Philosophy of Language » Lecture 6
We’ve mentioned entailment before, but it’s time to get precise about it.
Entailment is a relation among propositions:
One sentence \(S\) can be said (derivatively) to entail another sentence \(S'\) just in case the intension of \(S\) (set of possible situations in which it’s true) \(⟦S⟧\) is included in the intension of \(S'\), i.e., \(⟦S⟧ \subseteq ⟦S'⟧\).
Consider Esmeralda is a ewe and Esmeralda is a sheep. Since it is necessarily true that all ewes are sheep, the intension \(⟦\)Esmeralda is a ewe\(⟧\) is included in the intension \(⟦\)Esmeralda is a sheep\(⟧\). So the proposition that Esmerelda is a ewe entails that proposition that Esmerelda is a sheep. Hence there is an entailment from the first sentence to the second.
Consider
Suppose I disagree; I say No, he hasn’t.
Something interesting: both (1) and my denial of it appear to entail that John drank.
That is: John has stopped drinking can’t be true unless John drank is true; but nor can it be false unless John drank is true.
This phenomenon, of a proposition that seems to require the truth of another proposition, regardless of whether the first proposition is true or false, is called presupposition (Birner 2013: 146–57).
In (1) the presupposition that John drank seems to be triggered by presence of the aspectual/change-of-state verb stop.
Lots of other words trigger presuppositions: (Birner 2013: 152–55; Beaver, Geurts, and Denlinger 2024: §1)
Lizzie knows that ducks lay eggs. (Factive verb: presupposes that ducks lay eggs.)
It was Sylvester who left the tap running. (Cleft: presupposes that someone left the tap running.)
Jonquil is crying again. (Iterative: presupposes that Jonquil cried before.)
Antony spoke rapidly. (Manner adverb: presupposes that Antony spoke.)
Actually all those examples presupposed something else: that the names involved referred, and that there are such people as Lizzie, etc.
If anything is asserted there is always an obvious presupposition that the simple or compound proper names used have a reference. If one therefore asserts ‘Kepler died in misery’, there is a presupposition that the name ‘Kepler’ designates something. (Frege 1892: 34)
For Frege, a presupposition is something like an assumption that must be made:
presuppositions concern either the way in which utterances signal assumptions, or, conversely, the way in which utterances depend on assumptions in order to be meaningful. … Frege’s proposal to model presupposition as definedness of reference provides the standard way of defining a semantic presupposition relation which is independent of the speaker. (Beaver 2001: 8)
If these are the kinds of ways presuppositions can be triggered, how can we identify what is presupposed? Consider one of our examples, and various entailments:
Lizzie knows that ducks lay eggs.
Ducks lay eggs. (Entailed by 6)
Lizzie knows something about ducks. (Entailed by 6)
The presupposition (7) is amongst the entailments of (6).
But (8) is also entailed by (6), and is not a presupposition of (6); rather, that is something we can conclude from (6).
What distinguishes (7) from (8)?
The proposal: presuppositions are those entailments of a proposition that remain entailed by embedding the proposition under various operators:
Lizzie doesn’t know that ducks lay eggs.
Does Lizzie know that ducks lay eggs?
Maybe Lizzie knows that ducks lay eggs.
While these all entail (7), they do not entail (8).
We say that while presuppositions project from the original sentence to the various complex sentences in which it is embedded, regular entailments do not project in that way.
Indeed we began by observing that presupposition projects under negation: that John hasn’t stopped drinking entails that John drank, as does that John has stopped drinking.
This is the negation test for presupposition:
The presupposition is constant under negation, whereas the entailment disappears under negation – which means that constancy under negation can distinguish between entailments and presuppositions. (Birner 2013: 150)
Some might elevate this to an analysis, since presupposition under negation is so robust:
Consider Frege’s example, Kepler died in misery, and its negation, Kepler didn’t die in misery.
According to Strawson presupposition, these claims both presuppose that there was someone named Kepler – a presupposition which is obviously not necessary.
We could conclude that the theory of unstructured propositions is incorrect; but the puzzle will recur if we have any theory of propositions – unstructured or otherwise – which endorses this thesis:
How could this thesis be rejected?
a semantic view of presupposition … would seem to require that we abandon the concept of a two-valued logical system … and accept … a system with at least one intermediate value of ‘neither true nor false’. (Birner 2013: 149)
The proposal seems to be that some meaningful sentences can fail to have a truth value (either true or false) when their presuppositions are not met.
This prompts us to query the bivalent equivalence between ‘\(P\) is false’ and ‘\(P\) is not true’ – given truth-value gaps, this equivalence fails.
