Do Ante Rem Mathematical Structures Instantiate Themselves?

Ante rem structuralists claim that mathematical objects are places in ante rem structural universals. They also hold that the places in these structural universals instantiate themselves. This paper is an investigation of this self-instantiation thesis. I begin by pointing out that this thesis is of central importance: unless the places of a mathematical structure, such as the places of the natural number structure, themselves instantiate the structure, they cannot have any arithmetical properties. But if places do not have arithmetical properties, then they cannot be the natural numbers. The self-instantiation thesis turns out to be crucial for the identification of mathematical objects with places in structures. Unfortunately, we have no reason to believe that the self-instantiation thesis is true.     

Circular Discernment in Completely Extensive Structures and How to Avoid such Circles Generally

In this journal, D. Rizza [11] (p. 176) expounded a solution of what he called ??the indiscernibility problem for ante rem structuralism??, which is the problem to make sense of the presence, in structures, of objects that are indiscernible yet distinct, by only appealing to what that structure provides. We argue that Rizza??s solution is circular and expound a different solution that not only solves the problem for completely extensive structures, treated by Rizza, but for nearly (but not) all mathematical structures.     

Brandom's Leibniz

I discuss an objection by Margaret Wilson against Robert Brandom's interpretation of Leibniz's account of perceptual distinctness. According to Brandom, Leibniz holds that (i) the relative distinctness of a perception is a function of its inferentially articulated content and (ii) apperception, or awareness, is explicable in terms of degrees of perceptual distinctness. Wilson alleges that Brandom confuses ‘external deducibility’ from a perceptual state of a monad to the existence of properties in the world, with ‘internally accessible content’ for the monad in that state. Drawing on Leibniz, I develop a response to Wilson on Brandom's behalf.     

Curves in Gödel-Space: Towards a Structuralist Ontology of Mathematical Signs

I propose an account of the metaphysics of the expressions of a mathematical language which brings together the structuralist construal of a mathematical object as a place in a structure, the semantic notion of indexicality and Kit Fine’s ontological theory of qua objects. By contrasting this indexical qua objects account with several other accounts of the metaphysics of mathematical expressions, I show that it does justice both to the abstractness that mathematical expressions have because they are mathematical objects and to the element of concreteness that they have because they are also used as signs. In a concluding section, I comment on the pragmatic element that has entered ontology by way of the notion of indexicality and use it to give an answer to a question Stewart Shapiro has recently posed about the status of meta-mathematics in the structuralist philosophy of mathematics.     

The Rise of the Machines: Deleuze's Flight from Structuralism

In this paper, I offer an account of the conceptual shift that occurs between the work completed by Gilles Deleuze prior to 1969 and his later work with Félix Guattari, beginning in 1972 with Anti‐Oedipus. Against previous interpretations, which have concentrated on the developments initiated by Deleuze, I argue for the primary importance of Guattari's influence, especially his insistence on a theory of “machinic processes.” The importance of these processes is made manifest in Deleuze and Guattari's move away from theories of structuralism. In order to carry out this task, I offer a close reading of Guattari's essay “Machine and Structure.” This essay was first written as a review of Deleuze's acclaimed work in Difference and Repetition and Logic of Sense and formed the basis for Deleuze and Guattari's first meeting. In the concluding sections of the paper, I show how the integration of the concept of the machine allows Deleuze and Guattari to develop a theory of the unconscious that operates outside of the boundaries traditionally set by structuralist analysis.     

Spinoza on the Essences of Modes

This paper examines some aspects of Spinoza's metaphysics of the essences of modes.2 ²I would like to thank John Carriero, Calvin Normore, Eliot Michaelson, Eileen Nutting, Paul Nichols, Alexi Patsaouras, Rachel Johnson and Sarah Jansen for reading and commenting on earlier versions of this paper. I situate Spinoza's use of the notion of essence as a response to traditional, Aristotelian, ways of thinking about essence. I argue that, although Spinoza rejects part of the Aristotelian conception of essence, according to which it is in virtue of its essence that a thing is a member of a kind, he nevertheless retains a different part of such a conception, according to which an essence is some structural feature of a thing which causally explains other, non-essential features. I go on to develop an account of Spinoza's metaphysics of essence, according to which essences, what he sometimes calls formal essences, are produced by the divine essence prior to and independent of the creation of finite modes, and according to which essences are the formal or exemplar causes of finite modes. I then argue that finite modes, in virtue of the formal essences which they actualize, are genuine causal relata. Finally, I offer some speculations about Spinoza's answer to the question, ‘Why, in a necessitarian cosmos filled with formal essences, should there be temporal finite modes at all?’     

