1. Nothing

Nothing” is the complement of “everything

One of the most interesting things, about which whole books have been written, is nothing. It can be quite a challenge to talk about nothing, despite the success of a select few. On one hand, it is impossible for us to say what nothing is, since nothing does not exist. On the other hand, “nothing” (the word that represents nothing) certainly does exist, despite the fact that its referent does not. In other words, “nothing” is not nothing.[29]

Nothing” means no thing in the domain of discourse. It becomes rather elusive when it is taken to exist, in the sense that “nothing” is something. According to our definition, it is not the case that nothing is something; nothing is not something. So is nothing nothing? If it is not yet clear, it is easy to get caught in a substantial semantic quagmire by talking about nothing.[30]

Nothing” is a reference which does not validly reference something. Everything was previously defined by saying that it occupies every position along every dimension which was used to characterize that domain. Nothing, the complement of everything, necessarily occupies no position along any dimension. Hence, it does not exist: the reference to it, however, does exist (otherwise we could not talk about it, or even ask if it existed). As nothing does not exist, it cannot be said to have any properties (or lack any properties). It is tempting to say that it has the property of not existing, but existence is a property only of references, not of the things to which they refer.[31]

At first glance, the utility of a concept which does not correspond to anything in the real world does not seem terribly high. Why would I say that “I have zero of something” as opposed to saying “I do not have something” ? The former formulation contradicts the notion of “having” . Despite these objections, it is sometimes convenient for a language to have a zero-element . If a language has references, but it does not have the reference known as nothing, then it is more difficult to talk about mental things which do not exist. Things which do not exist are all denotationally equivalent, both to each other and to the reference nothing. For example, if one is asked how many people have set foot on Mars, and an answer is mandatory, then the concept of zero is required (which is a near analogue of nothing).

[29] Nothing” is a valid concept, but it does not correspond to anything in the world (it has no spatial extent). So, it is a reference, but it is not a valid reference.

[30] The lack of a clear denotation for the referential level of a thing is probably responsible for much of the confusion about nothing. There is a distinct difference between a thing and a reference to that thing. This book uses quotes to denote the latter, such that “apple” is a reference to ‘apple’ .

[31] If existence were not restricted to references, it would presuppose existence just to talk about something.