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Are Sentences in Fiction True/False?

Updated on January 12, 2015

Fictional Characters


Sentences in Fiction

Let us lay out some technical terminology we need to use. Let's take a grammatically correct sentence, or at least an intelligible sentence, of a language like English to be conveying or expressing a meaning: call this meaning the "proposition" expressed by the sentence. Many different sentences can express the same proposition. There can be grammatically correct English sentences that express no proposition - they are meaningless or nonsensical. Check out Lewis Carroll's famous nonsensical sentences from Alice in Wonderland or some of his other works. Whether a sentence expresses a proposition (has a meaning) or not is not a matter of psychological conviction: a user of the language may well take a nonsensical sentence to be meaningful; this does not make the sentence meaningful even to him: whether a sentence expresses a proposition or not is an objective matter. The competent user of the language is the judge and this "competent user" is an idealization but this only shows that languages, like games, have a normative or prescriptive and rule-based constitution to them. For example, the competent player or follower of baseball knows that the rule about 3 strikes is the right rule; nothing changes even if a local majority of people insist that it is otherwise. It is not correct - so, it is not correct even for them, although they don't realize it - that the rule about strike-outs is exactly three. "Correct" has a normative force that orders. It is absurd to say, as many people are heard saying today, that the wrong view is "true for the person who is mistaken." In some sense this is trivial: sure, the mistaken person is mistaken precisely because he or she takes a false statement for being true. But "true" is itself a prescriptive term: it order or compels. So, in the deeper sense of true, "the rule is true for her, even though it is not true" is itself a nonsensical sentence expressing a contradiction: "even though true, the rule can be not true."

We could take a theoretical view that truth is actually dependent on personal opinion. Most apparent proponents of this view, repeating a slogan, have not thought this position through. This is the view attributed to Protagoras of classical antiquity. A sophisticated exposition of this theory is possible - and, as we know form Aristotle's considerable labor in rebutting the view - the Protagoreans understood the implications of their position. One important consequence of this theory is that we have to abandon the logical law of non-contradiction: if two people contradict each other, while both expressing their opinions, they both have to be correct on the Protagorean view.

Let us now take the kind of sentence that has subject and predicate. Not every sentence of the language has this form but there is something fundamental about this structure of sentences that allows for developing the logic known as Predicate Logic, In modern logic, relations are themselves handled as many-places predicates. For instance "a is between b and c" is to be considered as relating three terms (named by "a", "b" and "c") as arguments of a three-place predicate, "between." If we symbolize this predicate by "B", we can symbolize the above sentence as "B(a, b, c)." This clever idea is due to Gottlob Frege; it had eluded Aristotle in antiquity.

The grammar of predicate logic as a formal language instructs us to put together predicate letters, like "F," with variables, which can be symbolized by "x." "Fx" means "the item referred to by x has the attribute F." Except that "x" does not refer to anything in particular as it is a variable. Thus, "Fx" is not a sentence; it is called a propositional function or open sentence. It does not have a truth-value. One method, due to Tarski, uses variable terms like x in constructing models (by using what a special way of assigning valuations) but this is an advanced topic. Truth-values are {True, False}, which we can write as {T, F}. Now, if the variable falls under the scope of a quantifier phrase like "all" or "some", we have a sentence that expresses a proposition and has a truth-value. The two classical quantifiers are "all" and "some." "Some" means "at least one" or "not no one," It does not mean "a few." Non-classical quantifiers can be easily defined. With names, like {a, b, c, ...}, there is no problem: placed next to predicate letters, for example as in "Fa," we have sentences that express propositions. "Fa" means "the item named or labeled by a has the attribute F." Variables and individual names or labels are known as TERMS. So, TERMS = {a, b, c, ...} or {x, y, z, ...}

An old, and intriguing, problem we face has to do with existence. This, obviously, plays a prominent role in the discussion of the logic of propositions in fictional settings. If we are told that "Fa", we may want to infer from this that there is an object referred to by "a" and this object has the property F or Fs'. This, however, creates a problem. A famous sentence in the history of logic is "the present King of France is bald." To express the proposition of this sentence we can treat the expression "the present kind of France" as a term (like a name)/ This is not the option chosen by Bertrand Russell, one of the founders of the standard modern logic (although there are alternative systems, of course.) As a term, this expression would not be referring: a natural choice, perhaps, is to withhold truth value from the proposition: this may mean either that the proposition is not true or false or that it actually a third, non-classical truth-value which is "neither true nor false." The standard formal systems are strictly bivalent - they admit exactly the two truth values True and False.