The Possibility of Psychic Conflict in Seneca's De Ira

This paper explores the potential for psychic conflict within Seneca's moral psychology. Some scholars have taken Seneca's explicit claim in De Ira that the soul is unitary to preclude any kind of simultaneous psychic conflict, while other interpreters have suggested that Seneca views all cases of anger as instances of akrasia. I argue that Seneca's account of anger provides the resources for accommodating some types of simultaneous psychic conflict; however, he denies the possibility of psychic conflict between two action-generating impulses, thus rejecting the phenomena of genuine akrasia and enkrateia. Although superficially counterintuitive, Seneca's cognitivist account of anger, according to which anger is complex and requires assent to the propositions that ‘I have been wronged’ and ‘I ought to seek revenge’, renders his denial of akrasia and enkrateia more plausible.     

Subsistence Needs,Human Rights,and Imperfect Duties

I address the usefulness of thinking about a human right to subsistence within conceptions of human rights grounded in ordinary moral reasoning. I argue that that natural rights should be understood as rights in rem, with their dynamism constrained by the requirements of justification and their scope constrained by the distinction between perfect and imperfect duty. I then suggest that many of the most pressing demands which the moral significance of subsistence needs create are plausibly imperfect duties, and so cannot correlate to a natural right to subsistence. This restricts the helpfulness of a human right to subsistence in our reasoning about what we owe to others.     

Enkratic Agency

An enkratic agent is someone who intends to do A because she believes she should do A. Being enkratic is usually understood as something rationality requires of you. However, we must distinguish between different conceptions of enkratic rationality. According to a fairly common view, enkratic rationality is solely a normative requirement on agency: it tells us how agents should think and act. However, I shall argue that this normativist conception of enkratic rationality faces serious difficulties: it makes it a mystery how an agent's thinking and acting can be guided by the enkratic requirement, which, as I shall further argue, is something that an adequate conception of enkratic rationality must be able to explain. This, I suggest, motivates exploring a different account of enkratic rationality. On this view, enkratic rationality is primarily a constitutive requirement on agency: it is a standard internal to agency, i.e., a standard that partly spells out what it is to exercise one's agential powers well.     

The Quasi-lattice of Indiscernible Elements

The literature on quantum logic emphasizes that the algebraic structures involved with orthodox quantum mechanics are non distributive. In this paper we develop a particular algebraic structure, the quasi-lattice ( \mathfrakI{\mathfrak{I}}-lattice), which can be modeled by an algebraic structure built in quasi-set theory \mathfrakQ{\mathfrak{Q}} . This structure is non distributive and involve indiscernible elements. Thus we show that in taking into account indiscernibility as a primitive concept, the quasi-lattice that ‘naturally’ arises is non distributive.     

Maximalism and Moral Harmony

Maximalism is the view that an agent is permitted to perform a certain type of action (say, baking) if and only if she is permitted to perform some instance of this type (say, baking a pie), where φ‐ing is an instance of ψ‐ing if and only if φ‐ing entails ψ‐ing but not vice versa. Now, the aim of this paper is not to defend maximalism, but to defend a certain account of our options that when combined with maximalism results in a theory that accommodates the idea that a moral theory ought to be morally harmonious—that is, ought to be such that the agents who satisfy the theory, whoever and however numerous they may be, are guaranteed to produce the morally best world that they have the option of producing. I argue that, for something to count as an option for an agent, it must, in the relevant sense, be under her control. And I argue that the relevant sort of control is the sort that we exercise over our reasons‐responsive attitudes (e.g., our beliefs, desires, and intentions) by being both receptive and reactive to reasons. I call this sort of control rational control, and I call the view that φ‐ing is an option for a subject if and only if she has rational control over whether she φs rationalism. When we combine this view with maximalism, we get rationalist maximalism, which I argue is a promising moral theory.     

New directions for nominalist philosophers of mathematics

The present paper will argue that, for too long, many nominalists have concentrated their researches on the question of whether one could make sense of applications of mathematics (especially in science) without presupposing the existence of mathematical objects. This was, no doubt, due to the enormous influence of Quine’s “Indispensability Argument”, which challenged the nominalist to come up with an explanation of how science could be done without referring to, or quantifying over, mathematical objects. I shall admonish nominalists to enlarge the target of their investigations to include the many uses mathematicians make of concepts such as structures and models to advance pure mathematics. I shall illustrate my reasons for admonishing nominalists to strike out in these new directions by using Hartry Field’s nominalistic view of mathematics as a model of a philosophy of mathematics that was developed in just the sort of way I argue one should guard against. I shall support my reasons by providing grounds for rejecting both Field’s fictionalism and also his deflationist account of mathematical knowledge—doctrines that were formed largely in response to the Indispensability Argument. I shall then give a refutation of Mark Balaguer’s argument for his thesis that fictionalism is “the best version of anti-realistic anti-platonism”.     

