Michele Paolini Paoletti – Università degli Studi di Macerata (michele.paolinip@gmail.com) Acta Analytica, 35(3)(2020): 421-437. Please quote only from the published version. Against Conjunctive Properties ABSTRACT: I put in question in this article the existence of conjunctive properties. In the second section, after having provided a characterization of conjunctive properties, I develop an argument based on the principle of ontological parsimony: if we accept that there are conjunctive properties in the universe then, ceteris paribus, our ontology turns out to be less ontologically parsimonious than if we reject them. Afterwards, in the third section, I distinguish between maximalist and non-maximalist and reductionist and non-reductionist theories of conjunctive properties., as well as between reductionist and non-reductionist theories that reject conjunctive properties. Such distinctions help to clarify the options at hand when accepting or rejecting conjunctive properties. In light of these distinctions, I then tackle two objections against the argument from ontological parsimony. Finally, in the remaining sections, I deal with two arguments defended by D. M. Armstrong for the existence of conjunctive properties: the argument from infinite complexity and the argument from causal powers. I show that there are several ways to resist these arguments and their conclusion. 1. Introduction. Consider Socrates. Socrates is both an animal and a rational being. Namely, admitting that there are properties in the universe, Socrates has both the properties of being an animal and of being rational. We are not concerned here with the nature of properties and of property-instantiation: maybe being an animal and being rational are particular properties (i.e., tropes), maybe they are universals; maybe Socrates exemplifies those properties, maybe he is a bundle of them. In any case, if Socrates is an animal and if he is a rational being, we stipulate that there are two propertyinstances here: that Socrates is an animal and that Socrates is a rational being. Moreover, that Socrates is an animal and that Socrates is a rational being is a conjunction of property-instances. Those who believe in the existence of the conjunctive properties claim that this conjunction of property-instances makes it the case that Socrates has the property of being an animal and being rational. Being an animal and being rational is a conjunctive property. In addition, some of those who believe in conjunctive properties could accept maximalism about them: for any property A and B (and C, and D, and…) had by something (where all such properties are different from one another), that thing also has the conjunctive property A and B (and C, and D, and…). Namely, every conjunction of property-instances is nothing but – or corresponds to – an instance of a conjunctive property. If Socrates has the properties of being an animal, of being rational and of being a philosopher, then Socrates also has the conjunctive properties of: being an animal and being rational; being rational and being a philosopher; being an animal and being a philosopher; being an animal and being rational and being a philosopher. On the contrary, other believers in conjunctive properties could reject maximalism. Namely, according to the latter, not every conjunction of property-instances is an instance (or corresponds to an instance) of a conjunctive property. In the aforementioned example, Socrates has the conjunctive property of being an animal and being rational, but he does not have the other conjunctive properties. The reason why we should only accept that conjunctive property could be the following: being an animal and being 1 Michele Paolini Paoletti – Università degli Studi di Macerata (michele.paolinip@gmail.com) Acta Analytica, 35(3)(2020): 421-437. Please quote only from the published version. rational is what it is for Socrates to be a human being, whereas the other conjunctive properties are not relevant for explaining anything about Socrates. Ceteris paribus, the second solution should be preferred in order to avoid proliferation of properties. For both solutions seemingly have the same explanatory power. The additional conjunctive properties introduced in the first solution do not explain anything. Thus, they are gratuitous additions of being. In this paper, I wish to argue against the existence of conjunctive properties both in light of the maximalist and the non-maximalist conception. In the second section, I shall introduce an argument from ontological parsimony. I shall try to show that, ceteris paribus, a theory accepting only simple (i.e., non-conjunctive) properties (in brief, S.P.T.) should be favoured over a theory accepting both simple and conjunctive properties (in brief, C.P.T.). For the sake of the argument, I shall also provide a characterization of conjunctive properties. In the third section, discussing my argument, I shall analyse two possible replies on behalf of conjunctive properties theorists. The first reply consists in pointing out that C.P.T. has more explanatory power than S.P.T. For the sake of the discussion, I shall draw a useful distinction between a reductionist and a nonreductionist version of S.P.T., as well as between a reductionist and a non-reductionist version of C.P.T. This move will broaden our perspective on conjunctive properties and introduce all the options one has when accepting or rejecting the latter. Such options will be evaluated both in light of their explanatory power and of their ontological parsimony. The second reply analysed in this section consists in arguing that the reductionist version of C.P.T. is more ontologically parsimonious than any other version. In the end, I shall argue that we should accept the non-reductionist version of S.P.T. In the fourth and fifth sections, I shall tackle two arguments formulated by David M. Armstrong for the existence of conjunctive properties. The first argument, examined in the fourth section, considers the possibility of there being only conjunctive properties in the universe. The second argument, examined in the fifth and final section, considers the idea that conjunctive properties confer unique causal powers, i.e., causal powers that cannot be conferred by any simple property at all in isolation. 2. The Argument from Ontological Parsimony. Ontological parsimony is a guiding principle for most ontologists. It can be formulated as follows: do not multiply entities beyond necessity. Consider two ontological theories T 1 and T2. Assume that T1 and T2 have the same explanatory power, i.e., that they explain all and only the same phenomena in the universe. T1 and T2 accept all and only the same entities, except for a certain class of entities, i.e., the Es: T1 rejects the Es, whereas T2 accepts them. Following the principle of ontological parsimony, we should favour T1. For ceteris paribus (i.e., given the same explanatory power and the admission of all and only the same further entities1) T1 has fewer entities than T2. 