Logical Abilities in Children: Volume 4 by Osherson Daniel N.;

Author:Osherson, Daniel N.;
Language: eng
Format: epub
Publisher: Taylor & Francis Group
Published: 2017-08-15T00:00:00+00:00

8.4 Properties of Derivations Evoked by Conceptual Domains

According to the plan of the last section, we seek to characterize sets of mental derivations in such a way that we may distinguish those of natural conceptual domains from those of unnatural or pseudoconceptual domains. It was seen in Section 8.2 that the mental derivations of a given conceptual domain are specified by an observationally and descriptively adequate model for that domain. Hence, we may proceed by attempting to distinguish the kinds of observationally and descriptively adequate models that are possible for natural and unnatural conceptual domains.

Let D1, ..., Dn be clear cases of natural conceptual domains of English. We seek properties common to the observationally and descriptively adequate models of D1,..., Dn. Let M(Di), for 1 ≤ i ≤, be the set of all observationally and descriptively adequate models for Di. For a given Di each model in M(Di) has certain formal properties, for example, (a) reliance upon a certain kind of algorithm employing rules of a special kind or ordered in a distinctive way, or (b) a primitive vocabulary of some restricted nature. For a set of formal properties, P, we shall say that Di is formalizable within the restriction P if and only if at least one member of M(Di) exhibits the properties P. Thus, one kind of generalization that might be true of D1, . . . , Dn has the following form: for some set of properties, P, each Di is formalizable within the restriction P. Expanded, such a generalization asserts that there is a set of formal properties, P, such that for each Di at least one observationally and descriptively adequate model of Di has the set of formal properties, P. If such a generalization were true of D1, ... , Dn—the clear cases of conceptual domains of English with which we started—then it might be proposed as a necessary condition on conceptual domains of English; that is, we might conjecture that every conceptual domain of English is formalizable within the restriction P. Such a hypothesis is subject to empirical test by attempting to formalize a new conceptual domain, not included among D1,... , Dn, within the restriction P.

However, finding such a necessary condition is not enough to distinguish the conceptual domains of English from pseudodomains based on concepts like (i)-(iii) of Section 8.1; for, such a condition might be true of all conceptual domains of English but be true also of some (or even all) pseudodomains as well. Rather, we seek a set of properties P such that every conceptual domain of English is formalizable within the restriction P, and no pseudodomain merely expressible in English can be formalized within the restriction P. For example, given that the concepts (i)-(iii) of Section 8.1 constitute an unnatural conceptual domain for humans, we desire a set of formal properties, P, such that the set of mental derivations evoked by those concepts is not formalizable in an observationally and descriptively adequate way within the restriction P.5

In practice, we

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