Keith Douglas
Recap
No feedback was received on last month’s column. On to the new matters for this one.
On Nothing
Leibniz’ question, “Why is there something rather than nothing?” has a presupposition (see the May 2025 column) one must analyze, namely that there could have been nothing. However, there are a bunch of “items that look like nothing, sorta”, where the “sorta” operator is due to Dennett. So, in order to further understanding of the complexities of matters that are adjacent to “nothing”, I briefly describe several of these areas which have proved important to me and some interrelationships. I take them up in arbitrary order. Which of these do you think that Leibniz had in mind?
Null object – In object oriented programming, a null object is one with no methods, no fields and is of its own type (in most languages). T. Hoare called it his billion dollar mistake, because including this special item into programming languages was “easy” but has arguably created more crashes than any other programming language feature. (Stuff will happen if a program tries to call a method or access the memory pointed to by a null object, usually crashes or behaviour that might create one if not handled.) His idea was so popular at the time and for years afterwards that we are still working on ways to deal with it – and it was 60 years ago this year that this error was made, if that’s what it was.
Null individual – Moving from programming and software to metaphysics, then. In various mereologies (studies of various part-whole relations), a null individual is a fiction (usually) introduced to make the resulting algebra neater. Peter Simons’ 1987 classic, Parts makes this claim, for example. He dismisses this as unnecessary. However, Bunge’s mereology (which is cited and criticized in these terms) has another purpose outside mereology narrowly construed, namely as inputs to a general scientific world view. A general conservation law is provable relatively easily once the null individual in place in the system. I asked Simons what he thought of this goal and why his excellent text doesn’t seem to take it into consideration. He regarded it as off-topic for the mereologist to worry about whether things suddenly come “out of nothing” or utterly annihilate. I disagree, for Bunge’s reasons – once he told me that theory of things includes “unusual” things like photons. I am actually reporting the conversations in reverse order, but no matter … And the null individual in Bunge’s system is definitely “no matter” – taken in itself (as an idealization). What is the metaphysical status of idealizations in YOUR world view?
Zero – I hold this to be one of the most amazing inventions ever (from India, in this case, it seems), and is in a way a basis for many of the others we discuss here. Mathematicians call the various zeroes the “identity” for various addition operations (a+0 = a, for all a in the set in question). The grade school sets of real and natural numbers are strictly speaking different, and a zero is defined for both – at least usually. There are so many mathematical theories that this is more complicated than it sounds. They are all very similar in the elementary case that moving between them is easy enough – fortunately, given elementary and high school teaching!
Empty string – Strings are a common data type in programming languages – either as a composite (in C, for example) or as a native type (in many modern programming languages). It used to be that I hated dealing with strongly typed strings – but that was because they were limited to an upper bound of length, like in Pascal, where 255 is (standardly) the maximum length one can allocate. Strings are also likely be to a target for domain driven design – and then the empty string becomes complicated. Why? The empty string is the (only) string with 0 characters (usually even in strongly typed languages strings are made up of, in part, characters, or can be easily treated as such). Unlike the null object, however, they still have a type. So operations on empty strings are supposed to be well defined, though in practice substringing them in some contexts produces errors. This is the equivalent of dividing by zero – just because 0 is a number (see above) does not make it always “usable”. However, there are definitely operations that one can perform – length, for example, of the empty string, is 0. The null object and the empty string are so likely in certain contexts that we have matters like String.IsNullOrEmpty so-called static methods, which object oriented purists find obnoxious. But it is too easy to weakly type derived object types and then have to scramble for interpretation. For example, now, many languages have a “IP address” type – beginning programmers might think “can’t I just use a string”. Well, maybe, in some languages, but one shouldn’t. What’s the hostname associated with the empty string? It isn’t defined; one has to then propagate the mistake to the hostname object type … and then it collides with the possibility that an IP address does not have a hostname (this is allowed) … Those who know about “domain driven design” or have heard about it – this is why it is so valuable as a practice!
Empty report – This is the “empty work product” I mentioned in last month’s column. I think it is sometimes very important to be able to tell the difference between not doing something because unneeded and we didn’t do it because we forgot to, or it hasn’t been done yet, etc. The first makes all reporting in my domain “needed”, but sometimes I can simply say: “Nothing needed further to do” as the report, and that’s it! This is the social equivalent of the strong typing of objects I mentioned; if you try to read the report and it is simply not there, one suffers the null object errors mentioned – as a person!
Empty set – Most set theories have one, the set with no elements (or no members). Further, in most set theories, the empty set is unique and well positioned to “represent” or “be” the number zero, or at least the natural number 0. This too makes calculations and axiomatization easier. However, the question about whether the empty set is in fact a (the?) zero is a question addressed in the philosophy of mathematics, and it is not exactly straightforward (though Platonistically and reductionistically inclined mathematicians are sure to disagree). P. Benaceraff’s classic paper “What numbers could not be” addresses this question. I for one as a fictionalist don’t actually care what the answer is – except fictionally. You can fictionally believe that the empty set and the natural number zero are the same fictional entity, for all I care (even philosophically). I do, though, think that the Platonist needs an answer to the question – and better, an answer to the epistemological question of “how do you know that?” I’m a fictionalist in mathematics in part because of this paper, though at the time I first read it some suggested to me it would do the opposite. Working mathematicians always say “Learn more (analysis, topology, algebra, number theory …) and then get back to me …” (My reply, quoting one of the greats, is “Das ist nicht Mathematik, das ist Theologie.”1)
Vacuum – This is a “place” where there is no matter, however understood. In the modern context we often speak as if vacuums (like in outer space) are empty of bodies at a certain scale (for example, that the hydrogen atoms are thus and so apart in the intergalactic “void”). However, this distinction is important – electromagnetic and gravitational fields propagate outwards at c so presumably there are (or will be? the tense here is hard for relativistic reasons) fields at least everywhere, so no true vacuums on that account. Descartes and pseudoBoyle were right! (Pseudo because although Hobbes accused Boyle of claiming he’d made a vacuum, there was no such claim.) This is because “empty?” can always be read “empty of what?” (And this might help with the Leibniz question!) Aside: A vacuum cleaner is an interesting item; I wondered as a child how one could clean with nothing or clean nothing itself. I always also hated them for the noise – for a nothing, they sure are loud! I leave it to the reader to figure out what you’d say to my childhood self about what they are, given the previous remarks.
- “This is not mathematics, this is theology” ↩︎