If it is stipulated that Frodo walked into Mordor, then it is stipulated that something walked into Mordor; I'll grant that logic.

Sure. What is stipulated is the Domain of discourse - the various individuals and predicates used in the fictional world.

It occurs to me that there are fictional creations in which such inferences do not hold. Hence, Nonsense as a genre.

It occurs to me that there are fictional creations in which such inferences do not hold. Hence, Nonsense as a genre. — Banno

Do you mean literature in which inconsistencies and contradictions abound. I'm trying to think of an example. Twain attributes some inconsistency to Fennimore Cooper's Deerslayer in the linked article. I read Deerslayer a few years ago and enjoyed it. Is poetic licence justification for inconsistency in literature?

I was more in mind of Lewis Carrol. Doesn't The Hunting of the Snark count as fiction? What I say three times is true, hence a new logic is born. Could the Bellman formalise this new system? If I say it four times and unsay it once, is it true or false?

I haven't read Lewis Carrol since I was a kid. I have read that he was also a logician.

According to that logic,

If you say three times that if you say something three times, then unsay it once it is false, then it is false.
If you say three times that if you say something three times, then unsay it once it is true, then it is true.

I guess...

Who did the original three-saying?

"Just the place for a Snark!" the Bellman cried,
As he landed his crew with care;
Supporting each man on the top of the tide
By a finger entwined in his hair.

"Just the place for a Snark! I have said it twice:
That alone should encourage the crew.
Just the place for a Snark! I have said it thrice:
What I tell you three times is true. — Lewis Carroll

To which we might add:

The method employed I would gladly explain,
While I have it so clear in my head,
If I had but the time and you had but the brain—
But much yet remains to be said.

What I tell you three times is true. — Lewis Carroll

Does the thrice-telling make it true, or does the Bellman tell it three times because it is true? Perhaps this is the much that yet remains to be said.

Does the thrice-telling make it true, or does the Bellman tell it three times because it is true? — Janus

Ah, and excellent point; and one that I think returns us to the incompleteness of fictional characters mentioned above and noted in the SEP article.

Given that the Bellman says other things, some of them undoubtedly true, yet this is the only one that he says three times. Hence that the Bellman says it three times is not, it seems , a necessary condition for truth. While not decisive, this perhaps mitigates against the theory that thrice-telling causes truth, and that rather thrice-telling implies truth.

This is further supported by the pivotal place of trust amongst the crew.

Right, so the incompleteness of fictional characters means that we can only infer about them what follows from what is told, and much may remain untold? Now you've gone and made me want to read the book.

we can only infer about them what follows from what is told — Janus

Perhaps; or is it that we can make such inferences as we see fit, and suit our purposes? Do we move to a paraconsistent logic, in which only statements made within the text or inferred therefrom are true, and all other statements neither true nor false?

Which raises the intriguing notion of a free, paraconsistent logic.

Do we move to a paraconsistent logic, in which statements made within the text or inferred therefrom are true, and all other statements neither true nor false? — Banno

Sounds like a good option.

Which raises the intriguing notion of a free, paraconsistent logic. — Banno

Maybe that's the salient difference between the logic of fiction and logic of fact. We say that propositions concerning what we don't know about the world, even what we cannot know about the world, must be true or false, even if we can never know it.

In the case of fiction, it would seem that propositions about what has not been told must be neither true nor false. Even if a later telling were to make them true or false, this would then be a "world" which has been altered or augmented; a "world" which was not prior to the later telling.

Imagine if there was a God (an author) and our world was like that...

it would seem that propositions about what has not been told must be neither true nor false. — Janus

But then what of spoilers - story facts kept till last? Are they neither true nor false until presented in the narrative?

@Snakes Alive

If you would,

E!t is true if t is an element in the domain, and otherwise false. — Banno

Is this correct? Or have I misunderstood?

Free logic would, in my humble opinion, open up the world of fiction - Tolkein's works, Doyle's works, etc. - to logical analysis.
— TheMadFool

You seem to think this would be problematic. Why shouldn't fiction be logical?

Holmes lived at 221b Baker Street. Why shouldn't we consider this to be true, within the context of the writings of Doyle and their derivatives? Is there an argument against this? — Banno

No, no. I have a recollection of wanting to make an argument about a fictional character about 6 months ago but I couldn't figure out how because of the vexing matter of existential import. I wanted an argument that has a nonexistent entity in it but it was impossible without also saying that the nonexistent exists.

It appears, prima facie, that the difficulty lies with the implied existence of $\exists x$. If I'm correct, free logic should have existence as a predicate. We might also need to look at the ontological aspects of categorical/sentential/predicate logic.

To be sure, it's the problems of free logic that are fun. — Banno

Excelente!

But then what of spoilers - story facts kept till last? Are they neither true nor false until presented in the narrative? — Banno

It seems story facts can't be true or false until irrevocably committed to print, because otherwise the author might change her mind. They could be true or false in the context of a draft or even the author's imagination, if nothing is written down, as long as she doesn't change her mind.

Yeah, that's right. On a classical logic, it will be true just in case t (that is, whatever object 't' denotes) is in the domain. On a free logic, it will be true just in case t is in the 'inner domain,' or domain of existents.

On a classical logic, E!t should be trivially true in any model, because every model has to assign to each individual constant a member of the domain. So just in virtue of naming t, you're committed to it existing in this sense. Everything exists.

On a free logic, E!t is not trivially true – it can be true on some models, and false on others, depending on whether t is in the domain of existent things. Some things don't exist (according to some models).

Cheers. In working through the stuff on negative semantics I lost track and wondered if I had this wrong.

