# 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**.