The Maximization of Falsifiability:

How To Acquire the Logic of

Implicatures from The Illogic of

Experience

Tom Roeper

UNIVERSITY OF MASSACHUSETTS

1.0 Introduction to an Intricate Interface

Deductive reasoning requires precision in the definitions of logical

words.The word “logic” itself refers to that notion, although in daily life

the term“ logical”, like virtually all words, is used with pragmatic

ambiguity and even wilful imprecision. The pragmatic force of real life

situations is very important when one addresses the acquisition question:

how does a child’s innate knowledge mesh with experience in order to

lead to the understanding of particular grammars.

The discussion to follow originates in elementary reasoning about

how we should conceive of the acquisition path. It does not reflect a

thorough background in philosophy, logic, the evidence of how

implicatures work, nor a thorough study of adult uses of logical terms,

nor a much-needed careful study of how children use logical terms in

naturalistic contexts beyond experimental contexts. An acute application

of what is already known will, one hopes, enhance the claims to follow,

but may challenge them as well. This discussion should be seen as a

prolegomena to the study of these questions, and a plea for pursuing one

angle on that interdisciplinary research.1

Learnability theory needs to be conceived of with sufficient

intricacy and sensitivity to meet the actual kinds of variation that

children experience every day. The argument below is that the concept

of Maximization of Falsifiability (MaxF) is ideally suited to the task.

This paper follows the theory of Anna Verbuk: that MaxF can apply to

the interface between pragmatics and semantics. I will present and

expand upon a few of the core examples in her work and seek to orient

it in a larger context.

Where do the complexities of real life entangle the acquisition

process? One place is the difficult dividing line between pragmatics and

semantics (Levinson (2000)). For instance, as we shall see, while some

unusual properties of quantifiers might simply be considered forms of

“pragmatic strengthening ” for adults and therefore irrelevant to the core

definition of logical terms, it may not be immediately evident to the child

that a property of pragmatics is not a property of the semantics and

therefore required in any exercise of deductive logic, independent of

context. The claim here is that a child’s apparent errors may reveal

more strict deductive reasoning than adult’s reasoning precisely because

their definitions of crucial terms may, briefly, carry stronger restrictions.

It appears that languages vary in what information is

1 Thanks particularly to Anna Verbuk for discussions. Chris Potts and Uli Sauerland made helpful remarks in various conversations, as did the audiences at the ZAS conference on intersentential anaphora, Tokyo Psycholinguistics Conference, and Tohuku University

included in quantificational terms. Terms in Dutch like “allemall” vary

across the meaning “often” “all the time” and “all kinds”.2 Terms like

“all the time” in English can mean either constantly or repeatedly.

Acquisition of such terms requires a lot of subtle work by children and

a capacity to register the nuances of triggering experiences.

1.1 Maximization of Falsifiability

Edwin Williams (1981) advanced an important idea for learnability

theory: the Maximization of Falsifiability (MaxF). The claim is that:

(1) a. A child’s initial representations (definitions) of words and nodes

are as rich as possible.

(1) a. A child’s initial representations (definitions) of words and nodes

are as rich as possible.

Definitions which are too broad are compatible with too many

interpretations, while highly specific definitions are quickly

contradicted by experience. In a word, vague or incomplete

representations are the enemy of learning. The impact of negative

information, which can change grammar, is strongest when the

definition of words are too precise and restrictive., which we will

illustrate shortly. In that sense, this theory adheres to the logic of the

Subset principle at the semantic level. (See Berwick (1985), Crain and

Thornton(1998)). New information expands the number of sentences

that the grammar accommodates by reducing grammatical restrictions,

which in turn gradually makes the rules more abstract.

