Thank you, Alex Norris, for such an intriguing question! Even though your question covers several complex philosophical fields (metaphysics and modality, standard and non-standard logic, philosophy of mind and language), I hope my answer will be as clear and complete as possible.
“There are things that do not exist.” This enigmatic sentence from A. Meinong sparked a never-ending philosophical controversy. As your question suggests, imagination and existence are quite different: there are things I didn’t imagine that do exist (e.g. the pangolin) and things that do not exist but I can imagine (e.g. Santa Claus).
Let’s focus on Santa Claus. A strange entity, isn’t it? I cannot see him or cross him in the street, but at the same time I can speak of him and make true or false claims about him; I might even have feelings towards him. So he must exist somewhere or somewhen, right? What’s more, isn’t it kind of contradictory to say that he doesn’t exist while still discussing him?
These are some of the reasons that pushed Meinong to accept these exotic entities in his metaphysics. According to Meinong, things like Santa Claus are concrete non-existent objects; that is, objects that possess the properties we usually ascribe to them (e.g. “a long white beard”) like ordinary objects do, but simply lack the property of existence.
The same goes for all we can imagine. For Meinong, all imaginable properties refer to something that “really exists”, even incomplete and impossible objects that violate fundamental principles of logic (e.g. the round square).
This last point led to a controversial philosophical debate.
Other philosophers, like D. Lewis, restricted the field to only possible objects. Paraphrasing Meinong, we might say that according to Lewis “there are possible things that exist.” Possibilia are objects “living” in non-actual worlds: the actual world is the one we’re living in, where M. Zuckerberg is Facebook’s CEO; but for Lewis there are other possible worlds, worlds in which for instance I am Facebook’s CEO and M. Zuckerberg is replying to your question.
One big problem with this idea is that Santa Claus seems to have not only actual properties, but also possible properties (since he could have been beardless). How is this to be interpreted? Should we say that there exists a possible object (beardless Santa) of a possible object (bearded Santa) or that bearded Santa is an actual object like you and me, which seems absurd?
Another position is artefactualism, according to which objects like Santa Claus are artifacts like cell phones but, unlike cell phones, they are abstract (non-concrete). Santa Claus would thus be a kind of abstract cultural entity created by generations of folk tales. This might sound intuitive, but the problem for artefactualism is that it automatically excludes all the concrete properties we usually assign to these entities (e.g. “Santa brings gifts to children”), and so we seem then to lose something significant about them.
If you remain unconvinced, you could always opt for the antirealist view: isn’t the mere fact that these objects look so strange and difficult to coherently analyze a good enough reason to say that they do not exist (period)?
What do you think? Do imagined things exist? Let us know in the comments.
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I studied in Geneva and Paris (University of Geneva and École Normale Supérieure) and I specialized in the philosophy of emotions, especially in the relationship between affective states and memory. My master's thesis dealt with nostalgia and represented an attempt to establish a general philosophical theory of this rich and complex emotion. Other areas of interest include moral emotions, metaethics and metaphysics, with a penchant for fictionality. I do not have any specific philosophical arguments in mind; however, I find that the works of Russell, Popper and Kripke are a must-read.