# Fallacy of Generalisation

## 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.