# How is synthetic knowledge produced in fictionalism?

With the Greek gods being fictional there is still objective knowledge - how many Greek female gods are there, etc. (Or if that's still too ambiguous, how many Greek gods are named Zeus). But "mining" this same repository of knowledge for synthetic/derived knowledge seems much less possible. E.g., what would Zeus do if X happened, where X is not something already depicted. Outside of the stipulations (e.g. there is a god name Zeus) I couldn't come up any objective, synthetic/derived knowledge. Rather, I'd be authoring the knowledge.

It seems to be a similar case for lots of other fictional knowledge, like Sherlock Holmes.

But when it comes to numbers, why can I endlessly come up with synthetic/derived knowledge even when treated fictionally? Why can I seemingly only do this with math and logic?

Maybe someone can come up with a fictional game like a complex version of cops and robbers where there is a lot of synthetic knowledge to be mined, but I struggled to do this with my limited imagination. It just doesn't seem like the math and logic case at all.

In math and logic, there is a lot of synthetic knowledge compared to the axioms (stipulations). Why can't we repeat that in other domains of fictionalism?

• You are on to the answer with your consideration about games. Suppose there was a Form of Games (AKA the "Intendo" of theories of intentional/practical reasoning), which can take any game (including itself) for an input, and output some or another game in turn. (There is a fantasy series, the Second Apocalypse books, with a game like this.) And consider, then, the difference between the choice and determinacy axioms, where the latter is defined game-theoretically. Another way to consider this is second-order fictionalism, or fictions about other fictions (or even about themselves). Commented Jul 8, 2023 at 2:51
• @KristianBerry I think you've found a good example with those two axioms, but they are mostly math leaning even in a game theory setting I dare say. (Here's a link I found to get get loosely acquainted with the AD blogs.cornell.edu/info2040/2018/11/12/…). I was hoping to find cases without such explicit use of math, but maybe you've shown math is kind of unique in fictionalism, and anything else has an authorship problem when going beyond the stipulations. If that's the case so be it, I couldn't come up with non-math cases Commented Jul 8, 2023 at 3:16
• I suppose for narrative fictions, synthetically rich franchises will have to be bulky and with good safeguards for consistency/continuity in place. Tolkien's legendarium comes to mind, but a vastly stronger case would be Brandon Sanderson's Cosmere stories. Modal fictionalists can help themselves to the diversity of possible/impossible-worlds talk, moral fictionalists can trace the consequences of utility functions or categorical imperatives. Aquinas could be taken as an unwitting example of how far religious fictionalism can tread (as far as angels fear not to tread, then). Commented Jul 8, 2023 at 3:22
• I should note that readers of one subset of Cosmere books deduced an until-then hidden element of local lore, purely by extrapolation from the "premises" Sanderson gave them in the until-then published texts. And the ability to identify the killer in a good mystery tale can be styled derivative in the intended way, maybe. Commented Jul 8, 2023 at 3:25
• @KristianBerry So a full compendium for a single deduction :) I'm not sure I buy "deduction" fully either...if Gandalf betrayed the fellowship, people would just dislike the stories, the knowledge derivable still seems simply up to the author. I dare think an author of fiction always has freedom. The religious example is pretty compelling to me (I don't know much about the other examples). I still don't get how we can set out to do fictional work and create such a factory for knowledge where everyone can get the same synthetic answers independently, unless its math in fictionalism. Commented Jul 8, 2023 at 3:52

The appearance of robust and expansive mathematical knowledge with fictionalist undertones might be symptomatic of the average mathematician's temperament: as a historical community, they are less minded towards competition, in part because getting oneself into the spirit of analyzing the outputs of bizarre (or at least esoteric) functions and sequences of functions means putting other people out of mind enough to where amour-propre is not triggered so much as in the often toxic fandoms of narrative fiction.

Still, rancor occurs: Kroenecker's vitriol vs. Cantor, Cantor's vitriol vs. the whole notion of infinitesimals, Brouwer's vitriol towards classical logic. One mathematician decades back expressed some dread regarding appeals to intuition like so:

A popular view is that axioms are self-evident truths concerning their domain. The difficulty with this view is that there is wide disagreement in the foundations of mathematics as to which statements are self-evident and if we restrict ourselves to the intersection of the statements that all mathematicians would regard as self-evident then the result will be quite limited in reach, perhaps coinciding with Q or slightly more.[4] Markov had a similar complaint with the employment of the related notion of being “intuitively clear”:

I can in no way agree to taking ‘intuitively clear’ as a criterion of truth in mathematics, for this criterion would mean the complete triumph of subjectivism and would lead to a break with the understanding of science as a form of social activity. (Markov (1962))

And Lawvere echoed such sentiments years later in his own way:

In ‘Diagonal arguments and Cartesian closed categories’ (Lawvere 69) we demystified the incompleteness theorem of Gödel and the truth-definition theory of Tarski by showing that both are consequences of some very simple algebra in the Cartesian-closed setting. It was always hard for many to comprehend how Cantor’s mathematical theorem could be re-christened as a “paradox” by Russell and how Gödel’s theorem could be so often declared to be the most significant result of the 20th century. There was always the suspicion among scientists that such extra-mathematical publicity movements concealed an agenda for re-establishing belief as a substitute for science. Now, one hundred years after Gödel’s birth, the organized attempts to harness his great mathematical work to such an agenda have become explicit.

