Michele Paolini Paoletti (Università degli Studi di Macerata) – michele.paolinip@gmail.com In: Bertini, D., Migliorini, D. (eds.) (2018), Relations. Ontology and Philosophy of Religion. Milan: Mimesis International: 109-122. Please quote only from published version. Bradley’s Regress: A Matter of Parsimony ) shall investigate in this contribution some solutions to Bradley s well-known regress. Moreover, I shall evaluate such solutions in light of the principle of ontological parsimony: all other things being equal, do not multiply entities (and types of entities) beyond necessity. This will show the advantages of accepting one peculiar solution to the regress, i.e., the one based on modes (particular properties that also ontologically depend on their bearers . )n section , ) shall present Bradley s regress. )n section , ) shall delve into some solutions to it. )n section 3, I shall introduce my own favourite solution, i.e., the mode solution, and I shall cope with some preliminary difficulties. In section 4 I shall introduce and clarify the principle of ontological parsimony. Finally, in section 5, I shall recall the solutions and I shall evaluate their degrees of parsimony. The overall conclusion of my argument will be that the mode solution is the most ontologically parsimonious solution to Bradley s regress. 1. Bradley’s Regress. )n this section, ) shall present Bradley s regress1. )n this context, Bradley s regress only concerns properties exemplification – though the original regress concerns the existence of relations in general. More precisely, as it was noticed by Vallicella2, Bradley s regress concerns the explanation of properties exemplification. Roughly, if properties are to be exemplified by their bearers and if one aims at explaining such a phenomenon, a vicious explanatory regress begins. Consider the seemingly true statement (1) Trump is a Republican. For most ontologists, such a statement – or the corresponding proposition – is made true by something in the universe. )t is made true by Trump s being a Republican, i.e., by the fact that Trump has the property of being a Republican. So far, so good. Yet, Trump could have existed even without having been a Republican. The property of being a Republican could have been exemplified by other entities – and not by Trump. Therefore, the relation between Trump and being a Republican call it exemplification seems to be an external one. External relations are not just grounded on their relata s existence, nor on their natures, nor on their intrinsic properties (i.e., the properties they have independently of the presence of any other entity)3. 1 See Francis Herbert Bradley, Appearance and Reality. 9th Edition (Oxford: Clarendon, 1930) and Collected Papers (Oxford: Oxford Univerty Press, 1969). See also Anna-Sofia Maurin, Bradley s Regress , Philosophical Compass 7(2012), 794-807. 2 William Vallicella, A Paradigm Theory of Existence. Onto-Theology Vindicated (Dordrecht: Springer, 2002). 3 See Michele Paolini Paoletti, Non-Symmetrical Relations, O-Roles and Modes , Acta Analytica 31(2016), 373-395. 1 Michele Paolini Paoletti (Università degli Studi di Macerata) – michele.paolinip@gmail.com In: Bertini, D., Migliorini, D. (eds.) (2018), Relations. Ontology and Philosophy of Religion. Milan: Mimesis International: 109-122. Please quote only from published version. Exemplification seems to be an external relation. For it is not just grounded on Trump s and being a Republican s existence, nor on their natures, nor on their intrinsic properties4. Here comes the trouble. Indeed, there should be an explanation as to why the exemplification relation holds between Trump and being a Republican. The exemplification relation itself could have existed even without relating Trump and being a Republican. Therefore, it seems that a further exemplification* relation must hold between Trump, being a Republican and the original exemplification relation5. Yet, in turn, exemplification* itself could have existed without relating those same entities. Thus, another exemplification** relation must be invoked, and so on, ad infinitum. What is troublesome here is not the existence of (possibly) infinite exemplification relations. What is troublesome is that explanation is always postponed. For exemplification* aims at explaining why the original exemplification relation, Trump and being a Republican are put together. Yet, exemplification** is in turn invoked to explain why exemplification*, the original exemplification relation, Trump and being a Republican are put together. And so on, ad infinitum. Here is a more precise statement of the argument: (i) if it is true that (1), then Trump exemplifies being a Republican; (ii) yet, if Trump exemplifies being a Republican, exemplification is an external relation between Trump and being a Republican; (iii) if (ii), then there must be an explanation as to why exemplification holds between Trump and being a Republican; (iv) thus, there must be an explanation as to why exemplification holds between Trump and being a Republican; (v) if (iv), then such an explanation cannot but invoke further exemplification relations, and so on, ad infinitum; (vi) thus, such an explanation cannot but invoke further exemplification relations, and so on, ad infinitum; (vii) it cannot be accepted that (vi): the regress is vicious. 