Leibniz on Infinite Numbers,Infinite Wholes,and Composite Substances

Leibniz claims that nature is actually infinite but rejects infinite number. Are his mathematical commitments out of step with his metaphysical ones? It is widely accepted that Leibniz has a viable response to this problem: there can be infinitely many created substances, but no infinite number of them. But there is a second problem that has not been satisfactorily resolved. It has been suggested that Leibniz's argument against the world soul relies on his rejection of infinite number, and, as such, Leibniz cannot assert that any body has a soul without also accepting infinite number, since any body has infinitely many parts. Previous attempts to address this concern have misunderstood the character of Leibniz's rejection of infinite number. I argue that Leibniz draws an important distinction between ‘wholes’ – collections of parts that can be thought of as a single thing – and ‘fictional wholes’ – collections of parts that cannot be thought of as a single thing, which allows us to make sense of his rejection of infinite number in a way that does not conflict either with his view that the world is actually infinite or that the bodies of substances have infinitely many parts.     

Internalism without Luminosity1

Internalists face the following challenge: what is it about an agent's internal states that explains why only these states can play whatever role the internalist thinks these states are playing?  Internalists have frequently appealed to a special kind of epistemic access that we have to these states. But such claims have been challenged on both empirical and philosophical grounds.  I will argue that internalists needn't appeal to any kind of privileged access claims.  Rather, internalist conditions are important because of the way in which we expect them to act as causal mediators between states of the world, on the one hand, and our beliefs and actions on the other.     

Keeping a Place for Metaethics: Assessing Elliot's Dismissal of the Subjectivism/Objectivism Debate in Environmental Ethics

Abstract: Robert Elliot claims that the metaethical distinction between subjectivism and objectivism is unimportant in environmental ethics. He argues that because a sufficiently sophisticated subjectivist can accommodate all the intrinsic value an objectivist can, even in apparently problematic situations where humans either do not exist or do not have the relevant values, and because metaethical commitments fail to have any normative or motivational impact on rational debate, it makes no difference whether an environmental ethicist is a subjectivist or an objectivist. Elliot's dismissal, however, is unjustified. As it turns out, objectivists argue differently from the way subjectivists do, are motivated differently from the way subjectivists are, and are able to make a greater range of intrinsic value claims than subjectivists are. If Elliot's arguments have any appeal at all, it is only because he blurs the fundamental metaethical distinction in the first place and defends a subjectivism so objectivist that it is almost unrecognizable as subjectivism.     

You meta believe it

Because of the privileged place of beliefs in explaining behaviour, mismatch cases—in which agents sincerely claim to believe that p, but act in a way that is inconsistent with that belief—have attracted a great deal of attention. In this paper, I argue that some of these cases, at least, are at least partially explained by agents believing that they believe that p, while failing to believe that p. Agents in these cases do not believe that ~p; rather, they have an indistinct first‐order, beliefy, representation that p. The indistinctness of this first‐order representation provides the leeway for the inconsistency seen in their behaviour.     

Rethinking Intrinsic Value

According to the dominant philosophical tradition, intrinsic value must depend solely upon intrinsic properties. By appealing to various examples, however, I argue that we should at least leave open the possibility that in some cases intrinsic value may be based in part on relational properties. Indeed, I argue that we should even be open to the possibility that an object's intrinsic value may sometimes depend (in part) on its instrumental value. If this is right, of course, then the traditional contrast between intrinsic value and instrumental value is mistaken.     

Sartre's Theory of Motivation

The aim of this article is to offer a novel reconstruction of Sartre's theory of motivation. I argue for four related claims: (a) Sartre's theory of motivation revolves around the Schelerian‐inspired notion of affectivity and the peculiar way affectivity provides us access to evaluative properties of the objects in our environment; (b) according to Sartre, the structure of intentional action, and in particular the act of choice and commitment to projects, is inextricably linked with “affectivity”; (c) the inextricable link between intentional action and affectivity is to be analyzed in terms of the fundamental structure of consciousness as being self‐present, thus making the agent nonpositionally aware of her choices and commitments; (d) an agent is motivated to act when her affective disclosure of value is in part constituted by the awareness of her commitments to relevant projects.     

