The absurdity of un-referenceable entities

by jessicata3 min read14th Mar 202021 comments


References (Language)Epistemology

Whereof one cannot speak, thereof one must be silent.

Ludwig Wittgenstein, Tractatus Logico-Philosophicus*

Some criticism of my post on physicalism is that it discusses reference, not the world. To quote one comment: "I consider references to be about agents, not about the world." To quote another: "Remember, you have only established that indexicality is needed for reference, ie. semantic, not that it applies to entities in themselves" and also "you need to show that standpoints are ontologically fundamental, not just epistemically or semantically." A post containing answers says: "However, everyone already kind of knows the we can't definitely show the existence of any objective reality behind our observations and that we can only posit it." (Note, I don't mean to pick on these commentators, they're expressing a very common idea)

These criticisms could be rephrased in this way:

"You have shown limits on what can be referenced. However, that in no way shows limits on the world itself. After all, there may be parts of the world that cannot be referenced."

This sounds compelling at first: wouldn't it be strange to think that properties of the world can be deduced from properties of human reference?

But, a slight amount of further reflection betrays the absurdity involved in asserting the possible existence of un-referenceable entities. "Un-referenceable entities" is, after all, a reference.

A statement such as "there exist things that cannot be referenced" is comically absurd, in that it refers to things in the course of denying their referenceability.

We may say, then, that it is not the case that there exist things that cannot be referenced. The assumption that this is the case leads to contradiction.

I believe this sort of absurdity is quite related to Kantian philosophy. Kant distinguished phenomena (appearances) from noumena (things-in-themselves), and asserted that through observation and understanding we can only understand phenomena, not noumena. Quoting Kant:

Appearances, to the extent that as objects they are thought in ac­cordance with the unity of the categories, are called phaenomena. If, however, I suppose there to be things that are merely objects of the un­derstanding and that, nevertheless, can be given to an intuition, although not to sensible intuition, then such things would be called noumena.

Critique of Pure Reason, Chapter III

Kant at least grants that noumena are given to some "intuition", though not a sensible intuition. This is rather less ridiculous than asserting un-referenceability.

It is ironic that noumena-like entity being hypothesized in the present case (the physical world) would, by Kant's criterion, be considered a scientific entity, a phenomenon.

Part of the absurdity in saying that the physical world may be un-referenceable is that it is at odds with the claim that physics is known through observation and experimentation. After all, un-referenceable observations and experimental results are of no use in science; they couldn't made their way into theories. So the shadow of the world that can be known (and known about) by science is limited to the referenceable. The un-referenceable may, at best, be inferred (although, of course, this statement is absurd in refererring to the un-referenceable).

It's easy to make fun of this idea of un-referenceable entities (infinitely more ghostly than ghosts), but it's worth examining what is compelling about this (absurd) position, to see what, if anything, can be salvaged.

From a modern perspective, we can see things that a pre-modern perspective cannot conceptualize. For example, we know about gravitational lensing, quantum entanglement, Cesium, and so on. It seems that, from our perspective, these things-in-themselves did not appear in the pre-modern phenomenal world. While they had influence, they did not appear in a way clear enough for a concept to be developed.

We may believe it is, then, normative for the pre-moderns to accept, in humility, that there are things-in-themselves they lack the capacity to conceptualize. And we may, likewise, admit this of the modern perspective, in light of the likelihood of future scientific advances.

However, conceptualizability is not the same as referenceability. Things can be pointed to that don't yet have clear concepts associated with them, such as the elusive phenomena seen in dreams.

In this case, pre-moderns may point to modern phenomena as "those things that will be phenomena in 500 years". We can talk about those things our best theories don't conceptualize that will be conceptualized later. And this is a kind of reference; it travels through space-time to access phenomena not immediately present.

