Quantifier Fallacy
Fallacies of Ambiguity
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Fallacy Name:
Quantifier Fallacy
Alternative Names:
None
Category:
Fallacy of Ambiguity > Scope Fallacy
Explanation:
This fallacy is a type of Scope Fallacy, in that
the scope of particular quantifiers like some or every shift during the
progress of an argument. The basic form of this fallacy is:
a. Every member M of a group bears the relation R to some X.
b. Therefore, some particlar X bears the relation R to every M.
In other words, it is argued that because everything in some class is related in some way to some thing, then there is one particular thing which has that relationship to every member of that class.
Examples and Discussion:
Here is an easy example that everyone should catch:
2. Every person has some moral values (premise). Therefore, there are some moral values which every person shares with everyone else (conclusion).
Obviously this argument is wrong - the mere fact that everyone has moral values does not logically mean that there are some particular moral values which we all share in common (this conclusion could be a true proposition, just not for the reason given). But why is it wrong?
Notice that there is a shift which occurs between the premise and the conclusion. The order, and hence the scope, of the quantifiers "every" and "some." In the premise, the quantifier "every" comes first and has the widest scope, whereas in the conclusion the quantifier "some" comes first and has the widest scope.
It doesn't seem like anyone would use such an argument and really mean it, but it does happen occasionally, for example in this attempted proof of the existence of God:
3. We all agree that every event has a cause. But that must mean that there is some cause for all the events. Why not simply call this cause "God"?
Once again, there is a shift in the order and scope of the quanitiers every and some. It is important to keep in mind that it is possible to write such an argument without using those key words, so you can't just rely on watching for them. Instead, you have to pay attention to nature of the claims being made.
It is, however, worth noting that reversing the argument is valid and is not a fallacy:
4. Some X has the relation R to every M. Therefore, every M has this relation R to some X.
How does this work? Just look at these two examples:
5. Every person is loved by someone. Therefore, there is someone who loves everyone.
6. There is someone who loves everyone. Therefore, every person is loved by someone.
Example #5 commits the Quantifier Shift Fallacy described above, but example #6 reverses the components of the argument. This is now a valid argument because it is true that if there exists any person who loves every other person, then we can conclude that every person must be loved by someone (i.e., by at least one person). Because the arguments are so similar, this may be a reason why the fallacy is made.
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