Many of the basic terms and concepts of critical thinking are also used in the "Boolean logic" of web search engines and other examples of database management. George Boole (1815-1864) was an English mathematician who devised a binary system of symbols for the analysis of logic. A binary system is one in which all the variables are either true or false, or in which they all have the value of either zero or one. Since computers are also binary systems, Boolean algebra seems a perfect fit. Boolean expressions that are widely used in search engines include such logical terms as:

• and
• or (the inclusive "or")
• xor (the exclusive "or")
• not

Consider this example: You want to search the web for information about the American novelist John Gardner, the author of The Sunlight Dialogues and other novels. Unfortunately, there is another contemporary novelist by the name of John Gardner, who has published many more titles, mostly mysteries and thrillers, and who has chosen to continue the James Bond series after the death of its originator, Ian Fleming. Now imagine various Boolean expressions that might help you limit your search results, and the problems those limitations have.

NOTE: With most search engines, putting several words in quotation marks means they are treated as a unit. Therefore, searching for "John Gardner" returns any page where the words "John Gardner" appear in that order (but not instances such as "Gardner, John" or "John C. Gardner"). Searching for John Gardner, without the quotation marks, will find all pages with the words "John" or "Gardner" ("or" because that's what is assumed unless another limiter is specified), in any order (including "Gardner, John" and "John C. Gardner," but also including "Annie John" and "Gardner McKay" as well as the sentence, "The gardner wants to use the john," unless letter case--capital or lower-case--can be specified).

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2. Sweeping generalization, though the generalization here is not that "accidents that occur over 55 mph have a higher fatality rate," which may be true, but rather the unstated generalization that "there should be no rise in the speed limit if it creates a higher fatality rate." This is a sweeping generalization as the sole determinant for rises, though it might be an important factor in a more complex determination of benefits versus liabilities. After all, if we accept that "there should be no rise in the speed limit if it creates a higher fatality rate" as the sole determinant, speed limits would never be raised from 0 mph (where fatalities are impossible) to 1 mph (where they are only unlikely). This could also be explained as a false dilemma, since you are being presented with two options, preserving the speed limit or risking lives, when there are other possibilities.

3. Sweeping generalization. There are many factors that go into traffic safety, and speed is only one of them. It would be quite possible to raise the speed limit while cutting fatalities, for example, by funding more safety engineering or greater safety enforcement. Of course, there may be a correlation between speed and fatalities, but the generalization becomes "sweeping" when it oversimplistically considers "speed" as the only possible cause of "fatalities."

4. Hasty Generalization. The only apparent support for the generalization that Fords "are terrible cars" is the speaker's single experience of owning one, and considering how many millions of Fords have been produced, one is obviously an insufficient basis for generalizing about all of them. This does not mean, of course, that Fords are not "terrible cars," only that we don't have enough information here to make a decision one way or the other.

5. Appeal to common belief. Is a "good" vacation policy merely one that the workers "like," or are there other considerations, such as its fairness, effectiveness, versatility, and so forth? A good vacation policy is probably not determined merely on its popularity. By contrast, things which are decided by common belief--the popularity of a song or an actor--can go from being "good" to "bad" without any change in the thing itself. So a rock song can be everyone's favorite (that is, "good") one week, and no one's favorite (that is, "bad") a month later, and still be the same song. But we can imagine a vacation policy that is "good," even though no one recognizes it, just as we can imagine such a policy that is "bad," even though everyone seems to like it (at least for a while). The question is whether popular opinion, or some other kind of judgment, should be used in determining the value or quality of something. When popular opinion is inappropriately used as the basis for such a determination, then it is a case of a fallacious appeal to common belief.

6. Sweeping generalization, although the generalization itself is unstated here. The person is implying that if you can buy cigarettes at 18, you should be able to do anything at 18, including gamble, and that would be the sweeping generalization.

7. Appeal to pity. This might just be a verifiable claim about the amount of work George put into the report, except that it is coupled with a plea not to fail him. Since the amount of work done is not necessarily an indication of the quality of the report, the speaker is hoping that the grader will feel sorry for George because of all his effort.