This reference is vague, in that it doesn't clearly define what things are modern phenomena, and also doesn't allow one to know ahead of time what these phenomena are. But it's finitely vague, in contrast to the infinite vagueness of "un-referenceable entities". It's at least possible to imagine accessing them, by e.g. becoming immortal and living until modern times.

A case that our current condition (e.g. modernity) cannot know about something can be translated into a reference: a reference to that which we cannot know on account of our conditions but could know under other imaginable conditions. Which is, indeed, unsurprising, given that any account of something outside our understanding existing, must refer to that thing outside our understanding.

My critique of an un-refererenceable objective physical world is quite similar to Nietzsche's of Kant's unknowable noumena. Nietzsche wrote:

The "thing-in-itself" nonsensical. If I remove all the relationships, all the "properties," all the "activities" of a thing, the thing does not remain over; because thingness has only been invented by us owing to the requirements of logic, thus with the aim of defining, communication (to bind together the multiplicity of relationships, properties, activities).

Will to Power, sec. 558

I continue to be struck by the irony of the transition from physical phenomena to physical noumena. Kant's positing of a realm of noumena was, perhaps, motivated by a kind of humility, a kind of respect for morality, an appeasement of theological elements in society, while still making a place for thinking-for-one's-self, science, and so on, in a separate magisterium that can't collide with the noumenal realm.

Any idea, whether it's God, Physics, or Objectivity, can disconnect from the human cognitive faculty that relates ideas to the world of experience, and remain as a mere signifier, which persists as a form of unfalsifiable control. When Physics and Objectivity take on theological significance (as they do in modern times), a move analogous to Kant's will place them in an un-falsifiable noumenal realm, with the phenomenal realm being the subjective and/or intersubjective. This is extraordinarily ironic.


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Another reason why unreferenceable entities may be intuitively appealing is that if we take a third person perspective, we can easily imagine an abstract agent being unable to reference some entity.

In map/territory thinking, we could imagine things beyond the curvature of the earth being impossible to illustrate on a 2d map. In pure logic, we imagine a Tarskian truth predicate for a logic.

You, sitting outside the thought experiment, cannot be referenced by the agent you imagine. (That is, one easily neglects the possibility.) So the agent saying "the stuff someone else might think of" appears to be no help.

So, I note that the absurdity of the unreferenceable entity is not quite trivial. You are assuming that "unreferenceable" is a concept within the ontology, in order to prove that no such thing can be.

It is perfectly consistent to imagine an entity and an object which cannot be referenced by our imagined entity. We need only suppose that our entity lacks a concept of the unreferenceable.

So despite the absurdity of unreferenceable objects, it seems we need them in our ontology in order to avoid them. ;)

The absurdity comes not from believing that some agent lacks the ability to reference some entity that you can reference, but from believing that you lack the ability to reference some entity that you are nonetheless talking about.

In the second case, you are ontologizing something that is by definition not ontologizable.

If there's a particular agent thinking about me, then I can refer to that agent ("the one thinking about me"), hence referring to whatever they can refer to. It is indeed easy to neglect the possibility that someone is thinking about me, but that differs from in-principle unreferenceability.

I don't believe in views from nowhere; I don't think the concept holds up to scrutiny. In contrast, particular directions of zoom-out lead to views from particular referenceable places.

Yeah, I'm describing a confusion between views from nowhere and 3rd person perspectives.

Do we disagree about something? It seems possible that you think "ontologizing the by-definition-not-ontologizable" is a bad thing, whereas I'm arguing it's important to have that in one's ontology (even if it's an empty set).

I could see becoming convinced that "the non-ontologizable" is an inherently vague set, IE, achieves a paradoxical status of not being definitely empty, but definitely not being definitely populated.

It seems fine to have categories that are necessarily empty. Such as "numbers that are both odd and even". "Non-ontologizable thing" may be such a set. Or it may be more vague than that, I'm not sure.

