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.