By Friederike Moltmann
Summary gadgets were a crucial subject in philosophy on account that antiquity. Philosophers have defended quite a few perspectives approximately summary gadgets by means of beautiful to metaphysical issues, issues concerning arithmetic or technological know-how, and, no longer on occasion, intuitions approximately common language. This e-book pursues the query of the way and even if normal language allows connection with summary items in a completely systematic method. via making complete use of latest linguistic semantics, it provides a far larger diversity of linguistic generalizations than has formerly been considered in philosophical discussions, and it argues for an ontological photo is particularly diverse from that usually taken with no consideration through philosophers and semanticists alike. connection with summary items similar to homes, numbers, propositions, and levels is significantly extra marginal than quite often held. in its place, typical language is quite beneficiant in permitting connection with particularized homes (tropes), using nonreferential expressions in obvious referential place, and using "nominalizing expressions," similar to quantifiers like "something." connection with summary gadgets is completed mostly basically by way of 'reifying terms', resembling "the quantity eight."
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Additional info for Abstract Objects and the Semantics of Natural Language
John likes honesty. b. John prefers honesty to charm. (52a) certainly does not mean that John likes all instances or all typical instances of honesty. Yet it also does not mean that John likes the abstract object that is the property of being honest. John’s mental state of liking is directed toward concrete instances of honesty, for example, instances that caused John’s attitude of liking or possible instances that John conceives of when making hypothetical judgments. Similarly, (52b) certainly does not require that John prefers any instance of honesty to any instance of charm.
Thus, the children denotes a sum of individuals, whereas collective NPs such as the group of children denote an atom relative to <. On this view, sums would be collections as many, whereas atoms would be collections as one. The Plurality Constraint stated in terms of the notion of an atom would require that predicates referring to the parts of an argument (but not the argument as a whole) apply only to non-atoms. “Kind term behavior” would have to be accounted for by distinguishing kinds that are sums, that is, sums of possible instances, and kinds that are atoms (the Siberian tiger).
Just as the predicate add in (79) is multigrade with respect to its second place, there are expressions that are multigrade functors, taking an unlimited number of entities in a certain order as arguments. Examples are the functors sum and sequence: (80) a. the sum of two and two and two b. the sequence of two and one and two A multigrade predicate (or a multigrade argument place of a predicate) may itself be plural or in fact multigrade with respect to one of its positions, and in the latter case, the multigrade position may itself be multigrade or plural with respect to any of its positions.