But so another thing about all this, about mathematics overall, is how relatively trivial or ethereal much of the "knowledge" we have therein turns out to be. Fiddling with obscure and subtle parameters usually results in only obscure and subtle variations (many functions do not as such "compound" their outputs, so to speak). It is often easy enough to accept insubstantial "facts" without too much ado, especially if the facts are internally conditional/hypothetical in form ("If there is a proper class of measurables, then Setop doesn't have a small dense subcategory," can be innocuously admitted even by someone otherwise allergic to the higher infinite or even transfinite numbers generally, say).

On the flip side are those genres of narrative fiction where commitments to "verisimilitude," "realism," or at least detail are a mainstay of successful contributors. Fictionalism about various scientific terms intersects fictionalism about the objects of science fiction, but we still find consensus and the appearance of knowledge in science and so we have the distinction between soft and hard science fiction proper. Fantasy worlds that obey "Magic A is Magic A" also leave room for readers to "figure out" how certain themes will ultimately be fulfilled (in the Wheel of Time series, for example, it was possible to pay close attention to the oracles of a side character and yet then deduce a major component of the central protagonist's victory over the final enemy). Before I ever set foot on the PhilosophySE, I actually became acquainted with the SE format via a subsection of the 17th Shard, an analysis site devoted to the works of Brandon Sanderson, which testifies to the "factoid-based" nature of those works. Sanderson himself explains how his "science fantasy" operates:

For a while now, I’ve been working on various theories regarding magic systems. There’s a lot to consider here. As a writer, I want a system that is fun to write. As a reader, I want something that is something fun to read. As a storyteller, I want a setting element that is narratively sound and which offers room for mystery and discovery. A good magic system should both visually appealing and should work to enhance the mood of a story. It should facilitate the narrative, and provide a source of conflict.

For example, in many fantasy stories, the protagonist has a crucially powerful implement at hand, but either shouldn't or can't use it very often, if ever. The magic doesn't so much as solve problems as it is the problem. Then, depending on the skill of the storyteller, describing how the characters actually solve those problems either comes across as meaningful/"realistic" (at least psychologically) or as, of course worse, quite contrived. Whether, "X is a good/optimal solution to narrative problem A," counts as fictionalistic knowledge, I'm not keen to say; there are apparently undecided, or undecidable, questions that can be posed relative to various stories, like, "How many times did Frodo smile over his lifetime?" even if there are also questions that are decided explicitly in the given text or which could be decided by inference from what the direct author or authoritative readership interpreted their own texts as implicitly saying. (But then how much of such a difference in decidability is there between, "How many inaccessible cardinals are there?" and, "How many hairs were there on Galadriel's head?")

One domain of discourse that seems to involve precise fictions with relatively stable, if internal, implications is the law. There is the phrase/concept of "legal fictions," for example, yet notwithstanding the pseudo-reality of entities like corporations or imputable guilt, theories about what some or another law is seem able to "knowledgeably" proceed on those entities' basis. At least, lawyers, judge, etc. often spend years upon years learning about precedents and other factor that inform their legal strategies and conclusions; whether their "knowledge" as such is on a par with the ocean of mathematics seems doubtful to me, but I haven't studied legal reasoning very much (or exercised it much myself), so I would hesitate before claiming that lawyers and judges "don't know" what laws are or mean (if I claimed that, it would be modulo a claim that there aren't enough "real" laws to know about in the required way).

• Your rich examples made me think of Asimov’s three laws of robotics too, so maybe there’s hope for narrative knowledge that isn’t just “how many hairs did Galadriel have”. But do the three laws or Sanderson’s magic rules entail anything the way math does? I remember wondering if some of the robot’s actions really were in violation or not, and the next synthetic bit of knowledge is not nearly as automatic as in math. Commented Jul 8, 2023 at 5:52
• undecidability is possible in math and narratives yes, but the point is there is a wealth of decidable knowledge to learn from even 5-10 axioms and postulates. Even the three laws of robotics - it’s not like I can objectively derive “did the robot harm her” unless Asimov wrote it so. I could always wonder if the robot was hacked or the laws were supervened by a newly introduced deity’s power. I’m only certain about the words written. Commented Jul 8, 2023 at 6:06
• Well, most stories are "about" particular events, so it would be hard to write them all out as deduction from first principles. Perhaps an alternative solution would be via some kind of well-patterned asemic writing, although whether the patterns would, at the end of the day, be one and all themselves mathematical, I'm not sure. There could be a boundary between fictionalist/pluralist math, and "hard" math, too (Koellner discusses this option in one of the SEP articles he contributed). Commented Jul 8, 2023 at 6:30
• in math we can say if you accept X axioms, you equally accept all synthetic/derived theorems from them. In any other fiction I can accept whatever, and I’ll be sitting there till the end of time not knowing what else I equally accepted. That’s where I’m at, I’ll have to approach this with fresh eyes later. Thank you for your help Commented Jul 8, 2023 at 6:55