Here is a little illustration of how it can work, and how quickly it

can work. Suppose the child hears either den (German) or the in front

of a noun. Let the child guess that it is an article. How should she

determine its properties. Suppose in both cases the child makes the

Maximal assumption about possible features associated with articles

(probably there are more than these in fact)

(2) a. English Child I saw the man

Masc

Sing

Accusative

Definite

b. German child: Ich sah den Mann

Masc

Sing

Accusative

Definite

The German child will be immediately right. The English child quite

wrong, but the Hypothesis lends itself to contradiction. In five minutes

the child might hear “I saw the woman” which cancels the gender

feature, then “I saw the girls” which cancels the singular feature, and

then “The girls came” which cancels the accusative feature leaving

only definiteness. There is no reason not to believe that a great deal of

micro-acquisition occurs—within a few hours---much like many steps

in the mastery of bicycle balance occur in the few minutes after a child

manages to stay on a bike. If the opposite strategy is

assumed—the/den = only definiteness--then the English child will be

right, but the German child will freely use den in nominative positions

and with plurals, etc. What will force a change. Hearing Der

(nominative) Mann is a nominative form, but also carries demonstrative

force, and therefore it might not be seen as an alternative blocking the

use of den. The child could easily continue with the assumption that

either der mann or den Mann is acceptable. The conditions for revision

are far more obscure if one seeks to add features.

It is interesting to ask how far MaxF can be applied. Not only

syntax but implicatures, as we will show, and also, following Verbuk and

Roeper (2006) the acquisition of Principle B in binding theory can be

understood from this perspective. Nevertheless, the concept of

Maximization of Falsifiability itself is an idealization that is surely too

strong. There must be contexts where a child does add to the definition

of words as well as subtract from them and at least a few contexts where

acquisition depends upon comparison of words and an application of the

“uniqueness” assumption that words have different meanings.

1.2 Innate Logic

A strong and important claim has been advanced by Cherchia

(2004): in essence, the principles of logic are innate and therefore a)

require no learning, and b) instantly engender implicatures which are

implicitly or explicitly computed all of the time. Acquisition evidence

(Papafragou (2006) and, Guasti et al (2004) , and others) have

suggested that the implicature consequences of these principles by

children are not immediately realized. Therefore it could be that the

entire capacity for computing implicatures must be triggered or mature,

or become available via an interface computation (see Reinhard (to

appear), although mixed evidence leaves such a conclusion rather

murky. Others (Papafragou and Tanatalou (2004), Papafragou (2006))

have claimed that the implicatures involving “world knowledge” are

particularized in a way that slows their acquisition. Horn (2005) argues

that pragmatics is present everywhere.

We will argue that the range of possible definitions of words with

logical force within Universal Grammar is much larger than usually

supposed. Consequently the task of isolating the logical force of words is

not straightforward and requires subtle, and pragmatically exact

experiences. Nevertheless deductive reasoning must eventually be

possible---even against pragmatics---and it supplies us with the capacity

to, for instance, build a theory of linguistics where grammaticality can be

identified without the requirement of compatibility with context. The

argument here is that the child must, in some domains, move from a

restrictive pragmatic definition to a broader semantic one. It could be an

implicit goal of growth, belonging to the whole species, to find

definitions that allow strict deductive reasoning free of pragmatic

qualifications. To put it differently, the efficiency of language in general

lies largely in guaranteeing meanings that are independent of context and

which can even support anti-pragmatic readings (see Hollebrandse and

Roeper (to appear)). Sentences like:

(3) John met every person in the world

have a meaning which is impossible. but its meaning is computed as

fast as any other sentence---as well as its implausibility, without any

particular context needed.

1.3 Inference and Implicature

Horn (2005) and Papafregou (2006) argue and provide evidence that

children can undertake particularized situational implicatures. We

argue that some of these implicatures belong to General Inference

which is needed to see what is not said, to infer motives, in every

conversation, and in many non-verbal situations. They should be kept

distinct from implicatures that are properties of words which are

immune to pragmatic modification. General inference, while deep and

complex, computes plausible, not implausible consequences of

situations.

In contrast, a statement like the following has a logical

implicature whether we can make sense of it or not:

(4) Some people are people.

implies automatically that Not all people are people, a conclusion with

which we have to struggle cognitively, using any kind of inference,

including a strong sense of irony or cynicism, to rescue from apparent

nonsense. Nevertheless the implicature is present.