1 I am well aware that theories have other theoretical virtues, such as consistency and fruitfulness. However, I assume here for the sake of the argument that T1 and T2, as well as all the other theories to be compared, are on a par with one another with respect to such virtues. The view of parsimony introduced here incorporates Barnes 2 Michele Paolini Paoletti – Università degli Studi di Macerata (michele.paolinip@gmail.com) Acta Analytica, 35(3)(2020): 421-437. Please quote only from the published version. Ontological parsimony either concerns types of entities or single entities within a certain type. The Es are a certain type of entities. Thus, T1 is more ontologically parsimonious than T2 with regard to the types of entities to be accepted. Yet, one could also consider all the single Es. If two theories T3 and T4 both accepted the Es, but T3 accepted fewer Es than T4, then, ceteris paribus, T3 should be favoured over T4. For T3 would be more ontologically parsimonious than T4 with respect to the number of single Es to be accepted. Ontological parsimony in types is often more relevant than ontological parsimony in the number of entities within a certain type. For philosophers do not aim at establishing how many entities of a certain type are there in the universe. For example: they do not aim at establishing how many properties are there in the universe or how many properties are instantiated by Socrates. They aim at establishing if there are certain types of entities with certain features: e.g., if there are properties. Moreover, within that type, they aim at establishing if there are certain subtypes: e.g., conjunctive properties2. Thus, we shall be primarily concerned here with ontological parsimony in types of entities3. However, on some specific issues, we shall also consider parsimony in the number of single entities. Consider now two property-instances: something is A and something is B. In general, believers in conjunctive properties accept that there is a third property here, i.e., the conjunctive property of being A and being B, which is instantiated by the very same thing that is A and B. For example, as we have already seen, if Socrates is an animal and if he is rational, then he also has the conjunctive property of being an animal and being rational. However, not all the conjunctive predicates such as “is so-and-so and so-and-so” denote conjunctive properties. For example, it seems to me reasonable to deny that the predicate “is an animal and is an animal” denotes the conjunctive property of being an animal and being an animal, which has the same extension of the property of being an animal and adds nothing to the sort of similarity grounded on being an animal. Thus, how can one distinguish between the conjunctive predicates that legitimately denote conjunctive properties and those that do not denote them? More generally, how can one distinguish between conjunctive and non-conjunctive properties? I ran into a similar problem in Paolini Paoletti (2017) when I tried to distinguish between positive and negative properties. In the end, I suggested the following solution: a property non-P referred to by a predicate “is not P” is negative iff (if and only if) what “is not P” means can only be expressed in purely negative terms. By “purely”, I mean to rule out mixtures of positive and negative terms. The idea behind this solution is that what a predicate means is nothing but the nature of the property to which that (2000)’s anti-superfluity principle. For, in my comparison of T1 and T2, I claim that we should not accept entities that do not improve the explanatory power of a theory. 2 I assume here that both those who defend the existence of conjunctive properties and those who reject them agree on there being a certain type of entities, i.e., that of properties. What is evaluated here in terms of parsimony – and of other theoretical virtues, such as explanatory power – is the distinction between at least two different subtypes, i.e., simple and conjunctive properties. 3 On ontological parsimony, see for example Daly (2010: 131-154) and Sober (2015). Moreover, I accept Nolan (1997)’s characterization of quantitative parsimony as parsimony in the number of entities within a type. 3 Michele Paolini Paoletti – Università degli Studi di Macerata (michele.paolinip@gmail.com) Acta Analytica, 35(3)(2020): 421-437. Please quote only from the published version. predicate aims at referring. Thus, what a negative predicate means is nothing but the negative nature of the property to which that predicate aims at referring. This means that even positive predicates such as “is at rest” can denote negative properties, insofar as what “is at rest” means can only be expressed in purely negative terms. Something analogous can be suggested with regard to conjunctive properties. Namely, I suggest that a property P and Q referred to by a predicate “is P and Q” (here I use “P” and “Q” as variables ranging over properties, that can possibly denote even one and the same property) is conjunctive iff (if and only if) what “is P and Q” means can only be expressed in purely conjunctive terms, i.e., by invoking conjunctions of properties. This rules out that “is an animal and is animal” can denote a conjunctive property. For what “is an animal and is an animal” means can also be exhaustively expressed in non-conjunctive terms, by appealing to the non-conjunctive predicate “is an animal” and the corresponding non-conjunctive property of being an animal. On the contrary, “is an animal and is rational” denotes a conjunctive property, i.e., that of being an animal and being rational. However, one problem suddenly arises. What the predicate “is an animal and is rational” means can also be expressed in non-conjunctive terms, by appealing to the non-conjunctive predicate “is human” and to the non-conjunctive property of being human – at least if we accept that “being human” denotes a non-conjunctive property distinct from being an animal and being rational (as the non-reductionist version of the conjunctive property theory discussed in section 3 does). Thus, on the suggested criterion, “is an animal and is rational” does not denote any conjunctive property. To amend this criterion, one could try to rule out – when expressing what “is P and Q” means – all the predicates that are different from “P” and “Q”. The criterion could be amended as follows: a property P and Q referred to by a predicate “is P and Q” is conjunctive iff, whenever one is required to invoke no other predicate but the conjuncts “P” and “Q”, what “is P and Q” means can only be expressed in purely conjunctive terms. The restriction introduced by “whenever” is meant to rule out that one can appeal to further predicates different from “P” and “Q” (e.g., the predicate “is human”) when expressing what “is P and Q” means. On this amended criterion, “is an animal and is rational” still denotes a conjunctive property. For if we wanted to clarify the meaning of that predicate we would need to appeal to the predicate “is human”, which is not a conjunct of “is an animal and is rational”. Please note that this criterion does not rule out the existence of conjunctive properties with more than two conjuncts. Nor does it rule out that the conjuncts could also be negative and/or non-simple properties (e.g., disjunctive ones). Now turn back to being an animal and being rational. Call the ontological theory that accepts such a third conjunctive property (in addition to the properties of being an animal and of being rational) – and all the other legitimate conjunctive properties - “conjunctive properties theory” or “C.P.T.”