Having recently helped out a bit on stage crew for a community theater production of Singin' in the Rain, I have been thinking quite a bit about what it is to be a stage prop. A few thoughts toward an account.
(1) In Kendall Walton's Mimesis as Make-Believe, he identifies a number of ways in which real objects may play a role in fictions and imaginations. He highlights three in particular:
(a) Prompters. Given a real object, we may be provoked by it to imagine something. Walton's example is that you might, on seeing a bear-shaped stump, imagine a bear. Prompters "induce us to imagine what otherwise we might not be imaginative enough to think of" (p. 22). One of the important uses of prompters, which is certainly relevant to stage props is that they coordinate imaginings, in such a way that the imaginings can converge spontaneously rather than by negotiation and stipulation. "The prompter coordinates the imaginings of the participants and also gives them grounds to expect such coordination---both without disruptive discussion" (p. 23). The particular definition given to prompters here, that they induce imaginations by provoking us to imagine particular things, means that they are somewhat limited in function. If you set out to carve a bear-shaped wooden statue, the statue might be a prompter for someone else, but it is not at any point a prompter for you while making it -- you are not imagining the bear because you see the bear-statue already in the wood, but you are instead imagining a bear and re-shaping the wood to conform to the imagination you independently have. (Of course, later, you might set it aside and then come across it and imagine a bear because of it, in which case it would be a prompter.) Thus prompters are important but have a limited role in our overall imaginative activities. They are associated with a very limited range of our imaginative experiences.
(b) Objects of Imaginings. One of the trickiest aspects of imagination is that we do not merely imagine in response to things (prompters), but we imagine things to be other things. We might imagine a stick to be a sword, a rag doll to be a baby, a table to be a fort, an arrangement on a stage to be London. "Things that a person imagines about are objects of his imagining" (p. 25). Prompters may be objects of imagining for what they prompt us to imagine, but they are not necessarily so, and likewise, the objects of imagining may prompt us to imagine those things that they are imagined to be, but not necessarily so. Walton suggests that one of the functions of an object of imagining is to substantialize what you are imagining. If you imagine a stump to be a bear, there is now physical thing, what could be called the "imaginary bear", that can be touched, avoided, looked at, and so forth.
(c) Props. We sometimes talk about truth in a fiction or fictional truth. Thus it is true in The Hound of the Baskervilles that Sherlock Holmes is a detective; it is true in a performance of The Tempest that Prospero has magical powers; it is true in Raphael's Il Parnaso that the god Apollo plays a lira-da-braccio; it is true with respect to Santa Claus that he can come down a chimney. (Walton wants to deny that fictional truth is actually a kind of truth; this denial is a point, I think, on which Walton's overall account goes very wrong, since my own view is that fictional truth importantly is a kind of secondary or derivative truth that has reference to truth in a more primary sense, but it matters less than it might because Walton can treat the use of 'truth' here as a useful fiction for those propositions that in context are 'to be imagined'.) Suppose you have two boys who have agreed for a game that a stump 'counts as' a bear; they sneak up on what they take to count as a bear, but in fact it turns out not to be one -- perhaps it is a boulder rather than a stump, and so doesn't count as a bear. Meanwhile, however, they later, to their surprise, stumble into a stump they hadn't known was there -- there was something counting as a bear there, all along, even though they did not know it. Stumps in this game are working as what Walton calls props. "Props are generators of fictional truths, things which, by virtue of their nature or existence, make propositions fictional" (p. 37); they "generate fictional truths independently of what anyone does or does not imagine" (p. 38). The stump, given a principle of generation (e.g., the agreement that stumps count as bears), makes it a fictional truth that there is a bear there.