2. Some Solutions. The first solution to Bradley s regress consists in rejecting the existence of properties nominalism about properties). If there is no property such as being a Republican, there is no need to unify that property 4 At least if it is legitimate to talk of intrinsic properties of further properties (e.g., the intrinsic properties of being a Republican). 5 Notice that, for the sake of the argument, exemplification* and the original exemplification relation could either be taken as two instances of some universal exemplification relation or as two distinct particular properties. 2 Michele Paolini Paoletti (Università degli Studi di Macerata) – michele.paolinip@gmail.com In: Bertini, D., Migliorini, D. (eds.) (2018), Relations. Ontology and Philosophy of Religion. Milan: Mimesis International: 109-122. Please quote only from published version. with Trump. I cannot evaluate here such a nominalist solution. For I can discuss here no general argument in favour of the existence of properties. What is clear is that, if one has sound reasons for accepting the existence of properties – and most ontologists think that there are such reasons –, then nominalism about properties is not a viable solution to Bradley s regress. Nominalism can also be restricted to certain entities. Indeed, another nominalist solution consists in denying that exemplifies denotes a relation (nominalism about exemplification)6. Still another nominalist solution is based on the rejection of facts such as Trump s being a Republican (nominalism about facts). If there are no facts, we do not need to face the problem of explaining the unity of objects and properties within facts, e.g., we do not need to explain why and how Trump and being a Republican are unified within the fact that Trump is a Republican. Yet, even if we rejected the exemplification relation and/or facts, we would still need to explain what distinguishes (on the one hand) the mere sum of Trump and the property of being a Republican from on the other hand Trump s being a Republican – whatever Trump s being a Republican may turn out to be. In other terms, we would still need to explain why Trump and being a Republican can both exist in a possible world where Trump is not a Republican. One could also claim that there is nothing to explain here. Namely, one could claim that the difference between the mere sum of Trump and the property of being a Republican and Trump s being a Republican is a brute, unexplainable one (brutalism). The premise to be rejected is (iii). This sounds unacceptable in terms of ontological parsimony, as we shall see in section 5. One classical solution to Bradley s regress consists in delving into the nature of properties. Properties are such that they are unsaturated or incomplete entities (incompleteness solution). Properties need to be saturated/completed by something else. Therefore, being a Republican is something that needs to be completed by entities such as Trump. This means that exemplification is not an external relation, but an internal one – against (ii). We should distinguish here between two distinct theses. It might well be true that being a Republican is something that needs to be completed by entities such as Trump, i.e., by Trump or by some other object. Yet, this does not entail that being a Republican is something that needs to be completed by Trump (and only by Trump) within the fact that Trump is a Republican. What needs to be explained here is the unity of the latter fact. On the contrary, we do not need to explain the unity of being a Republican with some object or other within some fact. Bradley s regress would be avoided only if one were to argue that being a Republican needs to be completed by Trump – and only by Trump –, which is a much more contentious thesis. 6 See Peter Schulte, (ow to link particulars to universals: Four versions of Bradley's regress refuted , Philosophia Naturalis 44(2007), 219-237. 