Ontic Structural Realism and the Principle of the Identity of Indiscernibles

Recently, there has been a debate as to whether or not the principle of the identity of indiscernibles (the PII) is compatible with quantum physics. It is also sometimes argued that the answer to this question has implications for the debate over the tenability of ontic structural realism (OSR). The central aim of this paper is to establish what relationship there is (if any) between the PII and OSR. It is argued that one common interpretation of OSR is undermined if the PII turns out to be false, since it is committed to a version of the bundle theory of objects, which implies the PII. However, if OSR is understood as the physical analogue of (sophisticated) mathematical structuralism then OSR does not imply the PII. It is further noted that it is (arguably) a virtue of OSR that it is compatible with a version of the PII for possible worlds.     

A Lewisian Semantics for S2

This paper sets out a semantics for C.I. Lewis's logic S2 based on the ontology of his 1923 paper ‘Facts, Systems, and the Unity of the World’. In that article, worlds are taken to be maximal consistent systems. A system, moreover, is a collection of facts that is closed under logical entailment and conjunction. In this paper, instead of defining systems in terms of logical entailment, I use certain ideas in Lewis's epistemology and philosophy of logic to define a class of models in which systems are taken to be primitive elements but bear certain relations to one another. I prove soundness and completeness for S2 over this class of models and argue that this semantics makes sense of at least a substantial fragment of Lewis's logical theory.     

Strong Necessitarianism: The Nomological Identity of Possible Worlds

Dispositional essentialism, a plausible view about the natures of (sparse or natural) properties, yields a satisfying explanation of the nature of laws also. The resulting necessitarian conception of laws comes in a weaker version, which allows differences between possible worlds as regards which laws hold in those worlds and a stronger version that does not. The main aim of this paper is to articulate what is involved in accepting the stronger version, most especially the consequence that all possible properties exist in all worlds. I also suggest that there is no particularly strong reason for preferring the weaker to the stronger version. For example, Armstrong's instantiation condition on universals entails that according to strong necessitarianism every property is instantiated in all possible worlds. But first we do not need to accept Armstrong's instantiation condition, in part because his arguments for it are forceful only for a contingentist about laws and properties. Secondly, even if we do accept the condition, the consequence that all properties are instantiated is not itself contradictory, so long as any form of necessitarianism holds. Strong necessitarianism is prima facie counter‐intuitive. But for that matter so is weak necessitarianism. Accepting either weak or strong necessitarianism requires denying the force of intuition in this area. And indeed we have every reason to deny the force of intuition and its primary source, imagination, concerning modal facts.     

A defence of informational structural realism

This is the revised version of an invited keynote lecture delivered at the 1st Australian Computing and Philosophy Conference (CAP@AU; the Australian National University in Canberra, 31 October–2 November, 2003). The paper is divided into two parts. The first part defends an informational approach to structural realism. It does so in three steps. First, it is shown that, within the debate about structural realism (SR), epistemic (ESR) and ontic (OSR) structural realism are reconcilable. It follows that a version of OSR is defensible from a structuralist-friendly position. Second, it is argued that a version of OSR is also plausible, because not all relata (structured entities) are logically prior to relations (structures). Third, it is shown that a version of OSR is also applicable to both sub-observable (unobservable and instrumentally-only observable) and observable entities, by developing its ontology of structural objects in terms of informational objects. The outcome is informational structural realism, a version of OSR supporting the ontological commitment to a view of the world as the totality of informational objects dynamically interacting with each other. The paper has been discussed by several colleagues and, in the second half, ten objections that have been moved to the proposal are answered in order to clarify it further.     

