Jason Turner

This chapter gives a regimented, formalized presentation of Donald Baxter’s theory of Composition as Identity. It highlights how Baxter’s theory differs from the more commonly discussed variant that David Lewis flirted with. Baxter’s theory depends heavily on his Theory of Aspects, which restricts Leibniz’ Law, and of Count-Relative Identity. The chapter interprets the latter as a form of Ontological Pluralism and generates a novel notation for the former. It proposes certain principles as axioms of Baxter’s theory, regiments them, and gives them an informal gloss. It also highlights other potential axioms as choice points for Baxterians. It ends discussing objections and remaining questions.

Ontological nihilism is the radical-sounding thesis that there is nothing at all. This chapter first discusses how the most plausible forms of this thesis aim to be slightly less radical than they sound and what they will have to do in order to succeed in their less radical ambitions. In particular, they will have to paraphrase sentences of best science into ontologically innocent counterparts. The chapter then points out the defects in two less plausible strategies, before going on to argue that strategies that look more promising, including one based on Quine's predicate-functor language, face the same defects.

This paper presents a philosophically illuminating explanation of the concepts, from mathematics and formal model theory, of filters and ultrafilters. If a propositional theory is just a set of propositions, then a filter is a propositional theory that is (i) consistent, (ii) closed under finite conjunction, and (iii) closed under implication. An ultrafilter is a filter that is also negation‐complete. I prove the central theorem on ultrafilters and explain how it is a propositional variant of Lindenbaum’s Lemma (which says that every consistent set of sentences can be expanded to a negation‐complete, consistent set). Next I introduce the idea of products and ultraproducts of filters and ultrafilters, which are models constructed from the filters or ultrafilters, and prove Łos’s theorem, which shows that the ultraproduct of an ultrafilter makes true all and only the sentences which express propositions in the ultrafilter.

Representationalism is a metaphysical theory of quantities which explains the fact that we use unit-relative numbers to represent quantities by appealing to intrinsic, non-numeric relations between individual quantities plus a representation theorem. While the theory is well-developed for quantities such as mass or length, that development has not been extended to "mixed quantities" such as kilogram meters per second or cubed meters per kilogram-seconds-squared. Since typical instances of nomic constants are given in mixed units, this lack of development has gotten tangled up in issues about the metaphysics of constants, including David Baker’s "Pandora" argument against comparativism about quantities. This paper develops a representationalist theory of mixed quantities and explores how it can be used, in tandem with another thesis, to answer Baker’s Pandora argument.

Ontological Nihilism. It’s an extreme view—to extreme to be defended by most, even though variants and close cousins have their champions. Turner 2010 argues against the view with a dilemma. Some have resisted one horn of the dilemma. Less attention has been paid to the dilemma’s other horn. But a variant of Ontological Nihilism can avoid that other horn: Global Nihilism, which attempts to describe an object-free world all in one go. Despite appearances, Global Nihilism cannot be eliminated on grounds of simplicity or parsimony. However, one may object to its implicit holism. The argument here is that we learn the world by encountering it one piece at a time, but the Global Nihilist cannot provide the metaphysical ‘pieces’ of the world needed to explain how we do this.

Neither special nor general relativity make any use of a notion of absolute simultaneity. Since A-Theories about time do make use of such a notion, it is natural to suspect that relativity and A-Theory are inconsistent. Many authors have argued that they are in fact not inconsistent, and I agree with that diagnosis here. But that doesn’t mean, as these authors seem to think, that A-Theory and relativity are happy bedfellows. I argue that relativity gives us good reason to reject the A-Theory, even though strict inconsistency isn’t that reason.

Ontological nihilism is the radical-sounding thesis that there is nothing at all. This chapter first discusses how the most plausible forms of this thesis aim to be slightly less radical than they sound and what they will have to do in order to succeed in their less radical ambitions. In particular, they will have to paraphrase sentences of best science into ontologically innocent counterparts. The chapter then points out the defects in two less plausible strategies, before going on to argue that strategies that look more promising, including one based on Quine's predicate-functor language, face the same defects.

This report provides practical recommendations for the design and execution of multicenter functional MRI studies based on the collective experience of the Function Biomedical Informatics Research Network. The study was inspired by many requests from the fMRI community to FBIRN group members for advice on how to conduct MC-fMRI studies. The introduction briefly discusses the advantages and complexities of MC-fMRI studies. Prerequisites for MC-fMRI studies are addressed before delving into the practical aspects of carefully and efficiently setting up a MC-fMRI study. Practical multisite aspects include: establishing and verifying scan parameters including scanner types and magnetic fields, establishing and monitoring of a scanner quality program, developing task paradigms and scan session documentation, establishing clinical and scanner training to ensure consistency over time, developing means for uploading, storing, and monitoring of imaging and other data, the use of a traveling fMRI expert, and collectively analyzing imaging data and disseminating results. We conclude that when MC-fMRI studies are organized well with careful attention to unification of hardware, software and procedural aspects, the process can be a highly effective means for accessing a desired participant demographics while accelerating scientific discovery. © 2012 Wiley Periodicals, Inc.

