LOT 2: The Language of Thought Revisited

A main thread of the debate over mathematical realism has come down to whether mathematics does explanatory work of its own in some of our best scientific explanations of empirical facts. Realists argue that it does; anti-realists argue that it doesn't. Part of this debate depends on how mathematics might be able to do explanatory work in an explanation. Everyone agrees that it's not enough that there merely be some mathematics in the explanation. Anti-realists claim there is nothing mathematics can do to make an explanation mathematical; realists think something can be done, but they are not clear about what that something is.

I argue that many of the examples of mathematical explanations of empirical facts in the literature can be accounted for in terms of Jackson and Pettit's [1990] notion of program explanation, and that mathematical realists can use the notion of program explanation to support their realism. This is exactly what has happened in a recent thread of the debate over moral realism (in this journal). I explain how the two debates are analogous and how moves that have been made in the moral realism debate can be made in the mathematical realism debate. However, I conclude that one can be a mathematical realist without having to be a moral realist.     

Ernst Cassirer's Neo-Kantian Philosophy of Geometry

One of the most important philosophical topics in the early twentieth century – and a topic that was seminal in the emergence of analytic philosophy – was the relationship between Kantian philosophy and modern geometry. This paper discusses how this question was tackled by the Neo-Kantian trained philosopher Ernst Cassirer. Surprisingly, Cassirer does not affirm the theses that contemporary philosophers often associate with Kantian philosophy of mathematics. He does not defend the necessary truth of Euclidean geometry but instead develops a kind of logicism modeled on Richard Dedekind's foundations of arithmetic. Further, because he shared with other Neo-Kantians an appreciation of the developmental and historical nature of mathematics, Cassirer developed a philosophical account of the unity and methodology of mathematics over time. With its impressive attention to the detail of contemporary mathematics and its exploration of philosophical questions to which other philosophers paid scant attention, Cassirer's philosophy of mathematics surely deserves a place among the classic works of twentieth century philosophy of mathematics. Though focused on Cassirer's philosophy of geometry, this paper also addresses both Cassirer's general philosophical orientation and his reading of Kant.     

Locke's Theory of Demonstration and Demonstrative Morality

Locke famously claimed that morality was capable of demonstration. But he also refused to provide a system of demonstrative morality. This paper addresses the mismatch between Locke's stated views and his actual philosophical practice. While Locke's claims about demonstrative morality have received a lot of attention it is rare to see them discussed in the context of his general theory of demonstration and his specific discussions of particular demonstrations. This paper explores Locke's general remarks about demonstration as well as his claims about demonstration in natural philosophy, mathematics, and morality. Careful attention to these detailed discussions motivates a reevaluation of Locke's views on demonstrative knowledge of morality. Specifically, while Locke did believe that some demonstrative moral knowledge might be in‐principle available to us he also believed that facts about the difficulty of demonstration meant that this knowledge would in‐practice be largely unattainable.     

The Ethics of Price Gouging

An analysis of the contemporary moral debate over price gouging can advance multiple readings of the challenging biblical episode which depicts Jacob's purchase of the birthright. Ethical considerations, such as the maximization of welfare, preservation of choice, and promotion of virtue are evaluated and then applied to the biblical text recounting the sale of Esau's birthright. Did Jacob act ethically in his purchase of ravenous Esau's birthright, or did he seize a propitious opportunity to exploit Esau's predicament? Is Esau responsible for spurning his birthright, or was he misled as he claims Jacob had “supplanted me these two times: he took away my birthright; and, behold, now he has taken away my blessing” (Genesis 27:36)? An ethical analysis of Jacob's and Esau's intentions and actions in the transaction uncovers the Bible's position on the sale and on the larger moral debate.     

