Some Objections to Abstract Creationism

Comments on David Friedell's "Creating Abstract Objects"

David Friedell, “Creating Abstract Objects”, Philosophy Compass, Vol. 16, Issue 10 (October 2021): e12783, pp. 1-11.

In discussing the abstract artifact theory of fictional characters, it is useful to consider some of the possible objections that might be made to it. This gets us into a very sprawling and unruly philosophical literature, so, lest we get lost in the forest, we need a guide to some of the major sights. Friedell’s “Creating Abstract Objects” is an especially useful article for this purpose; it focuses particularly on the question of ‘abstract creationism’, the idea that abstract objects may be created.¹ Along the way, Friedell builds an excellent argument for one of our key ideas here: that issues like this end up having ramifications for the wide regions of philosophy.

Focusing on abstract creationism allows Friedell to cast a very large net:

Abstract creationists about musical works think that Beach’s Gaelic Symphony is an abstract object that Beach created. Abstract creationists about fictional characters think that Emma Woodhouse is an abstract object that Jane Austen created. There are abstract creationists about many other kinds of objects, such as arguments, words, internet memes, installation artworks, bitcoins, and restaurants. (p. 1)

Most of the discussion on these subjects, however, has been in the context of musical works and fictional characters, so these are what might be called the reference points for this entire field of discussion. The major opposing positions are what Friedell calls materialism (these objects are concrete rather than abstract) and Platonism (these objects are abstract, but are not created). In discussions of musical works, these are often characterized in terms of their different implications for the creatability, audibility, and repeatability of the works. Many of the arguments back and forth are about the failure or success of one or the other approach to give a reasonable account of these properties, which are difficult to pull together into a single account. Abstract creationism is often seen as doing very well, for the most part, with these, having the advantages of Platonism without some of the less intuitive claims, but this does not mean it has escaped all criticism. Friedell gives several major families of objections people have put forward against it (we will group them slightly differently by putting vague existence and vague identity objections together)

CAUSAL OBJECTIONS

To say that an author creates a fictional character makes it sound as if the author is a cause and the fictional character is an effect. However, many people hold that abstract objects cannot be either causes or effects. The obvious objection is that this gives us reason to think that if a fictional character is an abstract object, it cannot be created at all. Friedell, however, notes that there are other causal objections. For instance, musical works seem to cause enjoyment; if abstract objects aren’t causes, then it seems that musical works can’t be abstract objects.

The most obvious line of thought in response would be to deny the position that abstract objects cannot be causes or effects. Perhaps abstract objects are not causally inert. When we look at the kinds of things that are candidates for being abstract objects, there are times that we talk about them as if they weren’t causally inert. Mathematical proofs, like musical works, can cause enjoyment (or so we sometimes say), but if anything is an abstract object, it seems that a mathematical proof would be. The objector will surely come back with an argument that this ‘causation’ is not in fact causation at all, and that we can explain the effect without appealing to the abstract object as any kind of cause.

A more subtle response to the objection would be to accept that abstract objects are causally inert but hold that they are still in some relevant sense created. That is, you could deny that creation requires causation in any strict and proper sense. Perhaps it just requires dependence of some kind, or some other relation, that we nonetheless still think of as a reason to classify some abstract objects as ‘created’. Perhaps the composer never actually interacts with or affects the musical work she composes, but the musical work has a connection to the composer that we tend to model as causation-like, or that some people metaphorically represent as causation, and this is just one of the things we mean when we say that the composer creates the symphony. If you have a doghouse, there is also the singleton set of which the doghouse is the one and only element. Creating the doghouse can be seen as creating the set, even though the set is an abstract object and you yourself never actually do anything directly with it. A problem with this is that it becomes difficult to pin down such a relation that still makes works of art what we would usually call works of art.

Assessing objections like these requires us to consider quite a few other things:

As we have seen, causal objections pressure abstract creationists to either reject the view that abstracta are causally inert or adopt the Thomassonian line that people create causally inert abstracta. As Falguera et al. (2017) suggests, it might help us to think more about what it means for an object, whether abstract or concrete, to be causal. Metaphysicians focus on event-causation and agent-causation but largely overlook object-causation. A theory of object-causation could help us evaluate whether abstracta are causal. It could also help us evaluate Thomasson’s claim that it’s possible to create causally inert objects. (p. 4)

(Issues of object-causation are one of the things we hope to explore down the road.)

