A user's guide to
the Tolerance Principle. A discussion of the conceptual and
methodological issues in how to use the Tolerance Principle for
The Tolerance Principle was developed
in 2002: a draft paper can be found here. The examples and
narratives were crude, the formal result was not available (as it
was provided by Sam Gutmann a bit later), but the main idea has
remained the same.
Gutmann's proof led to an earlier
publication in 2005. Few cared but the Penn folks. In 2006 I
gave a job talk at Penn, ostensibly for a historical linguistics
slides are attached here.
The initial goal was modest. In my earlier work (KLNL, Chapter 3), I reported evidence that children learn and organize irregular verbs by rules. For instance, a rule "Change Rime to ought" takes care of verbs such as catch, think, buy, bring, teach, seek, and verbs such as say-said, lose-lost, sleep-slept, etc. fall under the rule of Vowel Shortening triggered by suffixation. In other words, the traditional approach to irregular morphology with rules going back to Bloch (1947) and SPE is correct, and the holistic storage/retrieval account is incorrect.
results raise a sharp question: How does the child figure out
the "ought" rule is applies to a fixed number of words whereas
the "-ed" rule is general and can apply to any verb. Children
may occasionally over-use the -ed rule (go-goed) but no
one ever says hatch-haught on the analogy of catch-caught.
Given the ubiquity of exceptions in language, a general solution
must be found. Furthermore, some deficiencies in
the variational approach to language acquisition developed in
also call for a principled distinction between noise and
exception in learning.
the formal solution was worked out in 2002, it took many years
to understand the scope of problems at hand, and accumulate a
large number of cross-linguistic case studies. A brief outline
is as follows.
Chapter 1: Border Wars
tension between rules and exceptions, and productivity, in
language. Why this has remained an unresolved question and how
it has poisoned the water for so long.
Chapter 2: The Indispensability of Rules
A review of statistical facts of language especially morphology
and children’s acquisition of morphology with focus on
productivity. Contrary to popular beliefs, productivity
should be understood as a categorical notion in language,
judging from the now extensive cross-linguistic studies of
Chapter 3: The Tipping Point
Using the Elsewhere Condition as a basic principle of language, as well as a performance/processing model, derive the mathematical principle of productivity, what I call the Tolerance Principle:
Chapter 4: Signal and Noise
A very detailed study of the acquisition of English inflectional
morphology and nominalization morphology, the treatment of
metrical stress in English and its acquisition, and the
important case of German noun plurals where a very small rule
(‘add -s’) can be productive. The entire discussion is driven by
the equation, using child-directed language data.
Chapter 5: When Language Fails
predicts complete lexicalization when the number of exceptions
to a rule exceeds the threshold. I show that this leads to
morphological gaps: without a productive rule, you only know the
derived form if you hear it otherwise ineffability arises.
Detailed numerical studies for gaps in Russian (Morris Halle's
famous 1973 paper), English “stride-strode-stridden” gap,
Spanish verbal inflections in the third conjugation, and the
masc. sg. genitive in Polish and its acquisition. The Tolerance
Principle also provides an integrated theory of language
acquisition, variation, and change, in that it provides/predicts
the conditions under which language change is actuated. As a
case study, the theory explains why—and when—the so-called
dative sickness in Icelandic started to take shape in the late
Chapter 6: The Logic of Evidence
completely new conceptualization of the indirect negative
evidence business in language acquisition, especially in syntax.
Instead of thinking about retreating from over-generalization, a
derivative application of the Tolerance Principle ensures that
the child is much more careful before generalizing. Shows how
the learner may acquire that adjectives such as “asleep” do not
allow attributive in NPs (“*the asleep cat”), and how to resolve
Baker’s classic problem of dative construction acquisition (“*I
donated the museum a painting”). A critique of previous
proposals, including Bayesian models of inference, is also
Chapter 7: On Language Design
How the current study impacts traditional problems in
linguistics, and how it leads to a simplification of the theory
of UG and language learning, with a reduced role for
domain-specific innate knowledge of language, leading to an
arguably more plausible solution to the problem of language
evolution. A novel account of why language learning must start