Composition as a Kind of Identity

Composition as identity, as I understand it, is a theory of the composite structure of reality. The theory’s underlying logic is irreducibly plural; its fundamental primitive is a generalized identity relation that takes either plural or singular arguments. Strong versions of the theory that incorporate a generalized version of the indiscernibility of identicals are incompatible with the framework of plural logic, and should be rejected. Weak versions of the theory that are based on the idea that composition is merely analogous to (one-one) identity are too weak to be interesting, lacking in metaphysical consequence. I defend a moderate version according to which composition is a kind of identity, and argue that the difference is metaphysically substantial, not merely terminological. I then consider whether the notion of generalized identity, though fundamental, can be elucidated in modal terms by reverse engineering Hume’s Dictum. Unfortunately, for realists about possible worlds, such as myself, who understand Hume’s Dictum in terms of duplicates, the elucidation never gets off the ground; for modal primitivists, the elucidation may succeed in capturing some general notion of identity, but it’s characterization is too general to target the particular notion of identity, tied to classical mereology, that is the object of my theorizing. In the end, I have little to offer the skeptic who claims not to understand the relevant notion of generalized identity, or not to take it to be compulsory in providing an account of the structure of reality.     

The contingency of composition

There is widespread disagreement as to what the facts are concerning just when a collection of objects composes some further object; but there is widespread agreement that, whatever those facts are, they are necessary. I am unhappy to simply assume this, and in this paper I ask whether there is reason to think that the facts concerning when composition occurs hold necessarily. I consider various reasons to think so, but find fault with each of them. I examine the theory of composition as identity, but argue that the version of this doctrine that entails universalism is unwarranted. I consider the claim that the a priority of such facts leads to their necessity, but give a defence of substantial contingent a priori truths. I ask whether the contingency of such facts would lead to unwelcome possibilities, but argue that it does not. Next, I argue against the thought that the Lewis–Sider argument against restricted composition might give us reason to accept the necessity of universalism. Lastly, I respond to two objections from the 2006 BSPC. I conclude in favour of the contingency of the facts concerning when some things compose some thing.

Structural Essentialism and Determinism

The paper tries to develop Bartels’s modern essentialism as a structural-role theory of identity for spacetime points. I adopt Hoefer’s idea of denying primitive identity for this theory and apply it to GTR and prerelativistic physics to find different versions of essentialism and different definitions of determinism which are coherent with them. I also try to argue that modified essentialism helps us to refute objections raised against essentialism and offers us the best understanding of prerelativistic and relativistic theories.     

The Fundamental Theorem of World Theory

The fundamental principle of the theory of possible worlds is that a proposition p is possible if and only if there is a possible world at which p is true. In this paper we present a valid derivation of this principle from a more general theory in which possible worlds are defined rather than taken as primitive. The general theory uses a primitive modality and axiomatizes abstract objects, properties, and propositions. We then show that this general theory has very small models and hence that its ontological commitments—and, therefore, those of the fundamental principle of world theory—are minimal.     

Semantic Primitivism and Normativity

Kripke-Wittgenstein meaning scepticism appears as a serious threat to the idea that there could be meaning-constituting facts. Some people argue that the only viable response is to adopt semantic primitivism (SP). SP is the doctrine that meaning-facts are sui generis and irreducibly semantic. The idea is that by allowing such primitive semantic facts into our ontology Kripke's sceptical paradox cannot arise. I argue that SP is untenable in spite of its apparent resourcefulness. No version of SP can account for the normative and practical aspects of meaning while remaining non-reductive. A sparse, basic SP does not adequately deal with the sceptical paradox. A richer SP, with an added intuitive epistemology, can only explain the practical aspect of meaning by aligning itself with reductive use-based accounts of meaning. SP with essential relations between meanings and meaning-bearers could possibly avoid these problems, but we have no reason to think such a version of SP is really non-reductive. I conclude that Kripke-Wittgenstein meaning scepticism should not lead us to adopt SP, instead we should re-examine use-based, dispositionalist accounts of meaning.     

