Reference: how do linguistic terms come to denote things?
Position: Reference dualism
As we’ve seen a few chapters above, semantics is about the reference (or denotation) of expressions in our language, about the truth value of our statements, and about the meaning (or connotation) of expressions. It is crucial to distinguish these general linguistic matters from the semantics of the formal language used in our ontology. I’ve tried to dispel misunderstandings by calling the latter "logical semantics". The formal language and its semantic interpretation in terms of ontology is prior to notions of ordinary objects and concepts that we will encounter here...
But let’s come back to our linguistic semantics... The matters of reference, truth and meaning are intermingled to a degree that theories of reference often seem to be talking at cross-purpose. I’ll try to simplify by considering three questions.
What is reference?
Conceptually, the answer is simple: reference is a relation between an expression-type and an object. It realizes the familiar mechanism whereby the name-type "Everest" denotes the object that is Mount Everest. Formally we will write: \[\mathbf{D}\texttt{"Everest"}\big[e\big]\] That may seem out of place. Previous paragraphs were about metaphysics or modality, and didn’t seem to assume the existence of language or of humans. Here I’m introducing expressions from a natural language (English) out of the gate. But the point of formal semantics is that the workings of our natural language point us to a deeper truth that’s part of the fabric of our world, whether a single word was ever spoken or not. Despite the use of concrete natural-language examples, the formalism should make that evident.
In the above, \(\mathbf{D}\) represents the denotation relation. \(\texttt{"Everest"}\) stands for the name-type (as opposed to the token: every time I have written that word in this section I’ve minted a new token; but it’s always the same type). \(\big[e\big]\) is the ordinary object, a mountain located in the Himalaya. The only constraint on objects of reference is that they exist in an ontological sense. But that still leaves us with a broad playing field that includes concretes objects as well as all abstract objects.
Colloquially it may seem that Everest is referring to something as concrete as it gets, but it’s important to remember that in our framework, ordinary objects are equivalence classes. I cannot direct my thoughts towards a specific heap of atoms that would mentally represent Everest (and no other heap would). Even if I could, atoms are not fundamental and discourse about them is ordinary discourse already: it’s "turtles all the way down" towards whatever fundamental substance there is, which we do not know yet, and thus cannot think or speak about.
Therefore, better to consider that all statements about the concrete world will be made by referring to ordinary objects. Since ordinary objects correspond to a specific kind, the denotation relation involves a choice of a kind, through the ordinary object it picks out. It was implicit, but easy to guess that \(\big[e\big]\) is of the kind "mountain". It is nonetheless instrumental, since some things can be "the same mountain" but not "the same rock" as a concrete Mount Everest. That is how natural language works as well: except in especially ambiguous situations, it should be clear what kind of thing an expression denotes to competent speakers.
What grounds reference?
Or to put in another way: in virtue of what do expressions refer? I will eschew the distinction between "direct" and "mediated" reference. Ultimately, reference is grounded in something, which we can call the mediator between language and object. As we’ve seen in various sections, the ground is two-fold.
On the descriptivist model, expressions refer by virtue of a certain descriptive content that identifies an object as the referent. For instance: "the King of England".
On the causal model, they refer in virtue of a causal chain, or rather of a "web of usage" that harks back to an original baptism.
The descriptivist way is generic: any sort of semantic expression can be denoted in that way (by talking of "semantic expression", I aim to exclude logical or formal connectives like "and" or "the"). The causal model is rather restrained to singular objects; on the linguistic side, proper names, kind names and demonstratives are archetypes. It is conceivable that I hear of "William IV, some king" and never associate any descriptive content to him beyond being a monarch, which does not single out an individual. Yet I can ascribe to specific beliefs about \(\texttt{"William IV"}\) , which can be evaluated based on which properties or relations the human being \(\big[ W_4\big]\) did satisfy. The chain of use on which this is grounded goes through my teachers, the authors of books I’ve read, back to people who knew William, and ultimately to his parents.
This could seem a bit of a specious distinction: after all, an ordinary object like \(\big[ W_4\big]\) is defined via certain properties: it is a set that includes all concrete objects that (1) satisfy the property of being human and (2) "are the same human" as a distinguished instance \(w_4\). The latter relation is also defined by properties, for instance "having as parents \(\big[ f\big]\) and \(\big[ m \big]\)" or "having DNA code that includes ’...’". This all amounts to a canonical definition or \(\big[ W_4\big]\), and isn’t that descriptive content?
Well, the key point is that canonical descriptions are typically not known by the speaker. To use a common example, Saul Kripke insists that natural kinds like "water" refer by virtue of a causal chain. Nowadays, we have good candidates for a canonical definition such as "a liquid that is mostly \(\textrm{H}_\textrm{2}\textrm{O}\)". But by pointing to the transparent liquid they saw in river or falling from the sky and calling it water, people initiated a causal-historical chain that for the most part has always denoted the same ordinary liquid as it does today, even as, for most of human history, the concept \(\textrm{H}_\textrm{2}\textrm{O}\) was not known, thought about or spoken about. In contrast, to refer by virtue of descriptive content requires mastery of that content. If someone speaks of "the longest-serving Taoiseach", it is hard to see how they could use that description to pick out a specific human whilst not knowing what a Taoiseach is.
Should we even talk about reference?
It’s always good to revise our priors. There have been many who’ve expressed doubts about the concept of reference itself. Does it amount to anything useful or is it hopelessly simplistic? Quine famously called reference "inscrutable". His point was that by considering language on the one hand, and the way the world is on the other, we can make educated guesses about what exactly words refer to, but there will never be a way to adjudicate between various hypotheses. Quine does have a point: there is multiple realizability when looking at a specific world and a specific context of utterance. And reference alone is indeed inscrutable.
That does not mean that reference as a concept should be discarded, only that it’s inseparable from a theory of meaning. Our theory of meaning will not be an overlay on the theory of reference but rather its foundation. Anticipating a bit: meanings will be construed as functions from worlds (our actual world or other possible worlds) and scenarios (representing epistemic states, for instance but not limited to the cognitive state of an ideal language user) to referents. The exact referent could then vary depending on the mode (belief, fear, hope...) or the context of utterance, since those would be reflected in the scenario of evaluation. Lastly, it’s always good to remind ourselves that lots of fine distinctions we may be tempted to make (for instance between "blue", "blueness", "being blue") do not require different referents since the possible difference in truth valuation will depend on pragmatics or on the mechanics of specific natural languages.