Abstract
An important step in the development of a theory of what I have called ‘controversial’ comprising entities (entities designated by terms such as ‘class’, ‘manifold’, ‘collection’, ‘aggregate’, etc.) is the clear distinction between talk of the many comprised entities, on the one hand, and talk of the entity which comprises them on the other hand. It seems natural to consider the latter as simply a peculiar mode of the former, one in which the many are ‘spoken of as one’. Indeed, it may turn out that the comprising entity is identical to the many comprised entities. However, the question whether this is so can only be considered with clarity if our thought and talk of the former is clearly distinguished from our thought and talk of the latter.
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References
As Frege notes (Frege 1895, 92), Husserl similarly observes that there are two ways in which an entity can belong to a class-as-extension, in his 1891 review of the same work of Schröder’s work.
Le niewski, however, took his account to constitute the claim that distributive classes do not exist. He clearly equated the view that a distributive class exists with the view that a distributive class is a single entity. See Küng 1963, 108–115.
The argument regarding the example of the heart is found in Rescher 1955; that regarding the example of the house is found in Cruse 1979. Doubts regarding the transitivity of is a part of can also be found in Lowe 1989, 95 (n. 9).
Note that in some types of set theory the term `set’ is used to refer to all such classes. In set theories of other types a distinction is drawn, among entities designated by `class’ in this wide sense, between entities designated by `set’ and entities designated by `class’ in a narrower sense. See, e.g. Machover 1996, 16.
For example, Frege assumes that a wood is a collective class of many trees; see Frege 1895, 87. For Legniewski’s similar view, see Kiing 1963, 105f.
See, for example, Russell 1919, 183; Grossmann 1983, 209–10, 214–216.
Grossmann, for example, claims that the null class is a convenient fiction, and that this was also the position of the originator of set-theory, Cantor, himself. See Grossmann 1983, 214–15.
For a discussion of the existence of such entities, see Simons 1987, 41–43.
Indeed, David Lewis proposes to conceive of the null class as concrete, by identifying it with the mereological sum of all individuals, which is itself a concrete individual. See Lewis 1991, 10–15.
Grossmann provides two further reasons for thinking that classes are abstract (see Grossmann 1983, 209–16). I do not think his reasons are convincing, but there is no need to take issue with him on these points in the present context.
See Russell 1903, 68–9. Conditions under which the existence of a class as one must be denied are conditions which lead to contradictions such as the one known as Russell’s Paradox. They are discussed in the chapter `The Contradiction’, Russell 1903, 101ff.
Notwithstanding the indeterminacy of the notion in these respects, according to the account I have offered so far, it is already sufficiently determinate to be contrasted with the notion Russell took `collection’ to connote in Russell 1903, 69.By assuming as he does that a collection is refereed to by means of an expression of the form `A1 and A2 and… and
I understand the relation between temporally unmodified notions and temporally modified ones in the way explained by Simons (1987, 176–8).
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Meirav, A. (2003). Types of Comprising Entities. In: Wholes, Sums and Unities. Philosophical Studies Series, vol 97. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0209-6_3
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DOI: https://doi.org/10.1007/978-94-017-0209-6_3
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