Alright, cool. 👌In general I think reference needs to be treated as a vague object to handle paradoxes (something along the lines of Hartry Field's theory of vague semantics, although I may prefer something closer to linear logic rather than his non-classical logic) -- and also just to be more true to actual use.

I am not able to think of any argument why the set of un-referenceable entities should be paradoxical rather than empty, at the moment. But it seems somehow appropriate that the domain of quantification for our language be vague, and further could be that we don't assert that nothing lies outside of it. (Only that there is not some thing definitely outside of it.)

Also -- it may not come across in my other comments -- the argument in the OP was novel to me (at least, if I had heard it before, I thought it was wrong at that time and didn't update on it) and feels like a nontrivial observation about how reference has to work.

The un-referenceable may, at best, be inferred (although, of course, this statement is absurd in refererring to the un-referenceable).

Would you also say that a lot of mathematics is absurd in this sense? For example, almost all real numbers are un-nameable (because there uncountably many real numbers, but only countably many names you could give a number).

There are a few things to say about this:

  • cousin_it is right about the undefinability of definability in ZFC.
  • Even the undefinable reals are taken to be in the "domain of discourse". They remain "accessible" in some infinitary sense (e.g. corresponding to some infinite bit string expansion) even if they aren't finitely definable.
  • Also, the predicate of being a real number in ZFC is definable. So the real numbers are definable in aggregate.
  • The physics case is about references like "the objective world" which are singular and aren't any kind of infinitely long name.
  • In the case of the reals, a skeptical perspective will note that there exists a countable model of ZFC (by Löwenheim-Skolem), hence reals "could be" a countable set from the perspective of ZFC. Our formal systems may, thus, lack the capacity of referencing truly uncountable sets.

I think Jessica is right on this point. Within a system like ZFC, you can't define the system's own definability predicate, so the sentence "there are numbers undefinable in ZFC" can't even be said, let alone proved. (Which is just as well, since ZFC has a countable model, and even a model whose every member is definable.) The same applies to the system of everything you believe about math, as long as it's consistent and at least as strong as ZFC.

there are ... only countably many names you could give a number.

If we take a name to be any pronounceable string pointing to a specific entity*, then in what way is that set limited? If you construct a list of syllables used for all names, and even limit your search to the items that start "the number", you can always take an existing number name and append a syllable from that list to create a new name. That's pretty much how set theory establishes integers, as I understand it.

I think there is a difference between "unnameable" and "unremarkable so far, so nobody's bothered to name it", which does describe nearly all numbers.

*This is an extremely narrow definition, but functional for this application. It could be extended to include any reproducible symbol including those that can be pronounced, scribed, or thought.

The existence of uncomputable/unnameable reals is usually asserted on the basis of some kind of continuity or absence of gaps.

Likewise in more concrete cases. If physics is correct in asserting that there is stuff beyond our cosmological horizon,then that is stuff we can never know about.

Quote: "Un-referenceable entities" is, after all, a reference.

Sortof. "Un-referenceable enitities" is a reference to something, but it's specifically a reference to a class of entity, not a reference to an entity. Speaking politely, I'd consider this to be a borderline 'weasel words' strategy.

To be frank, your argument style and word choices are really terrible if you're trying to get me to rethink reductionism/physicalism. (I am a strong reductionist.) Consider this sentence:

"Any idea, whether it's God, Physics, or Objectivity, can disconnect from the human cognitive faculty that relates ideas to the world of experience, and remain as a mere signifier, which persists as a form of unfalsifiable control."

This is a terrible sentence:

- Ideas are information. We have a lot of math for that.

- Ideas can't disconnect from anything. What does "Any idea ... can disconnect from" even mean?

- "The human cognitive faculty that relates ideas to the world of experience" We call this the act of modeling data in machine learning. There are huge quantities of literature on this. I see none of that referenced here.

- "An idea ... remain as a mere signifier"? What is that supposed to mean? Taken one way, you could say that as information, ideas are strictly and only signifiers. This section of the sentence is incredibly sketchy.

