Existential import refers to a proposition establishing the truth of which requires a pre-belief in the subject class members’ existence. There have been two views with regards to the treatment of existential imports: the traditional Aristotelian standpoint and the modern Boolean standpoint. To understand existential import, we make use of two propositions, I and O. The subject terms that have designated the classes are not empty.
In Aristotelian standpoint, the A and E propositions are followed validly by I and O propositions through sub-alternation. Therefore the propositions of A and E require having an existential import. A proposition that does not have an existential import cannot be used to derive a proposition with an existential import (Pankaj). For Aristotle, the statement “All unicorns have one horn” requires that we believe in the existence of unicorns. The interpretation developed by George Boole on certain positions opposes that standpoint by denying that existential import exists in all universal propositions. The Boolean logic sees an argument being termed invalid due to its premise lacking an existential import to be an existential fallacy. The Boolean standpoint would term the argument that “All cats are animals; therefore some cats are animals” to be fallacious on an existential level (Wreen).
Ordinary language arguments require an acute translation into categorical propositions in standard form to ascertain and test their validity. For interpreting ‘only,’ one basic example of the form ‘Only A are B’ is when signs use the term ‘Employees only.’ It implies that only Employees are allowed. This means that such signs by using ‘only’ intends to regard anything that does not have a certain property to be excluded. If we use ‘A only if B,’ that translates in standard form to ‘not A if not B,’ or ‘if not B, then not A.’ The use of ‘the only’ further enables us to make arguments without the ambiguities present with the use of ‘only’ (Hardegree). For instance, if we say “only venomous spiders are dangerous.”
There can be four different interpretations using ‘only’ in this case. But if we use “the only dangerous spiders are venomous spiders” or “venomous spiders are the only dangerous spiders” then it is more evident. The general form here is: ‘the only AB are CD’ or ‘CD are the only AB.’ Additionally, saying ‘the only A things are CD’ can be symbolized and paraphrased to be ‘the only A are CD.’ This gives us an example of how ‘only’ can differ from ‘the only’ when translating ordinary language.
Hardegree, Gary M. Symbolic Logic: A First Course. 3rd. McGraw-Hill College, 1999.
Pankaj. The Existential Import of Propositions. 2012. 10 April 2018. <http://www.preservearticles.com/201106017320/the-existential-import-of-propositions.html>.
Wreen, Michael. “Existential Import.” Crítica: Revista Hispanoamericana de Filosofía 16.47 (1984): 59-64. <https://pdfs.semanticscholar.org/fee7/5f6f0eb97dfcabeefdd6286a239c08a4b70e.pdf>.