Inductive argumentation is one of the most common of the properly-used logical constructions. An Inductive argument comes to its conclusion only after it has considered all of the facts. Once the thinker has enough evidence s/he makes the “inductive leap” and
produces a conclusion. Trial attorneys, for example, use induction to put the evidence
together to make the case. If the jury agrees with the lawyer’s logic, they will agree that
his/her conclusion is correct/accurate. TV’s Dr. House compiles test results and other
facts until the diagnosis is made.
Obviously it is possible to use induction improperly: exclude facts from the theory that might otherwise compromise its conclusion
; add facts that are obviously marginal or coincidental but which seem to “prove” your theory; draw conclusions which are unprovable…
As a teacher, I collect “facts” as I teach a unit, and then I make conclusions: they liked task X more than task Y; they yelled less often
; they remained focused longer--------conclusion: they loved the Shakespeare unit!
Once people reach a conclusion through inductive reasoning, they can use the general rule for themselves.
They loved the Shakespeare unit last time. If I do the same things next time, the students will love the Shakespeare unit again.
If you wish to challenge an inductive argument, you can only challenge the conclusion
; the facts that lead to the conclusion are obviously beyond dispute (or they wouldn’t be called “facts”)
a. Hasty Generalization: the sample is too small to support an inductive generalization
about a population
b. Unrepresentative Sample: the sample is unrepresentative of the sample as a whole
c. False Analogy: the two objects or events being compared are relevantly dissimilar
d. Slothful Induction: the conclusion of a strong inductive argument is denied despite
the evidence to the contrary
e. Fallacy of Exclusion: evidence which would change the outcome of an inductive argument is excluded from
Exercise in Inductive Argument
Below are some simple inductive arguments, with some evidence presented and a conclusion (which is in bold). Score each argument out of 4, as follows: 0-very poor; 1-some probability perhaps, but not very convincing; 2-partially true perhaps, but the evidence is not as good as it could be to support the conclusion; 3-good; 4-excellent, with a conclusion arising naturally out of the evidence.
1. Piggy spends more time complaining about Jack than he does trying to equip himself with food and shelter. Clearly Piggy is selfish.
2. Christopher assaulted a policeman and at least two of his classmates. He is violent.
3. The driver's blood alcohol level was three times the legal limit. Three separate witnesses indicate that he was driving on the wrong side of the road without lights on, and the preliminary analysis indicates that he was speeding well above the limit. And the brakes on the car are defective. He might be to blame in the accident.
4. We have conducted an experiment ten times under standard conditions in which we added a small piece of zinc to hydrochloric acid. Every time hydrogen gas was produced. Thus, the interaction of zinc and hydrochloric acid under similar conditions will always produce hydrogen gas.
5. The people of Quebec clearly do not want to separate from Canada
. In the last referendum on separation, the people of Quebec rejected the referendum question by a margin of 51 to 49 percent.
6. In this poem, nature is always described as "green," "verdant," "ripe," "blooming," and "fertile." The writer is here suggesting that nature is a rich source of life.
7. Odysseus obviously has a very cruel streak
. We see this when he grinds out the eye of Polyphemos, the Cyclops, with a sharpened and burning pole and at the end when he slaughters the suitors and punishes the servants, some of them very brutally.
8. The Liberal candidates promised that if re-elected they would control rising tuition costs. Once returned to office, they only limited the tuition raises for families earning below $160 000. They are all liars.
9. Some released sex offenders have committed new offences. We should never release any sex offenders, since they will re-offend.
10. Several scientists have said that greenhouse gases are increasing. We must urge governments to pass strict legislation controlling industrial and automobile emissions.
: Pick 3 of the conclusions that are flawed, and for each provide an improved version.
Read the following essay and see how the author has assembled facts and drawn an interesting, but perhaps not persuasive conclusion.
Quantifying the Roe Effect
Regular readers of this column know that for some time we have been pushing a pet theory about the political effect of abortion. We refer not to the issue of abortion but to the practice, and our theory is that abortion is making America more conservative than it otherwise would be.