What we talk about when we talk about epistemic justification

Stewart Cohen argues that much contemporary epistemological theorizing is hampered by the fact that ‘epistemic justification’ is a term of art (rather than something we all pretheoretically understand) and one that is never given any serious explication in a non-tendentious, theory-neutral way. He suggests that epistemologists are therefore better off theorizing in terms of rationality, rather than in terms of ‘epistemic justification’. Against this, I argue that even if the term ‘epistemic justification’ is not broadly known, the concept it picks out is quite familiar, and partly because it’s a term of art, justification talk is a better vehicle for philosophical theorizing. ‘Rational’ is too unclear for our philosophical purposes, and the fact that ‘epistemic justification’ gets fleshed out by appeal to substantive, controversial theses is no obstacle to its playing the needed role in epistemological theorizing.     

Wittgenstein on Set Theory and the Enormously Big

Wittgenstein's conception of infinity can be seen as continuing the tradition of the potential infinite that begins with Aristotle. Transfinite cardinals in set theory might seem to render the potential infinite defunct with the actual infinite now given mathematical legitimacy. But Wittgenstein's remarks on set theory argue that the philosophical notion of the actual infinite remains philosophical and is not given a mathematical status as a result of set theory. The philosophical notion of the actual infinite is not to be found in the mathematics of set theory, only in a certain associated philosophy – what Wittgenstein calls a certain kind of “prose”.     

The Astounding Assumption of Infinite Life

The multimillennial philosophical discussion about life after death has received a recent boost in the prospect of immortality attained via technologies. In this newer version, humans generally are considered mortal but may develop means of making themselves immortal. If “immortal” means not mortal, thus existing for infinity, and if the proposed infinite‐existing entity is material, it must inhabit an infinite material universe. If the proposed entity is not material, there must be means by which it can shed its material substance and exist nonmaterially. The article examines arguments for how an infinite life would be possible given current physical understanding. The paper considers a Pascalian‐style wager weighing the likelihood of adjusting to existence wholly within a finite universe versus betting on there being some way to construe the universe(s) as a viable medium for infinite beings. Conclusion: the case for a finite being to exist infinitely has little viable support.     

Nominalizing Quantifiers

Quantified expressions in natural language generally are taken to act like quantifiers in logic, which either range over entities that need to satisfy or not satisfy the predicate in order for the sentence to be true or otherwise are substitutional quantifiers. I will argue that there is a philosophically rather important class of quantified expressions in English that act quite differently, a class that includes something, nothing, and several things. In addition to expressing quantification, such expressions act like nominalizations, introducing a new domain of objects that would not have been present in the semantic structure of the sentence otherwise. The entities those expressions introduce are of just the same sort as those that certain ordinary nominalizations refer to (such as John's wisdom or John's belief that S), namely they are tropes or entities related to tropes. Analysing certain quantifiers as nominalizing quantifiers will shed a new light on philosophical issues such as the status of properties and the nature of propositional attitudes.     

A Different Type of Individualism in Zhuangzi

Individualism is not only a Western tradition. In the Zhuangzi we can also identify some elements which may be appropriately attributed to “individualism.” However, due to its particular cultural and philosophical background, Zhuangzian individualism has unique characteristics, which distinguish it from the variety of other individualist thoughts that have emerged in the West. Zhuangzi has a dynamic and open view on individual “self,” considering individuals as changing and unique beings rather than fixed and interchangeable “atoms”; he sets the unlimited Dao as the ultimate source for individuals to conform to, thus releasing individual mind into a realm of infinite openness and freedom. The Zhuangzian individualism is “inward” rather than “outward,” concentrating on individual spirit rather than material interests and rights in social reality. The individualism in the Zhuangzi provides a spiritual space for the development of individuality in ancient China. It also provides an alternative understanding of individual as an existence.     

Wittgenstein and logic

In his Tractatus Logico-Philosophicus Ludwig Wittgenstein (1889–1951) presents the concept of order in terms of a notational iteration that is completely logical but not part of logic. Logic for him is not the foundation of mathematical concepts but rather a purely formal way of reflecting the world that at the minimum adds absolutely no content. Order for him is not based on the concepts of logic but is instead revealed through an ideal notational series. He states that logic is “transcendental”. As such it requires an ideal that his philosophical method eventually forces him to reject. I argue that Wittgenstein’s philosophy is more dialectical than transcendental.     

Should We Be Talking About Ethics or About Morals?

