Existential import

Describes a situation in which a statement implies the existence of a term’s extension without providing sufficient evidence for it. This applies to statements in both everyday language as well as in formal systems (such as logic).

When it comes to fallacies, the concept of “existential import” is particularly interesting when the term actually refers to an empty set but is treated as if it described something that exists.

An “existential import” can occur on two different levels: a linguistic one and a logical one.

To explain both of these cases, let’s consider the following statement:

“Giant squids are deep-sea creatures.”

It is noteworthy that “giant squids” (Architeuthis dux) were long dismissed as mere sailors’ yarn, since these creatures appeared only in stories told by seafarers and were never actually caught e.g. in fishing nets. It was not until the 20th century that their existence was finally proven.

At first glance, the statement above describes only one characteristic of the genus Architeuthis, namely that it lives in the deep sea. Upon closer examination, however, it implies another characteristic as well, namely that such creatures actually exist (Enthymeme).

From today’s perspective, it makes sense to simply assume that such a widely accepted fact is common knowledge. However, things become somewhat more complicated if one were to encounter the same statement in, say, the 19th century – that is, before Giant Squids were “discovered” by scientists. In that case, there would be several possible interpretations:

• If the speaker attempts to use such phrasing to give the impression that the question of existence has long been settled and can therefore simply be implied, this constitutes a case of loaded language.

• Assuming instead that the existence or use of the word “giant squid” automatically implies the existence of the animal it describes constitutes an ontological fallacy.

At first glance, both of these might sound a bit far-fetched when viewed from today’s perspective. After all, we now know that giant squids exist. Just try, if you will, to substitute “giant squid” with any other fictional creature:

― “Nessie lives in Loch Ness, Scotland.”
― “Bigfoot is a protected species in parts of the U.S.”
― “Unicorns are creatures with magical healing powers.”

In all these cases, the existence of the creatures described by the terms “Nessie,” “Bigfoot,” or “unicorn” is merely implied. If this is not substantiated in the broader context, one should approach such statements with a healthy dose of skepticism.

Even within formal systems such as logic, a tacit existential import can be problematic. To better explain the problem in a logical context, let’s use a slightly modified statement:

“All Giant squids are deep-sea creatures.”

By adding the quantifier “all” we turn the phrase into a positive universal statement. At least within the logical systems covered on this website, such a statement explicitly has no existence condition.

This means that even the following statement is both valid and true:

“All unicorns are immortal.”

The reason for this is that if no unicorns exist in the first place, none could ever die.

Similarly, the statement “all giant squids are deep-sea creatures” is necessarily true if such creatures do not exist at all – and it is conditionally true (the condition being that they really are deep-sea creatures) if they do exist. In short: the question of existence is, when it comes to such logical statements, a lot less important than it is in everyday language.

However, this changes when we try to draw specific inferences from such statements. For example, it is generally the case that we can always derive a (weaker) existential statement from a (strong) universal statement. For example, based on “all flowers have blossoms”, one might conclude: “There exist flowers that have blossoms”. It should therefore be possible to do the same with unicorns or giant squids:

“There exist unicorns that are immortal.”
“There exist giant squids that are deep-sea creatures.”

However, an important side-effect of this transformation is the introduction of “existence” as a property. Whilst we were able to deal quite well with empty sets in the universal statement form, now we first need proof that the terms actually refer to something that really exists.

In the case of flowers and (nowadays) giant squids, we can accept an implied introduction of existence as a logical enthymeme, since we possess general knowledge about the world and know that these things exist. In the case of unicorns, however, one should not do so, as they are, in fact, mythical creatures that have no existence in reality.

In context of logic, the existential fallacy sums up various problems associated with such empty sets.

Specifically, in the context of syllogism, explicit proof of existence is expressly required for the following forms of inference: Barbari, Bamalip, Calemos, Camestros, Celaront, Cesaro, Darapti, Felapton and Fesapo. Further details can be found in the respective articles.

Not every reference to existence (not even every false one) constitutes a fallacy. Rather, this involves introducing existence into an argument without providing evidence that the subject actually exists. Such an import can be performed by simply implying it – as we have seen in the examples above – but even an explicit introduction can be illegitimate if there is a lack of evidence to justify it.

An explicit import could take, for example, the following form:

“Let’s assume that unicorns really do exist – then it follows that …”

Whether an import is implicit or explicit does not in itself determine whether or not it is legitimate. What matters instead is whether it remains clear throughout the subsequent argument that it is based on an unproven assumption – and whether this assumption is ultimately resolved.

In formal systems such as mathematics, the explicit introduction of an unproven assumption is a recognised method. A well-known example is the origin of the so-called “imaginary number”: it was initially introduced simply as an unproven assumption¹⁾; only over time did it become apparent that this assumption is coherent with mathematics (and extremely useful).

A similar method is called “proof by contradiction” (reductio ad absurdum): in this method, an assumption is (explicitly) introduced in order to show that it leads to a contradiction – and can therefore be refuted. Here, too, the assumption remains identifiable as such and is resolved at the end.

The situation is different when unproven assumptions are introduced into arguments as if they were established facts, without ever actually being substantiated. In such cases, we often encounter some form of circular reasoning: the assumption is treated as a premise from which conclusions are then drawn, which in turn appear to confirm the original assumption.

This tactic is particularly prevalent in conspiracy theories and pseudoscientific arguments, but it also crops up in everyday discourse – where it is all too often not recognised for what it is: a manipulative rhetorical device.

• Enthymeme
• Existential fallacy
• Ontological fallacy
• Vacuous truth