"The most obvious and compelling sources of resistance to an exclusive commitment to kinds with essences are the sciences themselves. The kinds of objects investigated by the sciences are sometimes describable in terms of essences, but often resist this sort of description. The traditional view that kinds are ontologically distinguished by essences has a storied past, but many of the kinds one theorizes about and experiments on today simply do not have any such things. Many of these kinds are groups whose members need have no distinguishing properties in common, and this clearly violates the stipulation that essences comprise sets of properties that are necessary and jointly sufficient for kindhood. I will refer to kinds with essences and those without as essence kinds and cluster kinds, respectively. Canonical examples of essence kinds are familiar from physics and chemistry. The kind essence of an electron, for example, consists in a handful of determinate, state-independent causal properties (specific values of mass, charge, and spin) that are characteristic of all and only members of this kind. But not all kinds fit this model.
The best-known examples of cluster kinds are derived from attempts to explicate the species concept in biological taxonomy. It is generally agreed that the search for essences here has failed. For example, neither morphological nor genetic properties will do, due to intra-species variation and overlap with other species. Reproductive isolation is also often cited as the mark of a species. Imagine that such isolation could be accounted for in terms of sets of intrinsic properties shared by certain individuals which unite them reproductively and isolate them from others. This proposal is also inadequate to the task of specifying essences, for several reasons: hybridization violates reproductive isolation, and when it occurs offspring are sometimes fertile, thus compounding the problem; some subpopulations within species mate successfully with other sub-populations but not with all; focusing on these sorts of reproductive criteria ignores asexual species entirely. Furthermore, in keeping with both intuition and biological practice, membership in a species cannot be conceived in terms of necessarily possessing distinctive morphological or reproductive properties (that are jointly sufficient), for a sterile tiger would still be a tiger, as would a tiger with only three legs, or an albino. I will consider the different concepts of species in the next section, but for now let it suffice to say that none of them identifies species with essences as traditionally understood, in terms of intrinsic properties that are both necessary and jointly sufficient for membership.
Given the absence of kind essences for various things widely regarded as kinds, it is now common to relax the essence criterion in the demarcation of many scientifically sanctioned categories of objects. In such cases membership in a kind is usually described in terms of metaphors: clusters, family resemblance, or as Hacking (1991, p. 115) puts it, ‘strands in a rope’. These are polythetic kinds, meaning that the possession of a clustered subset of some set of properties, no one of which is necessary but which together are sufficiently many, entails kind membership. NE [The New Essentialism], which endorses the traditional appeal to essences in distinguishing kinds, is not surprisingly uncomfortable with cluster kinds."
(Chakravartty, Anjan. Metaphysics for Scientific Realism: Knowing the Unobservable. Cambridge: Cambridge University Press, 2007. pp. 157-8)
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"The standard alternative to kinds associated with necessary and sufficient conditions (‘definable kinds’, or to use a term that some scientists employ, monothetic kinds) is what is sometimes referred to as “cluster kinds” or polythetic kinds. Though cluster theories are familiar to philosophers and psychologists alike, they are mostly understood as theories of concepts or categories, rather than theories of kinds.
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To avoid confusion I will try to be a bit more precise concerning the difference between monothetic and polythetic kinds. A monothetic kind is one that is associated with a property or set of properties each of which is singly necessary for membership in the kind and all of which are jointly sufficient. A polythetic kind is one that does not satisfy this condition. Members of a monothetic kind possess all and only the same properties, qua members of that kind, whereas members of a polythetic kind may not possess all and only the same properties qua members of that kind. In particular, if a kind is associated with a complex construction of properties, such as K1 = P1 & (P2 v P3), or K2 = P1 & (P2 v P3) & P4, then we cannot consider such a kind monothetic, on pain of stripping the distinction of any significance. The whole point of a cluster kind is that there is no unique set of properties that all and only members of that kind possess by virtue of being members of that kind. Two individuals can be members of K1 not by virtue of possessing exactly the same set of properties; for example, individual i1 might possess just P1 and P2, while i2 possesses just P1 and P3. Hence, K1 and K2 are not characterized by necessary and sufficient conditions for membership as ordinarily understood. If necessary and sufficient conditions were watered down in such a way as to allow these kinds, then the distinction between monothetic and polythetic kinds would disappear."
(Khalidi, Muhammad Ali. Natural Categories and Human Kinds: Classification in the Natural and Social Sciences. Cambridge: Cambridge University Press, 2013. p. 16)
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"The polythetic species concept was introduced by Beckner (1959) to replace the classical notion of universal class. He gave the name polytypic (later changed to polythetic) to classes that are defined by a combination of characters, each of which may occur also outside the given class and may be absent in any member of the class. The nature of polythetic classes can be illustrated by the following example (Sattler, 1986). Suppose a species is defined by a set of five properties Fl, F2, F3, F4 and F5. If these properties are distributed in the way shown in Table 2.1, the class will be polythetic. This example represents a polythetic class because each individual possesses a large number of the properties (i.e. four out of five), each property is possessed by a large number of individuals and no property is possessed by all individuals. Contrary to the situation with universal classes, no single property is either necessary or sufficient for membership in a polythetic class. The concept of polythetic class is extremely useful for dealing with biological entities endowed with intrinsic variability, since it can accommodate individual members that lack one or other character considered typical of the class. In this kind of class, certain elements may evolve and there is no difficulty in reconciling class membership with phylogenetic change. This makes a polythetic species similar to a fuzzy set (Beatty, 1982; Kosko, 1994) with boundaries that are modifiable and not uniquely defined. The view that species are sets has been elaborated by Kitcher (1984)."