TEMPORAL OBJECTIONS

Abstract objects are often thought of as eternal in some way. Sometimes this seems to be understood as a sort of omnitemporality, at other times as a sort of atemporality, and perhaps there are other ways to think of it. But whichever way you think would be most relevant, it’s possible to question whether something created could be eternal in this way. For instance, we usually think that something created has to begin to exist, which doesn’t seem very eternal.

An obvious line of thought one might have in response is to deny that abstract objects have to be eternal (in whatever way that is understood). Perhaps numbers are but musical works are not. Friedell notes that there is an argument, given by Juvshik, that contemporary physics seems to indicate that anything that can be temporally located must be spatially located, which is one of the things people are usually trying to deny of novels or fictional characters or other alleged abstract artifacts.

Friedell seems to put some weight on this as a serious objection, but we are not so sure – not because it’s not a serious objection but because it’s difficult to know how much of a problem it actually is, or even what about it is a problem. Physicists, after all, are usually not even thinking about fictional characters or musical works when they draw these conclusions, so it’s unclear whether the conclusions are even relevant to talking about such things. Further, scientific theories are among the major candidates for abstract artifacts; if a physicist says that something with temporal location has a spatial location, is he really committing himself to saying that the theory of general relativity, itself, has an identifiable spatial location, just like a massive object does, given that it was created by Albert Einstein? Can we give exact coordinates, or even just use coordinates to identify the exact spatial region, where the theory of general relativity is itself to be found? Could we, in principle, refute modern physics by coming up with a very good argument showing that a fictional character, despite its invention being temporally measurable, has no location in space? If this objection is relevant, then it seems that this is in principle possible. But it would be somewhat surprising if we either confirmed or disconfirmed advanced physical theories by pointing to true facts about Nancy Drew or mystery novels or the Battle of the Pelennor Fields. To the human eye it’s not clear how they would even be relevant.

Friedell focuses on other responses to the objection. One could hold that some abstract objects have a spatial location. Chess is an abstract artifact; but it does seem that you can say that there was a time when chess was only in India. Or perhaps, they don’t exactly have a spatial location in the ordinary sense, but in some other sense; certainly you could argue that physics doesn’t really require determinate, definite location (what is the determinate, definite location of an electron in an atom?), but can countenance at least the possibility of things that have a merely indeterminate location in region, or location in only a relative or loose sense, or even just some kind of spatial measurement that doesn’t identify a particular location at all.

The other possibility is to argue that abstract artifacts don’t even have temporal location. Can something come to be timelessly? Or can something be temporal but not in the way that is relevant to Juvshik’s argument?

All of these considerations are clearly connected to the question of what it means for abstract artifacts to be abstract.

VAGUENESS OBJECTIONS

One worry that you could have is what the implications of these abstract artifacts might be for our view of existence generally. This leads to the vague existence objection:

Suppose that Beach created Gaelic Symphony. It seems there is no precise nanosecond when she brought the symphony into existence. It seems indeterminate when it first existed. The worry is that this indeterminacy requires the word or concept “exists” to be vague, a state of affairs that many theorists (e.g., Lewis, 1986; Markosian, 1998; Sider, 2001) find implausible or even incoherent. Deniers of vague existence think it’s fine for an object to be vaguely red if it appears somewhere between red and orange. Likewise, objects may be vaguely round or vaguely tall. But deniers of vague existence think objects can’t vaguely exist. (p. 5)

There are a number of apparent cases of vague existence, and so the denier of vague existence will have to have strategies for showing that they are not really cases of vague existence, i.e., that the vagueness enters into the picture at some other point than existence. In fact, the problem raised above is just a general problem that applies to every kind of beginning to exist or ceasing to exist, and obviously if we deny that existence can be vague we will want to say that cases of beginning or ceasing to exist do not involve vague existence generally speaking. This objection then really amounts to saying that there is something about abstract artifacts that makes it so that no such strategy will work for them. It’s difficult to see how one would show this. This is particularly so given that ontologies allowing for abstract artifacts can be quite flexible.

Of course, an abstract creationist might well deny that it is indeterminate when the Gaelic Symphony first existed – perhaps the vagueness is epistemic rather than ontic – or simply affirming that, yes, indeed, some things exist vaguely.

