Fallacy of Generalisation
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Fallacy
Consider the argument:
| \(\displaystyle \text {All } \ \ \) | \(\displaystyle a\) | \(\text {are}\) | \(\displaystyle b.\) | ||||||||||
| \(\displaystyle \text {All } \ \ \) | \(\displaystyle b\) | \(\text {are}\) | \(\displaystyle c.\) | ||||||||||
| \(\displaystyle \text {All } \ \ \) | \(\displaystyle c\) | \(\text {are}\) | \(\displaystyle d.\) | ||||||||||
| \(\displaystyle \text {Therefore, all } \ \ \) | \(\displaystyle a\) | \(\text {are}\) | \(\displaystyle d.\) |
... which can be epitomised by:
| \(\displaystyle \text {All } \ \ \) | \(\displaystyle \text {cats}\) | \(\text {are}\) | \(\displaystyle \text {mammals.}\) | ||||||||||
| \(\displaystyle \text {All } \ \ \) | \(\displaystyle \text {mammals}\) | \(\text {are}\) | \(\displaystyle \text {animals.}\) | ||||||||||
| \(\displaystyle \text {All } \ \ \) | \(\displaystyle \text {animals}\) | \(\text {are}\) | \(\displaystyle \text {organisms.}\) | ||||||||||
| \(\displaystyle \text {Therefore, all } \ \ \) | \(\displaystyle \text {cats}\) | \(\text {are}\) | \(\displaystyle \text {organisms.}\) |
... which one has to admit seems plausible.
On the other hand, consider the argument:
| \(\displaystyle \text {Most } \ \ \) | \(\displaystyle a\) | \(\text {are}\) | \(\displaystyle b.\) | ||||||||||
| \(\displaystyle \text {All } \ \ \) | \(\displaystyle b\) | \(\text {are}\) | \(\displaystyle c.\) | ||||||||||
| \(\displaystyle \text {Most } \ \ \) | \(\displaystyle c\) | \(\text {are}\) | \(\displaystyle d.\) | ||||||||||
| \(\displaystyle \text {Therefore, most } \ \ \) | \(\displaystyle a\) | \(\text {are}\) | \(\displaystyle d.\) |
... an example of which reasoning may be:
| \(\displaystyle \text {Most } \ \ \) | \(\displaystyle \text {champion chess players}\) | \(\text {are}\) | \(\displaystyle \text {human.}\) | (There are some which are computers, of course.) | |||||||||
| \(\displaystyle \text {All } \ \ \) | \(\displaystyle \text {humans}\) | \(\text {are}\) | \(\displaystyle \text {organisms.}\) | ||||||||||
| \(\displaystyle \text {Most } \ \ \) | \(\displaystyle \text {organisms}\) | \(\text {are}\) | \(\displaystyle \text {monocellular.}\) | ||||||||||
| \(\displaystyle \text {Therefore, most } \ \ \) | \(\displaystyle \text {champion chess players}\) | \(\text {are}\) | \(\displaystyle \text {monocellular.}\) |
Well I don't know about you, but I've never been beaten at chess by an amoeba.
Such reasoning is referred to as a fallacy of generalisation.
Resolution
When processing statements in natural language into predicate logic such as the above, the word most must be interpreted in the same way as some.