While it might seem counter-intuitive at first, it is really quite

plausible to argue that children bring enormous inferential capacities to

the earliest stages of acquisition. In effect, when a sentence is not

understood, one tries to make inferences from individual words to

possible meanings. This occurs at the one-word stage. Every utterance

requires an interpretation for why it is said. The interpretive demand is

greater if your grammar is smaller. The child who hears:

“Milk!”

must be able to translate it into a range of meanings like “do you want

some milk” or “be careful and don’t knock over the milk carton” using

a lot of inferential power.

2.0 Projecting Restrictors

It is a fundamental feature of quantification that it carriesboth overt and covert restrictors:

(5) every child must wear a bathing suit

The quantifier every (Heim (1988)) is restricted by the noun child and by some property of the context, such as, in this class. Now we can ask: what constitutes a possible restrictor and how far does it get built into the quantifier itself. Here is where one can be unsure of what is entailed. Elementary time and location restrictions appear to be present without much contextual demands:

(6) the boy wearing a red shirt stole the fruit yesterday.

This sentence can mean a boy wearing the red shirt now or a boy wearing a red shirt during the robbery. A kind of optional default restriction to Here and Now seems to be present in many circumstances. Are there others? Piaget originally proposed that children

cognitively presupposed “simultaneity” in various tasks, but

Schmiedtova (2004) has shown that young children have the capacity to

make the distinction between what is simultaneous and what is not. We

argue that the phenomenon is not a cognitive unit but a part of the

system whereby implicatures are calculated. It fits the MaxF systematic

effort by children to over-restrict meanings in order to ultimately isolate

the correct meaning. Apparent misapplication of simultaneity could be

seeking an implicature where none is present, although perhsps it

sometimes is. Consider this case:

(7) Here are 500 bricks. Can you lift all of them?

The natural answer is “no, they would be too heavy”. But note that there is an implication of “all at once” that is not logically necessary. Surely one could lift them one by one. Many situations are open to an ambiguity here:

(8) a. Could you carry all your toys to your room?

This could mean all separately or all at once. Anna Verbuk reports (to appear) that children often reveal their restrictions in overt conversation. One 4.11 yr old child was asked if one animal had scratched all of another’s body and responded (“a card” means “no”),

(8) b. A. (4;11): A card. Because he didn’t do it all at once. Cause he

(=Tiger) was asking him (=Deer) to do it (=scratch Tiger’s body) all at

once, even though he didn’t say, “do it all at once

Many others offer similarly complex reasoning. From the perspective we are pursuing, the child is doing precisely the correct thing: he is maximizing the possible features associated semantically with “all”. The adult, by contrast, has this meaning as an implicature, a part of Pragmatic Strengthening if the context calls for it. It is not a part of the meaning of all when we engage in deductive reasoning. Could this meaning enter the logic of how quantifiers are interpreted elsewhere? Papafragou and Tantalou (2006) gave children sentences involving some whose implicature should be not all. They were given a scene of this general kind:

(9) 　 1. First two animals jump over the fence 2. Then another animal jumps over a fence

　3. Then a third animal jumps over a fence

When 6 year-olds were asked:

(10) “Did some of the animals jump over the fence”

they answered “yes” while adults answered “No”. This has been taken to mean that the children have not been able to process the implicature. However they are surely aware that all the animals have jumped over the fence and this implicature is far less complicated than many inferences that are implicitly made by toddlers.

If however children have applied the logic of MaxF to some as well as all, then we make precisely the correct prediction about the children’s “yes” answer as seeking a restrictor that allows “yes”:

(11) Did some of the animals jump over the fence at once?

Put in as a restrictor it would be:

(12) Did “some at once” of the animals jump over the fence?

If this logic holds for a wide variety of implicatures, then

we will expect the process to involve a great deal of quite specific experience. There are interesting examples that suggest that children might entertain quite unusual restrictors that apply in the domain of comparatives as well. Consider this dialogue from the Adam Files of Childes:

(13) Ursula: its much bigger Adam: it’s much smaller too Ursula: it’s much smaller! how can it be both!

Such forms of differentiation are not unknown in the adult language, but there is a default notion that bigger/smaller applies to the whole object. If the tail were bigger and the head were smaller we might say “one is both bigger and smaller than the other” with the implication to search for restrictions that would render the sentence non-contradictory. Now let us imagine what the range of possible restrictors could be for one quantifier: all. Then we will provide the kinds of experience which force the child to drop those excessive restrictors.