. C.P.T. is compatible with maximalism and non-maximalism about conjunctive properties. For maximalists, all conjunctions of property-instances give rise to legitimate conjunctive properties. For non-maximalists, only some conjunctions of property-instances give rise to legitimate conjunctive properties. 4 Michele Paolini Paoletti – Università degli Studi di Macerata (michele.paolinip@gmail.com) Acta Analytica, 35(3)(2020): 421-437. Please quote only from the published version. Call the ontological theory that rejects such a third conjunctive property – and all the other conjunctive properties – “simple properties theory” or “S.P.T.”. Here “simple” only means “non-conjunctive”. Therefore, in principle, S.P.T. could also accept properties “formed from” other properties, such as negative and disjunctive ones4. Assume, for the sake of the argument (though we shall put in question this assumption in the next sections), that C.P.T. and S.P.T. have the same explanatory power and that they differ only with respect to the admission or rejection of conjunctive properties. Namely, C.P.T. and S.P.T. accept all and only the same types of entities, except for conjunctive properties: C.P.T. accepts conjunctive properties; S.P.T. rejects them. Here is the first premise of my argument: (1) besides conjunctive properties, C.P.T. is also committed to simple properties – and S.P.T. is committed to simple properties as well. The reason why we should accept (1) is that each conjunctive property seems to be composed of simple properties. For example: being an animal and being rational seems to be composed of the simple properties of being an animal and of being rational. The conjunctive property of (being an animal or being rational) and being a philosopher is composed of the disjunctive (i.e., non-conjunctive and simple) property of being an animal or being rational and of the simple property of being a philosopher. Therefore, in addition to conjunctive properties, C.P.T. also accepts simple properties. S.P.T. accepts simple properties as well – provided that it differs from C.P.T. only with respect to the denial of conjunctive properties. The second premise of my argument is the following: (2) ceteris paribus, an ontological theory that accepts both conjunctive and simple properties is less ontologically parsimonious than an ontological theory that only accepts simple properties (and rejects conjunctive ones). Justifying (2) is not difficult. If two theories have the same explanatory power and they accept all and only the same types of entities except for the Es (this is what is meant by the “ceteris paribus” clause), 4 Given my characterization of simplicity, being an animal and all the other simple properties mentioned here need not be borne by the most fundamental entities of the universe – if any – in order to be simple. I also assume that properties such as being an animal and being rational are bona fide, existing ones. However, if one does not believe in their existence, one can choose other examples involving other properties. Another point is worth mentioning here. According to Swoyer (1998), there are at least two ways of interpreting compound properties such as conjunctive ones. The first way asserts that they are literally composed of or formed from other properties – this is the interpretation I implicitly assume here. The second way asserts that seemingly compound properties are such that one can specify them in complex/structured ways. Yet, such a specification expresses only the inferential relationships between those properties and further properties. It does not imply anything about their structure and complexity. It seems to me that, on this view, conjunctive properties are rebutted from the start. For “being an animal and being rational” either turns out to specify the inferential relationships between being human and being an animal and being rational (i.e., the former implies being an animal, as well as being rational) or that the properties of being an animal and being rational, when they are instantiated together, imply a certain set of further properties that they do not imply when they are instantiated in isolation. 5 Michele Paolini Paoletti – Università degli Studi di Macerata (michele.paolinip@gmail.com) Acta Analytica, 35(3)(2020): 421-437. Please quote only from the published version. then adding one further type of entities (i.e., the Es) in one of such theories is a gratuitous addition of being. There is no reason why we should add that further type of entities. The conclusion of my argument is the following: (3) therefore, ceteris paribus, C.P.T. is less ontologically parsimonious than S.P.T. Indeed, C.P.T. and S.P.T. are instances of (2): C.P.T. is an ontological theory that accepts conjunctive and, by (1), simple properties; S.P.T. is an ontological theory that, by (1), accepts simple properties and rejects conjunctive properties. Since we should favour ontological parsimony in types of entities, ceteris paribus, S.P.T. should be favoured over C.P.T. Conjunctive properties are a gratuitous addition of being. 3. Two Replies and Four Options about Simple and Conjunctive Properties. There are two strategies to deal with this argument. First, one could argue against (1). Secondly, one could argue against C.P.T.’s and S.P.T.’s being instances of (2). The first strategy will be examined in section 4. The two replies that I shall consider in this section are examples of the second strategy. To analyse such replies, I shall draw a distinction between reductionist and non-reductionist versions of S.P.T. and C.P.T. More generally, my discussion will highlight the options one has when accepting or rejecting conjunctive properties. The first reply goes as follows: while it is true in general that (2), the “ceteris paribus” clause does not apply to C.P.T. and S.P.T. Therefore, C.P.T. and S.P.T. are not instances of (2). For C.P.T. has more explanatory power than S.P.T. – this also puts in question my assumption that S.P.T. and C.P.T. have the same explanatory power. Consider again the conjunctive property of being an animal and being rational. Accepting that property, C.P.T. can show that the (seemingly simple) property of being human is identical with the conjunctive property of being an animal and being rational – or that it is at least necessarily co-instantiated with the latter (i.e., as a matter of necessity, something has the property of being human if and only if it has the conjunctive property of being an animal and being rational). Thus, C.P.T. can somehow explain what it is for something to be human, i.e., being a rational animal. C.P.T. can actually come out in two different versions. A reductionist version of C.P.T. admits that there are three (irreducible) properties here: the simple properties of being an animal and of being rational and the conjunctive property of being an animal and being rational – assuming that such properties are not reducible to further properties. Being human is nothing but/is identical with the conjunctive property of being an animal and being rational. Let me call this version “C.P.T.R.”5 The target of the reduction is the property of being human. Following van Gulick (2001), I take “reduction” here in a very broad sense. Reduction relations include, among others, identity relations, elimination, full grounding, etc. Namely, it is compatible with my usage of reduction that the property of being human turns out to be identical with the other properties at stake, as well as that it is eliminated in favour of the latter or that it exists, though being fully grounded on the latter. Readers could characterize reduction as they prefer in this context. 