This gives rise to an explicitly non-classical definition of presupposition:
| \(P\) | \(∼P\) (Kleene 1952) | \(¬P\) (Bochvar 1937: 93) | \(!P\) (Bochvar 1937: 91) |
|---|---|---|---|
| True | False | False | False |
| Neither | Neither | True | False |
| False | True | True | True |
Consider the following examples
Observe that (14) entails (13), but not vice versa.
The gappy approach can handle this fact – let not in (13) be ‘\(¬\)’ (i.e., 13 means it isn’t the case that the man is happy), while un- in (14) means ‘\(∼\)’.
But quite apart from having to reject the plausible thesis of bivalence, this hypothesis about un- seems quite implausible – since ‘\(∼\)’ operates at the level of the proposition, not the predicate.
If we take it at face value, un- is an operator that takes a predicate to its ‘opposite’ – in the case of unhappy, the property of not merely lacking happiness but positively possessing traits contributing to sadness.
Almost all cases of natural negation occur, not sentence initially, but attached to the main verb phrase – as Katz (1977: 238) put it, in English ‘negative elements do not behave like the connectives ‘and’ and ‘or’ but like adverbs’ (cf. Horn and Wansing 2022: §1.1).
There will thus tend to be a potential ambiguity of attachment, seen in this schematic contrast:
This attachment ambiguity allows us to draw a distinction between lacking a property and having its ‘opposite’ property, without needing any failures of bivalence.
This might give us some handle on some cases of presupposition.
Consider factives like (6) (Lizzie knows that ducks lay eggs). There is a natural opposite state to knowledge – not merely failing to know, but not-knowing, i.e., being ignorant:
Clearly (6) and (17) both entail ducks lay eggs: one cannot be ignorant of something untrue. (Though of course one must fail to know it!)
This will explain some of our presupposition data, if we make the assumption that, sometimes, people understand doesn’t know as meaning is ignorant of – i.e., so that (9) can be used to express (17).
This assumption will need to be generalised, i.e., in many cases, \(a\) is not-\(F\) will need to be taken to express \(a\) is \(G\), where \(G\) is the ‘opposite’ property.
This proposal might help with factives (e.g., both remember \(P\) and forget \(P\) entail \(P\)) and with aspect verbs (e.g., both stop \(\phi\)-ing and continue \(\phi\)-ing entail that there is \(\phi\)-ing going on).
The proposal so far is that we often understand not \(F\) as denoting an ‘opposite’ predicate, even though – strictly speaking – not is a complementing negation.
An alternative approach would be to understand natural language not as (almost) never a complementing negation; it almost always expresses a presupposition-preserving internal negation (Horn 1985).
All of our example presupposition triggers, it is suggested, have natural negations that involve internal negation:
Lizzie doesn’t know (is ignorant) that ducks lay eggs.
It was not Sylvester [i.e., it was someone other than Sylvester] who left the tap running.
Antony spoke not-rapidly.
If this is right, the puzzle doesn’t arise: the negation involved in the definition of semantic presupposition isn’t complementing.
A challenge for this view is to predict in a systematic and principled way how this internal negation would work – note it makes no clear prediction about the negation of (4), Jonquil isn’t crying again.
A closely related puzzle for entailment-based accounts of presupposition comes from cases like these:
John hasn’t stopped drinking; in fact he never started!
Antony didn’t speak rapidly; in fact, he didn’t speak at all.
In these cases we conjoin a negated sentence with the denial of its presupposition. The problem: the presupposition is supposed to be an entailment of the negation too, so this should be a flat out contradiction like
How can we successfully utter claims like (21), which (according to the semantic account of presupposition) should express contradictions?
The examples (21) and (22) are defective without a prior assertion of the sentence which ends up being negated.
This discourse constraint suggests that, while on the surface we are negating the asserted sentence, the addendum (and stress/focus, indicated by underlining) show that we are really targetting the presupposition (Birner 2013: §5.4; Beaver, Geurts, and Denlinger 2024: §3).
Horn (1985) characterizes cases such as [these] as instances of metalinguistic negation, in which, rather than negating the primary assertion (as with garden-variety negation), the speaker uses negation to object to virtually any aspect of the utterance at all, including for example the pronunciation of individual words (I didn’t eat the toMAHto, I ate the toMAYto) or, in this case, the presupposition. For this reason, metalinguistic negation require an appropriate prior utterance…. (Birner 2013: 158)
This metalinguistic negation isn’t a complementing operator (Horn 1985: 132–33):
Note in the last case that the semantic content of what is asserted is equivalent to what is cancelled.