Russell regimented the sentence - which means that he translated it properly by using the formal symbolic language he had constructed. This corrects the apparent grammar of the sentence. While most people may well be misled by the apparent grammar, the logical grammar can prove elusive as it can be at variance what the surface grammar suggests. The example we are considering here is a famous case of this. Although most students of logic today think that Russell made the wrong choice, it goes without saying that the logical grammar of propositions is not always apparent in following the apparent grammar.

To render the proposition expressed by the sentence "the present king of France is bald" have to be able to express uniqueness (THE present King of France we are talking about) and then to attribute to the entity denoted by this phrase the property of being bald. Of course, there is no such entity; no one can be referred to by the phrase "the present King of France," The philosopher and mathematician Bertrand Russell came up with a clever way of circumventing an apparent difficulty. What item in the domain of entities in the current world are we to name by "k" if "k" is the name of "the present King of France?" Russell decided that "the present king of France," which is a definite description is NOT a name, as we already mentioned. Surveyed, most thoughtful users of the language would probably disagree with this. This seems counter-intuitive from the standpoint of linguistic usage and is not a popular solution anymore. Russell treated the phrase "the present King of France" by means of what we called above "regimentation." He paraphrased it, to capture the proper logical form as he thought, by: "there is such an entity in the relevant domain, which is unique, and which is bald." We don't need to go into details as to how uniqueness is to be expressed. (At any rate, if you are curious: identity is needed in the formal language and then uniqueness of the item possessing property F is rendered as: there is an x such that, for all y that F, the referent of y = the referent of x, and x Fs. There is another, logically equivalent, way: for all x there is a y, such that y Fs if and only if the referent of x = the referent of y.)

Notice that the regimentation Russell imposes makes the propositional content a conjunction: there is a unique x, and this x Fs. Conjunctions can be true if and only if both of their conjuncts are true. Since it is not true that there is such an entity as the current king of France in the relevant domain, the whole statement above becomes false. Russell struggled for years over a glitch that results from this. The statement "the present king of France is NOT bald" would also have to be false, given the regimentation; but this statement seems to negate the one about the king being bald and, to that extent, should be accounted true as the negation of the false. Actually, there is scope ambiguity in this last sentence: the scope of negation can be the whole earlier sentence or only the part about the baldness-attribute of the referent (the king.) This is what Russell capitalized on to overcome this conundrum but this is something that has no bearing on our present discussion because it seems that the Russellian solution does not work at all in the case of statements in fictive contexts.

Russell's solution leaves us in the lurch when it comes to mythical, fictional, and other non-existent characters. All the statements in fiction would be false - at least those that are about fictional characters, because there may be references to non-fictional characters in fiction-- although, again, there may be such references which, although to actual characters, are themselves constructed fictively. Indeed, statements about non-fictional characters who are mentioned in fiction might not be true either: when Jesus is sentenced to death by the Pope in Dostoevsky's Karazamov Brothers, this is a reference whose possibly both referents are not fictional (Dostoevsky might have some specific Pope in mind) but the evaluation of the narrative is clearly independent of bringing up domains of entities from historical contexts.

Perhaps we could just give special fictive domains even when such domains are not at all, and can never be or have been, actual. This is not a problem at all but a problem arises when this solution is implemented. To go back to the preceding example, Russell's regimentation leaves us with referents for "Jesus" and "the Pope" which are not in the domain of actual things in the world; as characters in the novel, these two entities are not actual even given that both Jesus and some Pope the author may have had in mind have been actual historical figures. Or should we stagger the domain? Perhaps the referent of Jesus intended by the author is the historical Jesus but the referent of the Pope name is not intended as a historically focused denotation. We are already beyond standard predicate logic insofar as we have quantifiers ("all" and "some") ranging over more than one model-domain.

