Abstract
Properties as set of individuals, or of features? Worlds, or propositions? Time-points, or events? Preference, or choice? Natural kinds, or similarity? In modern analytic philosophy it is standard to take (i) individuals as basic, and properties as defined in terms of them; (ii) worlds as basic, and propositions as defined in terms of them; (iii) time-points as basic, and intervals as constructions out of them; (iv) preference as basic, and optimal choice as defined in terms of them; and (v) natural kinds as basic, and similarities as defined in terms of them. In this chapter we show that in all cases the other direction is possible as well. Most of the constructions used are well-known. But by putting them collectively on the table we hope to show that the constructions have something in common, and that it is not always clear which perspective is ontologically less committing.
We would like to thank the anonymous reviewers for this volume, as well as the volume editors
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Notes
- 1.
If we think of the extensional counterpart, this means that ‘some bike is red’ is true not because there actually exists a red bike, but rather that it is possible that such a bike exists. And indeed, what Leibniz considers to be the extension of a term (a set of individuals scattered around all worlds) is very much what in possible worlds semantics is its intension (cf. Leibniz 1966 and Ishiguro 1972, p. 49).
- 2.
This is what he believed, but he was not able to work out a full semantics for syllogisms with complex terms.
- 3.
Interestingly, Allen and Hayes define the notion of ‘meet’ ‘\(:\)’, as follows:
\(I{:}J\) iff\(_{def}\)\(I < J \wedge \lnot \exists K,L(I < K \wedge K \sim L \wedge L < J)\).
- 4.
For a necessary condition, see Lück (2006). In this paper it is also proven under which circumstances one can generate a continuous order of instants.
- 5.
Of course, it is not necessarily to define intervals as having open beginnings and closed ends. The other way is possible as well. Just to assume that it any convex set is an interval doesn’t give rise to endless descent even if \(\langle T,<^{**}\rangle \) is dense.
- 6.
This axiom is a finitary version of Sen’s Property \(\gamma \).
- 7.
Interestingly enough, this is exactly analogue to what Klein (1980) intended to do in linguistics: the meaning of ‘taller than’ (or ‘better than’) should be defined in terms of the meaning of ‘tall’ (or ‘good’), not that of ‘tallest’ (or ‘best’).
- 8.
The existence of maximal similarity sets is, in general, guaranteed by Zorn’s Lemma.
- 9.
This is so, because in order for \(f(\langle 1,2\rangle ) \cap f(\langle 2,3\rangle ) \not = \emptyset \) it must be that \(\exists X: X \in f(1) \cap f(2) \cap f(3)\) such that \(\{1,2,3\} \subseteq X\), see below.
- 10.
Only after writing this chapter we discovered Paseau (2012), where something very similar was worked out very precisely. Paseau argues that resemblance similarity can be saved, but that the cost of assuming similarity relations between sets of individuals is probably a too high price to pay for a nominalist.
- 11.
The empty set will be similar to no other set.
- 12.
Because if \(p \in X\), it follows that \(p \subseteq \bigcup X\), we can do with only condition (ii). Notice that (ii) entails that all individuals in \(\bigcup X\) resemble each other.
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Rooij, R.v., Schulz, K. (2014). A Question of Priority. In: McCready, E., Yabushita, K., Yoshimoto, K. (eds) Formal Approaches to Semantics and Pragmatics. Studies in Linguistics and Philosophy, vol 95. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-8813-7_13
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