3 Michele Paolini Paoletti (Università degli Studi di Macerata) – michele.paolinip@gmail.com In: Bertini, D., Migliorini, D. (eds.) (2018), Relations. Ontology and Philosophy of Religion. Milan: Mimesis International: 109-122. Please quote only from published version. Along these lines, Baxter7 and Armstrong8 claim that being a Republican is partly identical with Trump, i.e., that exemplification is an internal relation that is necessitated by its relata (in this case, being a Republican and Trump) (partial identity solution). In a nutshell, being a Republican and Trump are partly identical with one another, so that (1) is nothing but a way of expressing such a partial identity. This amounts to rejecting (ii): partial identity flows from Trump and being a Republican. Yet, what would it happen in a world where Trump is not a Republican? Trump (our Trump) – if he is partly identical with being a Republican – could not exist in that world. In addition, being a Republican (the actual property of being a Republican) – if it is partly identical with Trump – could not exist in that world. This means that, in that world, there are (at best) counterparts of Trump and of being a Republican, i.e., entities that are very similar, though not identical with the actual Trump and the actual property of being a Republican. This is quite expensive from the ontological viewpoint, as we shall see in section 5. One could also bite the bullet by accepting Bradley s regress and by then arguing that the regress is not vicious, thus rejecting (vii) (non-vicious regress solution)9. Recall that what is troublesome in Bradley s regress is not the existence of infinite exemplification facts. What is problematic is that explanation is always postponed. According to this solution, even if explanation is always postponed, every step in the explanatory chain is explained by the next step, and so on, ad infinitum. That Trump exemplifies being a Republican is explained by exemplification* s holding between Trump, being a Republican and exemplification; that exemplification* holds between Trump, being a Republican and exemplification is explained by exemplification** s holding between Trump, being a Republican, exemplification and exemplification; and so on, ad infinitum. According to Grossmann10, exemplification is just like glue (glue solution). Glue does not need to be stuck with further glue to the objects it applies to. In a similar vein, it is part of the nature of exemplification that exemplification applies to Trump and being a Republican without any further exemplification* relation. Since this solution somehow resembles the incompleteness solution, I shall not discuss its shortcomings here. According to Vallicella11, one needs an external unifier (something similar to God) in order to unify Trump and being a Republican (external unifier solution). Such an external unifier self-determines itself to unify that object with that property and there is no need to appeal to further entities, nor to provide any further explanation. Donald L. M. Baxter, Instantiation as Partial Identity , Australasian Journal of Philosophy 79(2001), 449-464. David M. Armstrong, How Do Particulars Stand to Universals? , Oxford Studies in Metaphysics 1(2007), 139-153. 9 See Francesco Orilia, States of affairs. Bradley vs. Meinong , in Meinongian Issues in Contemporary Italian Philosophy, edited by V. Raspa (Frankfurt: Ontos, 2006), 213–238. 10 Reinhardt Grossmann, The Categorial Structure of the World (Bloomington: University of Indiana Press, 1983). 11 William Vallicella, A Paradigm Theory of Existence. Onto-Theology Vindicated (Dordrecht: Springer, 2002). 7 8 4 Michele Paolini Paoletti (Università degli Studi di Macerata) – michele.paolinip@gmail.com In: Bertini, D., Migliorini, D. (eds.) (2018), Relations. Ontology and Philosophy of Religion. Milan: Mimesis International: 109-122. Please quote only from published version. Finally, following some suggestions given by Meinertsen12, exemplification can relate itself to its own relata, i.e., to Trump and being a Republican (self-relating exemplification solution). Exemplification turns out to be a three-place relation between Trump, being a Republican and itself. What is still unclear in this solution is the following: why does exemplification relate itself to Trump and being a Republican in those possible worlds where Trump is a Republican, whereas it does not relate itself to Trump and being a Republican in those possible worlds where Trump is not a Republican? An explanation still needs to be provided. 3. The Modes Solution. Modes are particular properties that also ontologically depend on their bearers for their own identity and existence. For example, Trump’s being a Republican is a mode of Trump, that also ontologically depends on Trump for its identity (i.e., for its being the very mode it is) and for its existence (so that it cannot exist without Trump)13. Modes ground an interesting solution to Bradley s regress14. Modes are such that they are internally unified with their bearers , so to say. Trump’s being a Republican would not exist and it would not be the very mode it is, without there being Trump and without its being a mode of Trump – and of no one/nothing else. Therefore, it is not true that Trump and the mode Trump’s being a Republican could exist apart from one another. If Trump’s being a Republican