# Classification as a kind of distance function. Natural classifications

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Distance Function Mathematical Logic Computational Linguistic Natural Classification## Preview

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- 1.The concept of natural classification considered in the present article is a relative concept. Philosophers and methodologists are however often using an absolute concept of natural classification. By a natural classification they mean a classification based on essential affinities and differences of the objects classified. See for exampleV. Lenzen:
*Procedures of Empirical Sciences, International Encyclopedia of Unified Science*, I, 5, p. 31–35 (The University of Chicago Press, 1938). As regards this absolute concept the fundamental problem is that of the nature of essential affinities and differences. This problem of essence has been studied in Poland by prof. Roman Ingarden. In this article it is not considered.Google Scholar - 2.Cited fromF. Dannemann:
*Erläuterte Abschnitte aus den Werken hervorragender Naturforscher*, Leipzig, 1902, p. 247.Google Scholar - 3.Here is howJ. Venn in his
*Principles of Empirical Logic*(London 1907) describes the ideas of those systematists „who have spoken in favour of a ‘natural’ system of classification”. „They considered themselves, says Venn, to be in some way following Nature in their scheme of arrangement, and to be making their dispositions in such a way that the things which should stand nearest each other in their scheme, should be those which were actually most closely related” (p. 333/334) … They thouhgt that „on such a scheme those things were placed in close proximity which are actually ‘related to’ or in ‘affinity with’ each other” (p. 337). Let us note that Venn is using here our concept of the distance within a given classificatory system between the things belonging to the classification space.Google Scholar - 4.
- 5.I will be also using: a) the functors of the sentential calculus →, V, Λ, ≡, as shorthands for “if…then”, “or”, “and”, “if and only if” respectively; b) the following symbols of the calculus of classes: ∪, ∩, ∋, ∈, Λ (null class); c) the sign of identity “=”.Google Scholar
- 6.The corner quotation marks in the formulaOpen image in new window are meant to inform that what is spoken of is the corresponding function and not its value for the arguments
*x, y*. This value will be denoted byOpen image in new window. A similar notation will be used below in the case of relations. Thus for example the formulaOpen image in new window names the relation of*being smaller than*whereas “*x<y*” states that*x*is smaller than*y*.Google Scholar - 7.i. e. is reflexive, symmetric and transitive in sp\(\mathfrak{M}\).Google Scholar
- 8.By “the compoundOpen image in new window I mean the ordered triple the first element of which is the class
*S*, the second — a classification\(\mathfrak{M}\) (whose space is*S*), the third—the distanceOpen image in new window (which is defined in*S*).Google Scholar

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© Państwowe Wydawnictwo Naukowe 1961