Sacrifice and At-one-ment: Joseph de Maistre and Cudworth's Types and Shadows Admired

This article pursues the perhaps surprising interest of the Savoyard polemicist and counter-revolutionary philosopher Joseph de Maistre for the early work of the Cambridge Platonist Ralph Cudworth. I argue that their shared Platonism and fascination for the imagery of the Temple of the Hebrews helps explain this unlikely alliance. I refer to the innovative work of Margaret Barker on Temple imagery in Christian theology to elucidate the biblical dimension of the theory of correspondences employed by both men.     

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.     

New Perspectives on Agency in Early Modern Philosophy

ABSTRACT

This introductory article outlines the themes and aims of this special issue, which offers new perspectives on early modern debates about agency in two ways: First, it recovers writings on agency and liberty that have been widely neglected or that have received insufficient attention, including writings by Anne Conway, Henry More, Ralph Cudworth, William King, Gabrielle Suchon, Elizabeth Berkeley Burnet, Mary Astell, and Anthony Ashley Cooper, the Third Earl of Shaftesbury. Second, it reveals the richness of early modern debates about agency and liberty.     

Henry More as reader of Marcus Aurelius

ABSTRACT

I examine Henry More’s engagement with Stoicism in general, and Marcus Aurelius in particular, in his Enchiridion Ethicum. More quotes from Marcus’ Meditations throughout the Enchiridion, leading one commentator to note that More ‘mined the Meditations’ when writing his book. Yet More’s general attitude towards Stoicism is more often than not critical, especially when it comes to the passions. I shall argue that while More was clearly an avid reader of the Meditations, he read Marcus not as a Stoic but as a ‘non-denominational’ ancient moralist who confirms a range of doctrines that More finds elsewhere in ancient philosophy. In this sense More continues the Neoplatonic practice of downplaying doctrinal differences between ancient philosophers in order to construct a single ancient philosophical tradition. This is quite different from the approach of his contemporary and fellow Cambridge Platonist, Ralph Cudworth, who was keen to highlight doctrinal differences between ancient philosophers.     

Erkenntnistheorie der Zahldefinition und philosophische Grundlegung der Arithmetik unter Bezugnahme auf einen Vergleich von Gottlob Freges Logizismus und platonischer Philosophie (Syrian, Theon von Smyrna u.a.)

The epistomology of the definition of number and the philosophical foundation of arithmetic based on a comparison between Gottlob Frege's logicism and Platonic philosophy (Syrianus, Theo Smyrnaeus, and others). The intention of this article is to provide arithmetic with a logically and methodologically valid definition of number for construing a consistent philosophical foundation of arithmetic. The – surely astonishing – main thesis is that instead of the modern and contemporary attempts, especially in Gottlob Frege's Foundations of Arithmetic, such a definition is found in the arithmetic in Euclid's Elements. To draw this conclusion a profound reflection on the role of epistemology for the foundation of mathematics, especially for the method of definition of number, is indispensable; a reflection not to be found in the contemporary debate (the predominate ‘pragmaticformalism’ in current mathematics just shirks from trying to solve the epistemological problems raised by the debate between logicism, intuitionism, and formalism). Frege's definition of number, ‘The number of the concept F is the extension of the concept ‘numerically equal to the concept F”, which is still substantial for contemporary mathematics, does not fulfil the requirements of logical and methodological correctness because the definiens in a double way (in the concepts ‘extension of a concept’ and ‘numerically equal’) implicitly presupposes the definiendum, i.e. number itself. Number itself, on the contrary, is defined adequately by Euclid as ‘multitude composed of units’, a definition which is even, though never mentioned, an implicit presupposition of the modern concept ofset. But Frege rejects this definition and construes his own - for epistemological reasons: Frege's definition exactly fits the needs of modern epistemology, namely that for to know something like the number of a concept one must become conscious of a multitude of acts of producing units of ‘given’ representations under the condition of a 1:1 relationship to obtain between the acts of counting and the counted ‘objects’. According to this view, which has existed at least since the Renaissance stoicism and is maintained not only by Frege but also by Descartes, Kant, Husserl, Dummett, and others, there is no such thing as a number of pure units itself because the intellect or pure reason, by itself empty, must become conscious of different units of representation in order to know a multitude, a condition not fulfilled by Euclid's conception. As this is Frege's main reason to reject Euclid's definition of number (others are discussed in detail), the paper shows that the epistemological reflection in Neoplatonic mathematical philosophy, which agrees with Euclid's definition of number, provides a consistent basement for it. Therefore it is not progress in the history of science which hasled to the a poretic contemporary state of affairs but an arbitrary change of epistemology in early modern times, which is of great influence even today. This revised version was published online in August 2006 with corrections to the Cover Date.     