exists, it is a mode of Trump, i.e., it is had by Trump. The mode solution rejects premise (ii) of the argument for Bradley s regress. Exemplification is not an external relation. Either exemplification does not exist – as there are only objects such as Trump and modes such as Trump’s being a Republican – or it is an internal relation – that entirely flows from the very nature and existence of Trump’s being a Republican. Fraser MacBride15 has an objection against relational modes that can also be applied to the mode solution. Take a relational mode such as Romeo’s loving Juliet. According to MacBride, one cannot explain a relational mode s capacity to relate certain relata by including its relata in that mode s nature. Namely, one cannot explain Romeo’s loving Juliet’s capacity to relate Romeo and Juliet (and no other relatum) by making it the case that that mode s nature includes both Romeo and Juliet.In a similar vein, Bo Meinertsen, A Relation as the Unifier of States of Affairs , Dialectica 62(2008), 1-19. See John Heil, From an Ontological Point of View (Oxford: Clarendon, 2003) and E. Jonathan Lowe, The FourCategory Ontology: A Metaphysical Foundation for Natural Sciences (Oxford: Oxford University Press, 2006). 14 See Anna-Sofia Maurin, Trope Theory and Bradley Regress , Synthese 175(2010), 311-326, Peter Simons, Relations and Truthmaking , Proceedings of the Aristotelian Society. Supplementary Volumes, 84(2010), 199-213, and my Non-Symmetrical Relations, O-Roles and Modes . For a similar solution – that is not properly based on modes – see Jan Willem Wieland and Arianna Betti, Relata-Specific Relations: A Response to Vallicella , Dialectica 62(2008), 509-524. 15 See Fraser MacBride, Relations and Truthmaking Proceedings of the Aristotelian Society. Supplementary Volumes 84(2010), 161-179. 12 13 5 Michele Paolini Paoletti (Università degli Studi di Macerata) – michele.paolinip@gmail.com In: Bertini, D., Migliorini, D. (eds.) (2018), Relations. Ontology and Philosophy of Religion. Milan: Mimesis International: 109-122. Please quote only from published version. one cannot explain why Trump’s being a Republican characterizes Trump (i.e., it is exemplified by Trump and by no other object by including Trump in that mode s nature. I have argued against this objection in my Non-Symmetrical Relations, O-Roles and Modes . In a nutshell, one could either look for a reductionist or for a non-reductionist explanation as to why Trump’s being a Republican includes Trump. In the former case, if one looks for a reductionist explanation (i.e., an explanation in terms of further, more ontologically fundamental entities), one begs the question against the mode solution. For the mode solution assumes that modes are irreducible entities – though they partly depend on their bearers . Therefore, no reductionist explanation of the existence of Trump’s being a Republican can be given. Alternatively, if one looks for a non-reductive explanation of the existence of Trump’s being a Republican, one can appeal to further entities in order to provide such an explanation. One can claim that Trump has other modes that somehow make it the case that he is a Republican. Yet, in both cases, there is no need to explain the unity of Trump and of the property of being a Republican. For Trump’s being a Republican is already unified with Trump by its own nature. Let me stress that the mode solution is not analogous to the brute difference solution. According to the latter, the difference between the mere sum of Trump and the property of being a Republican and the fact that Trump is a Republican is a brute, unexplainable difference. According to the mode solution, there is nothing to explain here because there is no property of being a Republican that can exist apart from Trump. There are modes such as Trump’s being a Republican, Cheney’s being a Republican, Clinton’s being a Democrat, which are internally unified with their bearers , since they depend on the latter. Moreover, the mode solution could easily accept that properties are identical with property-instances. For there are only property-instances – or property-instances are the only entities that one needs to invoke together with their bearers in order to solve Bradley s regress16. 