Indiscernible universals

Universals have traditionally thought to obey the identity of indiscernibles, that is, it has traditionally been thought that there can be no perfectly similar universals. But at least in the conception of universals as immanent, there is nothing that rules out there being indiscernible universals. In this paper, I shall argue that there is useful work indiscernible universals can do, and so there might be reason to postulate indiscernible universals. In particular, I shall argue that postulating indiscernible universals can allow a theory of universals to identify particulars with bundles of universals, and that postulating indiscernible universals can allow a theory of universals to develop an account of the resemblance of quantitative universals that avoids the objections that Armstrong’s account faces. Finally, I shall respond to some objections and I shall undermine the criterion of distinction between particulars and universals that says that the distinction between particulars and universals lies in that while there can be indiscernible particulars, there cannot be indiscernible universals.     

Freedom of the Will in Plato and Augustine

There has been a recent surge of interest in ancient accounts of free will. It is surprising, then, that there have been virtually no attempts to discuss whether Plato had such an account. Those who have made an attempt quickly deny that such an account is present in the dialogues. I shall argue that if we draw a distinction between two notions of free will, it is plausible that some account of free will is, in fact, present in the dialogues, the Republic in particular. This is the first in depth search into the question and I demonstrate that the defender of a Platonic free will thesis has more resources than she first appears to. It also has the benefit of giving us an obvious source material for Augustine's discussion.     

Category-theoretic structure and radical ontic structural realism

Radical ontic structural realism (ROSR) claims that structure exists independently of objects that may instantiate it. Critics of ROSR contend that this claim is conceptually incoherent, insofar as, (i) it entails there can be relations without relata, and (ii) there is a conceptual dependence between relations and relata. In this essay I suggest that (ii) is motivated by a set-theoretic formulation of structure, and that adopting a category-theoretic formulation may provide ROSR with more support. In particular, I consider how a category-theoretic formulation of structure can be developed that denies (ii), and can be made to do work in the context of formulating theories in physics.     

(Probably) not companions in guilt

In this paper, I will attempt to develop and defend a common form of intuitive resistance to the companions in guilt argument. I will argue that (contra the companions in guilt argument) one can reasonably believe there are promising solutions to the access problem for mathematical realism that don’t translate to moral realism. In particular, I will suggest that the structuralist project of accounting for mathematical knowledge in terms of some form of logical knowledge offers significant hope of success while no analogous approach offers such hope for moral realism.     

Levi on Causal Decision Theory and the Possibility of Predicting One's Own Actions

Isaac Levi has long criticized causal decisiontheory on the grounds that it requiresdeliberating agents to make predictions abouttheir own actions. A rational agent cannot, heclaims, see herself as free to choose an actwhile simultaneously making a prediction abouther likelihood of performing it. Levi is wrongon both points. First, nothing in causaldecision theory forces agents to makepredictions about their own acts. Second,Levi's arguments for the ``deliberation crowdsout prediction thesis' rely on a flawed modelof the measurement of belief. Moreover, theability of agents to adopt beliefs about theirown acts during deliberation is essentialto any plausible account of human agency andfreedom. Though these beliefs play no part inthe rationalization of actions, they arerequired to account for the causalgenesis of behavior. To explain the causes ofactions we must recognize that (a) an agentcannot see herself as entirely free in thematter of A unless she believes herdecision to perform A will cause A,and (b) she cannot come to a deliberatedecision about A unless she adoptsbeliefs about her decisions. FollowingElizabeth Anscombe and David Velleman, I arguethat an agent's beliefs about her own decisionsare self-fulfilling, and that this can beused to explain away the seeming paradoxicalfeatures of act probabilities.     

In Defense of Common Content

Abstract

In this essay, I critically discuss a theory of utterance content and de re communication that Anne Bezuidenhout has recently developed in a series of articles. This theory regards the significance of utterances as more pragmatic in nature than allowed by traditional accounts; further, it downplays logical considerations in explaining de re communication, choosing instead to emphasize its psychological character. Included among the implications of this approach is the rejection of what can be called ‘common content’, or utterance content that is held in common by speaker and listener. After describing this theory, I argue that Bezuidenhout does not supply a compelling reason to prefer her account of utterance content over more traditional alternatives that make room for elements of content held in common between speaker and listener. Further, I argue that her account of de re communication supplies even more reason to reject the view of content to which she subscribes. In the end, it will be clear that she has no principled reason for rejecting common content.