I find this particular vocabulary to have some oddities. For instance, it seems to follow from Walton's account of prompters that there are things that prompt us to imagine things but are not prompters, because they are not provoking us to imagine anything in particular, but merely providing a sort of guiding line or exhortation for our imagining. It's important not to forget these other things, but perhaps there's not too much lost by using 'prompter' specifically in Walton's sense. However, if I have a stick that I am imagining to be a sword, and you start talking about the object of imagining, my own natural inclination is to assume that you are talking about the sword that you are imagining the stick to be; but in Walton's sense of 'object of imagining', the object of imagining is the stick. I can see the sense in this sense, but I also find this confusing and immensely discordant with our usual practice in talking about objects of imagining. So I would suggest that we distinguish these by calling that which is imagined to be something the material object of imagining and that which we imagine it to be the formal object of imagining. In this case, the stick is the material object of imagining and the sword is the formal object of imagining.
It's also the case that Walton's use of 'prop' is rather different from our ordinary use of the word 'prop'. For instance, in a stage play, what 'generates fictional truths' about a lamppost on the stage is first and foremost the play itself -- the references of the characters to it, their actions with respect to it, and so forth. You could have a purely imaginary lamppost, in the sense that there is no physical prop on the stage but everyone acts as if there were a lamppost in a particular spot. The principle of generation (the script, or perhaps the directorial instructions about how to implement the script, or perhaps the agreement of the actors about how to perform a scene in the absence of a prop) provides all that's needed to generate most of the fictional truths that are relevant to the lamppost; it's the actions of the actors, not the prop, that constitute the primary generators of fictional truths on a stage. If we add in the lamppost, this (a) facilitates the actors' work in generating the relevant fictional truths and relatedly (b) facilitates the audience's recognition of the fictional truths that are intended to be communicated. None of this has to do with generation per se of fictional truths. Any fictional truths that the lamppost would generate would have to be specifically concerned with its being a physical object (and, therefore, presumably, with its being a material object of imagining) -- for instance, that there is a lamppost visible in that location. Thus, props cannot be the only generators of fictional truths, and, indeed, it seems that they would always presuppose non-prop generators of fictional truths. On the other side, however, Walton's account of props means that 'prop' in his sense is astoundingly wide. Not only are stage props 'props', but the actors are props, and the stage is a prop, and the curtain is a prop, and in many contexts, the audience is a prop. And beyond that, the script on the page is a prop and the handbill that explain the play is a prop and the poster that advertises the play is a prop, and if someone records the play, the video is a prop, and if someone uses the video to paint a scene based on the play, the painting is a prop, and so forth.
Stage props can be prompters, and objects of imagining, and props in Walton's sense; but there is no straightforward way to use Walton's account of props to give much of an account of stage props. An interesting question is whether we can take Waltonian props to be a genus of stage props. Are all stage props always Waltonian props? And I think the answer is No. A reason to think not is that stage props are stage props offstage as well as onstage. If you have a cane waiting offstage to be used onstage, it is a stage prop, but it is not generating any fictional truths; it only does so when it becomes salient onstage, e.g., by an actor using it to walk. In scholastic terms, to be a prop in the Waltonian sense is a relation secundum dici, but to be a stage prop is a relation secundum esse -- the stage prop is the thing itself as capable of being related in certain ways, not its being able to be said to be proppish in function -- being a stage prop is a 'relative habitude' of the thing itself, not a relation to which the thing is further directed.
(2) One of the interesting things about stage props that needs to be considered is that all stage props represent something, but they themselves can be what they represent. If we put a piano on stage for the actors to work with in some way or other, that makes it a stage prop. But its purpose as a stage prop is to be what it is, a piano. In one sense, it's obviously not like the stick imagined to be a sword. It may not even be like a dull sword imagined to be a sharp sword; it could be like that (a defective piano standing in for a properly functioning piano), but depending on the context, it might be, and might need to be, a perfectly functioning piano that will be used as a functioning piano. On the other hand, it's not actually all that different. The piano is put on the stage to be a material object of imagining; it's just that the piano is a material object of imagining whose formal object of imagining is a piano. When you put a piano on a stage, it is not merely there; it is being put there to be imagined to be a piano. It's not as if you have all this host of things on stage that are imagined to be various things, and then you have the piano that is not imagined to be anything at all; on the contrary, its use in the play almost certainly requires us to imagine it to be a piano. The actual piano is also a fictional piano; it is true that the piano is related in various ways to things (e.g., an actor), and it is also fictionally true that the piano is related in those various ways to things (e.g., to the character we are imagining the actor to be). One thing that makes stage props interesting is that they are an obvious case in which the actual and the fictional overlap. I can pull out an actual, physical, really functioning pen, which is then fictionally, imaginatively, attributively a pen in the context of the play. To say that something is a pen in the fiction of the play does not imply that it is not an actual pen; to say that something is an actual umbrella is consistent with its also being a fictional umbrella. Obviously, we are not using the word 'fictional' here in an exclusionary sense that implies falsehood (that's the whole point), but the way the piano, or the pen, or the umbrella is related to other things means that it has a role in the ficiotn and therefore a status in the fiction that is constituted by what is true in the fiction. In the sense in which 'fictional' characterizes what is going on in the play, we cannot deny that the piano is also fictional. I mean, the fictional characters might play the piano, which can only be made sense of if the piano is fictional, even if we have a real piano being the fictional piano.
