Faulty link between premises and conclusion:
| Fallacy | Premises | other ‘evidence’ | ⇒ | Conclusion |
|---|---|---|---|---|
| missing the point | imply conclusion A | conclusion B drawn | ||
| overinterpreting | uncertain | definite | ||
| begging the question #1 | dubious premise ignored | |||
| begging the question #2 | validated by conclusion | circular reasoning | validated by premises | |
| equivocation | one meaning for key word | another meaning for same word | ||
| straw man | tested with bad example |
Case-dependent relationship between parts and whole:
| Fallacy | Premises | other ‘evidence’ | ⇒ | Conclusion |
|---|---|---|---|---|
| false extrapolation to whole | parts | attribute misapplied | whole | |
| false extrapolation to parts | whole | attribute misapplied | part | |
| false extrapolation to individual | general | attribute misapplied | individual | |
| hasty generalization | non representative individual | generalized | general |
Fallacies Resulting from Problems in a Premise
For scientists, few ‘victimless’ crimes are as outrageous as the burning of the Alexandria library, and with it the destruction of so much ancient knowledge and culture. One legend is that when the Muslim Amrou Ibn el-Ass captured Alexandria, he sought his caliph’s guidance on the fate of the library. Caliph Omar responded that the library’s books are either inconsistent or consistent with the Koran. If inconsistent, they are heretical; if consistent, they are redundant. In either case they should be burned. [Gould, 1990]
The story is apocryphal and, I suspect, wrong. The library was probably destroyed in 389 A.D., not 642 A.D., and the Muslims embraced other cultures and their science at a time when Christians were suppressing them. As a memorable example of false dichotomy, however, the story is unsurpassed.
A valid deduction does not imply a correct conclusion; accurate premises or assumptions are also essential. When reading a research paper, the scientist must seek and evaluate the premises. Incorrect or overlooked premises are probably the dominant source of incorrect scientific deductions, and these errors can take several forms:
- False dichotomy is an incorrectly exclusive ‘either . . .or. . .’ statement in one of the premises. When one choice is eliminated by another premise, the other choice is accepted incorrectly as the conclusion. The logic is valid, and if there truly are only two choices then the conclusion is valid:
