Many are reluctant to accept primitive modality into their fundamental picture of the world. The worry often traces to this thought: we shouldn't adopt any more primitive - that is, unexplained - notions than we need in order to explain all the features of the world, and primitive modal notions are not needed. I examine one prominent rival to modal primitivism, combinatorialism, and show that in order to account for all the modal features of the world the combinatorialist must (...) adopt two additional primitive notions. My own modal primitivist view takes as primitive the notion of incompatibility between properties or relations. I show how the non-modal notions that the combinatorialist must adopt as primitive may be analyzed using my notion. The upshot is that with respect to the number of primitive notions, my modal primitivist theory comes out ahead. (shrink)

In explaining the notion of a fundamental property or relation, metaphysicians will often draw an analogy with languages. The fundamental properties and relations stand to reality as the primitive predicates and relations stand to a language: the smallest set of vocabulary God would need in order to write the “book of the world.” This paper attempts to make good on this metaphor. To that end, a modality is introduced that, put informally, stands to propositions as logical truth stands to sentences. (...) The resulting theory, formulated in higher-order logic, also vindicates the Humean idea that fundamental properties and relations are freely recombinable and a variant of the structural idea that propositions can be decomposed into their fundamental constituents via logical operations. Indeed, it is seen that, although these ideas are seemingly distinct, they are not independent, and fall out of a natural and general theory about the granularity of reality. (shrink)

We argue that Armstrong's Combinatorialism allows for the possibility of nothing by giving a Combinatorial account of the empty world and show that such an account is consistent with the ontological and conceptual aims of the theory. We then suggest that the Combinatorialist should allow for this possibility given some methodological considerations. Consequently, rather than being 'spoils for the victor', as Armstrong maintains, deciding whether there might have been nothing helps to determine which metaphysics of modality is to be (...) preferred. (shrink)

The combinatorial theory of modality has long been dogged by the supposed problem that it entails that S5 is not the correct logic for metaphysical modality. In this paper, I suggest a modification to combinatorialism, to eliminate this tension with S5. I argue that the resulting view is more in the spirit of combinatorialism than the original position.

The object of this paper is to argue once again for the combinatorial account of possibility defended in earlier work. But there I failed fully to realise the dialectical advantages that accrue once one begins by assuming the hypothesis of logical atomism, the hypothesis that postulates simple particulars and simple universals at the bottom of the world. Logical atomism is, I incline to think, no better than ‘speculative cosmology’ as opposed to ‘analytic ontology’, to use Donald Williams’ terminology. It is, (...) however, not an implausible hypothesis given the current state of quantum physics. More important for our purposes here, the strictly combinatorial theory that flows rather naturally from the atomist metaphysics shows some promise of continuing to hold in a world that is not an atomist world. (shrink)

Much of the appeal of Armstrong’s combinatorial theory of possibility depends on the theory’s principle of recombination. Despite its centrality, the principle has received little attention in the critical literature on combinatorialism. In this paper, I first set out to discuss how to exactly formulate the principle; then, I show that some notable criticisms of combinatorialism are in fact criticisms to the principle of recombination that allegedly sustains the theory. I focus in particular on Sider’s ‘trickle down’ objection (...) concerning the recombination of mereologically complex wholes and on the objection that combinatorialism cannot account for so-called alien possibilities. The combinatorialist – I contend – can rebut both objections by fine-tuning the principle of recombination. (shrink)

In his recently published paper, ‘The Nature of Possibility,’ David Armstrong presents an account of possibility which, he correctly claims, is partly an elaboration of the early Wittgenstein's. Both are combinatorialists. That is to say, both hold that there is a fixed ontology of individuals, properties and relations whose combinations determine the range of all possible states of affairs, and therewith the range of all those totalities of states of affairs which they call possible worlds.But Armstrong's account, I believe, is (...) fatally flawed in ways that Wittgenstein's isn't. And this, I shall argue, is mainly because Armstrong is both an actualist, whose fixed ontology is one of actual individuals, properties and relations, and a reductionist, who tries to reduce the notion of possibility to that of ߢallߣ their combinations. Armstrong seems to think that Wittgenstein at least shares his actualism, and perhaps even his reductionism. (shrink)

Many contemporary philosophers accept Hume's Dictum, according to which there are no metaphysically necessary connections between distinct, intrinsically typed entities. Tacit in Lewis 's work is a potential motivation for HD, according to which one should accept HD as presupposed by the best account of the range of metaphysical possibilities---namely, a combinatorial account, applied to spatiotemporal fundamentalia. Here I elucidate and assess this Ludovician motivation for HD. After refining HD and surveying its key, recurrent role in Lewis ’s work, I (...) present Lewis ’s appeal to HD as providing a broadly axiomatic generating basis for the space of metaphysical modality, and canvas the prima facie advantages of the resulting combinatorial principle---HD ---as being principled, extensionally adequate and modally reductive. Most criticisms of Lewis 's combinatorialism have targeted seeming ways in which the theory overgenerates the desired space; I rather argue that HD seriously undergenerates the desired space in three different ways. For each way I argue that available means of overcoming the undergeneration either fail to close the gap, undermine the claim that HD is a principled generator of metaphysical modal space, undermine the reductive status of Lewis 's combinatorialism, or call into question the truth of HD. (shrink)

The core idea of David Armstrong’s combinatorial theory of possibility is attractive. Rearrangement is the key to modality; possible worlds result from scrambling bits and pieces of other possible worlds. Yet I encounter great difficulty when trying to formulate the theory rigorously, and my best attempts are vulnerable to counterexamples. The Leibnizian biconditionals relate possibility and necessity to possible world and true in.

At the outset of his instructive and thought-provoking paper, ‘The Nature of Possibility,’ Professor David Armstrong gives a succinct description, in itself almost complete, of his ‘combinatorial theory’ of possibility. He says: ‘Such a view traces the very idea of possibility to the idea of the combinations - allthe combinations which respect certain simple form- of given, actual elements’. We can perhaps start a bit further back than this. In explaining the idea of a ‘possible world,’ some philosophers begin with (...) the idea of ‘things being a certain way’ or ‘the way things are.’ From this idea a leap is made to ‘things might have been a certain other way’ or ‘ways things could have been.’ And here we already have possible worlds, or so some philosophers assure us: David Lewis, for example, says his talk of possible worlds is nothing but a ‘permissible paraphrase’ of this familiar and innocent-sounding locution, ‘ways things could have been.'. (shrink)

Many contemporary philosophers accept a strong generalization of Hume's denial of necessary causal connections, in the form of Hume's dictum (HD), according to which there are no metaphysically necessary connections between distinct, intrinsically typed entities. Hume's version of his dictum occurs during his investigation into the source of the idea of causal connection. The most powerful role that HD plays in Lewis's system concerns its providing a basis for, as Lewis puts it, a "principle of plentitude" that will guarantee "that (...) the worlds are abundant, and logical space is somehow complete". Lewis's combinatorialism promises to provide a principled, extensionally adequate, and reductive generator of metaphysical modal space. Beyond combinatorialism, there are many other accounts of metaphysical modality that need to be considered, not just with an eye to extensional adequacy but also to the clear desideratum to provide an account of the space of metaphysical modality that is principled. (shrink)

This article includes a basic overview of possible world semantics and a relatively comprehensive overview of three central philosophical conceptions of possible worlds: Concretism (represented chiefly by Lewis), Abstractionism (represented chiefly by Plantinga), and Combinatorialism (represented chiefly by Armstrong).

This paper focuses on the possibility of conceiving a form of ontological nihilism, starting from D. M. Armstrong’s combinatorialism. This possibility has been suggested by Efird and Stoneham, by means of proposing an alternative strategy to the ‘subtraction argument’. They claim that it is possible to sustain such nihilism trough the concepts of construction and totality state of affairs. However, this hypothesis will require the acceptance of non-instanciated universals, that is, platonic universals. Yet this is opposite to requirements that (...) are basic for a combinatorial theory, which should uphold that universals exist only in their instantiations. Then, the assumption of platonic universals results in high costs for a combinatorial naturalism, according to which only exists what is located in space and time. (shrink)

This paper focuses on the possibility of conceiving a form of ontological nihilism, starting from D. M. Armstrong’s combinatorialism. This possibility has been suggested by Efird and Stoneham, by means of proposing an alternative strategy to the ‘subtraction argument’. They claim that it is possible to sustain such nihilism trough the concepts of construction and totality state of affairs. However, this hypothesis will require the acceptance of non-instanciated universals, that is, platonic universals. Yet this is opposite to requirements that (...) are basic for a combinatorial theory, which should uphold that universals exist only in their instantiations. Then, the assumption of platonic universals results in high costs for a combinatorial naturalism, according to which only exists what is located in space and time. (shrink)

This paper focuses on the possibility of conceiving a form of ontological nihilism, starting from D. M. Armstrong’s combinatorialism. This possibility has been suggested by Efird and Stoneham, by means of proposing an alternative strategy to the ‘subtraction argument’. They claim that it is possible to sustain such nihilism trough the concepts of construction and totality state of affairs. However, this hypothesis will require the acceptance of non-instanciated universals, that is, platonic universals. Yet this is opposite to requirements that (...) are basic for a combinatorial theory, which should uphold that universals exist only in their instantiations. Then, the assumption of platonic universals results in high costs for a combinatorial naturalism, according to which only exists what is located in space and time. (shrink)

In the first part of this paper, I argue against the view that laws of nature are contingent, by attacking a necessary condition for its truth within the framework of a conception of laws as relations between universals. I try to show that there is no independent reason to think that universals have an essence independent of their nomological properties. However, such a non-qualitative essence is required to make sense of the idea that different laws link the same universals in (...) different possible worlds. In the second part, I give a positive argument for the necessity of at least some laws of nature, by showing with the example of a paradigmatic law of association that it consists in an internal relation between two universals which are determinables of the same class of determinates, where this relation is essential to both. Furthermore, I show that the necessity of laws of association could be accommodated within David Lewis' Humean metaphysics, but that it is incompatible with David Armstrong's combinatorialism. (shrink)

The question as to whether some objects are possible worlds that have an initial segment in common, i.e. so that their fusion is a temporal tree whose branches are possible worlds, arises both for those who hold that our universe has the structure of a temporal tree and for those who hold that what there is includes concrete universes of every possible variety. The notion of “possible world” employed in the question is seen to be the notion of an object (...) of a kind such that objects of that kind play a certain theoretical role. Lewis’s discussion of the question is thereby clarified but is nevertheless inadequate; his negative answer is correct but even from his combinatorialist viewpoint the rationale he provides for this answer is misguided. I explain why the combinatorialist advocate of concrete plenitude should hold that no object is a tree of possible worlds. Then I explain that for a different reason the nomic essentialist advocate of concrete plenitude should hold this much too. (shrink)

공가능성(compossibility) 개념은 라이프니츠 연구자들 사이에서 가장 활발하게 연구되고 있는 분야 중 하나이다. 이 논문에서 나는 우선 공가능성에 대한 영향력 있는 네 가지 해석들을 살펴보고 각 해석의 장단점을 지적한다. 더불어 나는 그동안 연구자들 사이에서 간과되었던 한 가지 문제를 지적한다. 공가능성에 대한 영향력 있는 해석들은 모두 명시적 혹은 암묵적으로 공가능성을 이행적(transitive)인 관계로 파악하고 있다. 그러나 나는 이 논문에서 라이프니츠가 공가능성을 비이행적인 관계로 이해하고 있음을 보임으로써, 공가능성에 대한 기존의 해석들에 대한 새로운 문제를 제기한다.

Armstrong's combinatorialism, in his own words, is the following project: "My central metaphysical hypothesis is that all there is is the world of space and time. It is this world which is to supply the actual elements for the totality of combinations. So what is proposed is a Naturalistic form of a combinatorial theory."2 Armstrong calls his central hypothesis "Naturalism." He intends his well−known theory of universals to satisfy this thesis. He now attempts to give a naturalistic theory of (...) modality. (shrink)

English title: Are combinatorialism and nomological realism compatible?

