Numbers and other mathematical objects are exceptional in having no locations in space or time or relations of cause and effect. This makes it difficult to account for the possibility of the knowledge of such objects, leading many philosophers to embrace nominalism, the doctrine that there are no such objects, and to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects. This book cuts through a host of technicalities that have obscured previous (...) discussions of these projects, and presents clear, concise accounts of a dozen strategies for nominalistic interpretation of mathematics, thus equipping the reader to evaluate each and to compare different ones. The authors also offer critical discussion, rare in the literature, of the aims and claims of nominalistic interpretation, suggesting that it is significant in a very different way from that usually assumed. (shrink)
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.. (shrink)
In the author’s previous contribution to this journal (Rosen 2015), a phenomenological string theory was proposed based on qualitative topology and hypercomplex numbers. The current paper takes this further by delving into the ancient Chinese origin of phenomenological string theory. First, we discover a connection between the Klein bottle, which is crucial to the theory, and the Ho-t’u, a Chinese number archetype central to Taoist cosmology. The two structures are seen to mirror each other in expressing the psychophysical (phenomenological) action (...) pattern at the heart of microphysics. But tackling the question of quantum gravity requires that a whole family of topological dimensions be brought into play. What we find in engaging with these structures is a closely related family of Taoist forebears that, in concert with their successors, provide a blueprint for cosmic evolution. Whereas conventional string theory accounts for the generation of nature’s fundamental forces via a notion of symmetry breaking that is essentially static and thus unable to explain cosmogony successfully, phenomenological/Taoist string theory entails the dialectical interplay of symmetry and asymmetry inherent in the principle of synsymmetry. This dynamic concept of cosmic change is elaborated on in the three concluding sections of the paper. Here, a detailed analysis of cosmogony is offered, first in terms of the theory of dimensional development and its Taoist (yin-yang) counterpart, then in terms of the evolution of the elemental force particles through cycles of expansion and contraction in a spiraling universe. The paper closes by considering the role of the analyst per se in the further evolution of the cosmos. (shrink)
When a person acts from ignorance, he is culpable for his action only if he is culpable for the ignorance from which he acts. The paper defends the view that this principle holds, not just for actions done from ordinary factual ignorance, but also for actions done from moral ignorance. The question is raised whether the principle extends to action done from ignorance about what one has most reason to do. It is tentatively proposed that the principle holds in full (...) generality. (shrink)
This paper defends the idea that there might be vagueness or indeterminacy in the world itself--as opposed to merely in our representations of the world--against the charges of incoherence and unintelligibility. First we consider the idea that the world might contain vague properties and relations ; we show that this idea is already implied by certain well-understood views concerning the semantics of vague predicates (most notably the fuzzy view). Next we consider the idea that the world might contain vague objects (...) ; we argue that an object is indeterminate in a certain respect (colour, size, etc.) just in case it is a borderline case of a maximally specific colour (size, etc.) property. Finally we consider the idea that the world as a whole might be indeterminate; we argue that the world is indeterminate just in case it lacks a determinate division into determinate objects. (shrink)
Van Fraassen defines constructive empiricism as the view that science aims to produce empirically adequate theories. But this account has been misunderstood. Constructive empiricism in not, as it seems, a description of the intentional features of scientific practice, nor is it a normative prescription for their revision. It is rather a fiction about the practice of science that van Fraassen displays in the interests of a broader empiricism. The paper concludes with a series of arguments designed to show that constructive (...) empiricism so understood is self-undermining. (shrink)
Integrative and naturalistic philosophy of mind can both learn from and contribute to the contemporary cognitive sciences of dreaming. Two related phenomena concerning self-representation in dreams demonstrate the need to bring disparate fields together. In most dreams, the protagonist or dream self who experiences and actively participates in dream events is or represents the dreamer: but in an intriguing minority of cases, self-representation in dreams is displaced, disrupted, or even absent. Working from dream reports in established databanks, we examine two (...) key forms of polymorphism of self-representation: dreams in which I take an external visuospatial perspective on myself, and those in which I take someone else's perspective on events. In remembering my past experiences or imagining future or possible experiences when awake, I sometimes see myself from an external or 'observer' perspective. By relating the issue of perspective in dreams to established research traditions in the study of memory and imagery, and noting the flexibility of perspective in dreams, we identify new lines of enquiry. In other dreams, the dreamer does not appear to figure at all, and the first person perspective on dream events is occupied by someone else, some other person or character. We call these puzzling cases 'vicarious dreams' and assess some potential ways to make sense of them. Questions about self-representation and perspectives in dreams are intriguing in their own right and pose empirical and conceptual problems about the nature of self-representation with implications beyond the case of dreaming. (shrink)
