Why Euclid’s geometry brooked no doubt: J. H. Lambert on certainty and the existence of models

J. H. Lambert proved important results of what we now think of as non-Euclidean geometries, and gave examples of surfaces satisfying their theorems. I use his philosophical views to explain why he did not think the certainty of Euclidean geometry was threatened by the development of what we regard as alternatives to it. Lambert holds that theories other than Euclid’s fall prey to skeptical doubt. So despite their satisfiability, for him these theories are not equal to Euclid’s in justification. Contrary to recent interpretations, then, Lambert does not conceive of mathematical justification as semantic. According to Lambert, Euclid overcomes doubt by means of postulates. Euclid’s theory thus owes its justification not to the existence of the surfaces that satisfy it, but to the postulates according to which these “models” are constructed. To understand Lambert’s view of postulates and the doubt they answer, I examine his criticism of Christian Wolff’s views. I argue that Lambert’s view reflects insight into traditional mathematical practice and has value as a foil for contemporary, model-theoretic, views of justification.     

Gamete Donation,the Responsibility Objection,and Procreative Responsibilities

Sophisticated arguments advanced by Harry Silverstein, David Boonin, and Jeff McMahan attempt to show that being responsible for an individual's existence need not result in an obligation to ensure that the needs of that individual are satisfied. While these arguments take place within the abortion debate, by extension they threaten causal accounts of procreative responsibility more generally. In this article, I defend causal accounts of procreative responsibility by showing that these arguments do not succeed, but without thereby undermining the permissibility of abortion. Further, while being causally involved in the existence of a person is not sufficient for acquiring procreative responsibilities, I argue that there is an especially strong case for ascribing such responsibilities to gamete donors.     

Spinoza’s Arguments for the Existence of God*

It is often thought that, although Spinoza develops a bold and distinctive conception of God (the unique substance, or Natura Naturans, in which all else inheres and which possesses infinitely many attributes, including extension), the arguments that he offers which purport to prove God’s existence contribute nothing new to natural theology. Rather, he is seen as just another participant in the seventeenth century revival of the ontological argument initiated by Descartes and taken up by Malebranche and Leibniz among others. That this is the case is both puzzling and unfortunate. It is puzzling because although Spinoza does offer an ontological proof for the existence of God, he also offers three other non‐ontological proofs. It is unfortunate because these other non‐ontological proofs are both more convincing and more interesting than his ontological proof. In this paper, I offer reconstructions and assessments of all of Spinoza’s arguments and argue that Spinoza’s metaphysical rationalism and his commitment to something like a Principle of Sufficient Reason are the driving force behind Spinoza’s non‐ontological arguments.     

Absolve You to Yourself: Emerson's Conception of Rational Agency

Ralph Waldo Emerson famously warned his readers against the dangers of conformity and consistency. In this paper, I argue that this warning informs his engagement with and opposition to a Kantian view of rational agency. The interpretation I provide of some of Emerson's central essays outlines a unique conception of agency, a conception which gives substance to Emerson's exhortations of self‐trust. While Kantian in spirit, Emerson's view challenges the requirement that autonomy requires acting from a conception of the law. The key to understanding Emerson's opposition to Kant rests in showing how obeying the law requires spontaneity on the part of the agent herself. Emerson's concerns about conformity and consistency further enrich the view of agency, argued for by Richard Moran, according to which we take responsibility for our minds by taking up a first‐person deliberative perspective on our minds. Conformity and consistency in one's thinking and acting permits society and one's own past to dictate when deliberation may come to an end, thereby undermining a crucial sense in which an agent, in taking up the deliberative perspective, has taken responsibility for her mind.     

On disagreement about perception

In this article I have tried to rebut certain types of arguments which purport to show not merely that God does not exist but that the notion of necessary existence is itself either self‐contradictory or senseless. In showing that it is not self‐contradictory I have allowed myself the luxury of a negative and a positive approach. Negatively, I have had to show that when the accusation of self‐contradiction is made, it is often accompanied, not by an argument but by a sheer assertion. On the rare occasions when an argument is forthcoming, the arguments, I have tried to show, have been invalid, not even, inconclusive. And to the extent that Kant may be said to have argued not simply the impossibility of a genuine proof of the existence of God, but indeed the impossibility of the concept of necessary existence, I have argued out the weakness of Kant's arguments, the most notable of which I have discussed in some detail. Finally, to establish the genuineness of the concept of necessary existence, positively, I have paradoxically made use of a notion from Russell's logic.     

