Gideon Rosen

According to neo-Fregean Platonism, abstraction principles—such as the principle that the direction of line a is identical to the direction of line b iff a and b are parallel—may in some cases be regarded as introducing new singular terms (e.g., “the direction of line a”) and as fixing the truth-conditions of genuine identity statements featuring them. If neo-Fregeanism is to vindicate Frege’s idea that a plausible philosophy of arithmetic can and should treat the natural numbers as a species of _object_, it must address the so-called “Caesar Problem”: the problem of explaining in general terms which objects given in other terms they are to be distinguished from. This chapter pilots a novel solution to the Caesar Problem via the notion of a _real definition_: a definition whose purpose is not to explain a meaning, but to characterize the essential nature of the thing introduced.

This chapter explores Fine’s suggestion that the ethical facts supervene on the natural facts, not as a matter of metaphysical necessity, but rather as a matter of normative necessity. The first part develops an argument against the metaphysical supervenience of the ethical, the main premises of which are ethical non-naturalism and Fine’s essentialist analysis of metaphysical necessity. The second part defends an analysis of normative necessity according to which P is normatively necessary iff P would have been the case no matter how the non-normative facts had been. The last part argues that the basic principles of ethics as the non-naturalist conceives them are indeed normatively necessary in this sense.

Conventional wisdom holds that pure moral principles hold of metaphysical necessity, from which it follows that it is metaphysically impossible for the moral facts to vary independently of the descriptive facts. Moral contingentists deny this, holding that the moral laws are in some cases like the laws of nature: metaphysically contingent, but necessary in a weaker sense. The present chapter makes a preliminary case for moral contingentism and defends the view against recent objections due to Lange (2018) and Dreier (2019).

Realists about metaphysics hold that the aim of the enterprise is to state the truth about the fundamental structure of reality and the principles by means of which reality as a whole is built up from that fundamental structure. Fictionalists hold, by contrast, that metaphysics aims to produce theories (or models) of the fundamental structure that satisfy certain self-imposed constraints: consistency with evolving science, coherence, plausibility by the standards of one or another philosophical subculture, and so on. This chapter distinguishes scientific metaphysics (the sort of metaphysics that rounds out the scientific image by settling theoretical questions unaddressed by scientists) from speculative metaphysics (the sort of metaphysics that tackles questions remote from science) and recommends a version of fictionalism about the latter.

This chapter explores bridge-law non-naturalism: the view that when a particular thing possesses a moral property or stands in a moral relation, this fact is metaphysically grounded in non-normative features of the thing in question together with a general moral law. Any view of this sort faces two challenges, analogous to familiar challenges in the philosophy of science: to specify the form of the explanatory laws, and to say when a fact of that form qualifies as a law. The chapter explores three strategies for answering these questions, all of which maintain that a moral law is a true generalization of the form [It is normatively necessary that whatever ϕs is (thereby) F].

Gideon Rosen discusses Kitcher’s recent critique of platonism and defense of formalism. Kitcher argues that any view that attributes a subject matter to mathematics, including platonism, has no good explanation of how symbol manipulation could lead to the discovery of new abstract objects. Hence there is a gap between the basis for mathematical claims and the ultimate standard of correctness in mathematics on the platonist view. In response Rosen argues that moderate platonism can answer Kitcher’s charge. Rosen is also critical of Kitcher’s formalism for failing to make sense of various aspects of mathematical practice, especially applied mathematics. The inability to make sense of mathematical practice is precisely the sort of concern Kitcher raises against the platonist.

A theory of moral responsibility should not just identify the conditions of moral responsibility; it should explain why those conditions are as they are. This chapter explores an account of responsibility that yields explanations of the desired sort. According to the Alethic View, for a person X to be morally responsible (praiseworthy or blameworthy) for an action A just is for the thoughts implicit in the moral reactive emotions to be true of X and A. These thoughts thus determine the basic conditions of moral responsibility.

This contribution to a symposium marking the 30th anniversary of Kit Fine’s “Essence and Modality” raises a general question for essentialist theories of modality: What sort of proposition can figure in the essence of a property? Several versions of Fine’s preferred “definitional” conception are explored. The main aim is to find a version of the theory that can secure the necessity of generative principles — e.g., the principles according to which complex entities are generated from simples — without opening the door to opening the door to bogus principles that would prove the existence of gods and angels.

Region R Question: How many objects — entities, things — are contained in R? Ignore the empty space. Our question might better be put, 'How many material objects does R contain?' Let's stipulate that A, B and C are metaphysical atoms: absolutely simple entities with no parts whatsoever besides themselves. So you don't have to worry about counting a particle's top half and bottom half as different objects. Perhaps they are 'point-particles', with no length, width or breadth. Perhaps they are extended in space without possessing spatial parts (if that is possible). Never mind. We stipulate that A, B and C are perfectly simple. We also stipulate that they are connected as follows. A and B are stuck together in such a way that when a force is applied to one of them, they move together 'as a unit'. Moreover, the two of them together exhibit behavior that neither would exhibit on its own — Perhaps they emit a certain sound, or glow in the dark — whereas C is..

This paper takes up a neglected problem for metaethical noncognitivism: the characterization of the acceptance states for agent-centered normative theories like Rational Egoism. If Egoism is a coherent view, the non-cognitivist needs a coherent acceptance state for it. This can be provided, as Dreier and Gibbard have shown. But those accounts fail when generalized, assigning the same acceptance state to normative theories that are clearly distinct, or assigning no acceptance state to theories that look to be intelligible. The paper makes the case for this and then asks: What should we conclude if the problem cannot be solved? We might conclude that since Egoism is clearly a coherent view, the argument amounts to a refutation of noncognitivism. But we suggest another possibility. There is, on reflection, something incoherent, or at least odd, in standard formulations of Egoism; noncognitivism predicts this and so provides an intriguing explanation for this fact.

Viewed from a suitable distance, David Lewis's ontological scheme is simplicity itself. Absolutely everything that exists, according to Lewis, is either a spatiotemporal particular, or a set theoretic construction from such particulars, or a mereological aggregate of such items. Set theoretic constructionalism is not an incidental feature of Lewis's system. The master argument of On the Plurality of Worlds is that a pluriverse composed of infinitely many concrete universes constitutes a “paradise for philosophers. Given his other views, his account of classes has profound implications for general metaphysics, implying as it does an account of the nature of properties and instantiation, propositions and propositional truth, the nature of events, and so on. But Lewis does not consider those implications. The aim of this chapter is to close the circle by bringing Lewis's mature account of sets into contact with his larger ontological scheme.