Does chemistry reduce to physics? If this means ‘Can we derive the laws of chemistry from the laws of physics?’, recent discussions suggest that the answer is ‘no’. But sup posing that kind of reduction—‘epistemological reduction’—to be impossible, the thesis of ontological reduction may still be true: that chemical properties are determined by more fundamental properties. However, even this thesis is threatened by some objections to the physicalist programme in the philosophy of mind, objections that generalize to the chemical case. (...) Two objections are discussed: that physicalism is vacuous, and that nothing grounds the asymmetry of dependence which reductionism requires. Although it might seem rather surprising that the philosophy of chemistry is affected by shock waves from debates in the philosophy of mind, these objections show that there is an argumentative gap between, on the one hand, the theoretical connection linking chemical properties with properties at the sub-atomic level, and, on the other, the philosophical thesis of ontological reduction. The aim of this paper is to identify the missing premises (among them a theory of physical possibility) that would bridge this gap. Introduction: missing elements and the mystery of discreteness The refutation of physicalism A combinatorial theory of physical possibilia Combinatorialism and the Bohr model Objections The missing premises and a disanalogy with mind. (shrink)

Set theory deals with the most fundamental existence questions in mathematics—questions which affect other areas of mathematics, from the real numbers to structures of all kinds, but which are posed as dealing with the existence of sets. Especially noteworthy are principles establishing the existence of some infinite sets, the so-called “arbitrary sets.” This paper is devoted to an analysis of the motivating goal of studying arbitrary sets, usually referred to under the labels of quasi-combinatorialism or combinatorial maximality. After explaining (...) what is meant by definability and by “arbitrariness,” a first historical part discusses the strong motives why set theory was conceived as a theory of arbitrary sets, emphasizing connections with analysis and particularly with the continuum of real numbers. Judged from this perspective, the axiom of choice stands out as a most central and natural set-theoretic principle (in the sense of quasi-combinatorialism). A second part starts by considering the potential mismatch between the formal systems of mathematics and their motivating conceptions, and proceeds to offer an elementary discussion of how far the Zermelo—Fraenkel system goes in laying out principles that capture the idea of “arbitrary sets”. We argue that the theory is rather poor in this respect. (shrink)

“There are no gaps in logical space,” David Lewis writes, giving voice to sentiment shared by many philosophers. But different natural ways of trying to make this sentiment precise turn out to conflict with one another. One is a *pattern* idea: “Any pattern of instantiation is metaphysically possible.” Another is a *cut and paste* idea: “For any objects in any worlds, there exists a world that contains any number of duplicates of all of those objects.” We use resources from model (...) theory to show the inconsistency of certain packages of combinatorial principles and the consistency of others. (shrink)

Can different material objects have the same parts at all times at which they exist? This paper defends the possibility of such coincidence against the main argument to the contrary, the ‘Indiscernibility Argument’. According to this argument, the modal supervenes on the nonmodal, since, after all, the non-modal is what grounds the modal; hence, it would be utterly mysterious if two objects sharing all parts had different essential properties. The weakness of the argument becomes apparent once we understand how the (...) modal is grounded in the nonmodal. By extending the ideas of combinatorialism so that we recombine haecceities as well as fundamental properties, we see how modal properties can be grounded in non-modal properties in a way that allows coincidence and yet also explains why there are differences in the modal properties of coinciding objects. Despite this, some de re modal facts are not grounded in the non-modal but instead are brute. However, although we cannot explain why a particular object has the basic modal properties it has, we can explain a closely related, semantic fact and, comparing the facts we can’t explain to more familiar brute facts, we understand why there should be no better explanation. As a result, we can see how coincidence is, after all, possible. (shrink)

This paper explores the prospects of a combinatorial account of modality. We argue against David M. Armstrong’s version of combinatorialism, which seeks to do without modal primitives, on the grounds, among other things, that Armstrong’s basic ontological categories are themselves subject to non-contingent constraints on recombination. We outline an alternative version, which acknowledges the necessity of modal primitives, at the level of ontology, and not just of our concepts.