5 6 Michele Paolini Paoletti – Università degli Studi di Macerata (michele.paolinip@gmail.com) Acta Analytica, 35(3)(2020): 421-437. Please quote only from the published version. On the other hand, a non-reductionist version of C.P.T. (i.e., C.P.T.N.) admits that there actually are four (irreducible) properties here: the simple properties of being an animal and of being rational, the conjunctive property of being an animal and being rational and the simple property of being human. Being human is necessarily co-instantiated with (but different from) the conjunctive property of being an animal and being rational. In turn, S.P.T. can come out in two different versions too. According to reductionist S.P.T. (i.e., S.P.T.R.), there are two (irreducible) simple properties here: being an animal and being rational. Again, the target of the reduction is the property of being human. According to non-reductionist S.P.T. (i.e., S.P.T.N.), there actually are three (irreducible) simple properties: being an animal, being rational and being human. While my discussion does not hinge on the acceptance on any particular theory of properties, one caveat should be added here. The non-reductionist version of C.P.T., i.e., C.P.T.N., implies the rejection of the necessary coextension criterion for the identity of properties. Namely, C.P.T.N. implies that it is not the case that properties P and Q are identical iff, as a matter of necessity, everything has P iff it has Q. The reason is simple: being human is necessarily coextensive with – yet distinct from – the conjunctive property being an animal and being rational. Therefore, C.P.T.N. is incompatible with those theories of properties that are committed to the necessary coextension criterion, e.g., set nominalism and resemblance classes nominalism. According to such theories, properties are sets or resemblance classes of particulars. Since necessary coextension is sufficient for establishing the identity between two sets or two resemblance classes, the properties of being human and of being an animal and being rational turn out to be identical qua sets/resemblance classes – contra C.P.T.N. On the other hand, S.P.T.R., S.P.T.N. and C.P.T.R. are not committed to the rejection of the necessary coextension criterion. For there are no necessary coextensive yet distinct properties within those theories. Consider S.P.T.N. It is true that, on S.P.T.N., as matter of necessity, everything is human iff it is an animal and it is rational. Yet, being an animal and being rational do not constitute any additional conjunctive property that is necessarily coextensive with – yet distinct from – the property of being human6. C.P.T.R. and C.P.T.N. have more explanatory power than S.P.T.R. For S.P.T.R. does not accept the existence of the property of being human. Therefore, there is no explanandum for S.P.T.R. (i.e., the property of being human, to be explained in its nature and existence) and, subsequently, no explanation for it. Of course, on behalf of S.P.T.R., one could counter that we do not need to accept the existence of properties such as that of being human, so that we need no explanation for them. However, this is at 6 See, for example, Orilia, Swoyer (2016) and Allen (2016). However, if reduction is characterized in nonidentitarian and non-eliminativistic terms, C.P.T.R. turns out to be committed to the rejection of the necessary coextension criterion too. Indeed, the reduced property (i.e., being human) – though reduced to being an animal and being rational – still exist and is distinct from the latter. Yet, being human is necessarily coextensive with being an animal and being rational. This does not happen with S.P.T.R. For there is no single property with which being human is necessarily coextensive. 7 Michele Paolini Paoletti – Università degli Studi di Macerata (michele.paolinip@gmail.com) Acta Analytica, 35(3)(2020): 421-437. Please quote only from the published version. odds with our taxonomies of the universe. Indeed, when we classify certain entities in the universe (i.e., human beings), we either use the property of being human, or the conjunctive property of being an animal and being rational. Or, to invoke two examples from fundamental physics, when we classify electrons and quarks, we either use the properties of being an electron and of being a quark, or respectively the conjunctive properties of being a lepton and having negative one electric charge and being a fermion and having +2/3 or -1/3 electric charge and having a baryon number of 1/3. These facts cannot be accounted for by S.P.T.R. For, on S.P.T.R., such taxonomies are invisible. C.P.T.R. does not accept the property of being human as such. Yet, it introduces the conjunctive property of being an animal and being rational as something that can explain (for example) the existence of a classificatory concept in our minds such as the concept of being human. C.P.T.N. accepts being human. Moreover, ceteris paribus, C.P.T.R. should be favoured over C.P.T.N. For ceteris paribus the former is more ontologically parsimonious than the latter in the number of single entities: both theories accept simple and conjunctive properties, but C.P.T.N. has one more simple property than C.P.T.R. (i.e., the simple property of being human). However, S.P.T.N. has the same explanatory power as both C.P.T.R. and C.P.T.N. According to S.P.T.N., the simple property of being human is necessarily co-instantiated with the simple properties of being an animal and being rational. The latter properties, when taken together, can somehow explain what it is for something to be human. In addition, S.P.T.N., rejecting conjunctive properties, is more ontologically parsimonious in types than both C.P.T.R. and C.P.T.N. It could be replied that S.P.T.N. is more theoretically complex than C.P.T.R. For the former needs to explain why the simple property of being human is necessarily co-instantiated with the simple properties of being an animal and being rational. To do this, it needs to introduce brute connections between properties, that should justify why being human is necessarily co-instantiated with being an animal and being rational, and not with being an animal and being a stone7. On the contrary, C.P.T.R. can just hold that whenever the conjuncts are instantiated together (i.e., being an animal and being rational) there is also a conjunctive property (i.e., being an animal and being rational). Yet, C.P.T.R. actually has two sorts of problems here. If it accepts maximalism (i.e., that every conjunction of property-instances gives rise to a conjunctive property), then it multiplies the number of single entities beyond necessity. If it rejects maximalism, it still needs to explain why only certain conjunctions of property-instances give rise to a conjunctive property. Therefore, in the latter case, it needs to perform a task analogous to the one performed by S.P.T.N. To do this, it seemingly needs to introduce brute connections between certain properties (i.e., the relevant conjuncts) and the conjunctive properties they give rise to. I also add one important remark. That being an animal and being rational must be taken together does not entail that they compose one further, conjunctive property. It only entails that there is a conjunction 7 Something analogous seems to happen with C.P.T.N. when it has to connect being human with being an animal and being rational. 