Luck egalitarianism is an approach within current distributive justice theory which aims to focus redistributive efforts solely upon disadvantages that ensue from bad luck. This article considers how central assumptions and themes of both luck egalitarianism and its critics parallel those of providence theology and share some of their concerns. These relate to problems such as the basis of equality, the extent and nature of our knowledge, and of course, the paternalism that assessing people’s responsibility over their own disadvantages involves. (...) I highlight the similarity of luck egalitarianism to the role of providence and providence theory thinking, and particularly the tension between egalitarianism as a theological concept and the condescension inherent to imitatio Dei ethics. I approach these issues by analyzing standard criticisms of the luck egalitarian project, espoused by Susan Hurley and Elizabeth Anderson. I then proceed to assess the values of luck egalitarianism itself and consider different models of providence, and the meaning of this analysis for normative ethics. The subject matter of this article is part of a wider comparison of distributive justice and providence theory, within which luck egalitarianism affords a very fruitful and highly relevant case study. (shrink)
According to one sort of epistemic relativist, normative epistemic claims (e.g., evidence E justifies hypothesis H) are never true or false simpliciter, but only relative to one or another epistemic system. In chapter 6 of Fear of Knowledge, Paul Boghossian objects to this view on the ground that its central notions cannot be explained, and that it cannot account for the normativity of epistemic discourse. This paper explores how the dogged relativist might respond.
Fictionalism about possible worlds is the view that talk about worlds in the analysis of modality is to be construed as ontologically innocent discourse about the content of a fiction. Versions of the view have been defended by D M Armstrong (in "A Combinatorial Theory of Possibility") and by myself (in "Modal Fictionalism', "Mind" 99, July 1990). The present note argues that fictionalist accounts of modality (both Armstrong's version and my own) fail to serve the fictionalists ontological purposes because they (...) imply that as a matter of necessity there exist many worlds. (shrink)
In Being Realistic About Reasons T. M. Scanlon argues that particular fact about reasons are explained by contingent non-normative facts together with pure normative principles. A question then arises about the modal status of these pure principles. Scanlon maintains that they are necessary in a sense, and suggests that they are ‘metaphysically’ necessary. I argue that the best view for Scanlon to take, given his other commitments, is that these pure normative principles are metaphysically contingent in some cases and necessary (...) only in a weaker sense. (shrink)
According to Parfit, the best version of Kantian ethics takes as its central principle Kantian Contractualism: the thesis that everyone ought to follow the principles whose universal acceptance everyone could rationally will. This paper examines that thesis, identifies a class of annoying counterexamples, and suggests that when Kantian Contractualism is modified in response to these examples, the resulting principle is too complex and ad hoc to serve as the 'supreme principle of morality'.
In Prior Analytics 1.15 Aristotle undertakes to establish certain modal syllogisms of the form XQM. Although these syllogisms are central to his modal system, the proofs he offers for them are problematic. The precise structure of these proofs is disputed, and it is often thought that they are invalid. We propose an interpretation which resolves the main difficulties with them: the proofs are valid given a small number of intrinsically plausible assumptions, although they are in tension with some claims found (...) elsewhere in Aristotle’s modal syllogistic. The proofs make use of a rule of propositional modal logic which we call the possibility rule. We investigate how this rule interacts and coheres with the core elements of the modal syllogistic. (shrink)
The paper examines the conditions under which we are responsible for actions performed under duress, focusing on a real case in which a soldier was compelled at gunpoint to participate in the massacre of civilian prisoners. The case stands for a class of cases in which the compelled act is neither clearly justified nor clearly excused on grounds of temporary incapacity, but in which it is nonetheless plausible that the agent is not morally blameworthy. The theoretical challenge is to identify (...) the excuse in such cases and to explain its basis. The paper argues that when mortal duress excuses in cases of this sort, it does so because the compelled act, though impermissible and freely chosen, nonetheless fails to manifest ‘an insufficiently good will’. The argument depends on a potentially controversial thesis in the ethics of concern, namely, that a thoroughly decent moral agent—someone who cares enough about morality and the values that underlie it—will not always be moved to do what he knows he ought to do. (shrink)