1. Persistence of Simple Substances University of Durham, November 19, 2009 Dr Jani Hakkarainen (University of Tampere) Dr Markku Keinänen (University of Turku)

2. Introduction Broad sense of persistence: identity over time Narrow sense: cross-temporal identity with qualitative change The problem of persistence concerns primarily explanation: what accounts for the persistence of an entity

3. Introduction Roxanne Marie Kurtz's (2006) approach to the problem of persistence in the narrow sense: 1.“alteration”: 1.“Any object that changes is the proper subject of the incompatible properties involved in the change.” 2.“survival”: 1.“If an object persists through change, then the object existing before the change is numerically identical to the one existing after the change. ” 3.“atemporal instantiation”/temporary intrinsics: 1.having intrinsic properties is not relativized to time 2.“If an object is the proper subject of a property, then (i) the object has that property, and (ii) facts about time and tense are irrelevant to the truth of the proposition that the object has that property. ”

4. Introduction Restriction to concrete particulars and especially to simple individual substances: –Simple substances do not have other individual substances as their proper parts –Basically, fundamental physical particles such as quarks and electrons

5. Introduction Michael Della Rocca’s (2009) distinction between 3D and 4D: –The difference between 3D and 4D consists in in virtue of which entities persist: 3D: in virtue of same entities (entities persist because of identity) 4D: in virtue of distinct entities “in virtue of”: metaphysical explanation i.e. entity or entities that ground persistence

6. Introduction Novel 3D: –Trope-bundle account of Strong Nuclear Theory (SNT) development of Simons (1994) Defense for the standard objections to 3D: 1)Temporal relativization of temporary intrinsics 2)Bradley’s regress 3)Coincidence, fusion and fission cases

7. Introduction Focus on ontic predication (substance-its properties) or truth-makers Standard 4D: an object has a spatio-temporal part corresponding to each point of space-time it occupies (geometric correspondence principle) SNT permits that objects are spatio-temporally extended simples i.e. spatio-temporally extended objects that do not have any further objects as their proper parts Assuming Eternalism and tenseless theory of time

8. Structure of the Paper 1)Introduction 2)Overview of the SNT 3)No Temporal Relativization of Ontic Predication 4)No Bradley’s Regress 5)Coincidence, Fusion and Fission Cases 6)Conclusion

9. SNT: Overview According to all trope-bundle theories, tropes are particular properties, i.e. tropes are: 1) concrete (spatio-temporal) particulars 2) having definite identity and counting conditions 3) categorially simple (either simple or all parts of tropes are further tropes) 4) having a thin nature to determine a single feature of the object possessing the trope 5) capable of occurring compresent with each other

10. SNT: Overview Rival trope bundle theories differ in the construction of substances out of the property tropes In independence theories (Williams 1953a, 1953b; Campbell 1990), substances are aggregates of mutually compresent tropes Dependence theories (Simons 1994; Denkel 1996, 1997) use the formal relations of rigid and generic dependence in constructing substances

11. SNT: Overview SNT is a dependence theory. According to SNT, each simple substance i has one or more nuclear tropes: –if there are more than one nuclear tropes, they are strongly rigidly dependent (SRD) on each other Nuclear tropes are necessary to substance i and determine the kind K to which i belongs –Background: SNT analyses the primitive substances of Ellis-type dispositional essentialism in terms of tropes To guarantee the diversity of the distinct tropes constituting the nucleus, the SNT assumes that each nuclear trope falls under a distinct highest determinable

12. SNT: Overview As the tropes of the substance of kind K, the nuclear tropes of i are generically dependent on tropes belonging to some distinct determinable kinds D 1, … D k There has to be a trope belonging to each of the kinds D 1, … D k and rigidly dependent on the nuclear tropes Either the kinds D 1, … D k are already occupied by the nuclear tropes of i or it also contains contingent tropes belonging to the rest of these kinds

13. SNT: Overview The contingent tropes of i are one-sidedly strongly rigidly dependent on the nuclear tropes Trope t is a part of substance i iff t is rigidly dependent only on the nuclear tropes of i To determine the spatio-temporal location of tropes, SNT assumes that –the trope aggregate formed by the nuclear tropes of i (n-bundle of i, for short) is figuring in the basic spatio- temporal relations Thus, the spatio-temporal location of the n- bundle determines the location of each nuclear trope

14. SNT: Overview Necessarily, if nuclear tropes exist, they are compresent with each other and the n-bundle To explain the location of contingent tropes, the SNT assumes that –the trope aggregates formed by each single contingent trope u of substance i and the nuclear tropes of i (c-bundles, for short) figure in the basic spatio-temporal relations, as well as n-bundles Thus, the location of the c-bundle determines the location of the contingent trope u

