A formal fallacy by which existence is implied in a logical operation that would require it to be proven first.
Take, for example, the following syllogism:
All animals are mortal. (true)
No unicorn is mortal. (vacuously true)
Therefore, there exists unicorns which are not animals.(existential fallacy)
On first glance, this resembles the Modus Camestros Show “Modus Camestros” in Syllogism FInder App, but it lacks the explicit existential import that this form normally requires. As a result, the conclusion here, which implies existence of unicorns is not valid.
- (Illicit) existential instantiation
Different types of logical statements may or may not refer to empty extensions of the terms used. Most notably, universal quantifications (like
all A are B) do not, wheras existential quantifications (like
some A are B) do imply existence.
This can lead to problems when the latter type is infered from earlier. A typical situation where this happens is when an existential quantification is inferred from a universal one. In principle, this is possible, as the existential quantifier is the weaker form of the two (Argumentum a Fortiori ), meaning that a statement like
all cars are vehicles obviously also implies that
some cars are vehicles.
What is less obvious, though, is that this inference is only possible because we know that cars actually exist. In other words, by our knowledge (which is external to the logical statements), we implicitly import existence into this transformation.
This becomes a problem with statements which refer to something that does not exist: “all unicorns are immortal” is vacuously true, meaning it is true specifically because no unicorns exist that could actually ever die. If we transform this into
there exist unicorns which are immortal, this implicit existential import goes wrong and we have arrived to a statement which is clearly not true.
For this reason, infering from a form that allows referring to an empty extension to one that does not, requires that the import is made explicit.
Such situations arise in a number of syllogisms, where an existential conclusion is derived from universal premises. In particular, this affects the modi Barbari, Bamalip, Calemos, Camestros, Celaront, Cesaro, Darapti, Felapton and Fesapo. In all of these, there is an additional requirement to explicitly validate the existential import for at least one of the terms used.
However, this fallacy is not limited to syllogistic inferences, but can happen whenever a statement which has an existential implication is derived from a statement that does not.
- The Existential Fallacy on Fallacy Files