8 Michele Paolini Paoletti – Università degli Studi di Macerata (michele.paolinip@gmail.com) Acta Analytica, 35(3)(2020): 421-437. Please quote only from the published version. of property-instances. If it were claimed that all (or at least some of) the conjunctions of propertyinstances imply the existence of conjunctive properties, this would beg the question in favour of C.P.T. Indeed, why should those who hold S.P.T. accept that conjunctions of property-instances imply the existence of conjunctive properties? In sum, this first reply to my argument only shows that S.P.T.N. should be favoured over S.P.T.R. In addition, ceteris paribus, S.P.T.N. should be favoured over both C.P.T.R. and C.P.T.N. For S.P.T.N. rejects one type of entities: conjunctive properties. The second reply to my argument can be easily dealt with. According to this reply, the reductionist version of C.P.T., i.e., C.P.T.R., should be favoured over the non-reductionist version of S.P.T., i.e., S.P.T.N. For C.P.T.R. rejects the simple property of being human as a basic constituent of one’s ontological inventory of the universe. C.P.T.R. reduces being human to the conjunctive property of being an animal and being rational. Thus, C.P.T.R. is more ontologically parsimonious than S.P.T.N. with respect to the number of the basic constituents of the universe. This is a non sequitur. S.P.T.N. is still more ontologically parsimonious than C.P.T.R. in the number of existing properties. For S.P.T.N. accepts only one type of properties: simple properties. On the contrary, C.P.T.R. accepts two types of properties: conjunctive and simple properties. The reply would be successful in one case, namely, if the conjunctive property of being an animal and being rational, though existing, were less ontologically fundamental than the simple properties of being human and of being rational. In this case, C.P.T.R. would be more ontologically parsimonious than S.P.T.N. in the number of basic entities, as it would have two simple properties as ontologically basic – rather than three. This case presupposes an important distinction between existing and being basic. C.P.T.R. now accepts that there exists a conjunctive property such as the one of being an animal and being rational. Yet, it denies that such a property is a basic one. For example: it denies that such a property must be invoked in order to explain something in the history of the universe. C.P.T.R. now resembles epiphenomenalism about mental properties. Epiphenomenalists claim that mental properties exist, even if they do not confer any causal power, so that they are not basic. In a similar vein, C.P.T.R. now claims that conjunctive properties exist, but they are not basic8. However, what would the difference between C.P.T.R. and S.P.T.R. amount to in this case? Both theories would recognize two simple properties as ontologically basic: being an animal and being rational. However, C.P.T.R. would also recognize the existence of one third, non-fundamental conjunctive property. Thus, ceteris paribus, C.P.T.R. would still be less ontologically parsimonious than S.P.T.R. with respect to the number of existing entities – even if they would contain the same number of basic entities (i.e., two simple properties). Moreover, C.P.T.R. would be at least as ontologically parsimonious as S.P.T.N. if S.P.T.N. accepted that the property of being human exists but it is not basic. The option that is 8 This new version of C.P.T.R. fits well with Schaffer (2015)’s characterization of the principle of parsimony: do not multiply fundamental entities without necessity. For some criticisms of Schaffer’s theses, see Baron, Tallant (2016). 9 Michele Paolini Paoletti – Università degli Studi di Macerata (michele.paolinip@gmail.com) Acta Analytica, 35(3)(2020): 421-437. Please quote only from the published version. open for being an animal and being rational (i.e., existing and not being basic) is also open for being human. One could also try to combine both replies. Namely, it could be argued that C.P.T.R., by accepting conjunctive properties as existing, non-basic entities, would have more explanatory power than S.P.T.R. In addition, C.P.T.R. would be more ontologically parsimonious than S.P.T.N. in the number of basic entities. Yet, the first thesis (i.e., that C.P.T.R. could both accept conjunctive properties as non-basic entities and have more explanatory power than S.P.T.R.) is untenable: if being an animal and being rational were irreducibly invoked for the sake of explaining something about being human, then that conjunctive property would turn out to be a basic entity. Either something increases the explanatory power of a theory or (aut) it is a non-basic entity. For being a basic entity seemingly implies, among other things, playing an irreducible explanatory role9. To summarize: I have defended the idea that one should favour S.P.T. over C.P.T. However, I have conceded that one should prefer a non-reductionist version of S.P.T., i.e., S.P.T.N., according to which three properties exist in our study case (i.e., being human, being an animal and being rational), though, as a matter of necessity, everything is human iff it is an animal and it is rational. 4. Armstrong I: the Argument from Infinite Complexity. David Armstrong (1978: 30-36) argues against (1) besides conjunctive properties, C.P.T. is also committed to simple properties – and S.P.T. is committed to simple properties as well, as follows. It is possible that all seemingly simple properties turn out to be conjunctive properties and that the conjuncts of such conjunctive properties then turn out to be further conjunctive properties, and so on, ad infinitum. Namely, for any property A, A can turn out to be nothing but B and C. Subsequently, B can turn out to be nothing but D and E and C can turn out to be nothing but F and G, and so on, ad infinitum10. If this is the case, C.P.T. is not committed to simple properties. Moreover, (2) does not apply to C.P.T. and S.P.T. For C.P.T. now claims that there are only conjunctive properties, as all seemingly simple properties are conjunctive properties. Of course, C.P.T. must be taken in its reductionist form C.P.T.R. Recalling our previous example, there is no property such as the property of being human. There are only the properties of being an animal and of being rational, as well as the conjunctive property of being an animal and being rational. Moreover, the properties of being an animal and of being rational are 9 This implication can be motivated as follows. I take something to be basic iff it does not depend on anything else and something else depends on it in some respect. Therefore, if A is basic, something depends on A in some respect, so that A irreducibly explains – or contributes to explaining – that thing in that respect. I talk here of “irreducible explanatory power” rather than of “explanatory power” simpliciter in order to stress the idea that the explanatory role played by basic entities cannot be played by other entities. Otherwise, basic entities would not be basic. 10 On Armstrong’s view of conjunctive properties, see also Armstrong (1975). 