science

Levels of adequacy

Levels of adequacy is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Levels of adequacy rather than just read about it. In short: In his work Aspects of the Theory of Syntax (1965), Noam Chomsky introduces a hierarchy of levels of adequacy for evaluating grammars (theories of specific languages) and metagrammars (theories of grammars). These levels constitute a taxonomy of theories (a grammar of a natural language being an example of such a theory) according to validation.

Key takeaways

Levels of adequacy belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Levels of adequacy to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Levels of adequacy from memory before moving on to harder problems.

Reference excerpt

In his work Aspects of the Theory of Syntax (1965), Noam Chomsky introduces a hierarchy of levels of adequacy for evaluating grammars (theories of specific languages) and metagrammars (theories of grammars). These levels constitute a taxonomy of theories (a grammar of a natural language being an example of such a theory) according to validation. This taxonomy might be extended to scientific theories in general, and from there even stretched into the field of the aesthetics of art. This present article's use of the phrase as a terminus technicus should not be confused with its everyday language uses.

Motivation The "potency" criterion alluded to in the preceding section is somewhat ill-defined, but may include "exhaustiveness", "effectiveness', and an affective component as well. (Arguably, the taxonomy is also motivated by considerations of "elegance". This should not be confused with the application of the taxonomy in the field of aesthetics). As a metatheory, or "theory of theories", it becomes a concept of epistemology in the philosophy of science, rather than a mere tool or methodology of scientific linguistics. As Chomsky put it in an earlier work:

The theory of linguistic structure must be distinguished clearly from a manual of helpful procedures for the discovery of grammars.

The levels Observational adequacy The theory achieves an exhaustive and discrete enumeration of the data points. There is a pigeonhole for each observation. Descriptive adequacy The theory formally specifies rules accounting for all observed arrangements of the data. The rules produce all and only the well-formed constructs (relations) of the protocol space. ...the grammar gives a correct account of the linguistic intuition of the native speaker, and specifies the observed data (in particular) in terms of significant generalizations that express underlying regularities in the language. Explanatory adequacy The theory provides a principled choice between competing descriptions. It deals with the uttermost underlying structure. It has predictive power. A linguistic theory that aims for explanatory adequacy is concerned with the internal structure of the device [i.e. grammar]; that is, it aims to provide a principled basis, independent of any particular language, for the selection of the descriptively adequate grammar of each language. Theories which do not achieve the third level of adequacy are said to "account for the observations", rather than to "explain the observations." The second and third levels include the assumption of Ockhamist parsimony. This is related to the Minimalist requirement, which is elaborated as a corollary of the levels, but which is actually employed as an axiom.

Precursors in the philosophy of science It is suggested that the system of levels proposed by Chomsky in Aspects of the Theory of Syntax has its antecedents in the works of Descartes, Kant, Carnap, Quine, and others. Certainly the criterion of adequacy found in rationalism, specifically, rational empiricism, bear some resemblance to Chomsky's formulation. Since one of the key issues which Chomsky treats in Aspects is a supposition of a congenital endowment of the language faculty in humans, the topic ramifies into questions of innateness and a priori knowledge, since it is by reference to those questions that the third level of adequacy is to be sought.

Note This concept should not be confused with the "causal adequacy principle," which refers to Descartes' version of the ontological argument for the existence of God in his Meditations on First Philosophy.

Bibliography Chomsky, Noam. 1957. Syntactic Structures. The Hague: Mouton. Chomsky, Noam. 1964. "Current Issues in Linguistic Theory", in Fodor, J. A. and J. J. Katz (eds.), The Structure of Language: Readings in the Philosophy of Language, Englewood Cliffs, Prentice Hall: 50-118. Chomsky, Noam. 1965. Aspects of the Theory of Syntax. Cambridge, Massachusetts MIT Press. Chomsky, Noam. 1995. The Minimalist Program. Cambridge, Massachusetts: MIT Press. Chomsky, Noam. 2000. New Horizons in the Study of Language and Mind. Cambridge: Cambridge University Press.

References

External links Boeckx, Cedric, and Norbert Hornstein.The Varying Aims of Linguistic Theory. Online version at [2], accessed 2006-04-19.

Worked examples

Example 1 — a first encounter with Levels of adequacy

Start with the simplest possible case. Write down what Levels of adequacy claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Levels of adequacy before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Levels of adequacy ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Levels of adequacy

In research: Levels of adequacy appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Levels of adequacy in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Levels of adequacy is common in secondary-school and first-year university syllabi. It links to neighbouring topics Epistemology, Grammar, Noam Chomsky, so understanding it makes those chapters shorter.
In everyday life: Look for Levels of adequacy outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Levels of adequacy in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Levels of adequacy means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Levels of adequacy out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Levels of adequacy in simple terms?

Why does Levels of adequacy matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Levels of adequacy?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Levels of adequacy.