Continuants and Occurrents: Joseph Melia

In this paper I try to eliminate occurrents from our ontology. I argue against Simons' position that occurrents are needed to supply truthmakers for existential claims about continuants. Nevertheless, those who would eliminate occurrents still need some account of our willingness to assert sentences that logically entail their existence. Though it turns out to be impossible to paraphrase away our reference to occurrents, I show that the truthmakers for such sentences are facts that involve only continuants. This is enough to allow us to regard our ordinary talk about occurrents as fictional. Finally, I argue that a proper conception of the underlying temporal facts about continuants can both avoid the problematic tensed theory of time and the problem of temporary intrinsics.     

Fictional objects, non-existence, and the principle of characterization

I advance an objection to Graham Priest??s account of fictional entities as nonexistent objects. According to Priest, fictional characters do not have, in our world, the properties they are represented as having; for example, the property of being a bank clerk is possessed by Joseph K. not in our world but in other worlds. Priest claims that, in this way, his theory can include an unrestricted principle of characterization for objects. Now, some representational properties attributed to fictional characters, a kind of fictional entities, involve a crucial reference to the world in which they are supposed to be instantiated. I argue that these representational properties are problematic for Priest??s theory and that he cannot accept an unrestricted version of the principle of characterization. Thus, while not refuting Priest??s theory, I show that it is no better off than other Meinongian theories.     

The Ontology of Thisness

This paper seeks to give an account of what it is for an individual to instantiate thisness (i.e. primitive individual essence). Thisnesses are peculiar entities, and even those who endorse their existence and instantiation by objects/entities, have said very little about how an individual and its thisness are related. My approach will be to seek out a model for the instantiation of thisness by canvassing broadly Aristotelian accounts of the substance/attribute relation, and then by making appropriate modifications to the most likely candidates in order to accommodate an individual's instantiation of thisness. What will emerge is that the model with the most utility makes thisness redundant in the case of material substances. Nonetheless, I will suggest that a version of the model can be appropriately applied in the case of other individuals which might instantiate thisness: for example, events (where these are conceived as a fundamental category of ontology distinct from material substances).

     

The possibility of morality

Despite much discussion over the existence of moral facts, metaethicists have largely ignored the related question of their possibility. This paper addresses the issue from the moral error theorist’s perspective, and shows how the arguments that error theorists have produced against the existence of moral facts at this world, if sound, also show that moral facts are impossible, at least at worlds non-morally identical to our own and, on some versions of the error theory, at any world. So error theorists’ arguments warrant a stronger conclusion than has previously been noticed. This may appear to make them vulnerable to counterarguments that take the possibility of moral facts as a premise. However, I show that any such arguments would be question-begging.     

Platonism and anti‐Platonism: Why worry?

This paper argues that it is scientific realists who should be most concerned about the issue of Platonism and anti‐Platonism in mathematics. If one is merely interested in accounting for the practice of pure mathematics, it is unlikely that a story about the ontology of mathematical theories will be essential to such an account. The question of mathematical ontology comes to the fore, however, once one considers our scientific theories. Given that those theories include amongst their laws assertions that imply the existence of mathematical objects, scientific realism, when construed as a claim about the truth or approximate truth of our scientific theories, implies mathematical Platonism. However, a standard argument for scientific realism, the ‘no miracles’ argument, falls short of establishing mathematical Platonism. As a result, this argument cannot establish scientific realism as it is usually defined, but only some weaker position. Scientific ‘realists’ should therefore either redefine their position as a claim about the existence of unobservable physical objects, or alternatively look for an argument for their position that does establish mathematical Platonism.     

A powers theory of modality: or,how I learned to stop worrying and reject possible worlds

Possible worlds, concrete or abstract as you like, are irrelevant to the truthmakers for modality—or so I shall argue in this paper. First, I present the neo-Humean picture of modality, and explain why those who accept it deny a common sense view of modality. Second, I present what I take to be the most pressing objection to the neo-Humean account, one that, I argue, applies equally well to any theory that grounds modality in possible worlds. Third, I present an alternative, properties-based theory of modality and explore several specific ways to flesh the general proposal out, including my favored version, the powers theory. And, fourth, I offer a powers semantics for counterfactuals that each version of the properties-based theory of modality can accept, mutatis mutandis. Together with a definition of possibility and necessity in terms of counterfactuals, the powers semantics of counterfactuals generates a semantics for modality that appeals to causal powers and not possible worlds.     