As with existence, so with identity. At least some candidates for created abstract objects seem to be such that it is difficult, perhaps impossible, to say whether they are the same or different. Friedell notes an argument to such an effect by Everett, who tells a story of Frick and Frack in Frackworld:

Frackworld: No one was absolutely sure whether Frick and Frack were really the same person or not. Some said that they were definitely two different people. True, they looked very much alike, but they had been seen in different places at the same time. Others claimed that such cases were merely an elaborate hoax and that Frick had been seen changing his clothes and wig to, as it were, become Frack. All that I can say for certain is that there were some very odd similarities between Frick and Frack but also some striking differences (Everett, 2005, p. 629). (p. 6)

Are Frick and Frack the same fictional character? There seems to be no definite answer to the question.

Abstract creationists have several options here, as well. They can hold that, in fact, Frick and Frack are identifiably distinct characters (e.g., because they fill different roles in the narrative).

A variant of this possibility Friedell doesn’t discuss can perhaps be characterized using a (admittedly loose) analogy. -1 has two square roots, i and -i. Which is which? And it seems that we have to say that the only difference between i and -i is that they are sign-opposed square roots of -1. If we consider the common rotational interpretation of imaginary numbers, we can set i to be in any direction we please, and then -i will just be in the opposite direction. So there is an i and there is a -i, and they are distinct, but there really isn’t an answer to the question, “Which is which?” beyond one being the opposite of each other. Frick and Frack is an easier case. We are told that Frick and Frack have some “striking differences”, so we know that they are distinguishable. But that’s just all we know about them. We don’t know if they are distinguishable as persons or as something else (e.g., personas). The difference between this and the imaginary number case is that with the imaginary number case we seem to have hit the end of the line, but with Frick and Frack it is always possible that new information could help us answer further questions.

Another option is to hold that the answer here is just disjunctive – Frick and Frack are either different or the same – and that which of the two obtains is just something we don’t know rather than a fact about Frick and Frack.

As Friedell notes, whether these options are really workable in the long run depends on our view of fictional characters.

THE INADVERTENT CREATION OBJECTION

If we claim to be able to create abstract objects, what exactly is involved? It’s not immediately obvious, so it’s perhaps not surprising that some objections arise from this potential point of perplexity. Can you inadvertently create an abstract object?

Some abstract creationists hold that all creation of an abstract object is intentional; that is, it is specifically the intentionality or something necessarily connected with it that makes it so that the abstract object can be created. However, others hold that inadvertent creation is possible, and indeed it seems that you can point to apparent possible cases. One of the reasons you might be an intentionalist is that tying creation to intention gives one well-behaved answers to questions like, “When is it created?” or “By what means is it created?” If we accept inadvertent creation, we have to find other answers to these questions.

This is not to say that they are necessarily unanswerable. Friedell notes that abstract creationists are not the only ones who face these questions; in fact, it seems that you can have the same problems, and presumably analogous solutions, for all artifacts, including things like tables and chairs. Can you accidentally make a table? Can you, without actually intending to do so, invent a new kind of thing? There seem to be cases where this happens; either that is merely apparent, or we can in fact have inadvertent creation of artifacts, and we seem to get the same questions that we have for abstract artifacts.

*****

What all of these discussions seem to suggest is that the apparent problems that are faced by abstract creationism are not really exclusive to them. Many of the objections just turn on the difficulty of saying when something begins to exist, and you can find similar objections across the field of things that begin to exist. Others, like inadvertent creation, seem common issues that need to be discussed whenever we are considering artifacts or products of human action. As Friedell correctly notes, what this means is that abstract creationism is not an isolated position but one that feeds into, and is fed by, many different philosophical fields. Because of this, abstract creationists cannot focus too narrowly when developing their position, and, because of this, any argument for or against abstract creationism will have ramifications in wide areas of thought. This is always important to remember.

1. Most people who accept an abstract artifact theory are easily classified as abstract creationists, although there are possible exceptions. (That is, you could hold that the abstract artifact is not created, but something else that’s different but still relevant to its being classified as an artifact.) Many of the objections to abstract creationism are easily adaptable to most of these exceptions, though. It is also possible to have an abstract creationist view that does not hold that what is created is an artifact, but for our purposes here we can ignore this position.