The myth of the moral faculty: Response to Kirkby

David Kirkby argues that I have misrepresented Marc Hauser's conception of a moral faculty, in a way that invalidates my chief arguments against the existence and necessity of such a faculty. The core of Kirkby's challenge is that what Hauser lists as necessary conditions for the moral faculty to do its work are not themselves components of that faculty. I argue that there is no useful way to distinguish necessary conditions of moral judgments from the alleged moral faculty itself, and that even if we could do this, we would be left with an empty non-explanation of the supposed moral faculty that amounts to nothing more than the claim that we have a faculty that generates judgments of right versus wrong.     

NEWTON AND SPINOZA: ON MOTION AND MATTER (AND GOD,OF COURSE)

This study explores several arguments against Spinoza's philosophy that were developed by Henry More, Samuel Clarke, and Colin Maclaurin. In the arguments on which I focus, More, Clarke, and Maclaurin aim to establish the existence of an immaterial and intelligent God precisely by showing that Spinoza does not have the resources to adequately explain the origin of motion. Attending to these criticisms grants us a deeper appreciation for how the authority derived from the empirical success of Newton's enterprise was used to settle debates within philosophy. What I emphasize is that in the progression from More to Clarke to Maclaurin, key Newtonian concepts from the Principia (1687), such as motion, atomism, and the vacuum, are introduced and exploited in order to challenge the account of matter and motion that is presented in Spinoza's Ethics (1677). Building on this treatment, I use the arguments from More and Clarke especially to help discern the anti‐Spinozism that can be detected in Newton's General Scholium (1713). Ultimately, the Newtonian criticisms that I detail offer us a more nuanced view of the problems that plague Spinoza's philosophy, and they also challenge the idea that Spinoza seamlessly fits into a progressive narrative about the scientific revolution.     

Practical knowledge and the subjectivity of truth in Kant and Kierkegaard: The cover of skepticism

Kant developed a distinctive method of philosophical argumentation, the method of transcendental argumentation, which continues to have contemporary philosophical promise. Yet there is considerable disagreement among Kant's interpreters concerning the aim of transcendental arguments. On ambitious interpretations, transcendental arguments aim to establish certain necessary features of the world from the conditions of our thinking about or experiencing the world; they are world‐directed. On modest interpretations, transcendental arguments aim to show that certain beliefs have a special status that renders them invulnerable to skeptical doubts; they are belief‐directed. This paper brings Kierkegaard's thesis of the “subjectivity of truth” to bear on these questions concerning the aim of transcendental arguments. I focus on Kant's argument for the postulate of God's existence in his Critique of Practical Reason and show that Kierkegaard's thesis of the subjectivity of truth can help us construe the argument as both belief and world directed. Yet I also argue that Kierkegaard's thesis of the subjectivity of truth can help us understand the source of our dissatisfaction with Kant's transcendental arguments: It can help us understand that dissatisfaction as an expression of what Stanley Cavell calls the “cover of skepticism,” the conversion of metaphysical finitude into intellectual lack.     

Breaking Out of the Circle

What’s wrong with begging the question? Some philosophers believe that question-begging arguments are inevitably fallacious and that their fallaciousness stems from a shared “formal” deficiency. In contrast, some philosophers, like Robinson (Analysis 31:113–117, 1971) deny that begging the question is fallacious at all. And others characterize begging the question as an “informal” fallacy of reasoning that can only be understood with the aid of epistemic (as opposed to syntactic and semantic) notions. Sorensen (Analysis 56:51–55, 1996) joins this last camp by offering a powerful argument against both Robinson’s skepticism and fully formal approaches to the phenomenon. According to Sorensen’s view, question-begging is fallacious because it compromises the rationality of the question-beggar’s position. Though his argument forces Robinson into a peculiar dialectical position, it does little to elucidate the reasons why Robinson’s position is unstable and it fails to embody Sorensen’s own conception of rationally persuasive argumentation. I utilize this conception to show how Robinson is left with no easily identifiable grounds on which to deny the fallaciousness of begging the question. By advancing the dialectic between Sorensen and Robinson, I aim to show that our argumentative practices must take the perspectives of others seriously, whether or not those perspectives are rational.     

THE ONTOLOGICAL ARGUMENT AND THE DEVIL

The 'parody objection' to the ontological argument for the existence of God advances parallel arguments apparently proving the existence of various absurd entities. I discuss recent versions of the parody objection concerning the existence of 'AntiGod' and the devil, as introduced by Peter Millican and Timothy Chambers. I argue that the parody objection always fails, because any parody is either (i) not structurally parallel to the ontological argument, or (ii) not dialectically parallel to the ontological argument. Moreover, once a parody argument is modified in such a way that it avoids (i) and (ii), it is, ironically, no longer a parody – it is the ontological argument itself.     