Possible Worlds for Modal Primitivists

Among the most remarkable developments in metaphysics since the 1950’s is the explosion of philosophical interest in possible worlds. This paper proposes an explanation of what possible worlds are, and argues that this proposal, the interpreted models conception, should be attractive to anyone who thinks that modal facts are primitive, and so not to be explained in terms of some non-modal notion of “possible world.” I articulate three constraints on any acceptable primitivist explanation of the nature of possible worlds, and show that the interpreted models conception meets the three constraints.     

Expressive completeness in modal language

Conclusion The logics of the modal operators and of the quantifiers show striking analogies. The analogies are so extensive that, when a special class of entities (possible worlds) is postulated, natural and non-arbitrary translation procedures can be defined from the language with the modal operators into a purely quantificational one, under which the necessity and possibility operators translate into universal and existential quantifiers. In view of this I would be willing to classify the modal operators as disguised quantifiers, and I think that wholehearted acceptance of modal language should be considered to carry ontological commitment to something like possible worldsConsidered as two languages for describing the same subject matter, modal and purely quantificational languages show interesting differences. The operator variables of the purely quantificational languages give them more power than the modal languages, but at least some of the functions performed by the apparatus of operator variables are also performed, in a more primitive and less versatile way, by actuality operators in modal languages.A final note. Quine has written much on the inter-relations of quantifiers, identity, and the concept of existence. These, he holds, form a tightly knit conceptual system which has been evolved to a high point of perfection, but which might conceivably change yet further.²⁹ He has also dropped hints about the possibility of a simpler, primitive or defective version of the system, in which the quantifiers are not backed up in their accustomed way by the concept of identity. He has dubbed the resulting concept a pre-individuative concept of existence, or a concept of entity without identity. What would a pre-individuative concept of existence be like? Quine has sometimes suggested that one might be embodied in the use of mass nouns, but the identity concept is used in connection with stuff as well as with things: is that the same coffee that was in the cup last night? I would submit that modality provides a better case. In view of the comparative weakness of modal languages, compared to the explicitly quantificational ones Quine takes as canonical, there is surely a sense in which the concept of existence embodied in that disguised existential quantifier, the possibility operator, is a defective one. And as we have seen, one of the differences between modal operators and explicit quantifiers is that modal operators cannot be joined with the identity predicate in the way quantifiers with operator variables can. Surely, then, there is a sense in which ordinary speech, as opposed to the metaphysical theorizing of a Leibniz or a David Lewis, conceives of possible worlds as entities without identity.As should become obvious on reading it, this paper is inspired by the work of David Lewis, particularly his classic Counterpart Theory and Quantified Modal Logic, Journal of Philosophy 7, March 1968. I would like to thank Lewis and the referee for this journal for encouragement and advice. An earlier version of the paper was formulated in terms of Lewis's counterpart theory rather than in terms of individuals being in more than one world, but, since I considered only the case in which the counterpart relation was an equivalence, I Felt that the added complexity was not justified. Doing things in a counterpart-theoretic framework does produce two new classes of sentences of the non-modal language which lack translations in the modal: speaking of the properties individuals have simpliciter rather than of those they have at a world allows us to discuss relations obtaining between individuals in different worlds (e.g. the longer than relation obtaining between actual yachts and their counterparts), and the assumption that no individual is in more than one world allows a tricky way of asserting that there are at most n worlds without using the identity predicate between terms for worlds. Otherwise, given the assumption that the counterpart relation was an equivalence with at most one member of each equivalence class being in each world, the transition from the counterpart theoretic framework to the current one was perfectly straightforward.