If we regiment a statement like "Pope sentences Jesus to be crucified" in the Russellian manner, we opt for it being false. Something seems amiss here. If we played a game with winners and losers, the right answer would be "it is true that the Pope sentences Jesus to death in Dostoevsky's novel"; also, another right answer would be "it is false that the Czar sentences Jesus to death in Dostoevsky's novel." Yet, on Russellian regimentation the two are not distinguished. They both come out false. Or, if we tweak the domain so that we include Jesus, Pope and the Czar, we then make true the proposition "the Pope who sentenced Jesus to death and the Czar who didn't were contemporaneous" - but this something we don't want!

An alternative is to take such statements as being neither true nor false. Here we have an other problem. "Odysseus was the King of Ithaca" would be value-less - exactly like "Odysseus was the President of the United States." Yet, in a context of discussing or participating in a contest, for instance, you would surely expect that you are making a correct assertion if you lay down the first sentence and a false assertion if you lay down the second! This problem also rebounds against the Russellian solution, of course - for which, solution, both sentences are not value-less but false!

It has been suggested that sentences in fiction and other creative enterprises are not making truth-valued statements anyway; they play a different role, having rather to do with eliciting certain emotive reactions. Is this a satisfactory response? Rather not. See if you can think why not.

But, then, what is to be done? How are non-referring terms, which we have in fiction, to be treated? How are non-fictional sentences with non-referring terms to be treated? I hope that all this whets your appetite for the study of Logic. Classical Logic, though, which you get in the introductory textbooks, will only get you as far as Russell's solution to the problem, which, as we saw, is unsatisfactory. On the other hand, non-classical logics are themselves either extensions of the classical one or alternatives whose construction you can follow easily after you have studied the fundamentals. The earliest known puzzles that adumbrated use of a non-standard logic appear in the texts of Aristotle.

Aristotle pondered the problem of what is known as future contingents. Can what I say today when I make predictions about the future be true/false - can it have a truth-value? We saw how names may have no referents ("Odysseus" in the epic does not refer to an actual entity). Present statements about putative future events have no truth-makers: whatever makes them true, or fails so to make them, is not available. How can they be true/false when they are uttered, before the fact? Aristotle was puzzled because such statements are actually meaningful and, as such, they ought to have truth-value. Aristotle thought of treating such statements as value-less. Now, this is ambiguous. It can mean that these statements have no truth-value or that they have a truth-value but this truth-value is a third one (not true and not false but a third truth-value which, in this case, can be interpreted as "indeterminate.") Aristotle goes on to compute with valuelessness, which means that he treats it as a third value. See these examples to understand what we mean by computation: "if it is true that it is Monday today, and it is true that it is raining today, then it computes as true that both it is Monday today and it is raining today," We can write out this computation as T&T=T. "And" as a function yields true when it takes as arguments true and true, We can write it out as follows: &(T, T) = T. Can you tell what we mean by &(T, F) = F? I hope you get the point.

Aristotle's indeterminate value, call it "I", computes with negation like this: -I = I. Now, you can see easily that -T = F and -F = T. The negation of true is false and the negation of false is true. But the indeterminate is a "fixed point": its negation is also indeterminate. Now see what is going to happen, and this freaked out Aristotle.

We take contradictions to be always false. A contradiction has the logical form or pattern, "p & - p". For T and F, this works. Try all the combinations. But for the third value, I, it doesn't. We get, instead, I & - I = I & I = I. The negation of indeterminate is indeterminate. The conjunction we want to treat as the minimum of the two conjuncts with the ordering relation, from greater to lesser, being: T > I > F. So, the minimum of I and I is I! This means that I & I = I. As we saw, I & - I also yields I. So, we can have a truth-value for "p" such that "p & - p" is not false! This outraged Aristotle because, as we know from other of his lectures, he was convinced that all contradictions are false. This is called the law of non-contradiction. Aristotle thought that if this law is not obviously a law of logic, then what other logical law could be obvious?? Aristotle ended up wanting both to have his cake and to eat it too: he wanted statements about future events to be I but he also wanted all contradictions to be F. He can't have it both ways! Even Aristotle can be embarrassed sometimes.

Similar issues arise with the treatment of fictional sentences, if we take the view that such sentences do indeed express propositions with truth-values. Notice that I, above, is itself a truth-value. Earlier, we saw also an issue about reference and non-reference of names in predicate logic. What can be done with non-referring terms?

© 2014 Odysseus Makridis


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