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.     

The Kalām Cosmological Argument and the Infinite God Objection

In this article, we evaluate various responses to a noteworthy objection, namely, the infinite God objection to the kalām cosmological argument. As regards this objection, the proponents of the kalām argument face a dilemma—either an actual infinite cannot exist or God cannot be infinite. More precisely, this objection claims that God’s omniscience entails the existence of an actual infinite with God knowing an actually infinite number of future events or abstract objects, such as mathematical truths. We argue, however, that the infinite God objection is based on two questionable assumptions, namely, (1) that it is possible for an omniscient being to know an actually infinite number of things and (2) that there exist an actually infinite number of abstract objects for God to know.     

The First Antinomy and Spinoza

Scholars commonly assume that Kant never seriously engaged with Spinoza or Spinozism. However, in his later writings Kant argues several times that Spinozism is the most consistent form of transcendental realism. In the first part of the paper, I argue that the first Antinomy, debating the age and size of the world, already reflects Kant's confrontation with Spinozist metaphysics. Specifically, the position articulated in the Antithesis – according to which the world is infinite and uncreated – is Spinozist, not Leibnizian, as commonly assumed. In the second part of the paper, I raise the chief Spinozist challenge to the Antinomy, arising from Spinoza's reliance on a cosmological `totum analyticum' – an infinite whole which is prior to its parts. In conclusion, I begin to elaborate a defence of the Kantian position, confronting Spinoza's infinite whole with Kant's account of the absolutely infinite in his discussion of the sublime.     

Two Conceptions of Inequality

Abstract

Following Temkin's Inequality I take my point of departure in an individualistic approach according to which a situation is bad in respect of inequality to the extent individuals in it have egalitarian complaints. After having criticised some of Temkin's notions of inequality, I argue that there are two proper egalitarian conceptions, the Equal Share Conception and the Place Conception. The first concerns how much welfare an individual can claim to have in order to have what she should have in virtue of equality. The second concerns an individual's egalitarian complaint in so far as it depends on her place in a situation's distribution of welfare. I argue that the first conception can be employed in a defence of Telic Egalitarianism against Derek Parfit's Levelling Down Objection and that the second one can explain why this objection may seem so convincing. I also argue that Telic Egalitarianism, understood according to the first conception, in one respect is preferable to Parfit's Priority View.     

What Kind of Theory is the Humean Theory of Motivation?

I consider an underappreciated problem for proponents of the Humean theory of motivation (HTM). Namely, it is unclear whether is it to be understood as a largely psychological or largely metaphysical theory. I show that the psychological interpretation of HTM will need to be modified in order to be a tenable view and, as it will turn out, the modifications required render it virtually philosophically empty. I then argue that the largely metaphysical interpretation is the only a plausible interpretation of HTM's central claim that desires are necessary conditions for motivation. This interpretation also fits better with the important roles that HTM plays in both moral psychological and metaethical debates. 1     

Improving the Metaphysical Argument Against Free Will

Abstract

Galen Strawson and Saul Smilansky have offered a well-known argument that free will does not exist because the control involved is so robust that it would require influence over an infinite series of prior decisions. (Strawson 1986, 1994, 2002, Smilansky 2000, 2002) Unfortunately, while this metaphysical argument has attracted widespread attention, it has garnered few adherents. Thus, in order to improve the metaphysical argument against free will, I offer a new interpretation of the argument, its fundamental principle, and its relationship to incompatibilism. I demonstrate that the central principle of the argument is just as defensible as the central principle of one of the major arguments for incompatibilism (namely, Robert Kane's argument from ‘ultimate responsibility’ in Kane 1996). Therefore, the metapysical argument against free will deserves much more respect than it currently receives.     

Which Kantian Conceptualism (or Nonconceptualism)?