Hobbes's Challenge to Descartes,Bramhall and Boyle: A Corporeal God

This paper brings new work to bear on the perennial question about Hobbes's atheism to show that as a debate about scepticism it is falsely framed. Hobbes, like fellow members of the Mersenne circle, Descartes and Gassendi, was no sceptic, but rather concerned to rescue physics and metaphysics from radical scepticism by exploring corporealism. In his early letter of November 1640, Hobbes had issued a provocative challenge to Descartes to abandon metaphysical dualism and subscribe to a ‘corporeal God’; a provocation to which the Frenchman angrily responded, but was perhaps importantly influenced. Hobbes's minimal realism was consonant with atheism, to which Descartes felt he was being forced. Moreover, Hobbes was unrelenting in his battle against Cartesian dualism, for which he saw Robert Boyle's experimental science as a surrogate.     

Redrawing Kant's philosophy of mathematics

This essay offers a strategic reinterpretation of Kant's philosophy of mathemat- ics in Critique of Pure Reason via a broad, empirically based reconception of Kant's conception of drawing. It begins with a general overview of Kant's philosophy of mathematics, observing how he differentiates mathematics in the Critique from both the dynamical and the philosophical. Second, it examines how a recent wave of critical analyses of Kant's constructivism takes up these issues, largely inspired by Hintikka's unorthodox conception of Kantian intuition. Third, it offers further analyses of three Kantian concepts vitally linked to that of drawing. It concludes with an etymologically based exploration of the seven clusters of meanings of the word drawing to gesture toward new possibilities for interpreting a Kantian philosophy of mathematics.     

Freedom and Necessity in Marx's Account of Communism

This paper considers whether Marx's views about communism change significantly during his lifetime. According to the ‘standard story’, as Marx got older he dropped the vision of self-realization in labour that he spoke of in his early writings, and adopted a more pessimistic account of labour, where real freedom is achieved outside the working-day, in leisure. Other commentators, however, have argued that there is no pessimistic shift in Marx's thought on this matter. This paper offers a different reading of this debate. It argues that there are two visions of the good life in Marx. However, it suggests that these two visions cannot be understood in terms of a simple shift between a ‘young’ and ‘mature’ Marx. Rather, it claims that Marx moves between these two visions throughout his writings. In this way, it suggests that Marx's intellectual development on this issue is best understood as an oscillation rather than a shift. Once this interpretive claim is advanced, the paper then moves on to consider some potential causes and implications of Marx's life-long oscillation between two different conceptions of the good life.     

The Surveyability of Mathematical Proof: A Historical Perspective

This paper rejoins the debate surrounding Thomas Tymockzko’s paper on the surveyability of proof, first published in the Journal of Philosophy, and makes the claim that by attending to certain broad features of modern conceptions of proof we may understand ways in which the debate surrounding the surveyability of proof has heretofore remained unduly circumscribed. Motivated by these historical reflections, I suggest a distinction between local and global surveyability which I believe has the promise to open up significant new advances in the philosophy of mathematics.     

The Existential Sources of Phenomenology: Heidegger on Formal Indication

Abstract: This article contributes to the contemporary debate regarding the young Heidegger's method of formal indication. Theodore Kisiel argues that this method constitutes a radical break with Husserl—a rejection of phenomenological reflection that paves the way to the non‐reflective approach of the Beiträge. Against this view, Steven Crowell argues that formal indication is continuous with Husserlian phenomenology—a refinement of phenomenological reflection that reveals its existential sources. I evaluate this debate and adduce further considerations in favor of Crowell's view. To do so, I analyze the young Heidegger's account of phenomenological communication and argue that it further reflects the continuity that Crowell identifies: as he does with reflection, Heidegger refines Husserl's account of phenomenological communication and sheds light on its existential sources.     

Kant and Husserl on the Contents of Perception

This paper focuses on the contents of perception in Kant's first Critique and Husserl's later writings. Both Kant and Husserl are known for their appeal to synthesis in their transcendental accounts of perceptual experience and objective judgment. Especially regarding Kant, the precise nature of perceptual synthesis has recently been the cause of much debate. Whereas some argue that for Kant perception must have nonconceptual content, others believe he is a conceptualist. After offering an alternative solution to this interpretative problem in Kant's philosophy, I turn to Husserl's later theory of perception. My main claims here are that Husserl departs from Kant specifically regarding (i) the sort of synthetic contents that govern affective perception and (ii) the role of conceptual capacities in the contents of attentive perception.     

