From the

recursive definition of [a.sub.l], we obtain the functional equation

In order to analyze the meaning of such

recursive definitions of procedures, Scott developed what nowadays is known as domain theory (see [1, 2] account of the theory and, also, [3, 4] for recent applications to computer science).

In the August 1970 Word Ways, Dave Silverman observed that

recursive definitions inevitably lead to the Chasing-one's-tail phenomenon.

Analyzing this statement in terms of the

recursive definition yields the following result.

For example, (1) is a discrete

recursive definition. There we have two subproblems to recursively deal with: D = 2; whose size is asymptotically 1/2 of the size of the original problem: [z.sub.1] = [z.sub.2] = 1/2, -1 [is less than or equal to] [s.sub.1,n] [is less than or equal to] 0, 0 [is less than or equal to] [s.sub.2,n] [is less than or equal to] 1; and there is exactly one call to each one: [w.sub.1] = [w.sub.2] = 1, [r.sub.1,n] = [r.sub.2,n] = 0.

(i) If an account of the common characteristics of the class of things that are artwork is to explain the sense or meaning of 'artwork', then the

recursive definition does not do this.

He also defined a notion of continuum and formulated steps toward a

recursive definition of spaces with a homogeneous dimension number.

Each instance definition is translated as a functional, abstracting over the

recursive definition of the overloaded variable.

(4) Oppy denies that 'the content of the noton work of art can be captured in some sort of

recursive definition which recapitulates the history of art'.

Derive an almost homomorphism from the

recursive definition of [p.sub.1] (Section 4.1).

The well-foundedness of many

recursive definitions is obvious enough to be verified automatically.

There is, of course, in Locke no idea of

recursive definitions of truth (or of any other semantic feature), but Locke can, surely, be interpreted as trying to say what a term's having meaning consists in, which is a thoroughly modem ambition.