@Srap Tasmaner

I'm interested in your answer to a question asked previously. You claimed

sentences found in fiction are literally false — Srap Tasmaner

In the SEP article the following example of a logical deduction is given: within the context of LOTR, Gollum hates the sun, and we can validly infer that something hates the sun.

You have claimed that "Gollum hates the sun" is false. Hence for you presumably the inference is invalid. Is that so?

I guess if I really wanted to do this, I'd assume fiction is a type of counterfactual, so you get your extensional semantics via possible worlds. Your nonsense category will show up as impossible worlds, I guess. That doesn't solve crossover problems directly. Doesn't Kripke write about this somewhere? How there can't turn out to be a "real" Sherlock Holmes, for instance.

Also as mentioned previously, that something exists cannot be the conclusion of an argument in free logic. Free Logic does not permit the expression of existence conditions.

So here we have the best attempt to formalise existence as a predicate for individuals. And it cannot be used to infer that some particular individual exists.

In particular, the logic shows that such arguments rely on question-begging.

Of the arguments of this type, two are of particular interest:

• Any necessary being exists (argument for God)
• I think therefore I am (Descartes)

Hence, another change of title for this thread.

Well, Kripke's semantics are usually a free logic. I doubt you have Lewis' counterfactuals in mind - he would have us think that Holmes actually exists in some possible world. Kripke would presumably say that the causal chain that leads form "Holmes" to it's referent leads to a fictional character, and hence cannot refer to a real character in another possible world.

But I take it you agree that the inference that in LOTR there is something that hates the sun is valid? That fictional sentences may be true within the fiction?

That fictional sentences may be true within the fiction? — Banno

Maybe? It's just hard to be sure what we mean by this.

Broadly, I'm not opposed to some kind of analysis that distinguishes internal and external frames of reference, however you do that, but it's not perfectly obvious how to do that formally.

What's more, people freely cross that boundary: "But in Chapter 3, Harry said ..." That sort of thing makes me suspect the "internal" frame of reference might actually just be shorthand for the external, just a condensed manner of speaking.

But I'm not wild about that approach either. For one thing, whatever analysis we arrive at for fictional objects ought to be able to support the fact that people care about fictional objects very nearly as if they were real. (At least as far as psychology is concerned, that suggests we're using some of the same machinery for understanding fictional worlds, and their furniture, that we use to understand the real one.)

Absolutely we expect fiction to be largely logical, except when it deliberately isn't. (William Burroughs, say.) That's a chunk of Mark Twain's critique of Cooper.

you can define it in a regular old first-order predicate logic, which is pretty much what you did above.

So we say, as a postulate governing its interpretation, that E!x iff ∃y[y=x]. — Snakes Alive

But then, this isn't very first-order, is it? More as though,

Quantifiers are (nothing but) predicates of formulae. — Snakes Alive

You're using predicates to refer to predicates (and other formulae including individual constants why not), instead of using them to refer to (only) individuals.

Which potentially is a problem if it isn't clear, and encourages equivocation between the x and the "x", the individual and the individual constant (use and mention, as ever), resulting in the obvious multiplicity of empty constants being used to excuse obvious baloney such as

the domain of non-existents. — Snakes Alive

Broadly, I'm not opposed to some kind of analysis that distinguishes internal and external frames of reference, however you do that, but it's not perfectly obvious how to do that formally. — Srap Tasmaner

An odd response, since free logic is exactly "how to do that formally". It also allows talk of both existent and nonexistent individuals within the same conversation.

But more over, if you are to care about the characters, you might begin by talking about them. That's what free logic permits.

As with all formal systems it provides a way of understanding the grammar of such conversations, of how it is that we can say things such as "Gollum is more famous than Gödel" without such claims being simply false.

But of course it's application is far broader than that.

My apologies, I'm not sure what to make of this.

So Epistemic Logic is the various logics that include predicates for belief and knowledge - yes? Where's that fit here?

But it's not true, nor even helpful, to think of fictional worlds as only existing in the mind of the author. Were this true, both Holmes and Frodo would have ceased to exist along with the minds of their respective authors. — Banno

Obviously, only Tolkien knew about Frodo before he wrote LOTR, no?

I don't see the point in NOT invoking epistemic logic into the discussion when thinking about works of fictions originally, (at least), existing in the mind of the author, and then his book or script after he or she decides to commence it into fiction for other people.

In {Eggs, Bacon}

~E!(Paris)

Paris doesn't exist in any sense?

Nice.

Paris doesn't exist in {eggs, Bacon}. Hence we might introduce the predicate "...is meat", the member of which is bacon; and conclude that Paris is not a meat; and "..."is breakfast", the members of which are both eggs and bacon, and conclude that Paris is not a breakfast.

We need a broader context in order to do more with Paris.

Sure. SO show us how to go about it. The point here is that free logic provides a suitable framework, and to explore how that framework might be used.

The difficulty I see with epistemic logic is that belief is a relation between a statement and an individual. But it's not just Tolkien who believes Frodo walked into Mordor. Hence my argument that statements about Frodo continue despite the demise of the author.

Paris doesn't exist in {eggs, Bacon}. Hence we might introduce the predicate "...is meat", the member of which is bacon; and conclude that Paris is not a meat; and "..."is breakfast", the members of which are both eggs and bacon, and conclude that Paris is not a breakfast. — Banno

I agree. The second there is a purpose or context which influences the truth conditions of E!, it should not be interpreted outside of it. E!, in what domain? Purpose or context choose the domain - therefore purpose and context choose what exists?