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
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 antipragmatic 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 carries
both 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 the
meaning 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 action
a. 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 house
6. 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 who
might 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, that
all = 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
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
２
For instance, Hollebrandse (2006) have interesting evidence that
Dutch children are misled by precisely this range of ambiguities.
１
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