(Claridge, M. F., H. A. Dawah, and M. R. Wilson. Species: The Units of Biodiversity. London: Chapman & Hall, 1997. p. 21)
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"The monothetic/polythetic distinction
Beckner (1959, p.21) sought to formalize Wittgenstein's notions, using the phrase "polytypic concept" vis-a-vis family, and the phrase "monotypic concept" vis-a-vis Aristotelian class. He defined a monotypic concept to be a concept whose extension is: A class (as) ordinarily defined by reference to a set of properties which are both necessary and suflicient (by stipulation) for membership in the class. Beckner presumed that the "extension" of a polytypic concept, on the other hand, would not be that for a monothetic concept: It is possible...to define a group K in terms of a set G of properties f1, f2,…,fn in a different manner. Suppose that we have an aggregation of individuals (we shall not yet call them a class) such that: (1) each possesses a large (but unspecified) number of the properties in G. (2) Each f in G is possessed by large numbers of these individuals; and (3) no f in G is possessed by every individual in the aggregate. By the terms of (3) no f is necessary for membership in this aggregate; and nothing has been said to warrant or rule out the possibility that some f in G is sufficient for membership in the aggregate. Nevertheless, under some conditions the members would and should be regarded as a class K constituting the extension of a concept defined in terms of the properties in G.
Sokal and Sneath (1963, pp. 13-14) changed the terminology to monothetic class and polythetic class; but they otherwise adopted Bechner's distinction, accepting and proselytizing polytypy as the rationale for a new direction they wished to give to numerical taxonomy: shifting emphasis away from monothetic dassification and towards computerized dustering schemes based on similarity (family resemblances)."
(Sutcliffe, J. P. "On the logical necessity and priority of a monothetic conception of dass, and on the consequent inadequacy of polythetic accounts of category and categorization." In New Approaches in Classification and Data Analysis, edited by E. Diday, Y. Lechevallier, M. Schader, et al., 55-63. Berlin: Springer, 1994. p. 57)
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"Polytypic Concepts: A class is ordinarily defined by reference to a set of properties which are both necessary and sufficient (by stipulation) for membership in the class. It is possible, however, to define a group K in terms of a set C of properties f1, f2,…, fn. in a different manner. Suppose we have an aggregation of individuals (we shall not as yet call them a class) such that:
1) Each one possesses a large (but unspecified) number of the properties in G
2) Each f in G is possessed by large numbers of these individuals; and
3) No f in G is possessed by every individual in the aggregate.
By the terms of 3), no f is necessary for membership in this aggregate; and nothing has been said to either warrant or rule out the possibility that some f in G is sufficient for membership in the aggregate. Nevertheless, under some conditions the members would and should be regarded as a class K constituting the extension of a concept defined in terms of the properties in G. If n is large, all the members of K will resemble each other, although they will not resemble each other in respect to a given f. If n is very large, it would be possible to arrange the members of K along a line in such a way that each individual resembles his nearest neighbors very closely and his further neighbors less closely. The members near the extremes would resemble each other hardly at all, e.g., they might have none of the f’s in G in common. Wittgenstein has emphasized the importance that concepts of this logical character assume in ordinary language, especially in that small segment of ordinary language that contains the semantical concepts of "meaning", "referring", "description", etc. He points out that all the members of such classes have a "family resemblance" to one another; he does not suggest a general term for classes of this kind. We shall call a concept C "polytypic with respect to C" if and only if it is E-definable in terms of the properties in G; its extension K meets conditions 1) and 2) above; and the E-defining test-procedure is intended to discover whether or not condition 1) is met. If the extension K in fact also meets condition 3), the concept will be said to be "fully polytypic with respect to G", or "fully polytypic" if C is understood.
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In the case monotypic concepts (concepts defined by reference to a property which is necessary and sufficient for membership in its extension), purely syntactical criteria guarantee the existence of an extension. If, for example, we have a number of classes w, x, y,…, any function of these classes (subject to certain type or stratification restrictions) is itself a class: either a class of elements or the null class. The satisfaction of syntactical requirements does not, however, guarantee the existence of a polytypic class."
(Beckner, Morton. The Biological Way of Thought. 1959. Reprint, Berkeley: University of California Press, 1968. pp. 22-3)
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"Biologists owe a debt of gratitude to Beckner (1959) for the first clear enunciation known to us of one important concept of natural taxa, a concept which Beckner calls "polytypic". Since this term and its converse, "monotypic", have meanings already well established in systematics, Sneath (1962) has suggested that "polythetic" and "monothetic" are better names (from poly: "many", mono: "one", thetos: "arrangement")."
(Sokal, Robert R., and Peter H. A. Sneath. Principles of Numerical Taxonomy. San Francisco: W. H. Freeman & Co., 1963. p. 13)
