On the realities and fictions in our languages

Whenever we express ourselves in language, we evoke fictional objects. Everything we talk about is fictional. Suppose you say “I ate fishball noodles today”. And suppose you really did eat “fishball noodles”. But in fact you didn’t. You ate a bunch of physical matter that resembles a bowl of Platonist “fishball noodle”, and of course we know the Platonist object doesn’t really exist in reality. And thus, we only describe imaginary objects that sort of convey a rough idea of actual reality, to willing listeners (who inevitably interpret the words in their own way, probably slightly different to what you actually intended). Of course, if your friend was actually beside you when you ate the noodles, then “the fishball noodles I ate yesterday”, although being a platonist concept in language, could be translated into those “real” noodles that he saw you eating. But I’m only talking about the ideas contained in the language, which is of course, without real world context, rather platonist.

This is the background, and it should be pretty obvious and non-controversial (I hope, because the stuff below is a bit crazy).

The more controversial question is this: given that we’re always talking about fictional and imaginary things in language, why do we say a bowl of “fishball noodle” is “real”? But we consider a fire breathing dragon as “fictional”? What about “honest politicians”? We can describe objects that (to human’s best of knowledge) do not exist in reality. We can even describe objects that defy logic and shouldn’t exist in logical worlds. Russell defined sets of all sets that don’t contain themselves — which was considered to be obviously so “fictional” (illogical) that naive set theory was considered invalid… but that didn’t deter millions of people talking about some omnipotent deity would be able to create a rock so heavy that it could not lift. We believe in uncountable real numbers, the numbers that defy our language to such extent that we cannot describe them all; we seriously contemplate oracle machines that defy logic by solving uncomputable problems within one step (which is proven impossible). We talk about all these weird things as if they were real — and if the justification is that the fictional objects are “real” because they are useful somehow, then why don’t we consider Harry Potter characters as “real”, because they are useful from various cultural and educational perspectives?

No matter where we draw the line between “reality” and “fiction”, most of us would agree that “fishball noodles” (even the platonic version) are more “real” than a set of all sets that don’t contain themselves… and we might want to draw a line somewhere to differentiate the two. But such “decision problems” relating to the “real world” are hard (see Buridan’s Principle. Leslie Lamport). One less draconian way to deal with this problem is to sort of roughly figure out “how fictional” a concept is, perhaps come up with some kind of “fictional score”, so that we don’t have to draw a hard line anywhere.

The question is, given that all concepts in languages are fundamentally fictional, how do we even define “how fictional” something is? We know that the number “1” is more real than (or at least as real as) most of the Real Numbers (TM) like sqrt(2). But how do we compare Pi=3.1415….. to a fire breathing dragon? You can say circles exist, therefore Pi is real. But in fact we’re only referring to platonic circles 🙂 Any circle in real life has to be imperfect, if only due to quantum weirdness. If we accept imperfect circles, drawn on (let’s say) paper, as proof of the “real-ness” of Pi, then any semi-competent artist can draw you a fire breathing dragon on the same piece of paper. You may also claim that a sphere is “real” since you can make a real sphere in the form of a ball, but hey I’m sure you can find 3d dragons in Toys-r-us too. I’m sure there are crazy people in the world who make dragon figures that really can breathe fire….

Anyway I’m not trying to claim dragons are real. It’s just that I don’t even know how to start comparing the “real-ness” or “fictional-ness” of concepts that don’t readily have a real life equivalent. We might be able to compare objects of the same “class” though. At least for “real-ness” function R, R(1) > R(Pi) > R(ω+1).

So let me end with difficult questions: how do we compare whether some concept is more “real” than another? Can we really say something is “real” whereas another is “fictional”?

（原文於 2016 年 3 月發佈，略有修輯）