10 Michele Paolini Paoletti – Università degli Studi di Macerata (michele.paolinip@gmail.com) Acta Analytica, 35(3)(2020): 421-437. Please quote only from the published version. identical with further conjunctive properties. To distinguish this version of C.P.T.R. from the version discussed in section 3 – which seemingly recognizes genuinely simple properties – I shall talk of “C.P.T.R.I.” – where “I.” stands for “Infinite”. Given C.P.T.R.I., there is only one type of properties: conjunctive properties. Thus, C.P.T.R.I. is at least as ontologically parsimonious in types as S.P.T.R. and S.P.T.N. Subsequently, (2) does not apply to C.P.T.R.I. in comparison with S.P.T. There are three important remarks to be done here. Such remarks show – at least in my opinion – where Armstrong’s argument from infinite complexity fails11. First, Casullo (1984) thinks that Armstrong’s argument begs the question against those who deny conjunctive properties. For it implicitly assumes that every conjunction of property-instances is identical with an instance of a conjunctive property. Let me expand a bit on this suggestion. Those who hold S.P.T. could provide an alternative interpretation of infinite complexity. They could claim that every instance of a simple property is identical with – or it necessarily comes together with – a conjunction of property-instances. In turn, the conjuncts are identical with – or they necessarily come together with – further conjunctions of property-instances. And so on, ad infinitum. The S.P.T. interpretation of infinite complexity is a legitimate one. In a nutshell, infinite complexity need not entail infinitely complex conjunctive properties. Take the property A. On the former alternative (“every property-instance is identical with a conjunction of property-instances”), every instance of the simple property A is identical with a conjunction of the property-instances of B and of C, and so on, ad infinitum. There is no property-instance of A as such, i.e., there is no property-instance of A distinct from the conjunction of property-instances of B and C. Let me call this reductionist alternative “S.P.T.R.I.” On the latter alternative (“every property-instance necessarily comes together with a conjunction of property-instances”), every instance of the simple property A necessarily comes together with a conjunction of the property-instances of B and of C, and so on, ad infinitum. Yet, the property-instance of A is distinct from the conjunction of property-instances of B and C. Let me call this non-reductionist alternative “S.P.T.N.I.” It can be argued that S.P.T.R.I. is problematic. When one “goes down” to B and C, the higher-level property-instances (of A) seemingly disappear – and the properties such as A seemingly disappear as well. Yet, the same difficulty affects C.P.T.R.I. Even in C.P.T.R.I. the property-instances of the seemingly simple properties and of the conjuncts disappear, as well as those same properties. Thus, one could favour S.P.T.N.I. There are also other ways to rebut Armstrong’s argument, e.g., by holding that it establishes the possibility (and not the actuality) of there being only conjunctive properties (see also Kraemer (1977) and Casullo (1984)) and by pointing out that the same sort of reasoning could show that there are only disjunctive or negative properties (see D. H. Mellor (1992)). Mellor (1991: 170-182) and (2012) has other arguments against complex properties in general. Yet, I shall not discuss them here, since they are based on more contentious principles (such as a certain criterion of identity for facts). For a discussion, see for example Oliver (1992) and Botterell (1998). 11 11 Michele Paolini Paoletti – Università degli Studi di Macerata (michele.paolinip@gmail.com) Acta Analytica, 35(3)(2020): 421-437. Please quote only from the published version. Be that as it may, C.P.T.R.I. and the S.P.T. readings of infinite complexity are on a par with respect to the number of types of properties to be admitted. True: S.P.T.N.I. accepts a higher number of properties than C.P.T.R.I. and S.P.T.R.I., since it maintains that A is a genuine property. However, this move is justified as a solution for a problem that affects both C.P.T.R.I. and S.P.T.R.I. (i.e., the disappearance of higher-level property-instances). Is there any reason for favouring the S.P.T. readings? Perhaps there is at least one reason having to do with intrinsic complexity. Conjunctive properties are less simple with respect to their composition. They are composed of further properties. This is not the case for simple properties. Thus, ceteris paribus, one might want to maintain that S.P.T. theorists accept the existence of simpler entities, to be favoured over more complex ones. Let me turn to my second remark to Armstrong’s argument from infinite complexity. Is infinite complexity a genuine and scientifically plausible possibility? Some philosophers believe that our world might be gunky, i.e., that every object in our world might be decomposable into further objects or, equivalently, that all the objects in our world might be composed of further objects12. However, the possibility of a gunky world does not entail that all the properties in that world are conjunctive. For all the infinitely decomposable objects in that world could only have simple properties. An object o1 with a property A could be composed of two objects o2 and o3. The latter could have two simple and nondecomposable properties B and C, even if o2 and o3 were in turn decomposable into further objects o4, o5, o6 and o7, and so on, ad infinitum. Thus, it is not necessary that gunky worlds only include conjunctive properties. My third and final remark is that a possible world that only includes conjunctive properties must actually be a world where further, non-conjunctive properties exist. Take our seemingly simple property A. If A is nothing but the conjunctive property B and C, then the conjuncts (i.e., B and C) share the higherorder property of being a conjunct of A. The higher-order property of being a conjunct of A is not a conjunctive one. Thus, there are also non-conjunctive, higher-order properties. In reply, one could try to argue against the existence of such higher-order properties. Yet, an additional argument against the latter would be required. Indeed, being a conjunct of A works in the same way as all the properties do in establishing a certain sort of similarity between two entities: the properties B and C are similar with respect to their being conjuncts of A and such a similarity is grounded on being a conjunct of A. Alternatively, it could be claimed that being a conjunct of A is no addition of being. For such a property and its instantiation flow from the existence and the nature of both B and C. If we take the conjuncts B and C, then we also have the higher-level property of being a conjunct of A. Remember that A is nothing but B and C. Therefore, it flows from the existence and the nature of both B and C that they are conjuncts of A, i.e., that they are conjuncts of B and C. 12 See for example Zimmerman (1996). 