MAXIMALITY,DUPLICATION, AND INTRINSIC VALUE

In this paper, I develop an argument for the thesis that ‘maximality is extrinsic’, on which a whole physical object is not a whole of its kind in virtue of its intrinsic properties. Theodore Sider has a number of arguments that depend on his own simple argument that maximality is extrinsic. However, Peter van Inwagen has an argument in defence of his Duplication Principle that, I will argue, can be extended to show that Sider's simple argument fails. However, van Inwagen's argument fails against a more complex, sophisticated argument that maximality is extrinsic. I use van Inwagen's own commitments to various forms of causation and metaphysical possibility to argue that maximality is indeed extrinsic, although not for the mundane reasons that Sider suggests. I then argue that moral properties are extrinsic properties. Two physically identical things can have different moral properties in a physical world. This argument is a counterexample to a classical ethical supervenience idea (often attributed to G.E. Moore) that if there is identity of physical properties in a physical world, then there is identity in moral properties as well. I argue moral value is ‘border sensitive’ and extrinsic for Kantians, utilitarians, and Aristotelians.     

Hudson on Receptacles

This note concerns a recent paper by Hud Hudson on the nature of 'receptacles'. It simplifies the mathematics in Hudson's paper, and it eliminates almost all of the topology in Hudson's arguments.     

Incarnation and the Divine Hiddenness Debate

This paper examines the debate that has arisen in connection with J. L. Schellenberg's work on divine hiddenness. It singles out as especially deserving of attention Paul Moser's proposal that the debate distinguish more clearly between classical theism and Hebraic theisms. This worthwhile proposal, I argue, will be unlikely to exert its full potential influence upon the debate unless certain features of Christian incarnation belief are recognized and addressed in connection with it.     

Argumentation,Adversariality, and Social Norms

Janice Moulton's “The Adversary Method: A Philosophical Paradigm” articulated several criticisms of the popular idea of philosophy as adversarial debate. Moulton criticizes it on epistemic grounds, arguing that philosophy's overreliance on adversarial debate is to the detriment of its goals. Some, notably Trudy Govier, have argued in favor of at least a minimal adversariality, governed by norms of respectful argumentation. This paper suggests that Govier's faith in these norms is misplaced, because it neglects the social circumstances of the arguers. While some authors have argued that politeness and aggression apply differently to those of different genders, this paper extends that analysis to social identities other than gender. In fact, given certain assumptions about the philosophy of language, engagement in polite adversarial debate may not even be possible for people occupying certain social locations.     

THE CASTRATION OF SIGNS: CONVERSING WITH AUGUSTINE ON CREATION, LANGUAGE AND TRUTH

This article takes as its starting point Nicholas Lash's use of the Buberian distinction between the basic words “I‐It” and “I‐You” to address the question of how the difference between God and creation is “displayed” within the world. Drawing on a rather different discourse—the semiotics developed by Augustine in the distinctions he makes between sign and thing, use and enjoyment—it seeks to explore the concrete shape that might be taken by practices that foster the speaking of the basic word “I‐You”, and which thereby manifest God's redemptive activity within the world, focusing specifically on practices of debate and argument. “What might a redeemed practice of debate look like?” is the question that this article seeks to answer.     

John Calvin on the Christian's Social Responsibility: Cultural Activist or “Modest Social Reformer”?

Recently there have been heated discussions between Reformed theologians who embrace the two‐kingdoms doctrine and proponents of the Neo‐Calvinist tradition on whether Calvin held social transformationist views. This article examines the debate and argues that Calvin did not interpret the kingdom as a progressive social‐transforming reality that gradually establishes God's future eschatological reign on earth. Instead, he regarded Christ's present reign as a “backward”‐reaching reality that restores God's original created order. At the same time Calvin did not make a sharp categorical distinction between the spiritual and civil realms but depicted the civil and spiritual order as two regiments of God's one reign that mutually aid and assist each other.     