4. Ontological Parsimony. The principle of ontological parsimony roughly states that, all other things being equal, we should only accept the ontological theory/-ies that posit(s) the smallest number of entities. More precisely: consider two ontological theories T1 and T2. Assume that T1 and T2 posit the same entities, except for certain entities Es. T1 accepts the Es, whereas T2 rejects the Es. If T1 and T2 have the 16 In his The Paradigm Theory of Existence, Vallicella has two other objections against the mode solution. First, substances (i.e., entities such as Trump) are murky additions of being. Yet, substances are implicitly included in all the solutions we discussed in section 2, so that they cannot only be a trouble for the mode solution. Secondly, some modes require external relations for their own existence. For example, Socrates’ being shorter than Simmias requires some external coordination or co-existence relation between Socrates and Simmias for its existence. Thus, one cannot avoid postulating external relations (such as exemplification) by only invoking modes. In reply, I have argued in my Non-Symmetrical Relations, O-Roles and Modes that external relations can be interpreted as modes. In addition, not every mode seemingly requires external relations. 6 Michele Paolini Paoletti (Università degli Studi di Macerata) – michele.paolinip@gmail.com In: Bertini, D., Migliorini, D. (eds.) (2018), Relations. Ontology and Philosophy of Religion. Milan: Mimesis International: 109-122. Please quote only from published version. same explanatory power and the same degrees of all the other theoretical virtues, we should accept T2 and reject T1. For T2 posits the smallest number of entities, since it rejects the Es. Of course, some clarifications are in order. First, one could reformulate the principle of ontological parsimony by only talking of fundamental entities, i.e., of entities that do not ontologically depend on further entities and on which further entities ontologically depend. Thus, if we accept this proposal, we should only accept the ontological theory/-ies that posit(s) the smallest number of fundamental entities17. For the sake of this paper, I assume that, if some entities are invoked to explain the unification of properties and their bearers i.e., to solve Bradley s regress), such entities can be taken as bona fide fundamental. Secondly, when evaluating the number of entities posited by theories, one could either consider types of entities, or singular entities. Therefore, all other things being equal, one should either accept the ontological theory/-ies that posit(s) the smallest number of types of entities, or one should accept the ontological theory/-ies that posit(s) the smallest number of singular entities. My intuition is that parsimony in the types of entities is more important than parsimony in the number of singular entities. However, both sorts of parsimony should be taken into account and, besides types, we should try not to multiply singular entities without necessity18. With this principle in mind, we can try to assess all the solutions to Bradley s problem presented in section 2. 5. Parsimony and Modes. The mode solution is committed to two types of entities: substances or objects – such as Trump – and modes – such as Trump’s being a Republican. It explains the unity of Trump’s being a Republican by claiming that the mode Trump’s being a Republican implies – by its own nature – that Trump is its bearer . We have already seen that nominalism about exemplification and nominalism about facts provide no explanation for the unity of the fact that Trump is a Republican. Therefore, they cannot be compared with the other solutions in light of their ontological parsimony. For the all other things being equal clause is not satisfied: the explanatory power is not the same, so that all other things are not equal. Nor can brutalism satisfy that clause. Moreover, brutalism posits three types of entities: substances, properties and facts. The incompleteness solution does not explain why being a Republican is completed by Trump – and only by Trump, in this particular case. In addition, it posits three types of entities too: substances, 17 See Jonathan Schaffer, What Not To Multiply Without Necessity , Australasian Journal of Philosophy 93(2015), 644-664. 18 See Chris Daly, An Introduction to Philosophical Methods (Peterborough: Broadview, 2010), 131-154, and Elliot Sober, Ockham’s Razors. A User’s Manual (Cambridge: Cambridge University Press, 2015). 7 Michele Paolini Paoletti (Università degli Studi di Macerata) – michele.paolinip@gmail.com In: Bertini, D., Migliorini, D. (eds.) (2018), Relations. Ontology and Philosophy of Religion. Milan: Mimesis International: 109-122. Please quote only from published version. properties and facts. In sum, both brutalism and the incompleteness solution posit more types of entities than the mode solution and they are endowed with less explanatory power. Consider now the partial identity solution. Even if this solution seems to have the same explanatory power as the mode solution, the partial identity solution needs to posit counterparts of Trump and of being a Republican. True: such counterparts are merely possible entities, because they are needed to explain why Trump is not a Republican in some other possible world. Yet, insofar as they play some explanatory role, they need to be included in that solution s ontology. Turn now to the non-vicious regress solution. Prima facie, this solution includes infinite