12 Michele Paolini Paoletti – Università degli Studi di Macerata (michele.paolinip@gmail.com) Acta Analytica, 35(3)(2020): 421-437. Please quote only from the published version. Yet, the claim “being a conjunct of A is no addition of being” does not imply here that being a conjunct of A does not exist. If no argument against higher-order properties is provided, it is legitimate to maintain that such properties exist. What is meant by that claim is that being a conjunct of A exists, but it entirely depends on B and C. Whenever you have B and C, you also have being a conjunct of A. Thus, the existence of being a conjunct of A entirely depends on B and C. Unfortunately, this opens the possibility of an infinite foundational regress. An infinite foundational regress is one in which the explanandum (or at least the relevant type of explanandum) is reintroduced in the explanans, and so on, ad infinitum. For example: Bradley’s regress is an infinite foundational regress. For one is committed to explaining the instantiation of a property P by an object o in terms of the instantiation of a relation of instantiation by both P and o. That further instantiation is then explained in terms of one further relation of instantiation, and so on, ad infinitum13. In an infinite foundational regress, the explanandum is never explained. This is what makes the infinite foundational regress vicious. In our case, the explanandum is the existence of being a conjunct of A. This is explained by the existence and nature of B and C. Yet, B and C are identical with further conjunctive properties: B is identical with D and E and C is identical with F and G. And so on, ad infinitum. Thus, B, i.e., the conjunctive property D and E, is what it is just because both D and E have the higher-order property of being a conjunct of B. The relevant type of explanandum (i.e., the existence of higher-order properties such as being a conjunct of B and being a conjunct of A) is reintroduced in the explanans. True: being a conjunct of B is explained by the existence and nature of both D and E. Yet, D and E are identical with further conjunctive properties, which are what they are just because their conjuncts share the property of being a conjunct of them. And so on, ad infinitum. 5. Armstrong II: the Argument from Causal Powers. Armstrong (1978: 30-36) has another argument for the existence of conjunctive properties: the argument from causal powers. According to Armstrong, properties ground real similarities between entities and they confer unique causal powers (i.e., causal powers that are not conferred by other properties). Take now two properties A and B. It seems that there could be some powers that are conferred by those two properties only when they are taken together. Such powers could not be conferred by A and B taken in isolation. For example: the power of rolling is conferred by the properties of being spherical and of being solid taken together. That power is not conferred by the property of being spherical by itself: a spherical thing needs to be solid in order for it to be able to roll. Spheres qua abstract, geometrical objects are spherical, but they cannot roll. Moreover, the power of rolling is not conferred by the property of being solid by itself: a solid 13 See for example Bliss (2013). 13 Michele Paolini Paoletti – Università degli Studi di Macerata (michele.paolinip@gmail.com) Acta Analytica, 35(3)(2020): 421-437. Please quote only from the published version. thing needs to be spherical in order for it to be able to roll. There are many solid, non-spherical things that cannot roll. Therefore, according to Armstrong, the power of rolling cannot but be conferred by the conjunctive property of being spherical and being solid. More generally, there are powers that cannot but be conferred by conjunctive properties. Such properties confer those unique powers. Thus, there exist conjunctive properties14. This also shows that (2) does not apply to simple and conjunctive properties. For conjunctive properties explain the presence of causal powers that cannot be explained only by simple properties. It is possible to reply that the power of rolling is not conferred by the conjunctive property of being spherical and being solid, but it is actually conferred by the corresponding conjunction of propertyinstances. However, many ontologists believe that properties (and not conjunctions of propertyinstances) are the only entities that confer causal powers. The non-reductionist version of S.P.T., i.e., S.P.T.N., can accept that there is one simple property that is necessarily co-instantiated with the relevant conjunction of property-instances and that is involved in conferring the relevant powers15. Alternatively, that simple property is co-instantiated with the relevant conjunction of property-instances only in the relevant context. For example: the simple property of being a ball is necessarily co-instantiated with the conjunction of instances of the properties of being spherical and of being solid. Alternatively, in some relevant context (e.g., if we talk of a ball), the simple property of being a ball is co-instantiated with that conjunction of property-instances. At any rate, the simple property of being a ball actually confers the power of rolling. There is no need to introduce the conjunctive property of being spherical and being solid in order to explain the existence of that power. However, let us concede that some properties introduce powers only when they are taken together – even without there being any simple property corresponding to their compresence. In this case, conjunctive properties turn out to exist only if one accepts the following principle: (P1) every casual power is conferred by necessity by some property or another taken by itself (i.e., not together with other properties). Given (P1), it is not possible that two (or more than two) distinct properties jointly confer a causal power. Moreover, causal powers necessarily flow from the nature of single properties: it is not possible that one has the relevant, single property, without also having the relevant causal powers conferred by that property. 14 It could pointed out that the power of rolling is also conferred by the conjunctive property of being cylindrical and being solid, so that it is conferred by different conjunctive properties. For the sake of simplicity, I shall leave this complication for Armstrong’s position aside. To sidestep it, one could try to single out a property P that only spherical and cylindrical objects share. One could then claim that the power of rolling is only conferred by the conjunctive property of being P and being solid. 15 Remember that property-instances are not identical with the objects that have the relevant properties: that Socrates is an animal and that Socrates is a rational being are two property-instances, whereas Socrates himself is not a property-instance. 