC network television show…entitled "Growing Up in the Age of AIDS".… I was one of nine guests on that live program.… …[A] single 45-second sound bite cost me a long journey and two hectic days in New York City.

Why…did I travel to The Big Apple for such an insignificant role? …I felt a responsibility to express the abstinence position on national television.… How sad that adolescents hear only the dangerous "safe sex" message from adults who should know better.

What follows, then, is what I would have said on television.…

Q: Why, apart from moral considerations, do you think teenagers should be taught to abstain from sex until marriage?

…[N]ot one of 800 sexologists at a recent conference raised a hand when asked if they would trust a thin rubber

sheath to protect them during intercourse with a known HIV infected person. … And yet they're perfectly willing

to tell our kids that "safe sex" is within reach and that they can sleep around with impunity.

Source: James C. Dobson, in a fund-raising letter for "Focus on the Family", February 13, 1992.