New Perspectives on an Old Debate: Friedrich Schleiermacher's Essay on Election

Abstract: This article analyses Schleiermacher's essay on election, which has not received the attention it deserves. I argue that it presents a significant advance in the debate about unconditional grace and the relation between redemption and predestination. While Schleiermacher defends the Augustinian‐Calvinist view of election, he criticizes the ideas of double predestination and eternal damnation (for the unbelievers). Thus, he wants to provide a new basis for Lutherans and Calvinists to settle or, at least, reconsider their longstanding controversy over the matter. After the publication of the essay in 1819, Schleiermacher's doctrine of election remained unchanged, except for minor modifications.     

Philosophy and “the method of fictions”: Maimon's proposal and its critics

Salomon Maimon argued forcefully for the indispensability of what he called “the method of fictions” in mathematics and physics, but also in philosophy. This last claim provoked critical responses from G. E. Brastberger, G. E. Schultze, and K. L. Reinhold. This paper offers a brief exposition of Maimon's “method of fictions” and an analysis of his response to critics of his claims concerning the employment of this method within philosophy.     

Putnam, Peano, and the Malin Génie: could we possibly bewrong about elementary number-theory?

This article examines Hilary Putnam's work in the philosophy of mathematics and - more specifically - his arguments against mathematical realism or objectivism. These include a wide range of considerations, from Gödel's incompleteness-theorem and the limits of axiomatic set-theory as formalised in the Löwenheim-Skolem proof to Wittgenstein's sceptical thoughts about rule-following (along with Saul Kripke's ‘scepticalsolution’), Michael Dummett's anti-realist philosophy of mathematics, and certain problems – as Putnam sees them – with the conceptual foundations of Peano arithmetic. He also adopts a thought-experimental approach – a variant of Descartes' dream scenario – in order to establish the in-principle possibility that we might be deceived by the apparent self-evidence of basic arithmetical truths or that it might be ‘rational’ to doubt them under some conceivable (even if imaginary) set of circumstances. Thus Putnam assumes that mathematical realism involves a self-contradictory ‘Platonist’ idea of our somehow having quasi-perceptual epistemic ‘contact’ with truths that in their very nature transcend the utmost reach of human cognitive grasp. On this account, quite simply, ‘nothing works’ in philosophy of mathematics since wecan either cling to that unworkable notion of objective (recognition-transcendent) truth or abandon mathematical realism in favour of a verificationist approach that restricts the range of admissible statements to those for which we happen to possess some means of proof or ascertainment. My essay puts the case, conversely, that these hyperbolic doubts are not forced upon us but result from a false understanding of mathematical realism – a curious mixture of idealist and empiricist themes – which effectively skews the debate toward a preordained sceptical conclusion. I then go on to mount a defence of mathematical realism with reference to recent work in this field and also to indicate some problems – as I seethem – with Putnam's thought-experimental approach as well ashis use of anti-realist arguments from Dummett, Kripke, Wittgenstein, and others.     

Akrasia,practical reason,and the diversity of motivation: A new defense of tripartition

In akrasia, an agent intentionally acts against her own judgment about what it is best to do. This presents many puzzles for the understanding of human motivation. The Socrates of Plato's Protagoras, for example, denies this is possible because he claims that all action is motivated by an agent's belief about what is best. Plato himself seems to reject this view in the Republic, appealing to three distinct sources of motivation. This paper takes Plato's side in the general debate, arguing for a new tripartite moral psychology. Because the akratic acts for a reason but against the conclusion of her practical reasoning, there must be a way of acting for reasons other than through reasoning about them. This way is desire. But once there is a division between reason and desire, a third capacity is needed to solve conflicts that can arise between them, the will.