Abstract
In the last chapter we saw that neoclassical mereology is only partly successful in accounting for features of wholes which were not satisfactorily accounted for by classical mereology. Numerous difficulties are associated with the ways in which neoclassical mereology accounts for important features of wholes — features whereby the existence of a whole seems to depend on the way its parts are conditioned; whereby more than one whole seems capable of being made up of precisely the same entities; and whereby wholes can survive the loss or gain of parts.
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References
Simons 1987, 212.
See van Inwagen 1990, 287 (note 13); Doepke 1982, 46–7; Simons 1987, 212.
See, for example, Russell 1903, 95–6; Grossmann 1983, 170–2.
On this question, see Boolos 1984.
Baxter 1988, 579.
See Baxter 1988. Throughout his discussion, Baxter uses the term ‘whole’, rather than ‘sum’ or ‘classical sum’. As I have noted above, however, there are straightforward reasons for thinking that a neoclassical sum is not identical to its parts. The reasons he gives, both for and against the view that the whole is identical to its parts, are at their most plausible if phrased with respect to the particular type of wholes we have been calling ‘classical sums’. To keep this clearly in mind, I have substituted his ‘whole’ for ‘sum’ throughout, where I take ‘sum’ as short for ‘classical sum’.
Baxter 1988, 578. Of course, people who are not professional philosophers are more likely to use the term ‘whole’ than ‘sum’ (indeed, they are not likely to debate about classical mereological sums). However, Baxter’s point is that in common sense thinking about wholes in general there is an inclination to assume that the whole is identical to its parts. Thus if common sense intuition is to be represented in a debate about classical sums, this would reasonably be done by attributing to common sense (according to Baxter) the belief that a sum is identical to its parts (SDP).
Baxter 1988, 578.
Baxter 1988, 578–9, substituting ‘sum’ for ‘whole’.
This response expresses what he calls the ‘Combination’ view, according to which… if there are six things then a seventh thing - the sum they are parts of - exist, and the six things collectively are the seventh thing. (Baxter 1988, 579; as before, substituting ‘sum’ for ‘whole’.)
However, as I have noted, Baxter himself finds this response unsatisfactory, although for different reasons. His main reason seems to be that the Combination view entails that all sums are multitudes, and this, he claims, commits us to atomism, and “one’s theory of parts and whole should not mandate atomism”. However, his response suffers from the unclarities noted with regard to the notion of a multitude, no less than does the Combination view itself. See Baxter 1988, 580.
Baxter 1988, 580. With regard to Baxter’s notion of a multitude see previous footnote.
Baxter 1988, 576–7.
Lewis 1991, 81–7.
Lewis 1991, 84–5.
Armstrong 1978, Vol. II, 37–8.
See Lewis 1991, 84–87.
Simons takes Lewis’s ultimate rejection of the claim that the sum is identical - strictly speaking - to its parts, to be incompatible with Lewis’s earlier claim that ‘given a prior commitment to cats, say, a commitment to cat-fusions is not a further commitment’ (Lewis 1991, 81). See Simons 1991, 396.
Lewis 1991, 87; substituting ‘sum’ for ‘fusion’.
Lewis 1991, 87; again, substituting ‘sum’ for ‘fusion’.
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© 2003 Springer Science+Business Media Dordrecht
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Meirav, A. (2003). Sums, Collections and All the Parts. In: Wholes, Sums and Unities. Philosophical Studies Series, vol 97. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0209-6_8
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