So the explanation of cases like (21) and (22) is that something other than the content is rejected; so their content can be perfectly consistent.
In fact, a presupposition is only cancellable when the sentence with the presupposition is embedded under some operator like negation (Beaver, Geurts, and Denlinger 2024: §3). Witness:
#Lizzie knows ducks lay eggs; in fact they don’t!
#Lizzie knows ducks lay eggs; in fact she doesn’t know anything about ducks!
The attempt to cancel the presupposition in (26) strikes us as just as bad – self-contradictory, in fact – as attempting to cancel a direct entailment in (27). The upshot is depicted in tbl. 2.
| Mere Entailments | Presuppositions | |
|---|---|---|
| Project from embeddings | no | yes |
| Cancellable when embedded | n/a | yes |
| Cancellable when unembedded | no | no |
One idiosyncratic feature of the discussion above was my deliberate avoidance of perhaps the most prominent and widely discussed presupposition trigger: definite descriptions like
This appears to presuppose there is a king of France – that is also entailed by the King of France isn’t bald, so meets our criteria for Strawsonian presupposition.
To deal more satisfactorily with this case, we’ll turn now to the semantics of definite descriptions.
A large literature on this (Neale 1993; Elbourne 2013; Ludlow 2023).
Jonquil is asleep.
The kid is asleep.
These look like they share grammatical form. They begin with (what looks like a) referring expression – a proper name in the case of (29), a definite description in the case of (30) – and predicate something of the thing referred to.
Both entail this:
Since (29) entails (31) via the principle if \(a\) is \(F\) then something is \(F\), it is natural to think that (30) makes use of a parallel principle.
The crucial question regarding whether (29) and (30) are semantically alike has turned out to be this: is (30) like (29) in presupposing that its leading NP refers?
Note both theories hold that the referent of the F, if there is one, is an F – in that way descriptions are held to be very different from Millian proper names. (Though see below.)
The presuppositional theory says that The King of France is a referring expression that is presupposed to have a referent in the simple subject-predicate sentence (32). Accordingly, this follows:
Despite (32) seeming true, it has a false consequence (33), and so must be false.
The evidence – from grammar and from logical role – suggests that definite descriptions are referring expressions. But then (32) must be false, contrary to appearances. Can we explain the evidence adequately without making false predictions?
Russell (Russell 1905: 481–82) offers this analysis of The \(F\) is \(G\):
There is at least one \(F\), and at most one \(F\), and every \(F\) is \(G\). (Neale 1993: 21)
Accordingly, (29) and (30) have quite different formalisations:
\(a\) is asleep.
There exists a unique kid and every kid is asleep.
Formally, (35) looks like this: \(\exists x (Kx \wedge \forall y (Ky \leftrightarrow x =y) \wedge Fx)\).
We may write: [The \(x\): Kid \(x\)] Asleep \(x\).
Note that (35) does entail (31) (There exists someone who is asleep), so we do explain that supposed piece of evidence for the presuppositional theory.
The presuppositional theory says that sentences headed by definites which fail to refer should exhibit the symptoms of presupposition failure – they should be neither true nor false, or should strike us as impossible to evaluate, or something like that.
But consider these examples (similar to some due to Neale (1993)):
Those don’t strike us as hard to evaluate; they are false, not gappy.
But these judgments are sensitive:
We are inclined to find (38) hard to evaluate. The contrast with (37), it is argued, is that (37) conflicts with known fact (e.g., that I clean my bathroom), while (38) does not. The explanation for the judgment of falsehood then isn’t the Russellian truth conditions, but something like a fall back strategy (von Fintel 2004: 295): ‘if we know a sentence cannot be true even if its referring phrases had referred, then we are inclined to think it false’.
There is evidence that favours Russell’s theory over the presuppositional alternative. Consider
This sentence is ambiguous. But if the Prime Minister is a referring expression – just like a proper name – PM, the logical form of the sentence is just Always (PM is Australian), and this is not ambiguous.
On Russell’s view, however, the logical form is more complex, and there is room for ambiguity in whether always takes wide or narrow scope:
Russell’s theory allows the different scope of the always to generate ambiguity in the sentence; since the sentence is ambiguous, that is evidence for Russell’s theory.
Even according to Strawson, not every use of a description is referential.
In (42), the underlined description occurs as a predicate in the sentence, used to predicate something (false) of Washington. Even if there is no greatest French chef, (42) is false.