We base this on two assumptions. First, that liberal and Democratic women are more likely to have abortions. Second, that children's political views tend to reflect those of their parentsnot exactly, of course, and not in every case, but on average. Thus abortion depletes the next generation of liberals and eventually makes the population more conservative. We call this the Roe effect, after Roe v. Wade, the Supreme Court's 1973 decision that established a constitutional right to abortion.
Some critics have objected that this is pure conjecture, but a new study by the Alan Guttmacher Institute
, a prochoice research group named for a onetime Planned Parenthood head, contains data that bolster the first assumption. We briefly noted the study yesterday, and now we've taken a look at the Guttmacher data for all 50 states. They show that there is indeed a statistical correlation between how a state voted in 2000 and its teen abortion statistics for each year.
Guttmacher actually produced two sets of abortion statistics: the abortion rate, or the number of abortions among girls and women age 1519 for each 1,000 women of that age range, and the abortion ratio
, the number of abortions in that age range divided by the number of pregnancies that ended in either live birth or abortion. In brief, the rate is the likelihood that any young woman will get pregnant and have an abortion, while the ratio is the likelihood that a pregnant young woman will have an abortion rather than carry her child to term.
We've prepared a pair of tables showing the ranking of the states by abortion rate and ratio along with the candidate who carried the state in 2000 and his margin of victory. You can also find the original Guttmacher study here (link in PDF); the table from which we drew the data appears on page 8. Some interesting findings:
* Of the 10 states with the highest teen abortion rates, Al Gore carried eight, and all by more than 10%. George W. Bush narrowly carried the remaining two
, Nevada (by 3.5%) and Florida (by less than 0.1%).
* Similarly, of the 11 states with the highest teen abortion ratios, Gore carried nine, all but one (Washington by 5.6%) by more than 10%. Bush carried two, by small margins: New Hampshire (by 1.3%) and Florida.
* Of the 20 states with the lowest teen abortion rates
, Gore carried only five: Maine, Vermont, Minnesota, Iowa and Wisconsin.
* Bush carried every one of the 20 states with the lowest teen abortion ratios.
* The District of Columbia, which Gore carried by 76.2%, had a higher teen abortion rate than any state, and a higher teen abortion ratio than any state except New Jersey and New York. (It is tied with Massachusetts.)
* The state that gave Bush his biggest margin, Utah (40.5%), had the lowest teen abortion rate and tied with Kentucky for the lowest teen abortion ratio.
* Wyoming, where Bush had his second biggest victory margin (40.1%), is something of an outlier. It ranked 14th, the thirdhighest among Bush states
, in both teen abortion rate and ratio.
The pattern is more dramatic when we depict it visually. We punched the numbers into Microsoft Excel and created a chart mapping the teen abortion rate for all 50 states against Gore's margin of victory (Bush's margin is indicated by negative numbers):
In the chart above, the coefficient of determination (R squared) is 0.4251, which means that 42.51% of the variation in teen abortion rates among states is "explained" by the variation in the presidential victory margin. This doesn't mean that either one causes the other, of course, but it does represent a significant correlation.
Here's a similar chart showing the presidential victory margin and the teen abortion
In this case
, R squared is 0.5445, an even stronger correlation. The abortion ratio may be a better proxy than the rate for a population's views on abortion, since it measures the behavior only of those women who actually face the choice of whether to abort or carry their pregnancy to term, ignoring those who avoid pregnancy in the first place.
This doesn't prove the Roe effect, which ultimately is conjectural in nature, resting as it does on a supposition about how the world would be different if the Supreme Court had not decriminalized abortion in 1973. But there now is evidence for the proposition that liberals and Democrats have more abortions
1. Is the argument persuasive?
2. Task: Try to build an inductive argument for each of the following:
a. Use inductive reasoning to show that we must spend more money to protect
b. Use inductive reasoning to show that Burlington is a good place to live.