- "which persists as a form of unfalsifiable control" Control against what? You haven't defined anything to control against. And why is it unfalsifiable? You haven't shown unfalsifiability, merely declared it. That is not sufficient.

Similarly in other places, you appear to be making extensive use of word mangling and creative word definitions. The map is not the territory; the label is not the thing. Being extremely strict about your labels, showing those labels map to something I care about, and crafting a strong, internally consistent set of arguments using those strictly defined labels is how you're going to convince people like me. I don't see that your posts so far do that.

Phrases like "the objective world" are typically taken to have meanings, where the meaning is as a kind of thing/entity that has properties, such as being physical. It would certainly be nonstandard to say that this isn't a reference, as it is, literally, a noun phrase, that is taken to correspond with some entity having properties.

I agree that "un-referenceable entities" could be a reference to a class (like an adjective) rather than a particular. However if I say "there exists an un-referenceable entity, which has properties x, y, and z" then that really looks like a reference to a particular.

I also think my arguments about referenceability of particulars also apply to referenceability of classes. For a reference to a class to be meaningful to some agent, it must in some way be related to that agent, e.g. to their observations/actions.

I'm going to ignore criticism of the last paragraph since it's not written to be compelling to people who don't, by that point, agree with the post's basic idea (which it seems you don't).

"However if I say "there exists an un-referenceable entity, which has properties x, y, and z" then that really looks like a reference to a particular" - It's a class that may only contain one if we choose the properties correctly

For a reference to a class to be meaningful to some agent, it must in some way be related to that agent, e.g. to their observations/actions.

I find that pretty vague. It doesn't have much meaning for this agent.

...if I say “there exists an un-referenceable entity, which has properties x, y, and z” then that really looks like a reference to a particular

Then don't. Or..why should that be a problem? Even Kant doesn't make positive claims about noumena or things in themselves.

How can there be an unreferenceable entity?

Perhaps I am missing the point of reference, but this phrase might be about something like:

  • If you've never seen an alien city, it might be difficult to describe it in advance. (reference to unknown parts of reality)
  • Things which cannot be referenced "directly"* - perhaps by existence. The members of the class of "colors we can see" for instance is one we know exists (has members, which we can point to). But colors we can't see may be a recently established phenomenon. While it could be "referenced", the reference didn't always point to a phenomenon with known examples - in fact its defining trait was that (via the known means at the time) it wasn't (easily, known to be) observable.


"Un-referenceable entities" is, after all, a reference.

But not to a single entity. Some expressions in ZFC uniquely refference a single real number. Ie or . All sorts of functions, roots trig functions ect can be expressed. There are countably many finite strings of symbols. The reals are uncountable, so the set of unreferenceable real numbers must be nonempty. But in general, testing if an arbitrary string really uniquely defines a value is not easy. It is equivalent to knowing if an arbitrary formula is true or false. So we need to work in ZFC+1. Within ZFC+1, there is a model of ZFC, and so you can take the set of all formulae that can be proved to uniquely define a number within the model, and then take the complement of it. (This is another source of subtlety, The reals within the model may not be the whole reals, which complement do you take)

This gets into some really complicated and subtle bits of model theory. Your paradox, like the set of all sets that don't contain themselves, is formed by the English language confusing concepts that are subtly different in formal maths.

But, a slight amount of further reflection betrays the absurdity involved in asserting the possible existence of un-referenceable entities. “Un-referenceable entities” is, after all, a reference

We have an answer to that: you can reference a class of entities ,as a class,that can't be referenced individually.

Part of the absurdity in saying that the physical world may be un-referenceable

Who do you think is saying that? I only know of assertions that parts of it other decoherent branches, or over cosmological horizons or inside event horizons...are inaccessible.

I always thought it was pretty funny when Lovecraft wrote about Un-namable on Indescribable Horrors for exactly this reason. Thanks for expanding on the thought!