exemplification relations. For each relation plays some role in explaining why some further exemplification relation holds between certain entities. Exemplification* is needed to explain why exemplification holds between Trump and being a Republican. In turn, exemplification** is needed to explain why exemplification* holds between exemplification, Trump and being a Republican. And so on. This seems to imply that there are four types of fundamental entities: facts, properties, substances and exemplification relations. Moreover, there are infinite, singular exemplification relations and facts. This is far from being ontologically parsimonious. In reply, one could restrict the principle of ontological parsimony to fundamental entities. One could then claim that singular exemplification relations are not fundamental. That some exemplification relation holds between its relata is explained by some further exemplification* relation, and so on, ad infinitum. No singular exemplification relation is fundamental. Yet, even if this were the case, exemplification relations as a type would still be fundamental. For they would be needed to explain – as a type – why properties are exemplified by objects. Moreover, the overall situation would turn out to be rather strange. Exemplification relations as a type would be fundamental, but no singular exemplification relation would be fundamental. How could this be the case? Namely: how could it be the case that a certain type of entities is fundamental, but no entity within that type is fundamental? Finally, facts would still be there and they would be counted as fundamental entities – at least if they were needed to explain something else. Thus, the non-vicious regress solution, even when it is modified as I have suggested, still needs to count three types of fundamental entities. One more general objection against my argumentative strategy is now in order. If facts depend on properties and objects, why should we count them as ontologically fundamental entities? Why can we not claim that the non-vicious regress solution – as well as the incompleteness solution – actually has only two types of fundamental entities, i.e., properties and objects? Both solutions now turn out to be at least as ontologically parsimonious as the mode solution. In order to deal with this objection, it is necessary to discuss my notion of fundamentality. I have claimed in section 4 that fundamental entities are all and only those entities that do not ontologically depend on further entities and on which further entities ontologically depend. On this view, facts do not count as 8 Michele Paolini Paoletti (Università degli Studi di Macerata) – michele.paolinip@gmail.com In: Bertini, D., Migliorini, D. (eds.) (2018), Relations. Ontology and Philosophy of Religion. Milan: Mimesis International: 109-122. Please quote only from published version. fundamental entities. Therefore, if one only needs to restrict the number of fundamental entities, the objection goes in the right direction. Yet, facts are presumably invoked within one s ontology in order to play some further explanatory role. Facts may be required as causal relata, or they can be invoked within laws of nature. Otherwise, there would be no need to accept facts. Define now fundamental* entities as all and only those nonfundamental entities on which further entities depend. Facts seem to be fundamental* entities. Moreover, it seems that, all other things being equal, one should be ontologically parsimonious in the number of types of both fundamental and fundamental* entities. For if we can do without certain types of fundamental* entities, if their explanatory role can be played by something else… why do we need those types of entities in our ontology? This introduces a caveat for the mode solution. The mode solution should be favoured over the fact solutions (i.e., the non-vicious regress and the incompleteness solutions) only if modes can play the same explanatory role of facts. I do not see any special difficulty for the mode solution here: in principle, whatever facts can do can also be done by modes. In addition, we may note that even modes are fundamental* entities, because they also ontologically depend on their bearers and they are taken to play some explanatory role. In comparison with the mode solution, both the glue solution and the external unifier solution posit one extra entity/type of entities: glue and the external unifier. Yet, glue and the external unifier do not belong to the category of properties. Otherwise, one should still explain how they are unified with Trump and being a Republican. Maybe the external unifier (i.e., God) is a substance, so that one only has two types of entities, i.e., substances and properties. (owever, God is an extra addition of being here, i.e., He is an extra singular entity we can avoid postulating if we accept the mode