15. SNT: Overview Two principles constraining the location of the c-bundle and the n-bundle: 1) As a trope aggregate, the c-bundle is mereologically constant: –if the c-bundle exists at some moment t, each of its proper parts must also exist at t –thus, if the c-bundle exists at t 1, the nuclear tropes of substance i and the n-bundle of i must also exist at t 1 –hence, the temporal location of the c-bundle is a proper or improper sub-location of the temporal location of the n-bundle

16. SNT: Overview 2) Since the c-bundle is a trope aggregate having the nuclear tropes of i as its constituents, the spatial location of the c- bundle must include the spatial location of the nuclear tropes –Consequently, at each moment in which the c-bundle exists, the spatial region occupied by the n-bundle is a proper or improper part of the spatial region occupied by the c-bundle.

17. SNT: Overview Every primitive substance i is a powerful particular having a centre of influence and an approximate size determined by the causal powers of i A trope has a centre of influence, which is its spatial location, but fails to have any definite size The centres of influence do not have different sizes The centre of influence of contingent trope u of i must include the centre influence of the nuclear tropes of i at each moment of its existence Thus, these tropes have exactly the same spatial location at each moment of their existence

18. No Temporal Relativization Tropes are not directly temporally relativized: –the locations of tropes are determined by the spatio-temporal relations in which the n-bundle and the c-bundle occur The relation between tropes and substance (ontic predication) is not temporally relativized either: –According to the SNT, a nuclear trope u is a property of substance i iff: [1] u is strongly rigidly dependent on i, [2] necessarily, if u exists, u is a proper part of i, and [3] u is necessarily compresent with i Conditions [1] – [3] hold atemporally and are not temporally relativized

19. No Temporal Relativization If u is a contingent trope of substance i, u is a property of substance i iff: [1] u is strongly rigidly dependent on i; [2] necessarily, if u exists, u is a proper part of i, [3’] necessarily the temporal region that u occupies (T(u)) is a proper or improper part of the temporal region occupied by i (T(i)), i.e., (T(u) < T(i); does not include “at t”/”t-ly”) the spatial location of u coincides with the location of i at each moment of u’s existence

20. No Temporal Relativization Condition [3’] does not involve any temporal relativization: 1)Temporal sub-location is not time- relativization; rather, it is atemporal part- whole relation, sharing temporal location 2)Temporary parthood is theoretically redundant in the SNT: it does not do any explanatory work but is accounted for by [1], [2], and [3'] instead.

21. SNT and Kurtz’s Theses SNT accepts Kurtz’s theses 1, 2 and 3.1 but rejects 3.2: –According to the SNT, simple substance i can instantiate incompatible contingent property tropes at the distinct moments of its existence (thesis 1) –Numerically identical substance i survives change because its nuclear tropes persist (thesis 2) –Neither property tropes nor the possession of tropes is temporally relativized: The temporal region occupied by a contingent trope u (and the corresponding c-bundle) is a proper or improper part of the temporal region occupied by substance i (thesis 3.1). –Facts about time are relevant to the truth of the proposition that a substance i possess intrinsic feature F determined by trope u (contra 3.2).

22. No Bradley’s Regress Systematic presentation: –assumption 1: relations are further entities to their relata –assumption 2: entities a and b are related by C –how is C related to a? –by assumption 1, by another relation C', which is a distinct entity from C and a –how is C' related to a? –by assumption 1, an additional relational entity C'‘ –so on ad infinitum If the analysis of ontic predication were vulnerable to this problem, it would collapse into infinite regress, which would be vicious

23. No Bradley’s Regress The regress halts at formal relations that are not distinct entities from their relata (denying assumption 1) 1)Trope aggregates bundled by strong rigid and generic dependences –formal ontological relations (as well as parthood): not further entities to their relata 2)The spatio-temporal relations between trope bundles relational tropes –extra entities to their relata and the regress gets off the ground –however, the relational tropes are related to their relata by strong rigid dependence –thus, the regress stops at these SRDs

24. Coincidence, Fusion, Fission Concern mainly (highly) complex substances SNT is about simple substances Thus, they do not pose any substantial problem for the SNT SNT permits spatial compresence of concrete entities In SNT, simple substances cannot divide or fuse

25. Thank you! Any comments are welcome: –markku.keinanen@utu.fimarkku.keinanen@utu.fi –jani.hakkarainen@uta.fijani.hakkarainen@uta.fi