A recent debate in Kant scholarship concerns the role of concepts in Kant's theory of perception. Roughly, proponents of a conceptualist interpretation argue that for Kant, the possession of concepts is a prior condition for perception, while nonconceptualist interpreters deny this. The debate has two parts. One part concerns whether possessing empirical concepts is a prior condition for having empirical intuitions. A second part concerns whether Kant allows empirical intuitions without a priori concepts. Outside of Kant interpretation, the contemporary debate about conceptualism concerns whether perception requires empirical concepts. But, as I argue, the debate about whether Kant allows intuitions without empirical concepts does not show whether Kant is a conceptualist. Even if Kant allows intuitions without empirical concepts, it could still be that a priori concepts are required. While the debate could show that Kant is a conceptualist, I argue it does not. Finally, I sketch a novel way that the conceptualist interpreter might win the debate—roughly, by arguing that possessing a priori concepts is a prior condition for having appearances.     

Phenomenology of Bodily Integrity in Disfiguring Breast Cancer

In this paper, I explore the meaning of bodily integrity in disfiguring breast cancer. Bodily integrity is a normative principle precisely because it does not simply refer to actual physical or functional intactness. It rather indicates what should be regarded and respected as inviolable in vulnerable and damageable bodies. I will argue that this normative inviolability or wholeness can be based upon a person's embodied experience of wholeness. This phenomenological stance differs from the liberal view that identifies respect for integrity with respect for autonomy (resulting in an invalidation of bodily integrity's proper normative meaning), as well as from the view that bodily integrity is based upon ideologies of wholeness (which runs the risk of being disadvantageous to women). I propose that bodily integrity involves a process of identification between the experience of one's body as “Leib” and the experience of one's body as “Körper.” If identification fails or is not possible, one's integrity is threatened. This idea of bodily integrity can support breast cancer patients and survivors in making decisions about possible corrective interventions. To implement this idea in oncology care, empirical‐phenomenological research needs to establish how breast cancer patients express their embodied self‐experiences.     

Contractualism,Person-Affecting Wrongness and the Non-identity Problem

A number of theorists have argued that Scanlon's contractualist theory both "gets around" and "solves" the non-identity problem. They argue that it gets around the problem because hypothetical deliberation on general moral principles excludes the considerations that lead to the problem. They argue that it solves the problem because violating a contractualist moral principle in one's treatment of another wrongs that particular other, grounding a person-affecting moral claim. In this paper, I agree with the first claim but note that all it shows is that the act is impersonally wrong. I then dispute the second claim. On Scanlon's contractualist view, one wrongs a particular other if one treats the other in a way that is unjustifiable to that other on reasons she could not reasonably reject. We should think of person-affecting wronging in terms of the reasons had by the actual agent and the actual person affected by the agent's action. In non-identity cases, interpersonal justifiability is therefore shaped both by the reason to reject the treatment provided by the bad suffered and the reason to affirm the treatment provided by the goods had as a result of existing. I argue it would be reasonable for the actual person to find the treatment justifiable, and so I conclude that Scanlon's contractualist metaethics does not provide a narrow person-affecting solution to the non-identity problem on its own terms. I conclude that the two claims represent a tension within Scanlon's contractualist theory itself.     

The Priority of the Now

This article motivates and develops a new theory of time: priority presentism. Priority presentism is the view according to which (i) only present entities exist fundamentally and (ii) past and future entities exist, but they are grounded in the present. The articulation of priority presentism is an exercise in applied grounding: it draws on concepts from the recent literature on ontological dependence and applies those concepts in a new way, to the philosophy of time. The result, as I will argue, is an attractive position that can do much of the same work in satisfying our intuitions about time as presentism, but without the ontological cost.     