2.1 Kinds of All The following are examples of possible extensions of

themeaning of all:

1. Kind: all = all kinds a. we have all Toyotas on our lot.

2. Variety: all = any possible selection a. we have all nationalities at Umass.

3. Collective: all = group actiona. we all lifted the table

4. Exclusive: all = all and only (possible, but not English)

a. he picked up all the toys.5. Adverbial: all = completely

a. he ran all the way around the house6. Adverbial: all = isolated (?)

a. he sat all by himself.7. Quotation: all = enthusiastic attribution

a. he was all “I can do it”

All of these example sentences are not far removed from the language of parents to children. It would be useful to do a study and see exactly which ones occur.

The common property of all is assumed to be exhaustivity. Is this property reliably honored? Consider a situation like this:

(14) [5 of 50 students are present at the start of class] Someone says with disdain: “all the students come late to this class”

If a child hears some version of this sentence, spoken with common exaggeration, he is entitled to assume: all = most. This would be a difficult assumption to overturn since in every situation where all is used, it would also be true of most.

How can we block such a modification? A careful look at the concept of restrictor suggests that it must indeed restrict. Suppose we tried to add a restrictor of the general form roughly speaking—to capture moments of casual overstatement--- to any quantifier.

This move would render the quantifier vague in a way that most

conceivable evidence could not rescue. By our logic, it would make

language unlearnable. Therefore the possible restrictors must

themselves be constrained. To state it informally: restrictors must

restrict and not expand the relevant domain.

It is quite possible that there is a further range of restrictors that apply which we have not seen and which, being short-lived, do not exhibit themselves overtly in the acquisition process. 2.2 Triggering Progress

Children have many informative experiences. The child whomight briefly entertain the idea that all = most would surely have some corrective experience, which imposes exhaustivity:

(15) [two of twenty toys are not picked up by a child] “you didn’t pick up all your toys

Similarly if the child assumed, which does not seem unnatural, thatall = all and only, experiences would arise, where one says:

(16)a. [person buys food and clothing] “I bought all the food” b. [adult reads a series of stories] “ I read all the stories”

where the reading for (16a) “all and only” is therefore ruled out and for(16b) the reading “all at once”. A great deal of learning via the MaxF principle would be accomplished silently (see Verbuk for discussion). It might be quite unclear 90% of the time that a child is using a more restricted form of the quantifier all.

3.0 The Path across Quantifiers

Are there implications here for the path of quantifier acquisition as a whole? One of the most startling facts is the wide disparity in the appearance of quantifiers. While their frequency is not equal, they all appear far more often than many other nouns and verbs that children readily acquire. Therefore any delay needs an explanation. While 2 yr olds use all easily, it has been found that every is very rarely used (deVilliers and Merchant (2006), Roeper et al (2006)). Only 18 instances of every+N were found among 10 children and they appeared between 4-5 years. As is well-known children make errors in the comprehension of “spreading” as well, allowing an object to treated exhaustively as well as a subject (every cowboy is riding a horse = every horse is being ridden by a cowboy). How does the child learn that all can have a collective reading but it is rare for every and excluded for each. Imagine this contextual contrast:

(17) Imagine: set of balls and bats

ball ball ball ball ball ball ball

bat bat bat bat bat bat bat

And now the instruction:

(18) “Point to all the balls” => child points to the whole row

(19) Now imagine this interchange:

“Point to every ball”

Child points to the whole row.

which elicits this Negative Trigger:

(20) “you didn’t point to every ball”

Such an experience is not implausible, but it might be that one could

only be sure that an experience of that kind occurred over the course of

several years, unlike the the/der learning procedure above.

Is there any mechanism that could make the process more efficient.

It is possible that the set of quantifiers are learned in a partly

paradigmatic fashion: blocking a restrictor on one becomes a block for

all. There is a range of options that the child seeks to capture, involving

contrasts in collectivity, proportion (most, few), and other factors that

interact with the notion of set. It would radically enhance acquisition

efficiency if the child eliminates a restrictor for the entire set at once,

moving a semantic property by MaxF into the pragmatic domain. Further

evidence might be needed to make individual quantifiers exceptions to

the set.