Reasonable Pluralism,Interculturalism, and Sterba on Question-Beggingness

In From Rationality to Equality, James Sterba (From rationality to equality. New York: Oxford University Press, 2013) argues that the non-moral, and non-controversial, principle of logic, the principle that good arguments do not beg-the-question, provides a rationally conclusive response to egoism. He calls this “the principle of non-question-beggingness” and it is supposed to justify a conception of “Morality as Compromise.” Sterba’s basic idea is that principles of morality provide a non-question-begging compromise between self-interested reasons and other-regarding reasons. I will focus, first, on Sterba’s rejection of the alternative Kantian rationalist justification of morality, and second, I discuss the logical principle of non-question-beggingness and I argue that Sterba is wrong to assume that there is a formal, logical requirement that a rational egoist must provide a non-question-begging defense of egoism. I argue that, like the Kantian, Sterba needs a more substantial conception of practical reason to derive his conclusion. My third focus is the problem of reasonable pluralism and public reason (Rawls in Political liberalism. Columbia University Press, New York, 1996; The law of peoples with the idea of public reason revisited. Harvard University Press, Cambridge, 1999). The Rawlsian principle of public reason is analogous to Sterba’s principle of non-question-beggingness. Sterba recognizes that public policies should respect competing perspectives and that a public conception of justice must be justifiable to all reasonable people. The problem is that that reasonable people disagree about fundamental moral questions. Rawls calls this the fact of reasonable pluralism. I argue that an intercultural conception of justice is necessary to provide a response to reasonable pluralism and a shared basis for public reason.     

Descartes,Malebranche and Leibniz: conceptions of substance in arguments for the immateriality of the soul

ABSTRACT

The most prominent early modern argument against materialism is to be found in Descartes. Previously I had argued that this argument relies crucially on a robust conception of substance, according to which it has a single principal attribute of which all its other intrinsic qualities are modes. In the present paper I return to this claim. In Section 2, I address a question that is often raised about that conception of substance: its commitment to the idea that a substance has a single such principal attribute. Gonzalo Rodriguez-Pereyra and Daniel Garber have argued that this claim relies on Descartes's identification of substance with attribute. But I argue that it relies on his view that a substance has a single, unitary nature. In Section 3, I examine the role of this conception of substance in arguments found in Malebranche and Leibniz and compare these arguments with Descartes's.     

Logic with numbers

Many people regard utility theory as the only rigorous foundation for subjective probability, and even de Finetti thought the betting approach supplemented by Dutch Book arguments only good as an approximation to a utility-theoretic account. I think that there are good reasons to doubt this judgment, and I propose an alternative, in which the probability axioms are consistency constraints on distributions of fair betting quotients. The idea itself is hardly new: it is in de Finetti and also Ramsey. What is new is that it is shown that probabilistic consistency and consequence can be defined in a way formally analogous to the way these notions are defined in deductive (propositional) logic. The result is a free-standing logic which does not pretend to be a theory of rationality and is therefore immune to, among other charges, that of “logical omniscience”.     

Two Conceptions of Conceptualism and Nonconceptualism

Though it enjoys widespread support, the claim that perceptual experiences possess nonconceptual content has been vigorously disputed in the recent literature by those who argue that the content of perceptual experience must be conceptual content. Nonconceptualism and conceptualism are often assumed to be well-defined theoretical approaches that each constitute unitary claims about the contents of experience. In this paper I try to show that this implicit assumption is mistaken, and what consequences this has for the debate about perceptual experience. I distinguish between two different ways that nonconceptualist (and conceptualist) proposals about perceptual content can be understood: as claims about the constituents that compose perceptual contents or as claims about whether a subject’s undergoing experiences with those contents requires them to possess the concepts that characterize those contents. I maintain that these ways of understanding conceptualism and nonconceptualism are orthogonal to one another. This is revealed by the conceptual coherence of positions in which the contents of experiences have both conceptual and nonconceptual features; positions which possess their own distinctive sources of philosophical motivation. I argue that the fact that there is a place in conceptual space for such positions, and that there may be good reason for theorists to adopt them, creates difficulties for both the central argument for nonconceptualism and the central argument for conceptualism. I set out each of these arguments; the Argument from Possession-Independence and the Epistemically-Driven Argument. I then try to show how the existence of mixed positions about perceptual content derived from a clear distinction between compositional and possessional considerations constitutes a significant obstacle for those arguments as they stand. The takehome message of the paper is that unless one clearly acknowledges the distinction between issues about the composition of perceptual content and issues about how subject’s capacities to undergo certain experiences relates to their possession of concepts one runs the risk of embracing unsatisfying philosophical arguments in which conclusions relevant to one conception of nonconceptual and conceptual content are grounded on arguments that concern only the other; arguments that cannot, in themselves, sustain them.     