In this sense it is a bit like an actor playing himself in a cameo. In the movie Last Action Hero, Arnold Schwarzenegger plays Jack Slater, a fictional character, who in the movie meets Arnold Schwarzenegger, who as a fictional character in the movie plays Jack Slater, a fictional character in the movie within the movie. When Jack Slater, played by Arnold Schwarzenegger, interacts with Arnold Schwarzenegger, played by Arnold Schwarzenegger, they are both fictional characters; it's just that Arnold Schwarzenegger, the actual person, is playing both a fictional character different from himself and also himself as a fictional character. So too the actual piano, which is playing itself as a fictional piano.
This is related to Walton's point about (material) objects of imagining substantializing our imaginations; stage props make fictions 'more real' by introducing what is non-fictional to serve fictionally. This could be by pure stipulation (like designating a section of the stage as a street), or it could be by symbolic representation (like using a stick to symbolize a sword), or it could be fictionally representing itself.
(All of this has some relevance, I think, to various philosophical positions that get grouped under the label 'fictionalism'. For instance, mathematical fictionalism is the position that mathematical objects are fictions. Well, okay, but as we see in the case of stage props, actors, self-referring fictions, and so forth, something being a fiction does not guarantee its being only a fiction, and you could very well be a mathematical realist and hold that mathematical objects are also fictions in some way -- e.g., you might analogize the role a mathematical object plays in a Euclidean proof to an actor's role in a play and take it that the real mathematical object is playing itself as a fictional role in the proof. The point is not whether this is an immediately attractive position in philosophy of mathematics; rather, the point is that when you've said that something is fictional, that does tell you something about how it works, but it rules out very little about what it could be. Fictional Troy turned out to be archeologically locatable.)
(3) In a play. we normally think of the play as actors doing things on the stage. But you can also think of it in terms of the under-play, in which the stage props (including things like most costumes, which are often wearable stage props) are moved on and off and around the stage. The under-play actually works a lot like the play; things have to go on and off stage on various cues, at various times, at various locations. The stage props are themselves the 'actors' of the under-play, although they differ from the actors in that they are not active but patient. They are the patients of the play, the things that do not themselves do but instead undergo. In this sense, there is a clear similarity between a stage prop and a puppet in a puppet show. The difference is that puppets symbolically represent actors, whereas stage props don't unless the stage prop is itself a puppet or something similar. A puppet show is in a sense all under-play, one representing a possible actual play, whereas in an ordinary play, the under-play is a fragmentary thing in which (for instance) chairs are brought off and on in a way that only gets its full meaning within the play itself. You could have postmodern play that was all under-play -- it would consist of a stage set with people doing nothing put moving chairs and things on and off the stage on various cues. It would be quite mysterious without the actual play, and probably would have difficulty keeping people's interest for the same lenght of time as an actual play which had the very same under-play.
What this highlights is that stage props have roles just as actors do. Roles are deontic structures. The piano ought to be out on the stage for such-and-such scene. The coatrack ought to have been removed by such-and-such scene. The table ought to be placed on the such-and-such side of the stage. To be a stage prop is to be something capable of participating in a deontic structure for a show, a role. This role may include any of Walton's functional statuses (prompter, material object of imagining, or Waltonian prop). This deontic structure in a play is established by the play itself -- the script and various decisions made for implementing it. In a magic show it would no doubt be established by the requirements of the magic tricks and the plan for their order. But it is only because there are such deontic structures that there are stage props.