Evidence that stakes don’t matter for evidence

Some philosophers have recently defended anti-intellectualism with respect to knowledge and evidence. In this paper, I assess anti-intellectualism about evidence, which claims a relation between one's evidence and the practical benefits or costs of being right or wrong about the propositions supported by that evidence. Proponents of anti-intellectualism generally regard their view as not at all obvious, but nonetheless strongly supported by appeal to our intuitive judgments about whether particular epistemic properties are instantiated in hypothetical cases. Anti-Intellectualism is thus taken by its proponents to be a surprising truth. I show that, though peoples’ explicit judgments about the general issue of whether or not non-epistemic factors make an epistemic difference are often in line with anti-intellectualism, their judgments about whether particular epistemic properties are instantiated in hypothetical cases do not display a pattern that would clearly support anti-intellectualism about evidence. Thus, anti-intellectualism about evidence is not entirely surprising, and intuitive assessments of hypothetical cases do not clearly support its truth.     

Ethics Beyond Moral Theory

I develop an anti‐theory view of ethics. Moral theory (Kantian, utilitarian, virtue ethical, etc.) is the dominant approach to ethics among academic philosophers. But moral theory's hunt for a single Master Factor (utility, universalisability, virtue . . .) is implausibly systematising and reductionist. Perhaps scientism drives the approach? But good science always insists on respect for the data, even messy data: I criticise Singer's remarks on infanticide as a clear instance of moral theory failing to respect the data of moral perceptions and moral intuitions. Moral theory also fails to provide a coherent basis for real‐world motivation, justification, explanation, and prediction of good and bad, right and wrong. Consider for instance the marginal place of love in moral theory, compared with its central place in people's actual ethical outlooks and decision making. Hence, moral theory typically fails to ground any adequate ethical outlook. I propose that it is the notion of an ethical outlook that philosophical ethicists should pursue, not the unfruitful and distorting notion of a moral theory.     

From Welfare to Rights without Changing the Subject

In this paper I introduce the ‘changing the subject’ problem. When proponents of animal protection use terms such as dignity and respect they can be fairly accused of shifting debate from welfare to rights because the terms purportedly refer to properties and values that are logically distinct from the capacity to suffer and the moral significance of causing animals pain. To avoid this problem and ensure that debate proceeds in the familiar terms of the established welfare paradigm, I present an expressivist analysis of animal rights vocabulary. When terms such as dignity and respect are understood in line with the theory of moral language use known as expressivism, proponents of animal protection that use these terms can escape the charge of changing the subject. Drawing upon Helm’s theory of love, I show how the usage of rights vocabulary can be respectable way for people to register their concern for the welfare of animals, even at times when it is unlikely that the animals concerned are suffering. Tying rights vocabulary to welfare via expressivism aligns the aims of animal rights with welfare without the theoretical problems associated with attempts to ‘reduce’ dignity or respect to natural behaviour or inherent value.     

Unlikely allies: embodied social cognition and the intentional stance

I argue that proponents of embodied social cognition (ESC) can usefully supplement their views if they enlist the help of an unlikely ally: Daniel Dennett. On Dennett??s view, human social cognition involves adopting the intentional stance (IS), i.e., assuming that an interpretive target??s behavior is an optimally rational attempt to fulfill some desire relative to her beliefs. Characterized this way, proponents of ESC would reject any alliance with Dennett. However, for Dennett, to attribute mental states from the intentional stance is not to attribute concrete, unobservable mental causes of behavior. Once this is appreciated, the kinship between IS??understood as a model of our quotidian interpretive practices??and ESC is apparent: both assume that quotidian interpretation involves tracking abstract, observable, behavioral patterns, not attributing unobservable, concrete, mental causes, i.e., both assume social cognition is possible without metapsychology. I argue that this affinity constitutes an opportunity: proponents of ESC can use IS as a characterization of the subpersonal basis for social cognition. In the process, I make my interpretation of IS more precise and relate it to current empirical literature in developmental psychology.     