Hume's Dictum (HD) says, roughly and typically, that there are no metaphysically necessary connections between distinct, intrinsically typed, entities. HD plays an influential role in metaphysical debate, both in constructing theories and in assessing them. One should ask of such an influential thesis: why believe it? Proponents do not accept Hume's arguments for his dictum, nor do they provide their own; however, some have suggested either that HD is analytic or that it is synthetic a priori (that is: motivated by (...) intuitions we have no good reason to question). Here I explore whether belief in HD is directly justified on either grounds. I motivate and present more formal characterizations of HD; I show that there are good prima facie cases to be made for HD's being analytic and for its being synthetic a priori; I argue that each of the prima facie cases fails, some things considered. I close by offering two suggestions for how belief in HD might be indirectly justified on argumentative grounds. (shrink)

This chapter contains sections titled: The Systematicity of Inference The Systematicity of Cognitive Representations The Compositionality of Representations Another Systematicity Argument Can Functional Combinatorialism Explain the Systematic Relations in Thought? Conclusion.

Armstrong’s combinatorial theory of possibility faces the obvious difficulty that not all universals are compatible. In this paper I develop three objections against Armstrong’s attempt to account for property incompatibilities. First, Armstrong’s account cannot handle incompatibilities holding among properties that are either simple, or that are complex but stand to one another in the relation of overlap rather than in the part/ whole relation. Secondly, at the heart of Armstrong’s account lies a notion of structural universals which, building on an (...) objection by David Lewis, is shown to be incoherent. I consider and reject two alternative ways of construing the composition of structural universals in an attempt to meet Lewis’ objection. An important consequence of this is that all putative structural properties are in fact simple. Finally, I argue that the quasi-mereological account presupposes modality in a way that undermines the reductionist aim of the combinatorialist theory of which it is a central part. I conclude that Armstrong’ quasi-mereological account of property incompatibility fails. Without that account, however, Armstrong’s combinatorial theory either fails to get off the ground, or else must give up its goal of reducing the notion of possibility to something non-modal. (shrink)

There cannot be a reductive theory of modality constructed from the concepts of sparse particular and sparse universal. These concepts are suffused with modal notions. I seek to establish this conclusion by tracing out the pattern of modal entanglements in which these concepts are involved. In order to appreciate the structure of these entanglements a distinction must be drawn between the lower-order necessary connections in which particulars and universals apparently figure, and higher-order necesary connections. The former type of connection relates (...) specific entities. By contrast, the latter type of connection is unspecific: it relates entities to some others. I argue that whilst there may be techniques that succeed in providing reductive truth conditions for sentences that say particulars and universals figure in lower-order necessary connections, such techniques cannot succeed in providing reductive truth conditions for sentences that say these entities figure in higher-order necessary connections. I conclude that this situation leaves reductionists with a dilemma. If they wish to affirm that there are particulars and universals then the project of reducing modality by positing these entities must be abandoned. Alternatively, they may continue to deploy their usual reductive techniques but then they must abandon the doctrine that there is more than one fundamental category of entity. (shrink)

It is widely agreed that properties play causal roles: they capture the causal powers of things. But do properties have their causal roles essentially? David Lewis did not think so. He adhered to the doctrine of quidditism, namely the doctrine that the identity of properties is primitive and that they can trade their causal roles. Quidditism is controversial. But Lewis did not see why he should want to reject it. He knew that he could avoid quidditism on the cheap by (...) treating individuals and properties alike in rejecting transworld multilocation of properties and endorsing a counterpart theory for properties. But he did not see why he should want to do so. In this article, I argue that Lewis should have wanted to endorse a counterpart theory for properties in order to reject quidditism. My argument concerns resemblance relations among properties. Another constitutive role of properties is that they capture objective resemblances between their instances. The premises of my argument are intuitive claims about resemblances among some properties that Lewis held on Humean grounds. (shrink)

In this paper I argue against Armstrong’s recent truthmaking account of possibility. I show that the truthmaking account presupposes modality in a number of different ways, and consequently that it is incapable of underwriting a genuine reduction of modality. I also argue that Armstrong’s account faces serious difficulties irrespective of the question of reduction; in particular, I argue that his Entailment and Possibility Principles are both false.