C endorses the doctrine of Composition as Identity, which holds that a composite object is (plurally) identical to its many parts, and entails that one object can be (plurally) identical to several others. In this dialogue, N argues that many‐one identity, and thus composition as identity, is conceptually confused. In particular, N claims it violates two conceptual truths: that existence facts fix identity facts, and that identity is no addition to being. In response to pressure from C, N considers several candidate interpretations of the first slogan. Each interpretation imagines God issuing a divine existential decree that counts as ‘fixing the existence facts’, and then considers what questions about identity are left open by it. N eventually hits on an appealing interpretation of the slogan that C can neither undermine nor accommodate, and uses it to interpret the second slogan as well.

The thesis of existentialism holds that if a proposition p exists and predicates something of an object a, then in any world where a does not exist, p does not exist either. If “possibly, p” entails “in some possible world, the proposition that p exists and is true,” then existentialism is prima facie incompatible with the truth of claims like “possibly, the Eiffel Tower does not exist.” In order to avoid this claim, a distinction between two kinds of world-indexed truth –and two associated kinds of modality –is needed. This paper embodies an attempt to develop a full account of just such a distinction.

In The Construction of Logical Space, Agustín Rayo defends trivialism, according to which number-involving truths are trivially equivalent to other, non-number-involving truths; picturesquely, ‘I have five fingers on my hand’ and ‘the number of fingers on my hand is five’ express the same fact, but carved up in different ways. A single fact thus has multiple structures. I distinguish two ways this might go: on the deflationary picture, facts get their structures from our linguistic practices, while on an inflationary picture, facts have multiple structures independently of language. I argue that Rayo’s view is best interpreted as deflationary. Thus interpreted, it blocks off an attractive solution to the old problems of intensionality. I further argue a that a semi-deflationary variant of Rayo’s view can make use of the attractive solution—but it thereby sacrifices the supposed mathematical benefits of trivialism

Compatibilism is the view that free will can exist even if determinism — the thesis that there is only one physically possible future at any given time — is true. In this thesis, I defend compatibilism by arguing against two of its main rivals. I first argue against necessary eliminativism — the view that free will is impossible — by deploying an attractive view of language (Lewis, 1983, 1984; Sider, 2001) to show that, so long as ordinary folk are liable to experience conflicting intuitions about how to use the term ‘free,’ it will refer to some property which is possibly exemplified. I then argue that libertarians — believers in free will who hold that it is incompatible with determinism — must reject either a naturalistic view of the world with no ontological commitments above and beyond those proscribed by science or the soundness of the best argument in favor of libertarianism (van Inwagen, 1983, ch. 3). Finally, I sketch a way a proponent of compatibilism can use my arguments against necessary eliminativists and naturalistic libertarians to offer a positive argument for compatibilism

The structuralist conception of metaphysics holds that it aims to uncover the ultimate structure of reality and explain how the world's richness and variety are accounted for by that ultimate structure. On this conception, metaphysicians produce fundamental theories, the primitive, undefined expressions of which are supposed to 'carve reality at its joints', as it were. On this conception, ontological questions are understood as questions about what there is, where the existential quantifier 'there is' has a fundamental, joint-carving interpretation. Structuralist orthodoxy holds that there is exactly one fundamental, joint-carving interpretation that an existential quantifier could have. This orthodox assumption could go wrong--either by there being too few fundamental-quantifier interpretations, or by there being too many. In this dissertation I examine the implications of these non-orthodox options. Someone who thinks there are too many fundamental-quantifier interpretations might think this means standard ontological debates are in some sense defective of 'merely verbal', or she might think instead that the different quantifiers show that there are different 'ways' or 'modes' of being. I argue that the first option runs into problems with a certain sort of realism about logic, but that there is no general problem with the second option, despite its longstanding bad philosophical reputation. I also argue that realism about logic gives us reason to think the dispute between someone who thinks there are many 'modes of being' in this sense and someone who thinks there is just one is not itself verbal. Finally, I turn to the case in which there are no fundamental quantifiers, arguing that it brings with it a host of theoretical problems we could avoid with quantifiers.

C endorses the doctrine of Composition as Identity, which holds that a composite object is identical to its many parts, and entails that one object can be identical to several others. In this dialogue, N argues that many‐one identity, and thus composition as identity, is conceptually confused. In particular, N claims it violates two conceptual truths: that existence facts fix identity facts, and that identity is no addition to being. In response to pressure from C, N considers several candidate interpretations of the first slogan. Each interpretation imagines God issuing a divine existential decree that counts as ‘fixing the existence facts’, and then considers what questions about identity are left open by it. N eventually hits on an appealing interpretation of the slogan that C can neither undermine nor accommodate, and uses it to interpret the second slogan as well

The free will defense is a theistic strategy for resisting the atheistic argument known as “the logical problem of evil.” It insists that God may have to allow some evil in order to get the greater good of creatures freely choosing to act rightly. Many philosophers have thought that the free will defense requires the truth of incompatibilism, according to which acts cannot be free if they are causally determined. For it seems that if compatibilism is true, God should be able to get the goods of free creatures acting rightly without any evil by simply creating a world where creatures are causally determined to always act rightly. I argue that this is not so. First I describe and motivate a compatibilist account of free will according to which, although God can create creatures which are both free and causally determined, the freedom of determined creatures depends on God’s not taking into account what they will be determined to do. I then show how, given such a form of compatibilism, God may be able to create free and determined creatures without being able to create creatures determined to always freely act rightly.