(4) One thing that is very important about a stage prop is that, as a stage prop, it is purely instrumental -- it is usually a separated instrument, although sometimes it could be a conjoined instrument. A stage prop is something that is for use on the stage for a show. Even if we have a rock, in using it as a stage prop, we in a sense 'artifactualize' it; it is no longer just a rock, but a rock to serve a purpose in a play or some other kind of show. You can take a rabbit and make it a stage prop in a magic show. Thus whether something is a stage prop is about whether it can be classified as an instrumental patient available for a role in a show. 'Availability for a show' is not a particularly precise thing; obviously the things in a prop lock-up for a theatre company are available for a show, and thus can be classified as instruments available for a show. An umbrella at a store is not a stage prop, but if someone buys it to be an umbrella in a show, then it is a stage prop. To be classified as available for a show requires there being some idea of the kind of show for which it could be available; the kinds of things that could be stage props for a magic show may overlap but are not necessarily the kinds of things that could be stage props for a tragedy. Tragedies in ancient Greece had props, but they were quite limited, in part because they were religious ceremonies, in part because there were expectations about how they could be done, and in part because the venues required that you only use things that would be easily visible to more or less everyone in what was effectively a stadium. They would likely have been puzzled as to how a rabbit, a top hat, and stick would function as stage props, having no conception of our magic show conventions, or how a pocket-watch would work as a stage prop in a modern drama, not being used to our relatively intimate stage-theater setting. Thus what can be a stage prop depends on what can be an actual show. There's no point trying to claim that Mount Rushmore is a stage prop unless you have the kind of show in which it could be a stage prop. Nonetheless, if you had such a show, absolutely nothing forbids Mount Rushmore from being a stage prop, i.e., classified as an instrumental patient available for a role in a show.
(5) One complication with the considerations in (4) is that a stage prop has different modes. A stage prop 'in storage', i.e., as available in a broad sense, is different from a stage prop 'in waiting', i.e., as available in the more immediate sense of 'ready to go'; and a stage prop 'in waiting' is different from a stage prop 'in use', i.e., actually being used specifically as a stage prop. Thus 'classified as an instrument available for a show' is not quite a complete account of a stage prop; you can have a stage prop that just stays in storage, available but never used, but what makes it a stage prop is that it is for being 'in use'. The old, technical way of making this distinction would be by saying that stage props can be potential and actual; thus stage props 'in storage' are potential stage props and stage props 'in use' are actual stage props. Unfortunately, this has also become a confusing way of talking, because there are two different things you can mean if you say that something is a potential X. You could mean that it is an X, but as being potential. You could also mean that it is not an X, but has the potential to become X. Potential being and actual being are both being; potential being is not nothingness. Likewise, a potential infinite and an actual infinite are both infinite; it's actually quite essential that a potential infinite not be finite. But we see in both cases that people get confused. In philosophy of mathematics, people repeatedly get Aristotle wrong by confusing his potential infinite (which is infinite) with an indefinite finite (which is not infinite); in metaphysics, a large number of mistakes get made by assuming that if something is potential it is not anything at all. Obviously, if we use this terminology here, both potential stage props and actual stage props are stage props.
While the terminology has the disadvantage of being confusing, it has the advantage of giving us roughly the right structure for reasoning. The stage prop 'in storage' (the potential stage prop) has to be partly activated as a stage prop to be a stage prop 'in waiting' (what the scholastics might have called the virtual stage prop), and the stage prop 'in waiting' has to be fully activated as a stage prop in order to be a stage prop 'in use'. These modes are related analogically; the potential stage prop and virtual stage prop exist to be an actual stage prop, to be not merely available for use, but available as actually being used.
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Kendall L. Walton, Mimesis as Make-Believe, Harvard University Press (Cambridge, MA: 1990).