4.0 Maximization of Falsifiability Elsewhere: Or, And, Reflexives,

and Binding Theory

These subtle ambiguities are not isolated. We find that words

like and, or, then have special features as well. Thus if we say John ate

meat ‘n rice or John ate meat and rice the former more naturally

associates with eating them together or “at once”. Bryant (2006) has in

fact shown that children may overapply the notion of simultaneity in

contexts where and occurs with gapping in German sentences roughly

like (the elephant brushes the lion, and the dinosaur __ the cat [=

dinosaur brushes the cat]). Adults do the two actions separately while

children struggle to do them at once.

Or allows both an inclusive and exclusive reading. For instance,

you can’t eat a hamburger or a lemonade allows the reading that you

can have lemonade in Russian. Verbuk has shown that children initially

give a default wide-scope to the negative in Russian, blocking that

reading, and Goro and Crain (2004) have made extensive studies along

the same lines in several languages.

Reflexives show the same kind of interesting ambiguity. In English

the expressions:

(21) a. John and Mary kissed themselves

b. John and Mary kissed

have different meanings. In (21a) each person only kisses him or

herself. In (21b) it is a joint activity (See Roeper and Roeper (2005) for

a game theory account, see also Rubinstein (2006)). If the joint activity

is chosen as the Default restriction, then evidence of distributivity will

occur for the reflexive, dropping the “joint” restroction, but never occur

for the empty object (21b).

In German the monomorphemic reflexive sich captures the joint

reading and the complex form sich selbst captures the distributive

reading. Iumguelzow and Roeper (in preparation) show that children

do not immediately choose the right meaning for each type of reflexive.

Similarly Verbuk and Roeper (2006) argue that children must exclude a

range of possible additional restrictions for reflexives like John hurt

himself, for instance physical, intentional, and subtle aspects of

perspective (see Levinson (2000)) before its parametric opposition to

the form him can be realized.

5.0 Conclusion

The emergence of implicatures, both conventional and

conversational, following the logic of MaxF in Verbuk (to appear)

requires us to imagine a very subtle process whereby semantic and

pragmatic factors are differentiated.

This argument applies the classic logic of learnability to the

learnability of logic. The child must have a method to discard potential

pragmatic restrictions on logical terms in order to isolate their logical

force. Only then does one generate an implicature for words like some

to the effect that it entails not all. Or that all operates without a time

restriction and therefore does not mean “all at once”.

The differentiated meaning under MaxF will encounter sharp

contrary evidence, either quickly or only when special circumstances

arise, that block the assumption that a circumstantial restrictor belongs

to the inherent eaning of the word. This predicts that each logical and

quantificational term (e.g. all, every, each) will have its own acquisition

path. This claim receives strong, straightforward evidence from the

naturalistic data. Several years separate the emergence of words like all

from the emergence of every.

The role of subtle triggering experience here needs to be kept

clearly in mind. If one takes a general approach, it may appear that

children need a frequent exposure to certain words in order to learn

them. This is true as a first order empirical generalization, but it does

not mean that frequency itself can be the source of discrimination. If

certain crucial environments for learning are quite rare, then it may

appear that greater frequency is needed when in fact what one needs is

more instructive experiences. Second language acquisition instruction

reflects this reality. Anyone who has learned a second language,

remembers environments where words seem to be used in a surprising

way when we thought we knew what they meant. Those are the

moments from which we learn, not from a statistical representation of

how often the word has occurred. Teachers, likewise, will often

compare two situations to explain how two similar words differ.

In sum, we have argued that issues at the interface between syntax,

semantics, and pragmatics require the same kind of learnability logic

that has been advocated for syntax alone. In fact, the diversity of

information that contributes to various possible restrictors makes the

need for efficient and constraining mechanisms to guarantee acquisition

success increasingly necessary.

Notes

2 For instance, Hollebrandse (2006) have interesting evidence thatDutch children are misled by precisely this range of ambiguities.

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