14 Michele Paolini Paoletti – Università degli Studi di Macerata (michele.paolinip@gmail.com) Acta Analytica, 35(3)(2020): 421-437. Please quote only from the published version. Since (i) the properties of being spherical and of being solid do not confer by themselves the causal power of rolling, and (ii) that causal power is conferred by necessity by some property or another taken by itself (an instance of (P1)), then (iii) there must be some third property that confers by necessity and taken by itself the causal power of rolling: the conjunctive property of being spherical and being solid. There are several ways to rebut this argument. First, without denying (P1), one could allow that the property of being spherical necessarily comes together with the property of being solid, so that the former property actually confers by necessity and taken by itself the causal power of rolling16. This would be the case if the property of being spherical included in its own nature the fact of coming together with the property of being solid. There are three problems with this solution. It rejects a priori the existence of non-solid spheres. It seemingly accepts that properties can have relational natures, i.e., that it is part of their nature (and necessary) that they come together with other properties. It does not actually “take by itself” the property of being spherical – since that property necessarily comes together with some further property. If you want to avoid these problems, there are some interesting alternatives. One radical alternative consists in denying (P1): (non-P1) it is not the case that: every casual power is conferred by necessity by some property or another taken by itself. Two options are available here – that are not mutually exclusive. First, some properties confer certain powers by necessity, but only when they are taken together with other properties. This can happen if it is part of the nature of the property of being spherical that it confers the power of rolling when it is coinstantiated with the property of being solid. In a similar vein, it is part of the nature of the property of being solid that it confers the power of rolling when it is co-instantiated with the property of being spherical. The “when-clause” is included in the natures of those properties17. 16 On the other hand, it is quite implausible that the property of being solid necessarily comes together with the property of being spherical. Thus, I shall not consider this possibility. 17 Note that the “when-clause” does not introduce conjunctive properties in the nature of the simple properties of being spherical and of being solid. For the “when-clause” only talks of co-instantiations of properties or, if you prefer, of conjunctions of property-instances. Moreover, the “when-clause” does not imply that those simple properties have relational natures: the existence of one of them does not necessarily imply the existence of the other. Let me add that, when Shoemaker (2007) talks of “conditional powers” conferred by properties, he is quite near to the point discussed here. I shall introduce Shoemaker’s conditional powers in a few lines. 15 Michele Paolini Paoletti – Università degli Studi di Macerata (michele.paolinip@gmail.com) Acta Analytica, 35(3)(2020): 421-437. Please quote only from the published version. This option does not imply that there are two distinct powers of rolling conferred by those properties (i.e.. the one conferred by being spherical and the one conferred by being solid) – nor that there are two distinct effects of the exercise of the power of rolling when the relevant object rolls. One and the same power of rolling is conferred by two distinct properties at once. Armstrong could reply that, following this hypothesis, the power of rolling is not a unique power, i.e., a power that is conferred by at least and at most one property. Unique powers allow us to find out what properties exist. For they allow us to find out all and only those properties we cannot get rid of when explaining what goes on in the universe. I reply, in turn, that there is a non sequitur in this reasoning. If it is part of the nature of the property of being spherical that it confers the power of rolling when it is co-instantiated with the property of being solid (and the other way round), then we still need both properties when explaining rolling. Thus, even if the power of rolling is not a unique one (since it is conferred by two properties), the properties of being spherical and of being solid cannot be dispensed with when explaining what goes on and what can go on in the universe. The second possibility is the following. Maybe there are causal powers that are not conferred by necessity by single properties. Maybe some powers are just contingently conferred by properties taken by themselves. Thus, the power of rolling is just contingently conferred by the property of being spherical, i.e., when that property is co-instantiated with the property of being solid – and the other way round for the property of being solid. Again: one and the same power is conferred by two distinct properties18. Finally, one could restrict (P1) to Shoemaker’s conditional powers19. The property of being spherical confers the conditional power of rolling if the object is also solid. The property of being solid confers the conditional power of rolling if the object is also spherical. In comparison with the first possibility discussed above, we do not claim here that it is part of the nature of the relevant properties (e.g., being spherical) that they confer those powers when they are co-instantiated with the other properties (e.g., being solid). On the contrary, the “when-clause” (or the “if-clause”) is now incorporated in the nature of powers. This solution is less ontologically parsimonious than the two options discussed above, as it distinguishes between two conditional powers: the one of rolling if the object is also solid and the one of rolling if the object is also spherical. However, it is more ontologically parsimonious in types than C.P.T. For C.P.T. now seemingly accepts three types of entities: simple (i.e., non-conjunctive) properties, conjunctive properties and powers. Within powers, it claims that there is only the power of rolling. The conditional powers solution accepts two types of entities: simple properties and powers. True: unlike C.P.T., it 18 I rule out that the power of rolling is just contingently conferred by the properties of being spherical and of being solid when taken together. For if the latter are taken together, they seem to confer that power by necessity: it seems that there cannot be solid and spherical objects that cannot roll. 19 See for example Shoemaker (2007: 24). 16 Michele Paolini Paoletti – Università degli Studi di Macerata (michele.paolinip@gmail.com) Acta Analytica, 35(3)(2020): 421-437. Please quote only from the published version. includes two powers rather than one. Yet, if parsimony in types should be favoured over parsimony in the number of entities, then the conditional powers solution should still be favoured over C.P.T.20 In a nutshell, Armstrong’s argument from causal powers can be dealt with by adopting different strategies. It is up to the reader to choose her favourite one. References. Allen, S. R. (2016). A Critical Introduction to Properties. London: Bloomsbury Armstrong, D. M. (1975). “Towards a Theory of Properties: Work in Progress on the Problem of Universals”. Philosophy, 50(192): 145-155 ______ (1978). Universals and Scientific Realism. Volume II: A Theory of Universals. Cambridge: Cambridge University Press Barnes, E. C. (2000). “Ockham’s Razor and the Anti-Superfluity Principle”. Erkenntnis, 53(3): 353-374 Baron, S., Tallant, J. (2016). “Do Not Revise Ockham’s Razor Without Necessity”. Philosophy and Phenomenological Research. Published in Early View on September, 7th, 2016. Bliss, R. 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(2001). “Reduction, Emergence and Other Recent Options on the Mind/Body Problem. A Philosophical Overview”. Journal of Consciousness Studies, 8: 1-34 Zimmerman, D. (1996). “Could Extended Objects Be Made Out of Simple Parts? An Argument for ‘Atomless Gunk’”. Philosophy and Phenomenological Research, 56: 1-29 18