solution. Finally, the self-relating exemplification solution still needs to explain why exemplification relates itself with Trump and being a Republican. Moreover, it posits three singular entities: self-relating exemplification, being a Republican and Trump. Self-relating exemplification and being a Republican might well belong to the same category of n-adic properties. Thus, we might still have the same number of types of entities as the mode solution, i.e., two. Yet, with respect to the number of singular entities, the self-relating exemplification solution is less ontologically parsimonious. For it posits at least three entities in correspondence with Trump s being a Republican: Trump, being a Republican and selfrelating exemplification. In sum, all other things being equal (and all other things are equal, at least as concerns explanatory power , the mode solution is more ontologically parsimonious than the other solutions to Bradley s regress. Before closing, let me anticipate and address three objections. First, it could be pointed out that the mode solution actually has at least the same commitments as certain other solutions. For universal properties could be still required in order to ground the similarities between modes. Therefore, the 9 Michele Paolini Paoletti (Università degli Studi di Macerata) – michele.paolinip@gmail.com In: Bertini, D., Migliorini, D. (eds.) (2018), Relations. Ontology and Philosophy of Religion. Milan: Mimesis International: 109-122. Please quote only from published version. mode solution actually accepts three types of entities: substances, modes and universal properties. In a similar vein, brutalism and the incompleteness solution accept three types of entities: facts, universal properties and substances. Yet, even accepting this point, I have argued that the explanatory power is not the same. Brutalism does not explain why facts are unified, whereas the incompleteness solution does not explain why a certain property is unified with a certain substance. On the contrary, there is no need to explain unification in terms of further entities within the mode solution. The second objection could go as follows. The mode solution is less ontologically parsimonious than certain other solutions in terms of the number of singular properties. For example, where the incompleteness solution only accepts the universal property of being a Republican, the mode solution has to introduce several modes, such as Trump’s being a Republican, Bush’s being a Republican, and so on. This objection does not take into account that the universalist solutions still need one further type of entities, i.e., facts. Moreover, they still need one singular fact in correspondence with every singular mode. This is far from making the universalist solutions ontologically less parsimonious. Thirdly and finally, one could look for an even cheaper solution, i.e., a solution based on tropes. I assume here that tropes are particular properties that do not depend on their bearers . )f there are only tropes – one could argue – and if substances are entirely dependent on tropes (e.g., if they are bundles of tropes), then we are committed to one type of entities: tropes. There seems to be no Bradley s regress for this solution. In reply, I have one dilemma for trope theorists. Either every collection – or bundle – of tropes corresponds to an object/substance such as Trump, or it does not. In the latter case, one should still need to explain why only certain collections correspond to objects. Without explaining this fact, only certain collections of tropes – and not all collections of tropes – would turn out to be fundamental entities. Therefore, trope theorists would still need to count two types of entities (or of fundamental entities): tropes and the relevant and fundamental collections of tropes. In a nutshell, if one chooses the second horn of the dilemma (i.e., that not every collection of tropes corresponds to an object), either the explanatory power of the trope theory diminishes, or there still are two types of entities (or two types of fundamental entities). Take the former case, i.e., every collection of tropes corresponds to an object such as Trump. This seems to run against our commonsensical intuitions. For example: the collection of some being a Democrat trope and of some being called Trump trope does not seem to correspond to any object such as a Trump the Democrat. Moreover, even if this were the case, there would be an overabundance of singular collection-objects that would violate the principle of ontological parsimony for singular entities. Finally, one would still need to explain why certain collection-objects (e.g., Trump the Republican) seem to be more important than others (e.g., Trump the Democrat) for our knowledge of the universe19. 19 This contribution has been revised by Richard Davies (University of Bergamo). 10