Abstract
Can there be relational universals? If so, how can they be exemplified? A monadic universal is by definition capable of having a scattered spatiotemporal localization of its different exemplifications, but the problem of relational universals is that one single exemplification seems to have to be scattered in the many places where the relata are. The paper argues that it is possible to bite this bullet, and to accept a hitherto un-discussed kind of exemplification relation called ‘scattered exemplification’. It has no immediate symbolic counterpart in any Indo-European natural language or in any so far constructed logical language. In order to remedy this, a notion called ‘many-place copula’ is introduced, too.
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Notes
It should perhaps be noted that Russell nonetheless in his popular The Problems of Philosophy says that universals do not exist in the same sense as things do: “we shall say that they subsist or have being, where ‘being’ is opposed to ‘existence’ as being timeless (Russell 2001, p. 57).” In his The Philosophy of Logical Atomism, however, he rejects such a way of talking see 1989, pp. 255–256). Since many philosophers think that universals and particulars must have different modes of being, it is worth noting that Russell ended up by believing that particulars are only complexes of universals (Russell 1962). Once he says that the existential quantifier is to the existence of things, properties, and relations as the genus fish is to the different species of fish (Russell 1959, pp. 231–238). To the view that the modalities possibility, actuality, and necessity must be different modes of being, he retorts that those who think in this way have not understood his distinction between propositions and propositional functions; primarily, these modalities apply only to propositional functions, and such functions are neither true nor false (Russell 1989, chapter V).
Note that a relational property predicate such as ‘taller than Socrates’ needs only the traditional one-place copula, ‘Simmias is (taller than Socrates)’, but a two-place relation predicate such as ‘taller than’ needs a two-place copula.
The expressions ‘are brothers’, ‘are lifting the piano’, and ‘are surrounding the house’ can of course be used in relation to a varying number of persons. For a defense of so-called ‘multigrade’ or ‘variably polyadic’ predicates, see (Oliver and Smiley 2004).
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Acknowledgments
I would like to thank Jan Almäng, François Clementz, Javier Cumpa, Barry Smith, and Christer Svennerlind for comments on an earlier version of this paper.
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Johansson, I. Scattered Exemplification and Many-Place Copulas. Axiomathes 23, 235–246 (2013). https://doi.org/10.1007/s10516-011-9155-y
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DOI: https://doi.org/10.1007/s10516-011-9155-y