This is straighforwardly handled on a Russellian account, which gives quantificational truth conditions for all description-involving sentences, roughly:
Things are a bit more complex though; Russell says that all definite descriptions occur in argument position, so he takes (42) to involve the is of identity – not predication!
This makes it challenging for Russellians to handle cases like this, where is must be predicative:
Return to our puzzle case (32).
On Russell’s formalisation, this is ambiguous over the scope of ‘not’ – whether it is internal or external:
This dissolves our puzzle.
Recall (28) (The King of France is bald).
Russell predicts that this is false: it entails the existence of a King of France, and there isn’t one.
But what about:
That seems also to entail the existence of a King of France (the internal negation isn’t bald looks equivalent to is hirsute)
And Russell can explain this too, since (47) has two readings, and does have a (false) narrow scope reading in (48):
For Russell, the existence of a King of France is a presupposition of one reading of (47), but a mere entailment of the other.
A distinction:
A speaker who uses a definite description attributively in an assertion states something about whoever or whatever is the so-and-so. A speaker who uses a definite description referentially in an assertion, on the other hand, uses the description to enable his audience to pick out whom or what he is talking about and states something about that person or thing. (Donnellan 1966: 285, my italics)
Both Strawson and Russell give theories according to which the F is always attributive – it cannot truly apply to a non-F. But is this right?
suppose that Jones has been charged with Smith’s murder and has been placed on trial. Imagine that there is a discussion of Jones’s odd behavior at his trial. We might sum up our impression of his behavior by saying, “Smith’s murderer is insane.” If someone asks to whom we are referring, by using this description, the answer here is “Jones.” This, I shall say, is a referential use of the definite description.…
the same difference in use can be formulated for uses of language other than assertions. Suppose one is at a party and, seeing an interesting-looking person holding a martini glass, one asks, “Who is the man drinking a martini?” If it should turn out that there is only water in the glass, one has nevertheless asked a question about a particular person, a question that it is possible for someone to answer. (Donnellan 1966: 285–86)
It’s also true in both of Donnellan’s cases that the presupposition of the sentence, according to both Russell and truth-value gap theories like Strawson’s (Strawson 1950), fails. Consider
According to Russell and Strawson, this entails/presupposes that there is a man drinking a martini; accordingly, the utterance should be defective – false or gappy.
But, says Donnellan, an utterance of (50) in the right circumstances needn’t be defective at all.
We may perfectly well interpret what a speaker says in uttering (50) as true, and come to believe something true about a particular man in response to an utterance of (50).
The Russellian (Strawsonian) has a ready response:
All this shows is that strictly false (gappy) sentences aren’t an obstacle to communication, if the circumstances are right. For communication is about what people believe. Suppose I know the martini glass contains water; if you say (50), I’ll think ‘That’s wrong, but if you believed that it was a martini, that would explain why you said it: so I think you’re talking about the person drinking water from a martini glass’. You believe the presupposition of the utterance, and that’s what enables me to understand it, and get a truth from it, even though its false and I know it’s false. I apply a principle of charity in the interpretation of your utterance, which enables successful communication.
This is a pragmatic explanation: what you said is false, but communication proceeds by another route.
Kripke introduces the idea of ‘speaker’s referent’, as distinct from semantic referent:
The speaker’s referent … is determined by a general theory of speech acts, applicable to all languages: it is the object to which the speaker wishes to refer, and which he believes fulfills the Russellian conditions for being the semantic referent. … in asserting the sentence he does, the speaker means that the speaker’s referent (the teetotaler) satisfied the predicate (is happy). (Kripke 1977: 266)
In these terms, speaker meaning is what speakers intend, and cooperative charitable hearers take up from what they hear – semantic meaning is the strict and literal content of what was said.
That these can come apart is key to understanding Donnellan’s cases within the standard assumption that the F denotes an F, but once more we will need to wait until we turn to pragmatics in lecture 9 to understand it more fully.
Suppose the throne is occupied by a man I firmly believe to be not the king, but a usurper. Imagine also that his followers as firmly believe that he is the king. Suppose I wish to see this man. I might say to his minions, “Is the king in his countinghouse?” I succeed in referring to the man I wish to refer to without myself believing that he fits the description. It is not even necessary, moreover, to suppose that his followers believe him to be the king. If they are cynical about the whole thing, know he is not the king, I may still succeed in referring to the man I wish to refer to. Similarly, neither I nor the people I speak to may suppose that anyone is the king and, finally, each party may know that the other does not so suppose and yet the reference may go through. (Donnellan 1966: 290–91)