8. Is this a fallacious appeal to fear? It might cause the listener to react out of fear of failure, but as long as this is a verifiable claim, not exaggerated in tone or consequence, then it is not a fallacy.

9. Appeal to common practice. Just because "everyone is doing it" doesn't make it right or acceptable. Note that this would not be an example of those variations on appeal to loyalty we've called "bandwagon" and "peer pressure." A related "bandwagon" claim would be, "I want a bike because biking is becoming the 'in' thing." A related "peer pressure" claim would be, "I want a new bike otherwise the kids at school will ignore me."

10. A triply loaded question. By answering "yes" or "no" you would only affirm or deny your enjoyment, while apparently agreeing that you did break your aunt's heart and that you were late for dinner. Shame on you!

11. Two wrongs make a right. The speaker is justifying making fun of someone else, on the grounds that the other person acts badly, as well. Never try to justify your wrongdoing on the basis of the wrongs committed by others.

12. Appeal to popular belief. The issue here is whether "the highest grossing film of all time" is a title to be decided by statistics or public opinion. And there may be a variety of statistics to look at: original and adjusted dollars, box-office only or other receipts, and so on. You could probably make an argument that the criteria used are finally subjective; but once those criteria are established, the pertinent statistics, and not popular opinion, establishes the winner.

13. Ad hominem. This is a case of attacking the individual instead of the argument the individual is making. Because the attack, in this case, comes even before the argument can be heard, this may also be considered an example of the special case of circular reasoning known as poisoning the well, in which the attack is designed to prejudice the listener before the argument is heard.

14. Fallaciously shifting the burden of proof. We should expect that anyone who claims Martians visit the Earth regularly would have the burden of proving that claim. Even the less fantastic claim that life, in whatever form, exists or existed on Mars is unsupported by any decisive evidence, and would also carry the burden of proof.

15. Sweeping generalization, although the generalization itself is left unstated here: if two languages are good, then three languages would be better. There are, certainly, professions and positions where multilingual qualifications are an advantage. But it would be much too broad to claim that knowing three languages will always land you a better job than knowing two languages.

16. Appeal to indirect consequences. The "slippery slope" of non-automatic consequences is clear here: increased availability, use, crime, and death, leading to destruction of the schools and society. And with each step down the slope, the consequences are more dire, but the causal connection is more tenuous. The point is that we should decide the question of legalizing drugs on its own merits, and not on the fear of a remote (and unlikely) result such as the collapse of society.

17. Margaret's claim is a sweeping generalization--the "dumb blonde" stereotype--and the rest of the claim here is an ad hominem attack on Margaret, based on the same sweeping generalization: don't listen to Margaret, because she is naturally a blonde, and blondes are dumb. Though such stereotypes are popular as jokes, they have no value in critical thinking.

18. This is based on a sweeping generalization--that "everyone who hangs out at the mall is cool"--but its application is the fallacy of peer pressure, which is an appeal to loyalty. The point is that, to be part of the "cool" group, you are under pressure to join them in hanging out at the mall.

19. Or maybe you don't deserve a raise! The assumption here is, "After two years, if I'm still making so little, there's something wrong with my boss." That could be a hasty generalization: to decide, we would need to know about other employees and their wages after a similar time. Or it could be a false dilemma: "either I get a raise or my boss is a jerk." This might also be an ad hominem attack, though that would be clearer if we were being asked to dismiss the boss's reasoning: ". . . I only make $5.95 an hour because my boss says I'm unreliable."

20. This doesn't seem to be a fallacy at all, maybe because the Rolling Stones are the best rock and roll band ever, but more because the first statement is an evaluative claim, supported by a verifiable claim of a similar evaluation among those friends. It cannot be an appeal to popular belief because which is "the best rock and roll band ever" is something that could legitimately be determined by popular opinion. The claim may not be true, but that doesn't make it necessarily fallacious.