GOD IN THE CAVE

When Finite and Infinite Goods was published in 1999, it took its place as one of the few major statements of a broadly Augustinian ethical philosophy of the past century. By “broadly Augustinian” I refer to the disposition to combine a Platonic emphasis on a transcendent source of value with a traditionally theistic emphasis on the value‐creating capacities of absolute will. In the form that this disposition takes with Robert Merrihew Adams, it is the resemblance between divine and a finite excellence that makes the finite excellence objectively of value, and it is the correspondence of an obligation to a divine command that makes the obligation objectively obligatory. I look closely at the complexity of this ethical division of labor—between the good and the right—mainly as it appears in the context of Finite and Infinite Goods, but also with attention to the broader corpus of Adams's writings, particularly his work on Leibniz and the essays of his that have been gathered together in The Virtue of Faith. I argue that there is a creative tension in his work between his desire to secure an objective basis for ethics and his affirmation of the value of grace, a love that is not proportioned to the excellence of its object. This tension, I further argue, ought to be resolved in the direction of grace.     

Husserl’s philosophy of mathematics: its origin and relevance

This paper offers an exposition of Husserl's mature philosophy of mathematics, expounded for the first time in Logische Untersuchungen and maintained without any essential change throughout the rest of his life. It is shown that Husserl's views on mathematics were strongly influenced by Riemann, and had clear affinities with the much later Bourbaki school.

THE NATURALIZATION OF SCRIPTURAL REASON IN SEVENTEENTH‐CENTURY EPISTEMOLOGY

Several scholars have claimed that the decline of revealed or Scriptural mysteries in the early Enlightenment was a consequence of the trajectories of Reformed theology in the sixteenth and seventeenth centuries. Reformed theology's fideistic stance, it is claimed, undermined earlier frameworks for relating reason to revealed mysteries; consequently, rationalism emerged as an alternative to such fideism in figures like the Cambridge Platonists. This article argues that Reformed theologians of the seventeenth century were not fideists but re‐affirmed Medieval claims about the eschatological concord of reason and revealed mysteries. Furthermore, the article suggests that early Enlightenment attitudes to religious mysteries owe more to innovations in Socinianism and Cambridge Platonism than to mainstream Reformed theology.     

From Cudworth to Hume: Cambridge Platonism and the Scottish Enlightenment

This paper argues that the Cambridge Platonists had stronger philosophical links to Scottish moral philosophy than the received history allows. Building on the work of Michael Gill who has demonstrated links between ethical thought of More, Cudworth and Smith and moral sentimentalism, I outline some links between the Cambridge Platonists and Scottish thinkers in both the seventeenth century (e.g., James Nairn, Henry Scougal) and the eighteenth century (e.g., Smith, Blair, Stewart). I then discuss Hume's knowledge of Cudworth, in Enquiry concerning the Principles of Morals, Enquiry concerning Human Understanding, The Natural History of Religion and Dialogues concerning Natural Religion.     

Modal Platonism: an Easy Way to Avoid Ontological Commitment to Abstract Entities

Modal Platonism utilizes “weak” logical possibility, such that it is logically possible there are abstract entities, and logically possible there are none. Modal Platonism also utilizes a non-indexical actuality operator. Modal Platonism is the EASY WAY, neither reductionist nor eliminativist, but embracing the Platonistic language of abstract entities while eliminating ontological commitment to them. STATEMENT OF MODAL PLATONISM. Any consistent statement B ontologically committed to abstract entities may be replaced by an empirically equivalent modalization, MOD(B), not so ontologically committed. This equivalence is provable using Modal/Actuality Logic S5@. Let MAX be a strong set theory with individuals. Then the following Schematic Bombshell Result (SBR) can be shown: MAX logically yields [T is true if and only if MOD(T) is true], for scientific theories T. The proof utilizes Stephen Neale’s clever model-theoretic interpretation of Quantified Lewis S5, which I extend to S5@.