Essential Properties and Non-Referring Terms: A Defense Against Counterexamples to Frege and Russell

This is an essay I wrote for Phil 345: Language and Mind taught by Professor James Joyce. I loved this class and liked this essay.

Many theories of language attempt to determine the truth values of sentences containing non-referring terms. In this essay, I will explain and examine how the theories of Gottlob Frege and Bertrand Russell deal with this problem and address some counterexamples.

Frege believed that every linguistic item, such as names, predicates, and sentences, contains two sorts of meaning, its sense and reference. The sense of a linguistic item is the descriptive content, which Frege calls “the mode of presentation”, that those who understand the term commonly associate it with. The reference of a linguistic item is the object or feature of the world that it picks out. To determine the sense and reference of a compound expression, such as a sentence, Frege introduces the Compositionality of Meaning. According to Frege, the meaning of a compound linguistic expression is determined by the meaning of its component parts. Thus, the sense of a sentence is determined by the sense of its parts, and the reference of a sentence is determined by the reference of its parts. Now, the question is what the reference of a sentence is. Frege believes that in the sentence, “Odysseus was asleep when they set ashore at Ithaca”, “Odysseus” does not refer. He argues that if we care about the sentence’s truth value, we care if “Odysseus” refers. Likewise, if we don’t care about the sentence’s truth value, we don't care if “Odysseus” refers. This means, by the Compositionality of Meaning, that the reference of a sentence is its truth value. Thus, to Frege, when a sentence contains a term that has no reference, by the Compositionality of Meaning, that sentence lacks a truth value.

On the other hand, Russell believed that every definite description could be replaced by a quantified statement. To understand Russell’s theory, we must introduce a couple of definitions. A singular term is a syntactic item that lets us talk about the objects it denotes or to which it refers. Examples of these are names (eg, “Hugh”) and definite descriptions (eg, “The author of this essay”). For a sentence to contain non-referring terms, it must contain singular terms, because only singular terms can have a reference or lack a reference. Russell makes an important point about singular terms (what he calls “denoting phrases”), that they have no meaning by themselves, but only in the context of use. Let us call this context of use a declarative sentence and give it the form “The P is Q”, where P is a singular term and Q is some property. Russell analyzes the meaning of the statement, “The P is Q” as “There exists an object x such that: x has property P, anything with property P is identical to x, and x has property Q”. The existential quantifier is important here. When we aim to determine the truth conditions of a declarative sentence, this means that every singular term in the sentence is associated with a “there exists this object”. Thus, if the term does not refer, meaning it does not exist, then the existential statement is false, and thus the sentence’s truth value is false.

Consider the following counter-example to both Frege’s and Russell’s views on sentences with non-referring terms:

Since there are no unicorns, Frege must maintain that the sentence “Unicorns are white” lacks a truth value, while Russell must maintain that it is false. Both are wrong because the sentence “Unicorns are white” is plainly true! After all, whiteness is part of the concept of a unicorn.

There are two main issues I have with this example. My first issue is as follows: the first sentence relies on the fact that unicorns not existing must mean the term “unicorn” lacks a reference. While it seems that Frege and Russell would maintain that, such a position is unclear. Frege says the reference of a proper name is a “definite object”, where he clarifies “this word to be taken in the widest range”, so it remains possible that a definite object may not necessarily have to be a physical object. Thus, I could imagine the reference of “unicorn” as the societal conception/idea of a unicorn. If you asked pretty much anyone what a unicorn is, there would be a very consistent description/response. While unicorns may not physically exist, there seems to be something that exists, namely, the collective idea of a unicorn. On the other hand, Russell’s view resides on the existential quantifier, where it is harder to justify whether an idea exists. Logically, the quantifier must pick from a set of things, i.e, we interpret Russell’s existential quantifier as ∃x∈W, where W is “our world”. The question of whether ideas (thoughts) are elements of our world is an entirely different metaphysical question that I may attempt to answer in a later essay, but not here. But in this context, such a fact would make Russell’s theory useless, since almost every statement would be true. This is because, for any false statement about the physical world (such as “Phil 345 is taught by Hugh Van Deventer”), I could imagine a scenario in which such a proposition is true (imagine if I were a young genius like Kripke and became a philosophy professor at age 19). So, for practicality, let us assume that the first statement is valid. This allows us to move on to the second statement, “the sentence 'Unicorns are white' is plainly true! After all, whiteness is part of the concept of a unicorn”. First, we must analyze what “Unicorns are white” predicates. I will take the stronger predication and say it means “All unicorns are white.” From earlier, I believe the reference of “unicorn” to be the idea of a unicorn. To analyze the truth conditions of this predicate, it is important to introduce the concept of essential and contingent properties. An essential property is a necessary property of an object, meaning that in every possible world in which that object exists, it is necessary for that object to have that property. A contingent property is a property of an object that the object does not need to have in possible worlds in which the object exists. Since I can imagine a non-white unicorn, say a purple unicorn (like Twilight Sparkle from My Little Pony), then whiteness is a contingent property of the idea of a unicorn. Yet, “all unicorns are white” seems to imply that whiteness is an essential property of the idea of a unicorn. So “Unicorns are white” is not plainly true; in fact, it is plainly false!

Now consider the following counter-example:

Since there are no bigfoots (bigfeet?), Frege must maintain that the sentence “Bigfoots have big feet” lacks a truth value, while Russell must say that it is false. Both are wrong because the sentence “Bigfoots have big feet” is plainly true! After all, bigfootedness is part of the concept of a bigfoot.

This example is very similar to the prior, so we can use the previous analysis to show that the fundamental point in this example is whether having big feet is an essential property of the idea of a bigfoot. I argue that it is, it is literally in the name. The idea of Bigfoot is this creature that has big feet. In folklore, its mentions are marked by its property of having big feet. Big footprints in forests are attributed as evidence for the existence of Bigfoot/Bigfoots. If we were to imagine a Bigfoot without big feet, that thing you imagine would cease being a Bigfoot. If you were to ask anyone to describe the idea of Bigfoot, big feet would be included in all those descriptions. Thus, I believe “Bigfoots have big feet” is in fact plainly true!

A very strong and reasonable objection to my analysis is: What is the idea of unicorns or Bigfoot? If someone just thought that bigfoots could have bigfeet, then using my same framework, they could argue any stance on what is or is not an essential property of unicorns or bigfoots. My solution is to apply Kripke’s Causal Theory of Reference to define such ideas. The chain is started by the first introduction of the term, which defines the properties of the idea. One thing to note is the fact that as time goes on, the meaning of the ideas can change. It would be interesting to consider a time when Bigfoot could mean something else, maybe everyone imagines a bear. Then this bigfoot, let us denote it bigfoot*, is part of a different language or is simply a different idea than our bigfoot. The essential qualities, then, would be the intersection of what every person who has heard the idea would describe as the minimum qualities of being that idea.