A puzzle about natural laws and the existence of God

The existence of natural laws, whether deterministic or indeterministic, and whether exceptionless or ceteris paribus, seems puzzling because it implies that mindless bits of matter behave in a consistent and co-ordinated way. I explain this puzzle by showing that a number of attempted solutions fail. The puzzle could be resolved if it were assumed that natural laws are a manifestation of God’s activity. This argument from natural law to God’s existence differs from its traditional counterparts in that, whereas the latter seek to explain the fact of natural laws, the former seeks to explain their possibility. The customary objections to the traditional arguments cannot be successfully adapted to counter this new argument, with one exception which has only limited effect. I rebut four claims that the theistic solution to the puzzle about natural laws is paradoxical, though I concede that one of these claims has merit. I consider four objections to the new argument but find three of them more or less unsatisfactory. The fourth, if successful, would undermine our claims to know the truth about the world.     

Two sorts of natural theology

Usually, natural theology is understood as the project of providing arguments for the existence of God. This project is endorsed by Moreland and Craig. McGrath, on the other hand, says that this project fails. In the first part of this article, I show how McGrath’s dismissal of arguments for the existence of God follows from his view of natural theology. In the second part, I argue that McGrath’s natural theology contains an accurate critique of Moreland and Craig’s way of doing natural theology, a critique that exposes two major problems in their treatment of the moral argument for the existence of God. In the third part, I propose a way of providing arguments for the existence of God that avoids the problems pointed out by McGrath, namely a way of arguing that seeks to show how theology may improve a certain non-theistic understanding of a natural phenomenon.     

Hilbert,logicism, and mathematical existence

David Hilbert’s early foundational views, especially those corresponding to the 1890s, are analysed here. I consider strong evidence for the fact that Hilbert was a logicist at that time, following upon Dedekind’s footsteps in his understanding of pure mathematics. This insight makes it possible to throw new light on the evolution of Hilbert’s foundational ideas, including his early contributions to the foundations of geometry and the real number system. The context of Dedekind-style logicism makes it possible to offer a new analysis of the emergence of Hilbert’s famous ideas on mathematical existence, now seen as a revision of basic principles of the “naive logic” of sets. At the same time, careful scrutiny of his published and unpublished work around the turn of the century uncovers deep differences between his ideas about consistency proofs before and after 1904. Along the way, we cover topics such as the role of sets and of the dichotomic conception of set theory in Hilbert’s early axiomatics, and offer detailed analyses of Hilbert’s paradox and of his completeness axiom (Vollständigkeitsaxiom).     

Kant's Argument that Existence is not a Determination

In this paper, I examine Kant's famous objection to the ontological argument: existence is not a determination. Previous commentators have not adequately explained what this claim means, how it undermines the ontological argument, or how Kant argues for it. I argue that the claim that existence is not a determination means that it is not possible for there to be non‐existent objects; necessarily, there are only existent objects. I argue further that Kant's target is not merely ontological arguments as such but the larger ‘ontotheist’ metaphysics they presuppose: the view that God necessarily exists in virtue of his essence being contained in, or logically entailed by, his essence. I show that the ontotheist explanation of divine necessity requires the assumption that existence is a determination, and I show that Descartes and Leibniz are implicitly committed to this in their published versions of the ontological argument. I consider the philosophical motivations for the claim that existence is a determination and then I examine Kant's arguments in the Critique of Pure Reason against it.     

Is happiness the supreme good? Some philosophical objections

Modern philosophy is characterised by various objections to the Aristotelian conception of happiness as the supreme good of human life. In this paper, I focus on the objections raised by two key thinkers of the modern period, namely Blaise Pascal and Friedrich Nietzsche. Both philosophers formulate important counter- arguments to the teleological claim that happiness is the highest good towards which all human beings naturally direct their efforts. Their target is not any specific definition of happiness as a particular kind of activity, or a particular kind of good. Instead, they express a more fundamental scepticism about the very possibility of happiness being the ultimate end of human life. As I show, Pascal's and Nietzsche's radical point is that, since reason alone can never answer for certain the question of whether or not happiness is the ultimate aim of human existence, philosophy should not concern itself with the question of happiness. The paper has three parts. I first sketch an outline of Pascal's sceptical argument with regard to happiness, and then present his positive definition of happiness, after which I do the same for Nietzsche. The third part is devoted to a critical assessment of their positions in light of an alternative argument developed by John Cottingham.