Intransitivity and Future Generations: Debunking Parfit's Mere Addition Paradox

ABSTRACT Duties to future persons contribute critically to many important contemporaneous ethical dilemmas, such as environmental protection, contraception, abortion, and population policy. Yet this area of ethics is mired in paradoxes. It appeared that any principle for dealing with future persons encountered Kavka's paradox of future individuals, Parfit's repugnant conclusion, or an indefensible asymmetry. In 1976, Singer proposed a utilitarian solution that seemed to avoid the above trio of obstacles, but Parfit so successfully demonstrated the unacceptability of this position that Singer abandoned it. Indeed, the apparently intransitivity of Singer's solution contributed to Temkin's argument that the notion of “all things considered better than” may be intransitive. In this paper, I demonstrate that a time‐extended view of Singer's solution avoids the intransitivity that allows Parfit's mere addition paradox to lead to the repugnant conclusion. However, the heart of the mere addition paradox remains: the time‐extended view still yields intransitive judgments. I discuss a general theory for dealing with intransitivity (Transitivity by Transformation) that was inspired by Temkin's sports analogy, and demonstrate that such a solution is more palatable than Temkin suspected. When a pair‐wise comparison also requires consideration of a small number of relevant external alternatives, we can avoid intransitivity and the mere addition paradox without infinite comparisons or rejecting the Independence of Irrelevant Alternatives Principle     

A Tale of Two Thinkers,One Meeting,and Three Degrees of Infinity: Leibniz and Spinoza (1675–8)

The article presents Leibniz's preoccupation (in 1675–6) with the difference between the notion of infinite number, which he regards as impossible, and that of the infinite being, which he regards as possible. I call this issue ‘Leibniz's Problem’ and examine Spinoza's solution to a similar problem that arises in the context of his philosophy. ‘Spinoza's solution’ is expounded in his letter on the infinite (Ep.12), which Leibniz read and annotated in April 1676. The gist of Spinoza's solution is to distinguish between three kinds of infinity and, in particular, between one that applies to substance, and one that applies to numbers, seen as auxiliaries of the imagination. The rest of the paper examines the extent to which Spinoza's solution solves Leibniz's problem. The main thesis I advance is that, when Spinoza and Leibniz say that the divine substance is infinite, in most contexts it is to be understood in non-numerical and non-quantitative terms. Instead, for Spinoza and Leibniz, a substance is said to be infinite in a qualitative sense stressing that it is complete, perfect and indivisible. I argue that this approach solves one strand of Leibniz's problem and leaves another unsolved.     

Infinite Reasoning

Our relationship to the infinite is controversial. But it is widely agreed that our powers of reasoning are finite. I disagree with this consensus; I think that we can, and perhaps do, engage in infinite reasoning. Many think it is just obvious that we can't reason infinitely. This is mistaken. Infinite reasoning does not require constructing infinitely long proofs, nor would it gift us with non-recursive mental powers. To reason infinitely we only need an ability to perform infinite inferences. I argue that we have this ability. My argument looks to our best current theories of inference and considers examples of apparent infinite reasoning. My position is controversial, but if I'm right, our theories of truth, mathematics, and beyond could be transformed. And even if I'm wrong, a more careful consideration of infinite reasoning can only deepen our understanding of thinking and reasoning.     

Loke on the Infinite God Objection

In a recent article, Andrew Ter Ern Loke raises several objections to Jacobus Erasmus and Anné Hendrik Verhoef’s exposition and response to the so-called ‘Infinite God Objection’ to the kalām cosmological argument. According to this objection, the argument against the possibility of an actual infinite brings into question the view that God’s knowledge is infinite. Erasmus and Verhoef’s solution to this objection, which Loke criticises, depends on an unusual account of omniscience. In this article, I respond to Loke and show that his objections are unsuccessful.     

Barth and Anselm: God,Christ and the Atonement

This article considers God, Christ and the atonement in the work of Anselm and Barth. It identifies key points of agreement regarding God's self‐assigned identity and the importance of dyothelitism; it discerns a marked divergence of opinion with respect to the atonement. Anselm construes the atonement in terms of a gift that Christ offers on behalf of sinful humankind. Barth, on the other hand, presents a view of atonement that builds on his revolutionary doctrine of election. He describes the cross as an event in which sin is ‘burned up’, cancelled and overcome within the time and space of God's being.