This article seeks to revisit the distinction between the words ethics and morals. First, we understand the word ethics to be focused on the way we seek to live our own life, and hence to connote a relativistic and essentially subjective perspective, whereas we understand the word morals to be focused on the way we should live our lives together, especially through sensitivity to viewpoints other than our own. Second, we perceive a usefulness in such a differentiation when the ethical values of those in a dilemmatic situation are conflicted in order to prioritize moral decision making in contemporary society. We argue that in our current era, characterized by a multiplicity of faiths and by pronounced value pluralism, a philosophical basis for moral decision making needs to be clearly attuned with intersubjectivity and interconnectivity among people. It should be able to determine principles of conduct toward others, no matter how one’s own ethical values, conceptions of the good, or life choices might differ from those of others. To do this, we relocate ethical decision making away from an essentially monological reflection on our own values and purposes into a social space wherein we have an inclusive, noncoercive, and reflective dialogue.     

Venturing Beyond Analytic Philosophy's “Best” Arguments to the Implied Inadequacies of Its Metaphilosophical Intuitions

Gary Gutting argues, in his recent book What Philosophers Know, that analytic philosophy provides a sizable collection of exemplary arguments that effectively yield a “disciplinary body of philosophical knowledge”—“metaphilosophy,” he names it—that is, specimens that define in a notably perspicuous way what we should understand as philosophical knowledge itself. He concedes weaknesses in the best‐known specimens, and he admits that, generally, even the best specimens do not provide answers to the usual grand questions. I admire his treatment of the matter but argue that the metaphilosophical issues are, normally, of a much grander gauge than that of his sort of specimen; that they require a much more open, informal sort of inquiry and exchange than that of the distinctive rigor of the classic specimens themselves; that analytic philosophy, not uncharacteristically, tends to ignore the metaphilosophical issue or takes the validity of its method of argument for granted; and that the issue itself invites an appraisal of competing second‐order conceptions of how philosophical argument proves fruitful. I proceed by way of the examination of cases drawn from Quine and Kripke.     

Socratic Film

This article is about a relationship between the Socratic practice of philosophy and the aesthetic practice of watching and appreciating film. The conclusion that I defend is that certain narrative films, like the elenctic method in the hands of Socrates, are philosophical tools for examining our cognitive and emotional life and thus for gaining insight into aspects of our character. In the early sections of the article I construct an analogy between the practice of watching narrative film and the practice of self‐examination through dialogue and reflection. I argue that good aesthetic practice in film appreciation is analogous to good philosophical practice in the manner of Socrates, and I treat the elenchus as a method of self‐examination rather than of conceptual analysis and Socrates himself as an examiner of people rather than of abstract concepts. In the later sections I discuss three films directed by Christopher Nolan—Memento (2000), The Prestige (2006), and Inception (2010)—as paradigm cases of Socratic film. I argue that these films show us something about ourselves by prompting extemporaneous emotional responses and cognitive judgments that we come, reflectively, to reject.     

Taking Stock of Infinite Value: Pascal’s Wager and Relative Utilities

Among recent objections to Pascal’s Wager, two are especially compelling. The first is that decision theory, and specifically the requirement of maximizing expected utility, is incompatible with infinite utility values. The second is that even if infinite utility values are admitted, the argument of the Wager is invalid provided that we allow mixed strategies. Furthermore, Hájek (Philosophical Review 112, 2003) has shown that reformulations of Pascal’s Wager that address these criticisms inevitably lead to arguments that are philosophically unsatisfying and historically unfaithful. Both the objections and Hájek’s philosophical worries disappear, however, if we represent our preferences using relative utilities (generalized utility ratios) rather than a one-place utility function. Relative utilities provide a conservative way to make sense of infinite value that preserves the familiar equation of rationality with the maximization of expected utility. They also provide a means of investigating a broader class of problems related to the Wager.     

Hallucination And Imagination

What are hallucinations? A common view in the philosophical literature is that hallucinations are degenerate kinds of perceptual experience. I argue instead that hallucinations are degenerate kinds of sensory imagination. As well as providing a good account of many actual cases of hallucination, the view that hallucination is a kind of imagination represents a promising account of hallucination from the perspective of a disjunctivist theory of perception like naïve realism. This is because it provides a way of giving a positive characterisation of hallucination—rather than characterising hallucinations in negative, relational, terms as mental events that are subjectively indistinguishable from veridical perceptual experiences.